On the Development of Macroscale Modeling Strategies for AC/DC Transport-Deformation Coupling in Self-Sensing Piezoresistive Materials

Goon Mo Koo, Purdue University

Abstract

Sensing of mechanical state is critical in diverse fields including biomedical implants, intelligent robotics, consumer technology interfaces, and integrated structural health monitoring among many others. Recently, materials that are self-sensingvia the piezoresistive effect (i.e. having deformation-dependent electrical conductivity) have received much attention due to their potential to enable intrinsic, materiallevel strain sensing with lesser dependence on external/ad hoc sensor arrays. In order to effectively use piezoresistive materials for strain-sensing, however, it is necessary to understand the deformation-resistivity change relationship. To that end, many studies have been conducted to model the piezoresistive effect, particularly in nanocomposites which have been modified with high aspect-ratio carbonaceous fillers such as carbon nanotubes or carbon nanofibers. However, prevailing piezoresistivity models have important limitations such as being limited to microscales and therefore being computationally prohibitive for macroscale analyses, considering only simple deformations, and having limited accuracy. These are important issues because small errors or delays due to these challenges can substantially mitigate the effectiveness of strain-sensing via piezoresistivity. Therefore, the first objective of this thesis is to develop a conceptual framework for a piezoresistive tensorial relation that is amenable to arbitrary deformation, macroscale analyses, and a wide range of piezoresistive material systems. This was achieved by postulating a general higherorder resistivity-strain relation and fitting the general model to experimental data for carbon nanofiber-modified epoxy (as a representative piezoresistive material with non-linear resistivity-strain relations) through the determination of piezoresistive constants. Lastly, the proposed relation was validated experimentally against discrete resistance changes collected over a complex shape and spatially distributed resistivity changes imaged via electrical impedance tomography (EIT) with very good correspondence. Because of the generality of the proposed higher-order tensorial relation, it can be applied to a wide variety of material systems (e.g. piezoresistive polymers, cementitious, and ceramic composites) thereby lending significant potential for broader impacts to this work. Despite the expansive body of work on direct current (DC) transport, DC-based methods have important limitations which can be overcome via alternating current (AC)-based self-sensing. Unfortunately, comparatively little work has been done on AC transport-deformation modeling in self-sensing materials. Therefore, the second objective of this thesis is to establish a conceptual framework for the macroscale modeling of AC conductivity-strain coupling in piezoresistive materials. For this, the universal dielectric response (UDR) as described by Joncsher’s power law for AC conductivity was fit to AC conductivity versus strain data for CNF/epoxy (again serving as a representative self-sensing material). It was found that this power law does indeed accurately describe deformation-dependent AC conductivity and power-law fitting constants are non-linear in both normal and shear strain. Curiously, a piezoresistive switching behavior was also observed during this testing. That is, positive piezoresistivity (i.e. decreasing AC conductivity with increasing tensile strain) was observed at low frequencies and negative piezoresistivity (i.e. increasing AC conductivity with increasing tensile strain) was observed at high frequencies. Consequently, there exists a point of zero piezoresistivity (i.e. frequency at which AC conductivity does not change with deformation) between these behaviors. Via microscale computational modeling, it was discovered that changing inter-filler tunneling resistance acting in parallel with inter-filler capacitance is the physical mechanism of this switching behavior.

Degree

Ph.D.

Advisors

Tallman, Purdue University.

Subject Area

Mathematics|Mechanics|Medical imaging|Nanotechnology|Polymer chemistry

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