A Fiber Bragg Grating (FBG)-Enabled Smart Washer for Bolt Pre-Load Measurement: Design, Analysis, Calibration, and Experimental Validation

A washer is a common structural element that is directly used along the loading path of a bolted connection. Pre-load on a bolted connection directly impacts its load bearing capacity and pre-load monitoring is an important aspect of structural health monitoring (SHM). With the change of the pre-load on a bolted connection, the loading force on the washer will change and, therefore, the outer diameter and outer circumferential length of the washer will change. Taking advantage of the high sensitivity and the small size of a Fiber Bragg Grating (FBG) sensor, we propose an innovative smart washer encircled by an FBG sensor that can directly measure the circumferential strain change and, therefore, the pre-load on the washer. For protection, the FBG is embedded in a pre-machined groove along the circumferential surface of the washer. A theoretical approach is used to derive the linear relationship between the applied load and the circumferential strain of the washer. To validate the functionality of the FBG-enabled smart sensor for in situ bolt pre-load monitoring, a simple but effective testing apparatus is designed and fabricated. The apparatus involves a bolt, the FBG-enabled washer, a metal plate, and a nut. The bolt has an embedded FBG along its axial direction for precise axial strain and, therefore, force measurement. With the calibrated axial force measuring bolt, in situ experiments on the FBG-enabled smart washers are conducted. Experimental results reveal the linear relationship between the pre-load and the wavelength of the FBG sensor encircling the washer. Both analytical and experimental results demonstrate that the proposed novel approach is sensitive to the bolt pre-load and can monitor in real time the bolt looseness in the entire loading range.


Introduction
As one of the most common types of structural connection, bolted joints are commonly used in civil structures, such as long-span bridges and high-rise buildings [1,2]. The pre-load of a bolt connection directly impacts its load bearing capacity and plays an important role in the structural wellbeing [1,2]. With the recent emphasis on and development of Structural Health Monitoring (SHM) [3][4][5][6][7], bolt pre-load monitoring has begun to receive attention and various methods have been proposed [8][9][10]. Wang et al. [11] conducted a review on bolted connection monitoring, which reviewed the acoustoelastic method [12], the piezoelectric active sensing method [13], and the piezoelectric impedance method [14]. This paper proposes a new approach to quantitative bolt looseness monitoring by using a Fiber Bragg Grating enabled smart washer for the entire range of the applied torque. In this research, the FBG sensor was embedded into a pre-machined circumferential groove which was located in the exterior washer surface. Since the washer is directly on the loading path of a bolted connection, the FBG-enabled smart washer is very sensitive to the pre-load changes and it can continue to monitor the pre-load during the entire loading range. By analyzing the wavelength change, different bolt looseness statuses can be monitored quantitatively. Experimental results demonstrate that the FBG-enabled smart washer is a simple, feasible, and quantitative method to monitor the pre-load level.

Fiber Bragg Grating (FBG)-Enabled Smart Washer: Principle and Design
The fiber Bragg grating, as shown in Figure 1, is a wavelength-dependent filter/reflector formed by introducing a periodic refractive index structure, with spacing on the order of a wavelength of light, within the core of an optical fiber [39]. When a light passes through the grating at a particular wavelength, called the Bragg wavelength, the light will be reflected [40]. The Bragg wavelength is expressed as where λ B is the Bragg wavelength, n is the effective refractive index of the FBG, and Λ is the grating period. This paper proposes a new approach to quantitative bolt looseness monitoring by using a Fiber Bragg Grating enabled smart washer for the entire range of the applied torque. In this research, the FBG sensor was embedded into a pre-machined circumferential groove which was located in the exterior washer surface. Since the washer is directly on the loading path of a bolted connection, the FBG-enabled smart washer is very sensitive to the pre-load changes and it can continue to monitor the pre-load during the entire loading range. By analyzing the wavelength change, different bolt looseness statuses can be monitored quantitatively. Experimental results demonstrate that the FBGenabled smart washer is a simple, feasible, and quantitative method to monitor the pre-load level.

Fiber Bragg Grating (FBG)-Enabled Smart Washer: Principle and Design
The fiber Bragg grating, as shown in Figure 1, is a wavelength-dependent filter/reflector formed by introducing a periodic refractive index structure, with spacing on the order of a wavelength of light, within the core of an optical fiber [39]. When a light passes through the grating at a particular wavelength, called the Bragg wavelength, the light will be reflected [40]. The Bragg wavelength is expressed as where λB is the Bragg wavelength, n is the effective refractive index of the FBG, and Λ is the grating period. When a broad-spectrum light signal is input to the Fiber Bragg Grating section, a reflected spectrum whose center wavelength is λB will be reflected and the remaining portion of light will transmit through. The reflected light can be used as an index to measure strain, temperature, or polarization changes by the Bragg wavelength shift. In this study, a commercially available coated FBG sensor was used to enable a washer to have the function to monitor the pre-load of a bolted connection. The length of the Bragg grating is 10 mm, the outer diameter of the fiber is 250 μm, and the diameter of the optical fiber core is 9 μm.
The smart washer design is illustrated in Figure 2a. The smart washer is formed by encircling the washer by an optical fiber with an FBG sensor. First of all, a smooth groove was pre-machined along the outer surface of the washer. Then, 502 glue was used to bond the fiber to the washer, after the sensor was attached to the washer. Epoxy resin was then used to strengthen the strain transfer between fiber and washer. Last, 704 glue was used to protect the fiber from damage. Figure 2b shows photos of a fabricated smart washer. In this research, the inner and outer diameters of the smart washer are 23 mm and 37 mm, respectively. The height is 5 mm. The depth and width of the groove are 1.5 mm and 2 mm, respectively. With the change of the pre-load on a bolted connection, the loading force on the washer will change and, therefore, the outer diameter and outer circumferential length of the washer will change, which is directly measured by the FBG sensor. Taking advantage of the FBG sensor, including its high sensitivity, the proposed smart washer can accurately measure When a broad-spectrum light signal is input to the Fiber Bragg Grating section, a reflected spectrum whose center wavelength is λ B will be reflected and the remaining portion of light will transmit through. The reflected light can be used as an index to measure strain, temperature, or polarization changes by the Bragg wavelength shift. In this study, a commercially available coated FBG sensor was used to enable a washer to have the function to monitor the pre-load of a bolted connection. The length of the Bragg grating is 10 mm, the outer diameter of the fiber is 250 µm, and the diameter of the optical fiber core is 9 µm.
The smart washer design is illustrated in Figure 2a. The smart washer is formed by encircling the washer by an optical fiber with an FBG sensor. First of all, a smooth groove was pre-machined along the outer surface of the washer. Then, 502 glue was used to bond the fiber to the washer, after the sensor was attached to the washer. Epoxy resin was then used to strengthen the strain transfer between fiber and washer. Last, 704 glue was used to protect the fiber from damage. Figure 2b shows photos of a fabricated smart washer. In this research, the inner and outer diameters of the smart washer are 23 mm and 37 mm, respectively. The height is 5 mm. The depth and width of the groove are 1.5 mm and 2 mm, respectively. With the change of the pre-load on a bolted connection, the loading force on the washer will change and, therefore, the outer diameter and outer circumferential length of the washer will change, which is directly measured by the FBG sensor. Taking advantage of the FBG sensor, including its high sensitivity, the proposed smart washer can accurately measure the pre-load on a bolted joint and detect the looseness of a bolted joint, as demonstrated in later sections. For the smart washer with the FBG sensor, the delicate part is the fiber with gratings (about 10 mm), which is embedded in the pre-machined groove on the washer with protection of glue and epoxy. The rest of the fiber can use commercially available steel-reinforced or Kevlar-reinforced fiber. Therefore, the smart washer design is suitable for practical applications.

Smart Washer-An Analytical Model
The smart washer that is proposed to monitor the bolt pre-load looseness is based on monitoring of the circumferential strain change by an FBG sensor whose wavelength changes with the circumferential strain. It is necessary to analyze the relationship between the pre-load and the circumferential strain. An in-service washer model is shown in Figure 3, which clearly shows that pre-load on the washer induces circumferential strain changes for the washer. For the smart washer with the FBG sensor, the delicate part is the fiber with gratings (about 10 mm), which is embedded in the pre-machined groove on the washer with protection of glue and epoxy. The rest of the fiber can use commercially available steel-reinforced or Kevlar-reinforced fiber. Therefore, the smart washer design is suitable for practical applications.

Smart Washer-An Analytical Model
The smart washer that is proposed to monitor the bolt pre-load looseness is based on monitoring of the circumferential strain change by an FBG sensor whose wavelength changes with the circumferential strain. It is necessary to analyze the relationship between the pre-load and the circumferential strain. An in-service washer model is shown in Figure 3, which clearly shows that pre-load on the washer induces circumferential strain changes for the washer.  An axial force on the bolt results in a uniform stress on the washer upper and lower surfaces, and the stress change can be expressed as where Δσ is the axial stress change of the washer, and A is the washer's upper surface area which is given as where D1 and D2 are the external and internal nominal diameters of the washer without torque applied, and D'1 and D'2 are the external and internal nominal diameters of the washer with torque applied as shown in Figure 3b,c. The axial strain change which is represented as Δεl is introduced as where E is the Young's modulus of the washer. According to the Poisson ratio, the transverse strain change ΔεD can be expressed as An axial force on the bolt results in a uniform stress on the washer upper and lower surfaces, and the stress change can be expressed as where ∆σ is the axial stress change of the washer, and A is the washer's upper surface area which is given as where D 1 and D 2 are the external and internal nominal diameters of the washer without torque applied, and D' 1 and D' 2 are the external and internal nominal diameters of the washer with torque applied as shown in Figure 3b,c. The axial strain change which is represented as ∆ε l is introduced as where E is the Young's modulus of the washer. According to the Poisson ratio, the transverse strain change ∆ε D can be expressed as Please note that the ∆ε D can also be expressed as where ∆D 1 is the pre-load decrease caused the external nominal diameter change, and the circumferential strain ∆ε c is given as where C 1 is the external circumferential without torque applied, and ∆C 1 is the pre-load decrease caused by the external perimeter change.
The relationship between the embedded Bragg wavelength change ∆λ w and the washer strain change ∆ε c can be presented as where k w is the strain sensitivity coefficient. From Equations (6) and (7), we know that ∆ε c is equal to ∆ε D . Substituting Equations (1)-(6) into Equation (7) gives the expression of ∆ε c as There is a linear relationship between the torque and the washer circumferential strain. The FBG wavelength can be expressed as where λ i is the initial wavelength, and µ and E are, respectively, the Poisson's ratio and Young's modulus of the washer.

Smart Washer-Calibration
The relationship between the axial stress and the wavelength of the FBG sensor was investigated though calibration tests. Figure 4 shows the calibration setup of the calibration test. Please note that the ΔεD can also be expressed as where ΔD1 is the pre-load decrease caused the external nominal diameter change, and the circumferential strain Δεc is given as where C1 is the external circumferential without torque applied, and ΔC1 is the pre-load decrease caused by the external perimeter change.
The relationship between the embedded Bragg wavelength change Δλw and the washer strain change Δεc can be presented as where kw is the strain sensitivity coefficient. From Equations (6) and (7), we know that Δεc is equal to ΔεD. Substituting Equations (1)-(6) into Equation (7) gives the expression of Δεc as There is a linear relationship between the torque and the washer circumferential strain. The FBG wavelength can be expressed as where λi is the initial wavelength, and μ and E are, respectively, the Poisson's ratio and Young's modulus of the washer.

Smart Washer-Calibration
The relationship between the axial stress and the wavelength of the FBG sensor was investigated though calibration tests. Figure 4 shows the calibration setup of the calibration test. The smart washer was loaded continuously from 0 kN to 20 kN with a load speed of 200 N/s. The strain change of the washer can be recorded by the universal testing machine. Three calibration tests were implemented and the results are plotted in Figure 5. Please note that the values of both the strain (the left ordinate) and the axial force (the right ordinate) are shown in Figure 5. The average experimental strain sensitivity coefficient of the FBG sensor is 0.8040 με/pm. The coefficient of regression association can be calculated by following equation and is found to be 0.9995: The smart washer was loaded continuously from 0 kN to 20 kN with a load speed of 200 N/s. The strain change of the washer can be recorded by the universal testing machine. Three calibration tests were implemented and the results are plotted in Figure 5. Please note that the values of both the strain (the left ordinate) and the axial force (the right ordinate) are shown in Figure 5. The average experimental strain sensitivity coefficient of the FBG sensor is 0.8040 µε/pm. The coefficient of regression association can be calculated by following equation and is found to be 0.9995: (11) whereŷ i and y i are the calculated regression value and measured value at the ith point, and y is the mean value of all measured sample points.
It is shown that the FBG smart washer sensor is stable and capable of measuring the axial stress level, which demonstrates the potential of the smart washer to monitor the looseness of a bolted connection. In addition, we did not experience noticeable loss of the light intensity for the washer that we have used during the experiments. We also noticed that there is no saturation in Figure 5, which shows the advantage of the FBG-based smart washer over the piezoceramic-based active sensing method which has the saturation issue [15][16][17]. where ˆi y and yi are the calculated regression value and measured value at the ith point, and y is the mean value of all measured sample points. It is shown that the FBG smart washer sensor is stable and capable of measuring the axial stress level, which demonstrates the potential of the smart washer to monitor the looseness of a bolted connection. In addition, we did not experience noticeable loss of the light intensity for the washer that we have used during the experiments. We also noticed that there is no saturation in Figure 5, which shows the advantage of the FBG-based smart washer over the piezoceramic-based active sensing method which has the saturation issue [15][16][17].

Experimental Setup
As shown in Figure 6, the bolt looseness test specimen, which consists of one metal plate, a bolt, and a nut with an option of adding a washer, is used in the research. The pre-load on the bolt is controlled by a torque wrench and the stress on the bolt is measured by a smart bolt that has an embedded FBG sensor. The experimental setup is illustrated in Figure 7. The torque wrench is used to apply the required torque to the specimen to explore the relationship between the applied torque and the bolt axial force that is measured by the smart bolt.

Experimental Setup
As shown in Figure 6, the bolt looseness test specimen, which consists of one metal plate, a bolt, and a nut with an option of adding a washer, is used in the research. The pre-load on the bolt is controlled by a torque wrench and the stress on the bolt is measured by a smart bolt that has an embedded FBG sensor. The experimental setup is illustrated in Figure 7. The torque wrench is used to apply the required torque to the specimen to explore the relationship between the applied torque and the bolt axial force that is measured by the smart bolt.
where ˆi y and yi are the calculated regression value and measured value at the ith point, and y is the mean value of all measured sample points. It is shown that the FBG smart washer sensor is stable and capable of measuring the axial stress level, which demonstrates the potential of the smart washer to monitor the looseness of a bolted connection. In addition, we did not experience noticeable loss of the light intensity for the washer that we have used during the experiments. We also noticed that there is no saturation in Figure 5, which shows the advantage of the FBG-based smart washer over the piezoceramic-based active sensing method which has the saturation issue [15][16][17].

Experimental Setup
As shown in Figure 6, the bolt looseness test specimen, which consists of one metal plate, a bolt, and a nut with an option of adding a washer, is used in the research. The pre-load on the bolt is controlled by a torque wrench and the stress on the bolt is measured by a smart bolt that has an embedded FBG sensor. The experimental setup is illustrated in Figure 7. The torque wrench is used to apply the required torque to the specimen to explore the relationship between the applied torque and the bolt axial force that is measured by the smart bolt.   The smart bolt was made by embedding a specially treated FBG sensor which includes two gripper tubes and two mounting supports into the center of the bolt. More detailed information can be found in [41]. With the help of the FBG sensor, the smart bolt can measure the axial forces when an external torque is applied. The design and a photo of the smart bolt are shown in Figures 8 and 9, respectively.

Relationship Between Pre-Load and External Torque with Help from a Smart Bolt
In the monitoring process, the bolted connection with a smart washer was fastened by applying external torque. Therefore, the relationship between applied torque and the axial load of the bolt should be first studied. The mechanical behavior of bolted joints during loosening and fastening was investigated [42][43][44][45]. The research results show that the torque applied to a bolted connection consists of three components [43,46]: (1) the torque to stretch the bolt; (2) the torque to overcome the friction in the threads of the bolt; and (3) the friction between nut face and bearing surface. In practice, it is appropriate to use the following equation to determine the torque to achieve a certain pre-load [47]: where F is the axial pre-load of the bolt, T is the applied torque, k is the torque-axial load coefficient determined by factors such as bolt type and lubricant, and d is the nominal diameter of the bolt. The relationship between the smart bolt strain change ΔεB and the embedded Bragg wavelength change ΔλB can be presented as The smart bolt was made by embedding a specially treated FBG sensor which includes two gripper tubes and two mounting supports into the center of the bolt. More detailed information can be found in [41]. With the help of the FBG sensor, the smart bolt can measure the axial forces when an external torque is applied. The design and a photo of the smart bolt are shown in Figures 8  and 9, respectively. The smart bolt was made by embedding a specially treated FBG sensor which includes two gripper tubes and two mounting supports into the center of the bolt. More detailed information can be found in [41]. With the help of the FBG sensor, the smart bolt can measure the axial forces when an external torque is applied. The design and a photo of the smart bolt are shown in Figures 8 and 9, respectively.

Relationship Between Pre-Load and External Torque with Help from a Smart Bolt
In the monitoring process, the bolted connection with a smart washer was fastened by applying external torque. Therefore, the relationship between applied torque and the axial load of the bolt should be first studied. The mechanical behavior of bolted joints during loosening and fastening was investigated [42][43][44][45]. The research results show that the torque applied to a bolted connection consists of three components [43,46]: (1) the torque to stretch the bolt; (2) the torque to overcome the friction in the threads of the bolt; and (3) the friction between nut face and bearing surface. In practice, it is appropriate to use the following equation to determine the torque to achieve a certain pre-load [47]: where F is the axial pre-load of the bolt, T is the applied torque, k is the torque-axial load coefficient determined by factors such as bolt type and lubricant, and d is the nominal diameter of the bolt. The relationship between the smart bolt strain change ΔεB and the embedded Bragg wavelength change ΔλB can be presented as The smart bolt was made by embedding a specially treated FBG sensor which includes two gripper tubes and two mounting supports into the center of the bolt. More detailed information can be found in [41]. With the help of the FBG sensor, the smart bolt can measure the axial forces when an external torque is applied. The design and a photo of the smart bolt are shown in Figures 8 and 9, respectively.

Relationship Between Pre-Load and External Torque with Help from a Smart Bolt
In the monitoring process, the bolted connection with a smart washer was fastened by applying external torque. Therefore, the relationship between applied torque and the axial load of the bolt should be first studied. The mechanical behavior of bolted joints during loosening and fastening was investigated [42][43][44][45]. The research results show that the torque applied to a bolted connection consists of three components [43,46]: (1) the torque to stretch the bolt; (2) the torque to overcome the friction in the threads of the bolt; and (3) the friction between nut face and bearing surface. In practice, it is appropriate to use the following equation to determine the torque to achieve a certain pre-load [47]: where F is the axial pre-load of the bolt, T is the applied torque, k is the torque-axial load coefficient determined by factors such as bolt type and lubricant, and d is the nominal diameter of the bolt. The relationship between the smart bolt strain change ΔεB and the embedded Bragg wavelength change ΔλB can be presented as Figure 9. A photo of the FBG-based smart bolt that is used to measure the axial loading.

Relationship Between Pre-Load and External Torque with Help from a Smart Bolt
In the monitoring process, the bolted connection with a smart washer was fastened by applying external torque. Therefore, the relationship between applied torque and the axial load of the bolt should be first studied. The mechanical behavior of bolted joints during loosening and fastening was investigated [42][43][44][45]. The research results show that the torque applied to a bolted connection consists of three components [43,46]: (1) the torque to stretch the bolt; (2) the torque to overcome the friction in the threads of the bolt; and (3) the friction between nut face and bearing surface. In practice, it is appropriate to use the following equation to determine the torque to achieve a certain pre-load [47]: where F is the axial pre-load of the bolt, T is the applied torque, k is the torque-axial load coefficient determined by factors such as bolt type and lubricant, and d is the nominal diameter of the bolt.
The relationship between the smart bolt strain change ∆ε B and the embedded Bragg wavelength change ∆λ B can be presented as where k b is the strain transfer constant coefficients. According to Equation (13), the Bragg wavelength change linearly corresponds to the smart bolt strain change. The bolt axial stress change ∆σ B is also linear with the strain change ∆ε B as where the E B is the Young's modulus of the bolt. The bolt axial stress change ∆σ B can be expressed as Substituting Equations (12)- (14) into Equation (15) gives the relationship between the applied torque T and the Bragg wavelength change ∆λ B as To study the relationship between the axial force and the applied torque, an experiment using the FBG smart bolt [39] to monitor the axial force was conducted. Because of the limitations of the torque wrench, it can only measure the increased torque. Therefore, the reversed process of pre-load looseness was investigated this study.
The designed torque loading process is from 0-120 N·m at intervals of 10 N·m. Since the torque in this paper was applied by a manual torque wrench, there was variation in torque increment in each loading case. In order to specifically show the relationship between the external torque and wavelength change, Figure 10 is plotted and a perfect linear fitting line between the external torque and wavelength change is obtained. Please note that the values of both Bragg wavelength (the left ordinate) and the axial force (the right ordinate) are shown in Figure 5. The linear relationship validates the correctness of the analysis of Equation (16), which confirms that the FBG-based smart bolt is an accurate tool to measure the axial loading on a bolted connection.
where kb is the strain transfer constant coefficients. According to Equation (13), the Bragg wavelength change linearly corresponds to the smart bolt strain change. The bolt axial stress change ΔσB is also linear with the strain change ΔεB as where the EB is the Young's modulus of the bolt. The bolt axial stress change ΔσB can be expressed as Substituting Equations (12)- (14) into Equation (15) gives the relationship between the applied torque T and the Bragg wavelength change ΔλB as To study the relationship between the axial force and the applied torque, an experiment using the FBG smart bolt [39] to monitor the axial force was conducted. Because of the limitations of the torque wrench, it can only measure the increased torque. Therefore, the reversed process of pre-load looseness was investigated this study.
The designed torque loading process is from 0-120 N·m at intervals of 10 N·m. Since the torque in this paper was applied by a manual torque wrench, there was variation in torque increment in each loading case. In order to specifically show the relationship between the external torque and wavelength change, Figure 10 is plotted and a perfect linear fitting line between the external torque and wavelength change is obtained. Please note that the values of both Bragg wavelength (the left ordinate) and the axial force (the right ordinate) are shown in Figure 5. The linear relationship validates the correctness of the analysis of Equation (16), which confirms that the FBG-based smart bolt is an accurate tool to measure the axial loading on a bolted connection.

Quantitative Monitoring of Bolt Pre-Load Using an FBG-Based Smart Washer
In this experiment, the pre-load is also controlled by the torque wrench. The instrumentation of the quantitative monitoring of the bolt pre-load is the same as that shown in Figures 6 and 7.
The bolt pre-load loading process is from 0-120 N·m at intervals of 10 N·m. With the increase of applied torque, the Bragg wavelength changes, as shown in Figure 11.

Quantitative Monitoring of Bolt Pre-Load Using an FBG-Based Smart Washer
In this experiment, the pre-load is also controlled by the torque wrench. The instrumentation of the quantitative monitoring of the bolt pre-load is the same as that shown in Figures 6 and 7.
The bolt pre-load loading process is from 0-120 N·m at intervals of 10 N·m. With the increase of applied torque, the Bragg wavelength changes, as shown in Figure 11. As shown in Figure 11, each step of the wavelength change is caused by the increased torque with an interval of 10 N·m from 0-120 N·m. Based on Figure 11, the relationship between the FBG wavelength and the axial force (pre-load) versus the applied torque based on experimental data is shown in Figure 12. Please note that the values of both the FBG wavelength (the left ordinate) and the axial force (the right ordinate) are shown in Figure 12. It is clear that a linear relationship is achieved without saturation.

Validation between Theoretical and Experimental Results
In order to validate the analytical model, a comparison study of theoretical and experimental results was conducted. Substituting Equation (12) into Equation (10), the relationship between torque and the FBG smart washer wavelength can be expressed as In this experiment, kw is 0.8040, which can be obtained from the calibration test; μ and E are the Poisson's ratio and Young's modulus of the washer, which are 0.32 and 2 × 10 5 Mpa, respectively; k is 0.1; and d is the nominal diameter of the bolt, which is 0.02 m in this experiment. In addition, D1 and D2 are 0.037 m and 0.023 m, respectively. The comparison of the theoretical and three experimental results is plotted in Figure 12.
In Figure 12, it can be seen that when the torque is larger than 30 N·m, the increase of the wavelength is around 10 pm when the torque has a 10 N·m increase. The results show that it is feasible to detect the pre-load degradation by monitoring circumferential strain change of the fabricated As shown in Figure 11, each step of the wavelength change is caused by the increased torque with an interval of 10 N·m from 0-120 N·m. Based on Figure 11, the relationship between the FBG wavelength and the axial force (pre-load) versus the applied torque based on experimental data is shown in Figure 12. Please note that the values of both the FBG wavelength (the left ordinate) and the axial force (the right ordinate) are shown in Figure 12. It is clear that a linear relationship is achieved without saturation. As shown in Figure 11, each step of the wavelength change is caused by the increased torque with an interval of 10 N·m from 0-120 N·m. Based on Figure 11, the relationship between the FBG wavelength and the axial force (pre-load) versus the applied torque based on experimental data is shown in Figure 12. Please note that the values of both the FBG wavelength (the left ordinate) and the axial force (the right ordinate) are shown in Figure 12. It is clear that a linear relationship is achieved without saturation.

Validation between Theoretical and Experimental Results
In order to validate the analytical model, a comparison study of theoretical and experimental results was conducted. Substituting Equation (12) into Equation (10), the relationship between torque and the FBG smart washer wavelength can be expressed as In this experiment, kw is 0.8040, which can be obtained from the calibration test; μ and E are the Poisson's ratio and Young's modulus of the washer, which are 0.32 and 2 × 10 5 Mpa, respectively; k is 0.1; and d is the nominal diameter of the bolt, which is 0.02 m in this experiment. In addition, D1 and D2 are 0.037 m and 0.023 m, respectively. The comparison of the theoretical and three experimental results is plotted in Figure 12.
In Figure 12, it can be seen that when the torque is larger than 30 N·m, the increase of the wavelength is around 10 pm when the torque has a 10 N·m increase. The results show that it is feasible to detect the pre-load degradation by monitoring circumferential strain change of the fabricated

Validation between Theoretical and Experimental Results
In order to validate the analytical model, a comparison study of theoretical and experimental results was conducted. Substituting Equation (12) into Equation (10), the relationship between torque and the FBG smart washer wavelength can be expressed as λ c = k w ·∆ε c + λ i = k w ·µ· 4 * T π·E·k·d·((D 1 ) 2 − (D 2 ) 2 ) In this experiment, k w is 0.8040, which can be obtained from the calibration test; µ and E are the Poisson's ratio and Young's modulus of the washer, which are 0.32 and 2 × 10 5 Mpa, respectively; k is 0.1; and d is the nominal diameter of the bolt, which is 0.02 m in this experiment. In addition, D 1 and D 2 are 0.037 m and 0.023 m, respectively. The comparison of the theoretical and three experimental results is plotted in Figure 12.
In Figure 12, it can be seen that when the torque is larger than 30 N·m, the increase of the wavelength is around 10 pm when the torque has a 10 N·m increase. The results show that it is feasible to detect the pre-load degradation by monitoring circumferential strain change of the fabricated smart washer with good repeatability. The linear relationship was obtained based on the repeated experimental data when the applied torque is higher than 30 N·m. The comparison shows that the theoretical analysis is slightly close to the experimental results. The experimental results validate the analytical ones. Once again, there is no saturation in Figure 12, which clearly shows the advantage of the FBG-based smart washer over the piezoceramic-based active sensing method which has the saturation issue [15][16][17].

Conclusions and Future Work
This paper developed a simple but effective Fiber Bragg Grating (FBG)-enabled smart washer to monitor the pre-load of a bolt connection and to detect bolt looseness during its entire loading range. The smart washer was formed by encircling the washer by an optical fiber with an FBG sensor that was embedded in a pre-machined groove along the outer surface of the washer. A theoretical approach was used to derive the linear relationship between the applied load and the circumferential strain of the washer, which was directly measured by the FBG sensor. Taking advantage of an FBG sensor including its high sensitivity, the proposed smart washer can accurately measure the pre-load on a bolted joint. To validate the functionality of the FBG-enabled smart sensor for in situ bolt pre-load monitoring, a simple but effective testing apparatus was designed and fabricated. Experimental results demonstrate the linear relationship between the pre-load and the wavelength of the FBG sensor encircling the washer. Both analytical and experimental results reveal that the proposed novel approach is sensitive to the bolt pre-load and can monitor in real time the bolt looseness in the torque loading range. Future work will include incorporation of a temperature compensation scheme with the smart washer and analytical study of strain transfer from the washer to the FBG sensor.