## 3 Results and Discussion
### Relationship between Load and Instrumental Signal  
Figure 6 shows the dimensionless average load-instrumental signal curve obtained in the two-point bending tests for the dataset about load and instrumental signal lower than the maximum load (P\({}_{\text{max}}\)) at 1-s time intervals. Additionally, the figure shows that the SDL as a vertical dashed line, which corresponds to the ratio between the lateral displacement of the strain gauge and the position of application of the loading nose concerning the embedment, \(\delta_{\text{B}}/\text{x}_{\text{o}}\), equals 0.3 [29]. For the loading range between 20 and 80 percent of maximum load, a linear model between the load (mN) and the instrumental signal (mV) was established. The parameters of the model, intercept (mN) and slope (mN/mV), are determined and presented in Table 3. The loading range was proposed to avoid the influence of the initial settling of the sensor, the effect of the loss of friction of the loading nose for large displacements, and the effect of the instrumental signal at the beginning of the test (V\({}_{\text{so}}\)). In addition to this, in Table 3, the confidence interval and the probability of the F value of Fisher, obtained through the regression analysis, are presented for each parameter. In Figure 6, a positive, dimensionless relationship between the load and the instrumental signal on each strain gauge is observed for the whole range of load values between zero and the maximum load [0, P\({}_{\text{max}}\)]. In the bending tests, two trends in the load-instrumental signal relationship were identified, which are explained by the position of the embedment relative to the strain gauge. These trends coincide with the results obtained in Figure 4.  
The first trend was a significant linear relationship that showed a coefficient of determination greater than 0.99 for all loading ranges, including the lateral displacements greater than the SDL. It corresponded to the embedment ratios between 0.3 and 0.45 (G1, G3, and G5). For these trends, the estimation error did not exceed 5% of the measured value (see Figure 7). Figure 6: Dimensionless average load–instrumental signal curve from the bending tests using 1-s time-weighted average values. The second trend corresponded to the strain gauges embedded on the edge or in the center of the sensing area (G2, G4, and G6) that showed a positive, non-linear relationship between load and instrumental signal. For small lateral displacements of the sensor, the linear trend between the load and the instrumental signal was significant. Nevertheless, the slope of the load-instrumental signal curve was two to four times greater than the slope of the first trend. This is due to the narrow range of variation of the instrumental signal compared to the range of variation of the load. This linear trend was significant for the whole loading range, but the coefficient of determination decreased to 0.93 (see Table 3) and the estimation errors exceeded 20% of the measured value (see Figure 7). It is worthwhile to highlight that, in Figure 6, none of the sensors showed the initial settling of the measuring system in the bending tests illustrated in Figure 5. This can be attributed to the fact that the performance of the load sensor of the INSTRON is compared with the performance of the strain gauge itself, thereby annihilating the effects of the initial settling of the sensor and obtaining a linear relationship between the load and the instrumental signal from the beginning of the test. Thus, the loss of linearity of the load-instrumental signal curve for loads lower than 20% of the maximum load can be attributed to the absence of a perfect embedment of the sensor. Additionally, for displacements greater than the SDL and close to 80% of the maximum load, an abrupt variation in the linear trend line, which has an error of overestimation greater than 15% of the measured value of the load, was observed (see Figure 7). This can be associated with the loss of friction between the loading nose and the surface of the strain gauge.