Characterization of Deformation of Bolts and Induced Stress Wave Propagation under Axial Tensile Stress

Abstract

The nondestructive testing technique used to evaluate the quality of bolt support by detecting the axial force is suitable for the bolt with a short construction time. For the bolt in the support state for a long time period, it may lead to the detection of small axial force only and ignore the fact that the bolt has entered the necking fracture stage, and thus fail to detect safety hazards in time. Three sets of parallel tests were conducted to solve the misjudgment of detection results due to the reduction of axial force when the bolt was in the necking fracture stage. Bolt deformation characteristics and stress wave propagation characteristics in bolts under axial tensile stress were studied by using the bolt tensile and stress wave detection test system which was modified and built independently. The results showed that (1) The diameter of the necking position decreases continuously during the tensioning process of the bolt and the rate of decrease increases abruptly during the necking fracture stage. (2) Due to the bolt stretching, the stress wave propagates in the bolt with different degrees of reflection and transmission, resulting in the attenuation of the stress wave energy; the energy attenuation ratio of the stress wave signal in the necking fracture stage reaches 35%, and the energy attenuation ratio increases exponentially as the necking continues to occur. (3) The frequency distribution of the stress wave signal during the bolt stretching process is from scattered to concentrated, the dominant frequency is gradually prominent and changes from low frequency to high frequency, the high-frequency signal is more sensitive to the cracks and necking of the bolt, and the dominant frequency is between 9500 and 10,000 Hz. (4) The average error of the stress wave method is 1.945% and the maximum and minimum values are 4.12% and 0.51%, respectively. The method is promising and provides a reference for the study of nondestructive testing of bolt stress waves in field support.

1. Introduction

Underground coal mining requires the excavation of a large number of roadways, which must be maintained open and stable in order to ensure coal mine safety [1]. Practical experience over the years has shown that bolt support is an economic and effective support method, and bolts can provide a certain support resistance to ensure the stability of the surrounding rock, and have an extension rate to adapt to the deformation of the surrounding rock, which is of great significance for coal mine safety [2,3]. The bolt is mainly subjected to tensile stress when it is in the support state, and when the tensile stress exceeds the bearing limit, the bolt will deform plastically until it fractures and lead to the failure of the support. The cumulative failure of the bolt eventually leads to accidents [4,5,6]. While coal mines focus on production, the quality of bolt support must be tested regularly to determine and solve safety hazards in a timely manner. However, the bolt project is a concealed project, and it is difficult to identify and investigate the quality problems effectively. The traditional bolt support quality inspection method is destructive and the number of sampling is small; hence, a nondestructive inspection method is required to investigate the characteristics of bolt deformation under tensile stress.

When the bolt is stretched, the mechanical properties of the bolt and the deformation inside the material change continuously as the stretching proceeds. Many scholars have analyzed the stress state and the stress–strain curve of the bolt stretching process through the bolt stretching test and concluded that the bolt stretching process can be divided into four stages, which are the elastic stage, yield stage, strengthening stage, and necking fracture stage [7,8,9]. These studies are much helpful for a better understanding of the bolt tensioning process and promote the development of bolt nondestructive testing technology. The study of bolt NDT technology is closely related to coal mine safety, and some scholars have been continuously researching and innovating bolt NDT technology for decades [10,11,12,13]. The core NDT techniques used nowadays are ultrasonic, acoustic emission, and stress wave methods. The advantages of the ultrasonic method are its applicability and penetration ability, high sensitivity, and high sensitivity to defects. However, when using ultrasonic waves to detect complex structures and irregularly shaped objects, wave attenuation is severe, so it is difficult to be used to detect composite rock formations and a variety of anchored media. The ultrasonic excitation frequency is high. The detection results are seriously affected by the defect location, shape, material and grain size, and other factors. The acoustic emission method is usually used to monitor the changes of parameters throughout the test process and is suitable for laboratory research to summarize the rules, but it is inconvenient to use for coal mine engineering and cannot be used to detect the state of bolts at a certain moment. The stress wave method has become an important method for the study of nondestructive testing of bolts because of its advantages of long measuring distance, low requirements for testing conditions, and easy operation, and a large number of scholars’ studies have provided a rich theoretical basis and signal analysis methods, and its applicability has been widely proven by field engineering applications [14,15,16]. The stress wave detection method does not lead to any damage to the bolt. When an excitation force is applied to the end of the bolt, a stress wave is generated at the rod end, which propagates along the rod towards the rod end and generates reflected and transmitted waves when it encounters the wave impedance interface, enabling the state of the bolt to be checked and tested by the waveform characteristics. Most of the existing studies on nondestructive testing of bolts have focused on the detection of bolt length [17], anchorage force [18,19,20], and anchorage quality [21,22], which provides data processing and interpretation methods for nonlinear and non-smooth signals [23,24,25,26]. However, in practical engineering applications, the nondestructive testing method of using axial force to assess the quality of anchor support is applicable to newly constructed bolts. For bolts that have been in support for a long time, the test results show that the axial force of the bolts is small, but the bolts may still have safety hazards. During the tensioning process of bolts at low loading speeds, the axial force increases first and then decreases after reaching the necking fracture stage when a fracture is about to occur, which is ignored by the nondestructive testing of the bolt axial force.

Based on the importance of bolt nondestructive testing to the safety and stability of coal mine roadways and the application of the stress wave reflection method in bolt nondestructive testing, this paper designs a bolt tensile and stress wave testing test system in order to solve the defects of the nondestructive testing technology of bolt axial force. The deformation characteristics of bolts under axial tensile stress and the propagation characteristics of stress waves in bolts were studied by means of experimental research and nonlinear stress wave data processing. Then, the connection between the two was found, and a nondestructive testing method based on the stress wave method to identify bolts in necking condition was proposed to provide a reference for the continued development of bolt nondestructive testing technology.

2. Bolt Tensile and Stress Wave Detection Test

In this paper, the bolt tensile test was conducted using the constructed bolt tensile and the stress wave detection test system. The stress wave detection device was used to obtain the stress wave data when the bolt was subjected to different axial displacements during the tensile test, and the deformation characteristics of bolts and stress wave propagation characteristics in bolts under axial tensile stress were studied.

2.1. Bolt Tensile Process Nondestructive Testing System

Figure 1 shows the pictures of the components of the test system, in which the bolt tensile and stress wave detection test system consists of a bolt tensile test bench, a stress wave detection device, and a bolt state monitoring device. The bolt tensile test bench was modified from the Teststar anchor testing machine, the stress wave detection device was SET-PWB-01 wireless bolt quality tester, and the bolt state monitoring device was designed according to the test requirements. The bolt tensile test bench can apply axial displacement to the bolt for tensile testing, and the displacement sensor and column sensor record the whole process displacement load data stored in the experiment console. The stress wave detection device is utilized to transmit the excitation signal into the bolt and record the waveform data of the stress wave propagation process for subsequent research. The bolt state monitoring device is used primarily to record the image data of the entire tensile test bolt deformation process.

Figure 2 is a schematic of the test system. The test system for the bolt tensile experiment can record the displacement, load, image, and stress wave data of the whole process completely, which is important for the study of bolt deformation characteristics and stress wave propagation characteristics.

2.2. Test Bolts

The test was conducted in parallel, taking three bolts with the same conditions to ensure that the test conditions (including temperature, humidity, test parameters, and testers) were consistent and to prevent the generation of accidental errors. The test was conducted with mining left-hand threaded steel bolts. Figure 3 shows a photo of the test bolts, and the specific parameters are listed in

Table 1. Bolt test parameters.

Bolt No.	Diameter (mm)	Length (mm)	Yield Strength (Mpa)	Ultimate Elongation
mg1	20	1200	500	15%
mg2	20	1200	500	15%
mg3	20	1200	500	15%

.

2.3. Test Method

To prevent the uneven contact surface between the bolt end face and the acceleration sensor from affecting the stress wave data, the bolt end face was polished to be rather smooth and flush. A scale was drawn on the bolt surface as a reference for the bolt deformation. The test is performed by controlling the axial displacement of the bolt through the bolt tension test bench and applying an axial load to the bolt. The stress wave data detection process is controlled by the roller shaker through the bolt nondestructive tester. Then, the acceleration sensor receives the stress wave data and transmits it back to the bolt nondestructive tester. The waveform data are recorded six times per test. The choice of displacement loading speed determines the rate of deformation of the bolt in the tensile process. The application of low stretching speed is conducive to adequate deformation of the bolt to ensure that ductile fracture occurs after the bolt has been stretched through the four stages of stretching. According to the tensile test standard regarding the test rate [27], the displacement loading speed was set to be 10 mm/min. Bolt nondestructive tester parameters mainly include the sampling rate, sampling points, channel gain, and emission energy. The experimental sampling rate is set at the maximum sampling rate of 1 MHz for the bolt nondestructive tester to ensure the accuracy of the stress wave signal obtained from the test. The number of sampling points determines the total length of the sampled signal, and the total length of the sampled signal should contain at least 2 stress wave propagation cycles of information, which are set to 6 k according to the experimental bolt length. The transmitting energy mainly controls the amount of energy emitted by the excitation, and the larger the energy value, the larger the signal amplitude generated by the excitation. The channel gain cooperates with the setting of the emission energy to achieve normal signal acquisition. In order to ensure that the stress wave signal acquired during the bolt tensioning process will not be clipped, the stress wave signal was debugged before the test. The channel gain and emission energy were set to be 50 dB and 10, respectively, and the signal could thus be acquired normally.

3. Test Results and Analysis

3.1. Deformation Characteristics of Bolts

3.1.1. Axial Load–Displacement Curve of Bolt Tensile Test

Figure 4 shows the axial load–displacement curve of each bolt, which belongs to one of the typical behaviors of metals and metal alloys. As can be seen from Figure 4, the bolts eventually undergo ductile fracture at low axial displacement loading rates. The occurrence of plastic deformation to ductile fracture of the bolts in tension is not a universal feature, so its characteristics need to be further studied to provide a reference for the research of nondestructive testing technology of bolts. The axial load–displacement curve of each bolt can be used to know which stage the bolt is in when any axial displacement is applied, and then the stress wave signals obtained from the test can be better studied in stages.

3.1.2. Bolt Tensile Deformation Characteristics

The bolt selected for the test was a common type of mining bolt with a length of 1200 mm. A comparison was made between blots of different lengths, but all other parameters were kept the same for all tested bolts. Figure 5 shows the axial (a,c) and radial (b,d) deformation curves of different parts of bolts of different lengths. It was found that the axial and radial deformation patterns of separate parts of bolts of different lengths are consistent, and the average sectional shrinkage rates of bolts that are 1200 and 2500 mm long are 54.64% and 55.24%, respectively, indicating that the tensile deformation characteristics of bolts of the same parameters have very little relationship with the length of bolts.

From Figure 5a,c, it can be seen that in the axial deformation rule of bolts at different locations, the deformation at both ends of bolts is less than the deformation at the center of bolts, but the difference is not significant, while the axial deformation of bolts near the fracture location is obviously much larger than other parts due to the effect of shrinkage. The radial deformation rule of bolts in different positions can be seen in Figure 5b,d. The bolt diameter variation rule is similar to the bolt transverse deformation rule. The deformation of the bolt diameter at both ends is smaller than the deformation of the bolt in the middle position, and the closer to the necking fracture position, the larger the deformation of the bolt diameter. The mg3 bolt diameter variation curves for different parts of the bolt differ from the mg1 and mg2 curves in that two distinct troughs appear in the mg3 curve (marked in Figure 5b) because the mg3 necking fracture location is closer to the center of the bolt.

The image data during the bolt tensioning process was recorded by the bolt state monitoring device, and the necking fracture process of the bolt and the diameter change rule of the necking fracture location when different axial displacements were applied to the bolt were collated and analyzed. Figure 6 shows the diameter change curve of the bolt shrinkage part. Due to the different amounts of axial deformation during bolt stretching, the tensile deformation ratio S is introduced. S is the axial displacement normalized by the total extension, and S is calculated by the following formula:

$$S=\frac{Axialdisplacement}{Totalextension}$$

(1)

As can be seen from Figure 6, the diameter change pattern is the same for different necking locations. The bolt undergoes uniform elastic-plastic deformation during the elastic phase, yielding phase, and strengthening phase, and the diameter change curve is slow. When the bolt reaches the necking fracture phase, its diameter changes drastically, the section at the necking decreases rapidly, and fractures are about to occur.

3.2. Stress Wave Propagation Characteristics of Bolt Tension Process

3.2.1. Stress Wave Signal Filtering Based on CEEMD Modal Decomposition Method

Noise appears in the data recorded from stress wave detection in the test process, so data filtering is needed to process the recorded signal. Commonly used filtering methods are digital filters, wavelet transforms, and modal decomposition methods. After determining the signal bandwidth, digital filters are mainly filtered by setting high pass, low pass, band pass, band reject, etc. Although the design is simple, it does not work well for nonlinear non-smooth signals, and the bandwidth cannot be determined for unknown signals. The wavelet transform method was first proposed to deal with nonlinear non-stationary signals, which has a solid theoretical foundation and can set soft and hard threshold noise elimination. However, detection signals acquired in engineering applications are highly variable, and the choice of soft and hard thresholds for wavelet noise cancellation can have a huge impact on the signal cancellation capability. The modal decomposition method is adaptive and can separate noise and useful signals according to different frequencies by the signal’s own characteristics. This signal-processing method does not require manual involvement and also avoids the generation of errors.

Complementary ensemble empirical mode decomposition is the commonly used modal decomposition method [28,29,30]. The first proposed method is empirical mode decomposition, which decomposes the complex signal into multiple smooth intrinsic mode components Intrinsic Mode Function and a residual term by frequency, and the Intrinsic Mode Functions of different frequencies can reflect the intrinsic characteristics of the original signal to a certain extent. However, the empirical mode decomposition algorithm has limitations and is prone to problems such as the modal confusion phenomenon and endpoint effects. After scholars’ continuous research and improvement, the complementary ensemble empirical mode decomposition method is proposed, which uses the addition of opposite white noise to the original signal for auxiliary decomposition, solving the problems of the empirical mode decomposition method, which is more effective for the processing of nonlinear non-smooth signals and widely used. Figure 7 is the flowchart of CEEMD decomposition.

Where cj(t) denotes the j-th IMF component finally obtained by CEEMD processing, c_ni denotes the j-th IMF component in group n obtained by EMD processing of the signal, R_n(t) denotes the residual term finally obtained by CEEMD processing, and r_i denotes the i-th residual term in group n obtained by EMD processing of the signal.

Based on complementary ensemble empirical mode decomposition, the process of filtering the original signal is described using the original data when the displacement of mg1 is zero as an example.

After exporting the data acquired by the bolt nondestructive tester, the original data were decomposed modally using complementary ensemble empirical mode decomposition programmed by numerical calculation software. Complementary ensemble empirical mode decomposition requires setting parameters such as the proportion of added noise and the number of summed averages. When the total averaging number is fixed, the error increases with the increase of the ratio of added noise; when the ratio of added noise is fixed, the more the total averaging number is and the closer the final result is to the real signal. According to the experimental debugging results, it is finally determined that the ratio of added noise and the number of summed averages are set to 0.01 and 10, respectively, and the decomposition effect is very good at this time. Decomposition results in 7 Intrinsic Mode Functions and 1 residual term, calculates the correlation number and energy of each IMF, takes the correlation coefficient greater than 0.2, and adds the IMFs with higher energy to attain the reconstructed signal. Figure 8 shows the CEEMD decomposition results of mg1-0.

Table 2. The cross-correlation coefficient between each IMF and the original signal and their respective energy ratios.

IMF Serial Number	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	R
cross-correlation coefficient	0.1107	0.7858	0.728	0.1393	0.0026	−0.0034	0.0017	−0.0013
energy ratio	0.73%	55.00%	41.55%	2.23%	0.21%	0.15%	0.08%	0.05%

shows the cross-correlation coefficients and energy ratios of each IMF component with the original data.

The cross-correlation coefficient and energy ratios of each IMF component to the original signal are calculated (Table 2).

The cross-correlation coefficient is calculated from the cross-correlation function and is a statistical measure used to indicate the degree of correlation between two signals, which can express the correlation between the IMF component and the original signal. The energy ratio indicates the weight of the IMF component in the original signal. It is obvious from the data in Table 2 that the number of cross-correlation coefficients between IMF2 and IMF3 is significantly greater than the other components, and energy summation accounts for 96.55% of the total energy. It can be observed that IMF2 and IMF3 basically contain the main features of the original signal and can be reconstructed as the feature components of the original signal to obtain the reconstructed signal.

3.2.2. Time and Frequency Domain Analysis of Stress Wave Signals at Different Stages of Bolt Tension

After filtering the original signals of the stress wave obtained during the bolt tensioning process by using the complementary ensemble empirical mode decomposition method, the reconstructed signals obtained were characterized in the time and frequency domains as follows.

①

Time domain feature analysis

Figure 9 shows the time domain diagram of the stress wave signal at different stages of bolt tension.

Figure 9a–i show the time domain plots of the stress wave signals of the bolt stretching to the elastic stage, yielding stage, strengthening stage, and necking fracture stage, respectively. By observing the time domain graph of the stress wave when different axial displacements are applied to the bolt, the amplitude of the stress wave decay continuously with time. The amplitude indicates the change of energy when the stress wave propagates in the bolt because the deformation of the bolt makes the stress wave propagate in the bolt with different degrees of reflection and transmission, resulting in the attenuation of energy. In order to show more intuitively the energy changes of stress wave propagation during bolt stretching, the incident energy, reflected energy, and attenuating energy of stress waves are calculated for different axial displacements of bolt stretching.

The incident and reflected energy magnitude of the stress waves could not be directly obtained because the bottom-end reflection could not be directly identified after the bolt stretched into plastic deformation. Therefore, the stress wave velocity in the free bolt was calculated first, and the bolt wave velocity was determined to be 5170 m/s. Then, the incident and reflected wave time intervals were determined by the bolt stretching length, and the time domain signals in the time range were integrated to obtain the incident and reflected energy magnitudes of the stress wave. The stress wave energy change curve during bolt tension is illustrated in Figure 10.

Figure 10 shows that the incident energy, reflected energy, and attenuating energy curves of the stress wave are consistent with the continuous application of axial displacement during the tensioning of the same bolt the incident energy increases rapidly and linearly in the tensile-elastic phase of the bolt and remains constant after reaching the plastic deformation phase with a slow increase in the incident energy. The reflected energy change curve of the stress wave is complicated, mainly due to the deformation occurring during the bolt stretching process, resulting in different degrees of attenuation of the stress wave energy. It can also be seen that the attenuating energy is increasing with the increase in tensile axial displacements. In the elastic phase, the bolt stretching makes the bolt thinner, the wavefront surface diffusion energy of the incident wave decreases, the sensor receives an increased signal, the incident energy increases, and the reflected energy attenuation increases accordingly. However, the incident energy, reflected energy, and attenuating energy increase linearly due to the reversible elastic deformation of the bolt, and no internal damage occurs. During the yielding stage, the reflected and transmitted energy of stress wave propagation in the bolt increases, showing that the attenuation energy continues to increase and the attenuation gradually becomes slower. At the beginning of the strengthening stage, the stress wave propagation in the bolt is similar to the yielding stage, and the attenuation energy of the stress wave also increases slowly. At the later stage of the strengthening stage, the attenuation of the stress wave energy starts to increase and the energy attenuation rate is accelerated. After reaching the necking fracture stage, cracks begin to appear in the bolt and necking occurs. When the stress wave propagation meets the crack and necking, the reflection and transmission are stronger, and the energy decay is more and faster than that in the later stage of strengthening.

After analyzing the incident energy, reflected energy, and attenuation energy at the moment of applying different axial displacements to the bolt, a stress wave energy attenuation ratio, i.e., the ratio of attenuation energy to incident energy, is proposed to determine the tensile state at the time of bolt detection. The stress wave energy attenuation ratio curve of the tensile process of the bolt is shown in Figure 11.

As can be observed in Figure 11, after converting the energy attenuation process occurring during the stress wave detection of the bolt tension process into the attenuation ratio, it is obvious that the trend of the stress wave attenuation ratio varies at different tension stages. The stress wave energy attenuation ratio increases linearly during the elastic and yielding phases, with an initial attenuation ratio of about 20%. After reaching the strengthening phase, the stress wave energy attenuation ratio remains at a relatively stable level, with a slight oscillation in the attenuation ratio of 33%. In the necking fracture stage, the stress wave energy attenuation ratio reaches 35% (marked with a purple dotted line in the figure) and increases exponentially until the bolt fractures. The analysis found that the energy attenuation ratio of the stress wave signal can be employed as an indicator for early warning when the bolt is necked, and the bolt is necked when the stress wave energy attenuation ratio reaches 35%. In addition, the energy attenuation ratio increases exponentially as necking continues to take place.

②

Frequency domain feature analysis

The Fourier transform of the time domain waveform of the stress waveform of the bolt stretching process was performed to obtain the frequency domain diagram at different axial displacements of the stretching. Figure 12 shows the frequency domain diagram of the stress wave signal at different stages of bolt tension.

Figure 12a,b shows the frequency domain diagram of stress wave detection in the elastic stage of bolt stretching. From Figure 12a, it can be seen that the dominant frequency of the stress wave signal is around 8 kHz when it is not stretched. The frequency domain diagram contains multiple wave peaks. With the application of axial displacement, the stress wave frequency concentrates toward 6 k–12 kHz and the dominant frequency is more prominent. Reaching the yielding stage, as shown in Figure 12c, the dominant frequency starts to increase slowly and the frequency interval becomes more concentrated, with frequencies mainly distributed in the 6 k–10 kHz frequency interval. Figure 12d–f shows the frequency domain diagram of the stress wave signal when the bolt is in the strengthening stage. There is a clear wave in the frequency domain plot in addition to the dominant frequency. The dominant frequency in the pre-strengthening phase is 8500 Hz and the second wave peaks at 9500 Hz. 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 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.

3.2.3. 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 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. During the intensification phase, although the curve segment shows a decreasing trend due to the oscillation of the energy attenuation ratio, the size of the diameter of the necking position does not correspond to the energy attenuation ratio. When the necking fracture stage is reached, there is a buffer zone in the curve, and the diameter reduction rate in the buffer zone is slow. At this time, the bolt necking has not yet shown obvious necking, cracks continue to develop, stress concentration appears, and after the stress concentration exceeds the limit of the bolt, a visible necking starts to appear, and the diameter reduction rate is rapid after the necking occurs.

In order to verify the correct correspondence between the stress wave signal attenuation energy ratio and the diameter of the bolt necking position in the bolt stretching process obtained from the test, the data of the diameter of the necking position and the energy attenuation ratio were fitted, as shown in Figure 14. The curve fitting results show that the data conform to the exponential distribution, and the fitted curve expression is shown in the graph. R² is the coefficient of determination. The closer to 1 means the better the fitting effect [31]. R² = 0.93876 means that the fitting formula can show the correspondence between the diameter of the bolt necking fracture location and the attenuation energy ratio during bolt stretching.

4. Experimental Verification of Bolt Necking Position Diameter Test Based on Stress Wave Energy Attenuation Ratio

The bolt tension test is performed using the bolt tension and stress wave detection test system. By observing the axial load–displacement curve of bolt tension, the bolt tension can be well controlled after reaching the tensile strength (when the axial load starts to decrease) and before the bolt fracture. At this time, the bolt is in the necking fracture stage, and stress wave nondestructive testing is performed. The stress wave results are processed and analyzed to obtain the stress wave energy attenuation ratio at this moment, and the corresponding bolt necking position diameter size is calculated according to the fitting formula above, and then compared with the bolt diameter size obtained from the bolt state monitoring device to calculate the error rate size of the stress wave method detection results.

A total of six sets of data were obtained from two bolts at three different random moments during the necking fracture stage using the stress wave method. The test results and errors of the validation experiments are shown in

Table 3. Validation of experimental test results and errors.

Specimen Number	Measurement Results (mm)		Detection Error (%)
	Bolt State Monitoring Device	Stress Wave Method
yz 1-1	18.112	18.02	0.51
yz 1-2	17.794	17.061	4.12
yz 1-3	15.319	15.089	1.5
yz 2-1	18.257	18.514	1.41
yz 2-2	18.035	17.709	1.81
yz 2-3	16.11	15.736	2.32

. Comparing the measurement results of the bolt state monitoring device with the detection results of the stress wave method, the average error of the detection results of the stress wave method was 1.945%, and the maximum and minimum values of the detection error were 4.12% and 0.51%, respectively, with a maximum difference of 3.61% in the detection error. Figure 15 shows the comparison of the measurement results and the error curve. It can be seen that the overall error of the stress wave method is small and stable, which indicates that it is feasible to use the stress wave signal energy attenuation ratio as the standard for detecting the diameter of the bolt necking position, and it can identify whether the bolt is in the necking fracture stage.

5. Conclusions

In order to study the deformation characteristics of bolts and stress wave propagation characteristics in bolts under axial tensile stress, an experimental study was conducted and verified using the custom bolt tensile and stress wave detection test system. Based on the work completed, the following conclusions can be drawn:

• After processing and analyzing the displacement, load, and image data obtained in the bolt tensile test and when the low loading speed is applied, it is found that the bolt tensile process undergoes four stages, and, finally, ductile fracture occurs. The change rule of the diameter of the bolt in the necking position during the tensile process elucidates the axial and radial deformation characteristics of bolts in different positions during stretching. It lays a foundation for better research on the propagation characteristics of stress waves in the bolt during the tensile process in stages.
• The time domain characteristic analysis of the stress wave signal during the bolt stretching process shows that the attenuation energy ratio of the bolt is generally increased. The deformation caused by the bolt tension makes the stress wave reflect and transmit in different degrees when it propagates in the bolt. It leads to the attenuation of stress wave energy, and the amplitude attenuation rule is different in the stress wave time domain diagram. The energy decay rate is faster in the elastic stage, yield stage, and necking fracture stage. The energy attenuation ratio is about 20% without stretching. When stretching to the elastic and yield stage, the attenuation ratio of stress wave energy increases linearly to 30–35%. After reaching the strengthening stage, the energy attenuation ratio of the stress wave remains at a relatively stable level, with slight oscillations between 33%. The attenuation of stress wave energy at the necking fracture stage reaches 35%. As necking continues to occur, the energy attenuation ratio increases exponentially.
• The frequency domain characteristic analysis of the stress wave signal during the bolt stretching process shows that the frequency distribution of the stress wave signal in the frequency domain ranges from scattered 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.
• Based on the fitting analysis of the test data, the fitting formula between the energy attenuation ratio of the stress wave signal and the diameter of the bolt necking position during the bolt stretching process is obtained. The verification test results showed that the error of the stress wave method is small and stable, which can effectively identify whether the bolt is in the necking state. The research in this paper demonstrates the successful application of the proposed method in the laboratory and provides a reference for research on nondestructive testing of bolt stress waves. Our future work will focus on field trials.