## 3 Test Results and Analysis
### Stress Wave Propagation Characteristics of Bolt Tension Process
#### 3.2.2 Time and Frequency Domain Analysis of Stress Wave Signals at Different Stages of Bolt Tension
As the bolt stretching proceeds, the dominant frequency amplitude decreases and the second wave peak frequency domain amplitude increases. Reaching the late stage of strengthening, the nucleation and growth of the microporous holes make the stress wave propagation blocked. The low-frequency signal passage rate decreases, the high-frequency signal increases, and the original second wave peak frequency becomes the dominant signal frequency. Figure 12g-i is the frequency domain diagram when the bolt is stretched to the necking stage. Due to the appearance of cracks and the occurrence of necking, the dominant frequency peak of the bolt is increasing, and multiple high-frequency peaks gradually appear. The high-frequency signals are more sensitive to damage. The reflection of the stress wave caused by the bolt necking makes the stress wave propagation period decrease and high frequencies appear. The  
Figure 11: Stress wave energy attenuation ratio of bolt tension process. (a) mg1; (b) mg2; (c) mg3. continued occurrence of necking also increases the energy of the stress wave reflection, and the dominant frequency amplitude shows an increase. The frequency domain of the stress wave signals continuously changes during the process of bolt stretching. In general, the frequency distribution in the frequency domain ranges from decentralized to centralized. The dominant frequency of the stress wave signal becomes more and more prominent with the stretching, and the dominant frequency of the stress wave changes from low frequency to high frequency. High-frequency signals are more sensitive to the cracks and necking of the bolt, and the dominant frequency of necking is between 9500 and 10,000 Hz. The frequency distribution characteristics of the stress wave signal can better assist in locating the stage of bolt tension, but a quantitative analysis is not feasible for the time being. 2.3 Analysis of the Energy Attenuation Ratio of Diameter-Stress Wave in the Necking Position during Bolt Tensioning  
After the bolt reaches its tensile strength and enters the necking fracture stage, the axial force begins to decrease. For bolts that have been in the support state for a long time with a small detected axial force, it is easy to overlook that the bolts may have entered the necking fracture stage and then mistakenly think that the bolts are in normal working condition so that safety hazards cannot be detected in time. Thus, the potential safety hazard cannot be found in time. After the bolt is stretched, elastic and plastic deformation occurs. According to the above study, the diameter of the bolt necking position is decreased during the stretching process of the bolt, and the time domain diagram of the stress wave signal of the bolt shows that the energy attenuation is increasing. Therefore, the diameter of the bolt necking position is used as the detection result, and the energy attenuation ratio of the stress wave signal is used as the detection standard, in order to find out the relationship  
Figure 12: Frequency domain diagram of the stress wave signal at different stages of bolt tension. (**a**) Unstretched; (**b**) Elastic stage; (**c**) Yield stage; (**d–f**) Strengthening stage; (**g–i**) Necking fracture stage. between the energy attenuation ratio and the diameter of the bolt necking position, so as to better predict the bolt necking condition and provide early warning. Figure 13 shows the diameter-stress wave energy attenuation ratio curve in the bolt necking position during bolt tensioning. As shown in Figure 13, the energy attenuation ratio of the stress wave signal increases, and the diameter of the bolt necking position shows an overall decreasing trend. The diameter of the bolt decreases basically linearly in the elastic and yielding stages of the tensile process, with a slow rate of diameter reduction.