Theory of piezoresistivity for strain sensing in carbon fiber reinforced cement under flexure

A theory is provided for piezoresistivity in carbon fiber reinforced cement (with and without embedded steel reinforcing bars) under flexure (three-point bending). The phenomenon, which involves the reversible increase of the tension surface electrical resistance and the reversible decrease of the compression surface electrical resistance upon flexure, allows strain sensing. The theory is based on the concept that the piezoresistivity is due to the slight pull-out of crack-bridging fibers during crack opening and the consequent increase in the contact electrical resistivity of the fiber-matrix interface. This work is an extension of prior theory, which concerns the effect of uniaxial loading on the volume resistance. The extension requires modeling the surface resistance and its change under flexure. The theoretical results on the piezoresistivity, both with and without rebar, are in good agreement with prior experimental results. Differences between theoretical and experimental results are probably due to minor damage and rebar debonding during flexure.