Abstract
Continuous fiber-reinforced composites exhibit complex failure mechanisms, often unapparent to the unaided eye. Using nanofiller modification to introduce self-sensing capabilities via the piezoresistive effect into these composites has been widely explored. However, to make meaningful predictions of the mechanical state of the composite, accurate piezoresistivity models are needed. Modeling efforts have largely focused on microscale piezoresistivity, often via utilizing computationally intensive resistor network models, which are limited to very small dimensions and consequently unsuitable in macroscale structural contexts. Furthermore, the role of the continuous fiber reinforcement has been widely overlooked; in other words, there has been little effort put into developing reliable analytical models for predicting conductivity changes in continuous fiber-matrix systems. To bridge this gap, this work proposes an analytical model predicting axial-strain induced transverse piezoresistivity in a nanofiller-modified polymer phase enveloping a continuous fiber reinforcement phase. An electrical concentric cylinders assemblage (ECCA) concept lies at the heart of this strategy. The model initiates with two concentric cylinders representing a reinforcing fiber surrounded by a nanofiller-modified conductive matrix. The system is homogenized to predict the transverse resistivity changes as a function of applied longitudinal strains and the constituent electro-mechanical properties. This is accomplished by imposing the concept of equal volumetric averages of current densities as well as utilizing existing tensor-based piezoresistivity relations for the nanofiller-modified matrix. The model studies transverse piezoresistive responses of CNF-epoxy composites with glass and conductive Kevlar 49 fibers at different volume fractions, and the outcomes will be compared to rule of mixtures predictions.
