## 3 Experimental Validation
### The Three-Point Bending Load Tests  
The three-point bending tests are performed as shown in Figure 6. The universal testing machine (UTM) controller sends to the trigger signal to UTM. Then, the loading step is controlled by displacement using the UTM. After each loading step, the multi-channel electrical impedance acquisition system measures the impedance signals of the FRCCs specimens. The loading steps consist of seven steps, i.e., 0.2 mm (1 st step), 0.4 mm (2 nd step), 0.6 mm (3 rd step), 0.85 mm (4 th step), 1 mm (5 th step), 1.25 mm (6 th step), 1.4 mm (7 th step), and no loading data (baseline data set) is also measured. The yielding region of the representative test specimen is observed from the 1 st step to the 4 th step, and the rupture region is revealed from the 5 th step to the 7 th step. The corresponding force-displacement curve of the test specimen is shown in Figure 7. Note that the data sets are obtained at 15 \({}^{\circ}\)C.  
Figure 8 shows the representative crack patterns initiated at the bottom of the specimen according to the loading steps. After applying bending loads up to 0.65 mm displacement, the cracking phenomenon is observed in the bottom view compared with the 1 st step (Figure 8a), as shown in Figure 8b. This visible crack occurs in the elastic region, called closed-type crack that can be restored. However, the sequentially created cracks, called open cracks showed in Figure 8c,d, cannot be restored. This is due to the sequentially created crack being in the plastic region.  
Figure 9 shows the representative Nyquist plots of each region according to the bending loading steps. For better visibility, Nyquist plots of each region are zoomed as shown in Figure 9.  
Figure 6: Experimental test setup.  
Figure 7: Representative force-displacement curve.  
The cracks are located in Regions C and D. Figure 9a,b show that the Nyquist plots are barely changed in the non-cracked regions, i.e., Regions A and B, while there are significant changes in the cracked Regions C and D, as shown in Figure 9c,d.  
Based on the DI computation using Equation (2), the crack location can be more clearly observed as shown in Figure 10. As the loading step is increased, DIs' are remarkably increased at the cracked Regions C and D. The physical meaning is that the steel fibers inside the FRCCs become more separated as the bending deformation progresses.  
In order to confirm the consistency of the test results, the similar tests are repeated using other three FRCCs specimens. The cracks similarly occur nearby the center location of the specimens due to three-point bending loads. The second and fourth specimens' cracks are initiated at Regions B and C, and the third specimens' cracks are initiated at Regions C and D. Figure 11 shows that remarkable DIs' are clearly observed at the cracked regions of each specimen. Although the DI value changing times are different depending on the FRCCs specimen, one can easily make the decision of the crack location using Figure 11. It is speculated that it is practically difficult to precisely control the fiber distribution and arrangement inside FRCCs during the manufacturing process. To secure the quantitative crack analysis, it is necessary to establish a standard FRCCs manufacturing process. According to the validation test results, it can be concluded that the proposed technique can measure instantaneously electrical impedance at multiple sensing regions, and crack detection, as well as localization, can be achieved without considering temperature change.  
Figure 8: The bottom view of the representative FRCCs specimen under bending loads: (**a**) 1 st step; (**b**) 4 th step; (**c**) 5 th step and (**d**) 6 th step.  
Figure 10: Damage index of representative specimen at **(a)** Region A; **(b)** Region B; **(c)** Region C and **(d)** Region D.  
Figure 9: The Nyquist plots obtained at at **(a)** Region A; **(b)** Region B; **(c)** Region C and **(d)** Region D.