Burial Depth Effect of Crack on the Lcr Wave Acoustoelastic Coefficient for Stress Measurement of Laser Cladding Coating

In this paper, the influence of burial depth of crack on stress measurement of laser cladding coating with the critical refracted longitudinal wave (Lcr wave) was discussed based on the Lcr wave acoustoelastic effect. The regular rectangular slots with different depths that were used to simulate the burial crack in coating was based on the equivalent theory. The experimental system including an ultrasonic wave generator, digital oscilloscope (2.5 GHz sampling rate), and two Lcr wave transducers (2.5 MHz center frequency) was used to collect the Lcr wave under different tensile loads, and the Lcr wave was denoised by using wavelet analysis technology, then the fracture morphology was observed using SEM. The results show that after the denoising by wavelet analysis technology, the signal-to-noise ratio of Lcr wave becomes bigger and the mean square deviation of Lcr wave becomes smaller. When the tensile load is within the turning point load, the difference in time of flight between Lcr wave increases linearly as the tensile load increases, and the deviation of the experimental results becomes obvious as the tensile load increases. When the tensile load is the same, as the burial depth of the slot increases, the nominal Lcr wave acoustoelastic coefficient decreases and tends to be stable gradually. At last, the experimental results are discussed based on the Lcr wave acoustoelastic effect and deformation theory, and it is analyzed that the uneven deformation caused by the interface in coating, anisotropic microstructure, and the burial crack is considered as the main reason.


Introduction
Stress plays an important role in the performances of coatings, so finding an effective method for stress measurement of coating appears to be particularly urgent. Generally speaking, the stress measurement method of coating can be divided into two categories, including the destructive method (such as drilling-hole method, tensile method, etc.) and non-destructive method (such as optical method, ultrasonic wave method, X-ray diffraction method, magnetic method, etc.) [1][2][3][4][5][6][7]. Due to non-destruction, convenient operation, safety, etc., the scholars' attention is attracted by the non-destructive technology, and its applications on stress evaluation also have been reported. While it should be noted that there is no absolute method for satisfying all the requirements of stress measurement, because there are lots of factors, including the characteristics, geometric shape, surface condition, etc., that should be taken into account to choose a method [8][9][10][11]. Compared with other non-destructive methods, the ultrasonic wave method has some significant advantages for evaluating stress, such as low cost, main process parameters for preparing the laser cladding Fe314 alloy coating are as follows: The laser power is 1.7 kW, the cladding velocity is 2 mm/s, and the feeding rate of powder is 16 g/min, respectively. To simulate the burial crack in coating, the regular rectangular slots with different depths were machined in the surface of Q235 steel, as shown in Figure 1. The widths of all the slots are 1.0 mm, and the burial depth of slots are 2.0, 2.5, 3.0, 3.5, and 4.0 mm, respectively. After that, all the coating samples are heat treated for relieving initial stress using the WZS-20 vacuum furnace (AOKE, Hangzhou, China), and its vacuum heat treatment parameters are listed in Table 1.

L cr Wave Acoustoelastic Theory
Under the definition of the three-dimensional plane of a medium in the orthogonal rectangular coordinate axis, shown in Figure 2, the complete tensorial description of the L cr wave acoustoelastic effect was deduced and expressed as follows [26,27]: where θ was the angle between the propagation direction of L cr wave and a 1 direction, V 0 L was the propagation velocity of L cr wave in an unstressed medium, K 1 and K 2 were L cr wave acoustoelastic coefficients along the a 1 and a 2 direction, σ 11 and σ 22 were the principal stress along the a 1 and a 2 direction.

Lcr Wave Acoustoelastic Theory
Under the definition of the three-dimensional plane of a medium in the orthogonal rectangular coordinate axis, shown in Figure 2, the complete tensorial description of the Lcr wave acoustoelastic effect was deduced and expressed as follows [26,27]: where θ was the angle between the propagation direction of Lcr wave and a1 direction, 0 L V was the propagation velocity of Lcr wave in an unstressed medium, K1 and K2 were Lcr wave acoustoelastic coefficients along the a1 and a2 direction, σ11 and σ22 were the principal stress along the a1 and a2 direction. If the propagation direction of Lcr wave was along the a1 direction, which was the loading direction, Equation (1) could be simplified as: where V1 was the propagation velocity of Lcr wave along the a1 direction. Based on the Lcr wave acoustoelastic theory, the result of K1>>K2 could be accepted [28], thus Equation (2) could be simplified as: When the propagation distance of Lcr wave was fixed, Equation (3) could be simplified as: where Δt was the difference in time of flight between Lcr wave, and σ was the stress.
Since the burial depths of cracks were different, the stress σ was replaced by the tensile load. Thus, Equation (4) could be written as follows: If the propagation direction of L cr wave was along the a 1 direction, which was the loading direction, Equation (1) could be simplified as: where V 1 was the propagation velocity of L cr wave along the a 1 direction. Based on the L cr wave acoustoelastic theory, the result of K 1 >>K 2 could be accepted [28], thus Equation (2) could be simplified as: When the propagation distance of L cr wave was fixed, Equation (3) could be simplified as: where ∆t was the difference in time of flight between L cr wave, and σ was the stress.
Since the burial depths of cracks were different, the stress σ was replaced by the tensile load. Thus, Equation (4) could be written as follows: where K was the nominal L cr wave acoustoelastic coefficient, F was the tensile load, and S was the cross-section area of the coating sample. From Equation (5), it can be known that when ∆t and F are determined, the K can be received, then the relation of the burial depth of crack and K can be determined.

The Cross-Correlation Theory
The cross-correlation function was usually used to calculate the difference in time of flight, and it can be expressed as: where R xy (τ) was the cross-correlation function, τ was the difference in time of flight between x(t) and y(t), and T was the signal period.
To eliminate the influence of the L cr wave amplitude on the difference in time of flight between signals, the cross correlation function was normalized and discretized [29], and it was defined as the cross correlation coefficient function ρ xy (τ) and written as follows: where ρ xy (τ) was the cross-correlation coefficient function, x(i) and y(i) were two different signals, and n was defined as the step length in this paper. It could be known that when the maximum of ρ xy (τ) was received, the difference in time of flight between signals could also be determined.

Experimental System for Stress Evaluation
The experimental system for stress measurement of laser cladding Fe314 alloy coating with the L cr wave consists of an ultrasonic wave generator (Olympus 5072 PR, OLYMPUS, Tokyo, Japan), digital oscilloscope (Tektronix DOP3034B, TEKTRONIX, Beaverton, OR, USA), and L cr wave transducers, including one transmitting transducer and one receiving transducer, which are designed by the authors. To meet the requirement of L cr wave sampling, the sampling rate is 2.5 GHz. For the best distance between two L cr wave transducers, the energy attenuation experiment of L cr wave propagating in coating was tested, and the results showed that when the center frequency of L cr wave is 2.5 MHz, the best propagation distance of L cr was 30 mm. In addition, the pressure holder of the L cr wave transducer was designed and employed to keep a constant pressure between L cr wave transducers and the coating surface. The calibration test of the L cr wave acoustoelastic coefficient was carried out using the SANS-CMT5205 static tensile testing machine (MTS-China, Shanghai, China).

Relation of the L cr Wave Acoustoelastic Coefficient and Burial Depth of Crack
To determine the L cr wave acoustoelastic coefficient, the L cr wave of coating with a rectangular slot was collected with the uniaxial static tension experiment. During the test, the maximal tensile load was the yield load of coating, and the loading rate was 0.5 kN/s. To collect the L cr wave of coating under different tensile loads, the preloads were determined beforehand, and each preload was held about 60 s, then the L cr wave was collected. In that process, the L cr wave transducers were placed on Materials 2020, 13, 2823 5 of 11 the top of the rectangular slot, and the L cr wave propagated along the loading direction. To avoid the influence of couplant between the L cr wave transducer and coating surface, the pressure on the L cr wave transducer was kept stably, and the L cr wave for each tensile load was collected five times repeatedly. Contrasting the L cr wave, it could be seen that under the same tensile load, there was almost no difference in the propagating time of L cr wave, it meant that the influence of the couplant on L cr wave could be ignored. In this paper, the first L cr wave of coating was analyzed and shown in Figure 3.  From Figure 3, it can be seen that for different burial depths, the change of Lcr wave along the time axis is very similar. As the tensile load increases, the Lcr wave gradually moves to the right along the time axis, it means that the propagation time of Lcr wave becomes longer. Since the propagation distance of Lcr wave is the same, the propagation velocity becomes lower as the tensile load increases. However, it should be noted that when the tensile load reaches a certain value, which is defined as a turning point load in this paper, as the tensile load increases, the change of Lcr wave is not continually regular as before, so the change on the propagation velocity of Lcr wave is irregular as the tensile load increases further. In addition, when the tensile load changes to the same, the change on the propagation time of Lcr wave is different as the burial depth changes gradually, while it is not very obvious. For that reason, the calculation accuracy of the difference in time of flight between Lcr wave seems very important. However, from the Lcr waveform, it can be seen that the noise is obvious, so the difference in time of flight is affected, which has been proven by the previous study. Therefore, the Lcr wave is denoised firstly, and the denoising parameters are optimized.
The wavelet analysis method is a commonly used method for denoising, and the main parameters of denoising include the mother wavelet, decomposition level, and the threshold method, which are discussed in this paper. From the waveform similarity, the db6 wavelet was chosen as the 14  From Figure 3, it can be seen that for different burial depths, the change of L cr wave along the time axis is very similar. As the tensile load increases, the L cr wave gradually moves to the right along the time axis, it means that the propagation time of L cr wave becomes longer. Since the propagation distance of L cr wave is the same, the propagation velocity becomes lower as the tensile load increases. However, it should be noted that when the tensile load reaches a certain value, which is defined as a turning point load in this paper, as the tensile load increases, the change of L cr wave is not continually regular as before, so the change on the propagation velocity of L cr wave is irregular as the tensile load increases further. In addition, when the tensile load changes to the same, the change on the propagation time of L cr wave is different as the burial depth changes gradually, while it is not very obvious. For that reason, the calculation accuracy of the difference in time of flight between L cr wave Materials 2020, 13, 2823 6 of 11 seems very important. However, from the L cr waveform, it can be seen that the noise is obvious, so the difference in time of flight is affected, which has been proven by the previous study. Therefore, the L cr wave is denoised firstly, and the denoising parameters are optimized.
The wavelet analysis method is a commonly used method for denoising, and the main parameters of denoising include the mother wavelet, decomposition level, and the threshold method, which are discussed in this paper. From the waveform similarity, the db6 wavelet was chosen as the mother wavelet. To get the distribution of frequency of L cr wave, the frequency domain of L cr wave of coating was extracted by using the FFT method, and the results were shown in Figure 4.  From Figure 4, it can be seen that under the 3 db theory, the main frequency domain of Lcr wave is in the range of 1.98~2.63 MHz. Compared with the center frequency of Lcr wave, the frequency domain distribution of noise can be determined. Based on that, the influence of decomposition level on the denoising result was discussed, and the results were shown in Figure 5.  Figure 5 shows that when the decomposition level is four, the noise cannot be separated from Lcr wave. When the decomposition level is five, the noise can be mainly separated from Lcr wave. When the decomposition level is six, the frequency domain of Lcr wave almost does not change compared with that of five levels. Thus, the five levels can meet the denoising requirement of Lcr wave. Based on that, the threshold method was discussed, and the result was shown in Figure 6.   From Figure 4, it can be seen that under the 3 db theory, the main frequency domain of L cr wave is in the range of 1.98~2.63 MHz. Compared with the center frequency of L cr wave, the frequency domain distribution of noise can be determined. Based on that, the influence of decomposition level on the denoising result was discussed, and the results were shown in Figure 5.  From Figure 4, it can be seen that under the 3 db theory, the main frequency domain of Lcr wave is in the range of 1.98~2.63 MHz. Compared with the center frequency of Lcr wave, the frequency domain distribution of noise can be determined. Based on that, the influence of decomposition level on the denoising result was discussed, and the results were shown in Figure 5.  Figure 5 shows that when the decomposition level is four, the noise cannot be separated from Lcr wave. When the decomposition level is five, the noise can be mainly separated from Lcr wave. When the decomposition level is six, the frequency domain of Lcr wave almost does not change compared with that of five levels. Thus, the five levels can meet the denoising requirement of Lcr wave. Based on that, the threshold method was discussed, and the result was shown in Figure 6.    Figure 5 shows that when the decomposition level is four, the noise cannot be separated from L cr wave. When the decomposition level is five, the noise can be mainly separated from L cr wave. When Materials 2020, 13, 2823 7 of 11 the decomposition level is six, the frequency domain of L cr wave almost does not change compared with that of five levels. Thus, the five levels can meet the denoising requirement of L cr wave. Based on that, the threshold method was discussed, and the result was shown in Figure 6. From Figure 6, it can be seen that compared with the denoising signal by using a soft threshold, the denoising waveform by using a hard threshold is smoother. In order to quantitatively evaluate the denoising result, the signal-to-noise ratio and the mean square deviation of Lcr wave after denoising were calculated and compared, and it was shown in Table 2.  Table 2, it can be known that compared with the results of the soft threshold, the signalto-noise ratio of the hard threshold is higher, and its mean square deviation is lower. The denoising theory indicates that a higher signal-to-noise ratio and lower mean square deviation means the better the denoising effect, so the hard threshold method is adopted in this paper. After that, the difference in time of flight between Lcr wave was determined by Equation (7). The previous studies indicated that the step length affected the accuracy of the difference in time of flight between signals, and one cycle was the most optimal step length [30]. Based on that, the difference in time of flight between Lcr wave was determined, and its relation with the tensile load was shown in Figure 7.  Figure 7, it can be seen that for different burial depths of slots, the whole trend of the difference in time of flight when the tensile load increases is very similar, but there are also some differences. For the similarities, the difference in time of flight increases linearly as the tensile load increases, which is consistent with the Lcr wave acoustoelastic theory. While when the tensile load reaches the turning point load, the difference in time of flight changes nonlinearly as the tensile load increases further. In addition, the deviation of curves from linearity becomes more obvious as the  From Figure 6, it can be seen that compared with the denoising signal by using a soft threshold, the denoising waveform by using a hard threshold is smoother. In order to quantitatively evaluate the denoising result, the signal-to-noise ratio and the mean square deviation of L cr wave after denoising were calculated and compared, and it was shown in Table 2.  Table 2, it can be known that compared with the results of the soft threshold, the signal-to-noise ratio of the hard threshold is higher, and its mean square deviation is lower. The denoising theory indicates that a higher signal-to-noise ratio and lower mean square deviation means the better the denoising effect, so the hard threshold method is adopted in this paper. After that, the difference in time of flight between L cr wave was determined by Equation (7). The previous studies indicated that the step length affected the accuracy of the difference in time of flight between signals, and one cycle was the most optimal step length [30]. Based on that, the difference in time of flight between L cr wave was determined, and its relation with the tensile load was shown in Figure 7. From Figure 6, it can be seen that compared with the denoising signal by using a soft threshold, the denoising waveform by using a hard threshold is smoother. In order to quantitatively evaluate the denoising result, the signal-to-noise ratio and the mean square deviation of Lcr wave after denoising were calculated and compared, and it was shown in Table 2. From Table 2, it can be known that compared with the results of the soft threshold, the signalto-noise ratio of the hard threshold is higher, and its mean square deviation is lower. The denoising theory indicates that a higher signal-to-noise ratio and lower mean square deviation means the better the denoising effect, so the hard threshold method is adopted in this paper. After that, the difference in time of flight between Lcr wave was determined by Equation (7). The previous studies indicated that the step length affected the accuracy of the difference in time of flight between signals, and one cycle was the most optimal step length [30]. Based on that, the difference in time of flight between Lcr wave was determined, and its relation with the tensile load was shown in Figure 7.  Figure 7, it can be seen that for different burial depths of slots, the whole trend of the difference in time of flight when the tensile load increases is very similar, but there are also some differences. For the similarities, the difference in time of flight increases linearly as the tensile load increases, which is consistent with the Lcr wave acoustoelastic theory. While when the tensile load reaches the turning point load, the difference in time of flight changes nonlinearly as the tensile load increases further. In addition, the deviation of curves from linearity becomes more obvious as the tensile load increases. For the differences, when the tensile load is the same, the difference in time of  differences. For the similarities, the difference in time of flight increases linearly as the tensile load increases, which is consistent with the L cr wave acoustoelastic theory. While when the tensile load reaches the turning point load, the difference in time of flight changes nonlinearly as the tensile load increases further. In addition, the deviation of curves from linearity becomes more obvious as the tensile load increases. For the differences, when the tensile load is the same, the difference in time of flight becomes lower gradually as the burial depth increases. For the above results, it is analyzed that the non-uniform distribution of stress caused by the slot and coating microstructure is the main reason.
Based on Equation (5), the difference in time of flight and tensile load within the turning point load was fitted with a linear function, so the relation of the fitting coefficient and burial depth of slot was received and shown in Figure 8. flight becomes lower gradually as the burial depth increases. For the above results, it is analyzed that the non-uniform distribution of stress caused by the slot and coating microstructure is the main reason. Based on Equation (5), the difference in time of flight and tensile load within the turning point load was fitted with a linear function, so the relation of the fitting coefficient and burial depth of slot was received and shown in Figure 8. As shown in Figure 8, it can be seen that as the burial depth of slot increases, the fitting coefficient decreases and tends to be stable gradually. To quantitatively describe the burial depth effect of slot on stress evaluation with Lcr wave, the result was fitted by the power function, and it could be expressed as: where Kʹ was the fitting coefficient, and D was the burial depth of slot.

Discussion and Analysis
First, from the interaction of Lcr wave and the medium, it can be known that the interface in coating and the anisotropic microstructure of coating caused by directional solidification are the main reasons for noise in the Lcr wave. The preparation method of coating shows that there are some interfaces between layer and layer, and it appears to be a circular arc, so the reflection of Lcr wave on the interface is very irregular, and the noise in Lcr wave is obvious.
Second, the Lcr wave acoustoelastic theory is the base for the experiment, so when the tensile load is within the turning point load, the difference in time of flight between the Lcr wave of coating varies almost linearly as the tensile load increases. However, it should be emphasized that the isotropic media is the premise of the Lcr wave acoustoelastic theory, while the microstructure of coating is obviously anisotropic, shown in Figure 1, so the experimental result is not very consistent with the Lcr wave acoustoelastic theory. It is analyzed that during the loading process of coating, the macroscopic deformation of coating is still in the elastic stage, but some small zones may be in the state of plastic deformation, which is not consistent with the deformation premise of the Lcr acoustoelastic theory. As the tensile load increases, the plastic deformation area becomes bigger gradually, so the deviation of the experimental result becomes more obvious. To prove it, the dislocation accumulation model for explaining plastic deformation was employed, and its model was shown in figure 9. As shown in Figure 8, it can be seen that as the burial depth of slot increases, the fitting coefficient decreases and tends to be stable gradually. To quantitatively describe the burial depth effect of slot on stress evaluation with L cr wave, the result was fitted by the power function, and it could be expressed as: where K was the fitting coefficient, and D was the burial depth of slot.

Discussion and Analysis
First, from the interaction of L cr wave and the medium, it can be known that the interface in coating and the anisotropic microstructure of coating caused by directional solidification are the main reasons for noise in the L cr wave. The preparation method of coating shows that there are some interfaces between layer and layer, and it appears to be a circular arc, so the reflection of L cr wave on the interface is very irregular, and the noise in L cr wave is obvious.
Second, the L cr wave acoustoelastic theory is the base for the experiment, so when the tensile load is within the turning point load, the difference in time of flight between the L cr wave of coating varies almost linearly as the tensile load increases. However, it should be emphasized that the isotropic media is the premise of the L cr wave acoustoelastic theory, while the microstructure of coating is obviously anisotropic, shown in Figure 1, so the experimental result is not very consistent with the L cr wave acoustoelastic theory. It is analyzed that during the loading process of coating, the macroscopic deformation of coating is still in the elastic stage, but some small zones may be in the state of plastic deformation, which is not consistent with the deformation premise of the L cr acoustoelastic theory. As the tensile load increases, the plastic deformation area becomes bigger gradually, so the deviation of the experimental result becomes more obvious. To prove it, the dislocation accumulation model for explaining plastic deformation was employed, and its model was shown in Figure 9.
with the Lcr wave acoustoelastic theory. It is analyzed that during the loading process of coating, the macroscopic deformation of coating is still in the elastic stage, but some small zones may be in the state of plastic deformation, which is not consistent with the deformation premise of the Lcr acoustoelastic theory. As the tensile load increases, the plastic deformation area becomes bigger gradually, so the deviation of the experimental result becomes more obvious. To prove it, the dislocation accumulation model for explaining plastic deformation was employed, and its model was shown in figure 9.  Figure 9 shows the process of plastic deformation caused by dislocation movement, an internal stress is generated and it can be expressed as follows: where τ g is the internal stress, τ is the shear stress on PQ surface, τ i is the resistance of dislocation in grain, L is the length of dislocation group, b is the Brinell vector of dislocation, and G is the shear modulus of metal. From Equation (9), it can be seen that as the dislocation number increases, the length of the dislocation group becomes longer, so the internal stress τ g becomes bigger gradually. When the internal stress becomes higher than the stress for moving the dislocation group, the dislocation moves from grain A to grain B, it means the deformation of grain A is transferred to grain B, meanwhile the internal stress is released. During the deformation process, the release and concentration of stress repeats many times until the plastic deformation can be observed. Considering the coating microstructural characteristic, the dislocation may be pinned by the interface in coating and the anisotropic microstructure, it means the stress concentration is formed, and there is a higher stress. While as the tensile load increases, the pinning effect of interface and microstructure on dislocation can be broken, so the dislocations continue to move, it means the stress is released. Therefore, the internal stress state changes during the loading process of coating, so the relation of the difference in time of flight and tensile load is not strictly linear as Equation (5). For the above analysis, it should be noted that the dislocation movement with many repetition times requires a well deformation capacity, so the SEM image of the coating fracture was observed and shown in Figure 10.  Figure 9 shows the process of plastic deformation caused by dislocation movement, an internal stress is generated and it can be expressed as follows: where τg is the internal stress, τ is the shear stress on PQ surface, τi is the resistance of dislocation in grain, L is the length of dislocation group, b is the Brinell vector of dislocation, and G is the shear modulus of metal.
From Equation (9), it can be seen that as the dislocation number increases, the length of the dislocation group becomes longer, so the internal stress τg becomes bigger gradually. When the internal stress becomes higher than the stress for moving the dislocation group, the dislocation moves from grain A to grain B, it means the deformation of grain A is transferred to grain B, meanwhile the internal stress is released. During the deformation process, the release and concentration of stress repeats many times until the plastic deformation can be observed. Considering the coating microstructural characteristic, the dislocation may be pinned by the interface in coating and the anisotropic microstructure, it means the stress concentration is formed, and there is a higher stress. While as the tensile load increases, the pinning effect of interface and microstructure on dislocation can be broken, so the dislocations continue to move, it means the stress is released. Therefore, the internal stress state changes during the loading process of coating, so the relation of the difference in time of flight and tensile load is not strictly linear as Equation (5). For the above analysis, it should be noted that the dislocation movement with many repetition times requires a well deformation capacity, so the SEM image of the coating fracture was observed and shown in Figure 10. From Figure 10, it can be seen that lots of dimples, which is the typical characteristic for a well plastic deformation capacity, appear in the surface fracture of coating, and means the above theoretical analysis is reasonable.
In addition, the stress concentration caused by the slot is another important reason for the experimental results. As well known, the stress concentration effect is a typical result caused by the crack, and the stress concentration effect becomes more obvious as the crack depth increases. It means that the stress concentration effect becomes more obvious as the burial depth of slot decreases in this paper, so when the tensile load is the same, the real stress becomes smaller as the burial depth of the slot increases gradually as shown in Figure 8. From Figure 10, it can be seen that lots of dimples, which is the typical characteristic for a well plastic deformation capacity, appear in the surface fracture of coating, and means the above theoretical analysis is reasonable.

Conclusions
In addition, the stress concentration caused by the slot is another important reason for the experimental results. As well known, the stress concentration effect is a typical result caused by the crack, and the stress concentration effect becomes more obvious as the crack depth increases. It means that the stress concentration effect becomes more obvious as the burial depth of slot decreases in this paper, so when the tensile load is the same, the real stress becomes smaller as the burial depth of the slot increases gradually as shown in Figure 8.

Conclusions
In this paper, the influence of burial depth of crack on stress measurement of laser cladding coating with L cr wave was discussed, and the experimental results were analyzed based on the L cr wave acoustoelastic theory and deformation theory. The results could be concluded as that: The structural interface and anisotropy of coating are the main reasons for the noise in L cr wave. Using the wavelet analysis theory, the L cr wave is denoised, and the optimal parameters are as follows: db 6, five decomposition levels, and hard threshold, respectively. For the coating deformation, it is not uniform because of the structural characteristics of coating, and it results in the difference between the experimental result and L cr wave acoustoelastic theory, which is explained by the dislocation accumulation. In addition, the stress concentration effect caused by burial crack is another reason for the difference between the experimental result and theoretical result. For the results, it can be known that as the burial depth of crack increases, the L cr wave acoustoelastic coefficient becomes smaller gradually.