Coupled Electromechanical Peridynamics Modeling of Strain and Damage Sensing in Carbon Nanotube Reinforced Polymer Nanocomposites

This work explores the computational modeling of electromechanical problems using peridynamics and in particular, its application in studying the potential of carbon nanotube (CNT) reinforced nanocomposites for the purpose of sensing deformation and damage in materials. Peridynamics, a non-local continuum theory which was originally formulated for modeling problems in solid mechanics, has been extended in this research to electromechanical fields and applied to study the electromechanical properties of CNT nanocomposites at multiple length scales.

Piezoresistivity is the coupling between the electrical properties of a material and applied mechanical loads, more specifically the change in resistance in response to deformation. This can include both, a geometric effect due to change in dimensions as well as the change in resistivity of the material itself. Nanocomposites referred to in this work are materials which consist of CNTs dispersed in a binding polymer matrix. The origins of the extraordinary piezoresistive properties of nanocomposites lie at the nanoscale where the non-local phenomenon of electron hopping plays a significant role in establishing the properties of the nanocomposite along with CNT network formation and inherent piezoresistivity of CNTs themselves. Electron hopping or tunneling allows for a current to flow between neighboring CNTs even when they are not in contact, provided the energy barrier for electrons to hop is small enough. This phenomenon is highly nonlinear with respect to the intertube distance and is also dependent on other factors such as the potential barrier of the polymer matrix.

To investigate this in more detail, peridynamic simulations are first employed to study the piezoresistivity at the CNT bundle scale by considering a nanoscale representative volume element (RVE) of CNTs within polymer matrix, and by explicitly modeling electron hopping effects. This is done by introducing electron hopping bonds and it is shown that the conductivity and the non-local length scale parameter in peridynamics (the horizon) can be derived from a purely physics based model rather than assuming an ad-hoc value.

Piezoresistivity can be characterized as a function of the deformation and damage within the material and thereby used as an in-situ indicator of the structural health of the material. As such, a material system for which real time in-situ monitoring may be useful is polymer bonded explosives. While these materials are designed for detonation under conditions of a strong shock, they can be damaged or even ignited under certain low magnitude impact scenarios such as during accidental drop or transportation. Since these materials are a heterogeneous system consisting of explosive grains within a polymer matrix binder, it is proposed that CNTs can be dispersed within the binder medium leading to an inherently piezoresistive hybrid nanocomposite bonded explosive material (NCBX) material which can then be monitored for a continuous assessment of deformation and damage within the material.

To explore the potential use of CNT nanocomposites for this novel application, peridynamic simulations are carried out at the microscale level, first under quasistatic conditions and subsequently under dynamic conditions to allow the propagation of elastic waves. Peridynamics equations, which can be discretized to obtain a meshless method are particularly suited to this problem as the explicit modeling of crack initiation and propagation at the microscale is essential to understanding the properties of this material. Moreover, many other parameters such as electrical conductivity of the grain and the properties of the grain-binder interface are studied to understand their effect on the piezoresistive response of the material. For example, it is found that conductivity of the grain plays a major role in the piezoresistive response since it affects the preferential pathways of current density depending on the relative ease of flow through grain vs. binder.

The results of this work are promising and are two fold. Peridynamics is found to be an effective method to model such materials, both at the nanoscale and the microscale. It alleviates some of difficulties faced by traditional finite element methods in the modeling of damage in materials and can be extended to coupled fields with relative ease. Secondly, simulations presented in this work show that there is much promise in this novel application of nanocomposites in the field of structural health monitoring of polymer bonded explosives.