## 3 Experimental Method
### Relationship between Electrical and Mechanical Strains  
A series of tensile tests were conducted to reveal a relationship between electrical strain and mechanical strain in plain-woven CFRP. A tensile testing machine TENSILON RTF 1310 was used to apply quasi-static loading by stretching the specimen of plain-woven CFRP with a constant displacement speed of 2 mm/min. After the specimen was stretched to the strain of 350 \(\mu\varepsilon\), the displacement was returned slowly until the specimen had original length. This cycle was done seven times to obtain reliable results. The electrical and mechanical strains were simultaneously recorded during the test to investigate the piezoresistive behavior in the CFRP. Figure 5 shows a schematic electrical circuit used to record the strains. The circuit used two Wheatstone bridges. The first bridge was connected to the strain gauge (TML FLA-5-11) to measure the mechanical strain in the CFRP. The second bridge was connected to two electrodes to measure the electrical strain alteration. In the second bridge, one dummy strain gauge was installed to assist the balancing of the bridge circuit resistances. This had to be done because the electric resistance of the CFRP is very small compared to the Wheatstone bridge resistances. The dummy strain gauge was pasted to a sufficiently rigid steel plate. Thus, no electrical resistance alteration generated by the dummy strain gauge. Both strain gauges attached in the CFRP and steel plate (as dummy strain gauge) have gauge factor (\(G_{sg}\)) of 2.09, electrical resistance (\(R_{sg}\)) of 120 \(\pm\) 0.3 \(\Omega\), and a gauge length of 10 mm. By using the bridges, the recorded data was voltage signal alteration only. This method, which used a Wheatstone bridge, was more beneficial than the four-wire method because the voltage change was usually small compared to initial resistance at the CFRP. As a consequence, the resistant alteration data obtained in the method would be more accurate. The voltage signals from each Wheatstone bridge are then filtered to eliminate noise signals and amplified by a strain amplifier TML DA-37A. From the first Wheatstone bridge circuit, the mechanical strain (\(\varepsilon_{m}\)) in CFRP can be evaluated by calculating Equation (10) as follows,  
\[\varepsilon_{m}\ =\ \frac{V_{m}\cdot K_{m}}{G_{sg}}, \tag{10}\]  
Figure 4: The electrical circuit for initial resistance evaluation in (**a**) wrap and (**b**) thickness directions. where \(V_{m}\) is DC voltage signal recorded from the first Wheatstone bridge circuit and \(K_{m}\) is an amplified voltage factor that can be adjusted in the first strain amplifier. From the second Wheatstone bridge circuit, an electrical strain (\(\varepsilon_{e}\)) can be then calculated as follows,  
\[\varepsilon_{e}\ =\ V_{e}K_{e}, \tag{11}\]  
where \(V_{e}\) is DC voltage signal recorded from the second Wheatstone bridge circuit and \(K_{e}\) is an amplified voltage factor that can be adjusted in the second strain amplifier. To obtain the optimal amplification of the voltage signal, the value of \(K_{m}\) is set to 1000 \(\mu\varepsilon\)/V for the first Wheatstone bridge circuit, whereas for the second Wheatstone bridge circuit, the value of \(K_{e}\) is set to 50 \(\mu\varepsilon\)/V. Furthermore, the voltage signals were also converted into a digital signal by the ADC prior to one displayed in the data recorder. Note that for each cyclic tensile test, the voltage signals were recalibrated. Thus, the signals always start from zero before the woven CFRP specimen was imposed by the tensile loading. Considering points \(a\) and \(b\) in Figure 5, the resistance between those points (\(R_{ab}\)) can be calculated as follows,  
\[R_{ab}\ =\ R_{CFRP}+2R_{c}+R_{sg}, \tag{12}\]  
The \(\varepsilon_{e}\) in Equation (7) can be derived by considering the alteration of electrical resistance recorded in the data recorder, which is sourced by the mechanical strain of the CFRP only.