Piezoresistivity of polymer-matrix carbon fiber filament in plane stress state

In this work, the relation between 2D- and 3D-strain based piezoresistive gauge factors for carbon fiber filament in plane stress states is developed theoretically. For measuring the gauge factors, carbon fiber filaments are attached to the base specimen surface at different angles. Their resistance response to multidimensional strain field is investigated by four-point bending tests. Piezoresistive models of carbon fiber filament in plane stress states are created using the test results. In the test setup, carbon fiber filaments are placed both on the tension side and the compression side. Both the models show that the piezoresistive response of carbon fiber filament is dominated by the longitudinal strain. Based on the inequality in the sensitivities to tensile strain and compressive strain, the piezoresistive models are modified further. The modified piezoresistive models reveal the following 3D-strain based gauge factors: 1.82 for longitudinal tensile strain, 1.64 for longitudinal compressive strain, 0.10 for transverse tensile strain, and -0.25 for transverse compressive strain. The 2D-strain based gauge factors depend not only on the polarity of the longitudinal strain and transverse strain, but also on the polarity of the strain in the thickness direction. The piezoresistive models are verified experimentally.