## 4 Characteristic Test and Analysis of the FBG Dynamometry Bol
### Test Results and Discussion  
#### 4.3.1 Analysis of the Results and Discussion of Test I  
The entire test process lasted for 20 min. The variation curve of the measurement data sensed by the testing machine, two groups of resistance strain gauges, and two groups of FBG sensors over time are shown in Figure 10.  
It can be seen in Figure 10 that the tension bolt in this test has experienced the elastic deformation stage, the yield deformation stage, and the plastic deformation stage. The tensile force when the test bolt yields is about 175 kN. In the elastic stage, the strain changes linearly with time. In the yield stage, the strain is evidently stable within a certain range. In the plastic stage, the strain slowly increases with time, and the deformation rate gradually decreases. The resistance strain gauge sensor can monitor the linear elastic process and the entire yield process of the tension bolt. After yielding, the strain gauge sensor fails. The failure of the strain gauge is due to the failure of the adhesive, which leads to the separation of the strain gauge from the anchor rod. However, due to the small size of the optical fiber, the adhesive can closely connect the optical fiber with the spring. Additionally, the spring  
Figure 9: Schematic diagram of the test equipment connection. can also protect the optical fiber, so that the FBG dynamometry bolt can monitor the linear elastic stage, the yield stage, and the partial plastic stage of the bolt tensile process. In the linear elastic stage, the sensing curve is almost straight. In the yield stage, the perceived strain is roughly maintained within a certain range and a jumping \"wavelet peak\" appears at the end of each yield. The \"wavelet peak\" can be used as a warning sign to detect the end-of-the-yield stage of the bolt rod. Then, at a certain time of plastic deformation, the adhesive between the spring and the bolt rod fails, which results in the failure of the FBG dynamometry bolt. After substituting the central wavelength measured by the FBG sensor in the elastic stage into Equation (13), the calculated strain of the FBG dynamometry bolt is the dependent variable, and the strain measured by the resistance strain gauge sensor in the elastic stage is the independent variable. The relationship curve between the dependent and independent variable is shown in Figure 11. The physical and mechanical parameters of the experimental materials are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material Parameters** & **Physical Symbols** & **Values** & **Units** \\ \hline Radius of bare fiber core & \(r_{\text{c}}\) & 62.5 & \(\mu\)m \\ Radius of the cladding layer & \(r_{\text{p}}\) & 125 & \(\mu\)m \\ Elastic modulus of the fiber & \(E_{\text{c}}\) & 72 & GPa \\ Shear modulus of the cladding layer & \(\text{G}_{\text{p}}\) & 400 & MPa \\ Bond length & \(L\) & 12 & mm \\ Spring length & \(L_{\text{s}}\) & 60 & mm \\ Bond width & \(D\) & 2 & mm \\ Thickness of the adhesive interlayer & \(h\) & 0.2 & mm \\ Shear creeps compliance & \(G_{\text{a1}}\) & 5 & GPa \\ Central wavelength initial value & \(\lambda_{\text{B1}},\lambda_{\text{B2}}\) & 1515.694 & nm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The physical and mechanical parameters of the experimental materials. Figure 10: Measurement results of each test instrument. The slopes of the 2 straight lines obtained by fitting are 0.97674 and 1.01735, which are approximately equal to 1. It shows that the strain measured by the FBG dynamometry bolt and the resistance strain gauge have a proportional relationship. At the same time, it can also be explained that the perceived strain calculated by Equation (13) is approximately equal to the theoretical value. The feasibility of Equation (13) is demonstrated.