Longitudinal Wave Defect Detection Technology Based on Ablation Mechanism

Abstract

For laser ultrasound in the thermoelastic mechanism, excitation of ultrasonic body wave signal is weak, it is not easy to realize the detection of deep defects inside the workpiece. While the ablation mechanism produces a high and practical ultrasonic signal-to-noise ratio, this paper is based on the generation mechanism of laser ablation excitation of ultrasonic waves, the establishment of laser ultrasound in the ablation mechanism in the aluminum plate excitation and propagation of ultrasonic numerical model, through the solution, obtained the ultrasonic acoustic field map, discussed the ablation mechanism of the laser ultrasonic body wave acoustic field directionality. Additionally, the preliminary verification of the validity of the model is presented. Then, in order to explore the application potential of high signal-to-noise ratio longitudinal waves in defect detection, defects of different depths are preset in the model for simulation calculations, and waveform and acoustic field analyses are performed on the simulation results to study the ultrasonic propagation paths inside the member and the interaction with the defects, and the transverse position and depth of the internal defects are judged by using B-scan imaging. Finally, experimental validation is carried out. The experimental results are highly consistent with the simulation model, and the defect experiments can qualitatively determine the location of internal defects and verify the practicality and accuracy of the model.

1. Introduction

Aluminum alloys are widely used in aerospace and automotive lightweight fields due to their extremely low density and excellent specific strength [1,2]. However, failure to detect and deal with internal defects in the production process may lead to structural failure and serious safety accidents. Therefore, timely and accurate detection of internal defects of aluminum alloy is extremely important to ensure the safe operation of mechanical structures [3,4]. At present, the more technically mature nondestructive testing methods at home and abroad include ray detection, magnetic particle testing, penetration testing, eddy current testing, and ultrasonic testing, among others. Ray detection [5,6] has the advantages of high sensitivity and the ability to detect volumetric defects, but for the detection of planar defects, it needs to be in the optimal direction of radiation. However, the rays are harmful to the human body, and the cost is high. Magnetic particle detection [7,8] can detect surface or near-surface defects in ferromagnetic materials, but it cannot be used for non-ferromagnetic materials or for the detection of internal defects. Penetration testing [9,10] can detect open defects on smooth metallic and non-metallic surfaces, but the operating procedures are strict and cumbersome, and the repeatability of the detected defects is poor. Eddy current detection [11,12] can detect surface and near-surface defects in conductive materials with high detection sensitivity, but it cannot detect internal defects, and it is difficult to estimate the shape and type of the defects. Ultrasonic inspection [13,14] can be used for any defect form in any material, but conventional ultrasound usually requires contact with the sample surface, which limits its use for detecting complex surface components or in special environments. Laser ultrasonic technology combines the advantages of high precision of ultrasonic detection and non-contact optical detection. It not only overcomes the limitations of traditional ultrasonic technology in the detection of large and complex components [15,16] but also realizes non-contact remote operation in extreme environments such as high temperature and high pressure [17,18]. It is not only used for the detection of many crystalline and mixed-phase crystalline materials [19,20,21] but is also applicable to the internal defect detection of many non-crystalline materials, such as plastics, rubbers, and composites [22,23,24]. Therefore, it is important to study the theory of laser ultrasound in the field of defect detection [25,26,27].

At present, the excitation mode of laser ultrasound can be divided into low energy thermoelastic mechanism and high energy ablation mechanism according to the energy intensity of the pulsed laser. Thermoelastic excitation can achieve complete non-damage to the surface of the workpiece, but its photoacoustic conversion efficiency is especially weak when the ultrasonic body wave signal is generated in the metal, which limits its detection of deep defects in the metal material [28]. For this reason, thermal bomb excitation requires other manipulations to improve the signal-to-noise ratio; Guo et al. introduced a glass constraint layer to enhance the excitation efficiency of the longitudinal wave in the low-energy thermoelastic mechanism and successfully detected the defects at a depth of 16 mm inside the specimen by using the high signal-to-noise ratio longitudinal wave excited [29]. Cui et al. studied the focusing and steering of the shear and longitudinal waves generated by seven fiber-optic phased array laser sources in the thermoelastic state through numerical simulation and developed a phased array laser ultrasonic testing system to achieve complete non-contact detection of internal cracks in thick metal samples [28]. In contrast, the high-energy ablation mechanism excites longitudinal waves with a high signal-to-noise ratio and propagates perpendicularly to the surface of the specimen, allowing direct and effective detection of defects within a metal sample. Tanak successfully detected internal small defects with a diameter of 100 μm in carbon steel samples by using laser-induced body waves in the ablation mechanism [30]. Choi S et al. studied the detection of internal defects using longitudinal waves excited by ablation through numerical simulation and experiments. The experimental results show that the longitudinal wave excited in the ablation state can be effectively used for internal defect detection [31]. Gao et al. pasted aluminum foil on the surface of the composite material to make it easy to ablate and obtained available signals to detect the delamination defects of the composite material [32]. In summary, although the ablation excitation method causes some damage to the surface of the specimen, the material damage caused by ablation is negligible in cases where the requirements for the surface properties of the material are not particularly high, e.g., prior to cleaning the surface during post-treatment of slab fabrication [33], or at extremes, e.g., under high-temperature conditions [34,35]. In recent years, most of the finite element simulation work based on laser ultrasonic testing technology has focused on sound field analysis under the thermoelastic mechanism [36,37,38]. Because the ablation mechanism includes complex physical phenomena such as material melting, phase change, vaporization and plasma formation, the numerical simulation of laser ablation excitation ultrasonic sound field process is relatively scarce. Therefore, this paper investigates sound field analysis and internal material defect detection based on finite element simulation of the ablation mechanism.

In order to explore the propagation process of ultrasonic wave generated by ablation excitation and the interaction process between sound field and defects when there are defects in the workpiece, in this paper, the absorbed laser energy is converted into the net reaction force exerted by the plasma on the surface of the workpiece. The finite element method is used to establish a simplified model of laser ultrasonic ablation and verify the validity of the model by the directivity of the body wave sound field. Furthermore, the model is extended to a defect detection model to explore the interaction mechanism between ultrasonic waves and internal defects of materials. At the same time, the workpiece containing prefabricated internal defects is tested to verify the correctness of the model.

2. Theoretical Basis and Simulation Model

2.1. Laser Ultrasonic Ablation Theory

The melting condition of the material is the result of the interaction of multiple factors. It depends on the inherent properties of the material itself, such as melting point, thermal conductivity and the characteristics of pulsed laser. For general metals, the threshold intensity required to achieve ablation needs to reach more than 107 W/cm² when a Q-switched pulsed laser is used. Ready [39] further pointed out that when the laser power density absorbed by the material exceeds a certain threshold $I_c$, the heat conduction effect can be neglected. This is because when the laser provides a high-power pulsed laser, the heat transfer is extremely fast, and the heat conduction process becomes no longer significant at this time. Therefore, the evaporation of metal materials depends almost entirely on its latent heat of evaporation. The expression of $I_c$ [40] is as follows:

$$I_{\mathrm{c}}\ge 2L\rho k^{1/2}{\tau }^{-1/2},$$

(1)

$$k=K/\rho c,$$

(2)

where $L$ is the latent heat required for solid evaporation, $\rho$ is the density of metals, $k$ is thermal diffusivity, $\tau$ is pulse duration, $K$ is thermal conductivity, and $c$ is the specific heat capacity of materials.

Omitting the intermediate process during the ablation process, such as temperature rise, thermal expansion, liquid phase transition, etc. And directly converting the absorbed laser energy into the elastic wave generated by the net reaction force. The net stress perpendicular to the surface can be expressed as follows [40]:

$${\sigma }_{\mathrm{net}}={\displaystyle \frac{I_A{(x,t)}^2}{\rho {\left[L+c\left(T_v-T_0\right)\right]}^2}},$$

(3)

$$I_A(x,t)=I_{0}f\left(x\right)g\left(t\right),$$

(4)

where $I_A$ is the laser intensity absorbed by the material, $T_v$, $T_0$, respectively, represents the vaporization point and initial temperature of the material. $I_0$ is the peak power of the incident pulsed laser, $f\left(x\right)$ and $g\left(t\right)$ respectively represents the spatial distribution and time distribution of the excitation light source.

2.2. Model Building and Parameter Setting

A two-dimensional plane strain model is established according to the actual size of the workpiece in Figure 1. The size of the aluminum plate is set to 70 mm × 20 mm. The net reaction force directly converted from laser energy is loaded into the AB section of the upper surface of the specimen. The thermodynamic properties of the materials [40] are listed in

Table 1. Main thermodynamic parameters of aluminum plate.

Parameter	Numerical Value
Constant pressure heat capacity (J/kg·K)	900
Latent heat of vaporization (kJ/kg)	10,778
Density (kg/m3)	2700
Evaporating point (K)	2790
Thermal conductivity (W/(m·K))	238
Young’s modulus (Pa)	70 × 109
Poisson’s ratio	0.33

.

In the Cartesian coordinate system, when the Gaussian pulsed laser irradiates on the surface of the material, the spatial distribution and time distribution of the excitation light source can be expressed as follows:

$$f\left(x\right)=\exp \left(-{\displaystyle \frac{{\left(x-x_0\right)}^2}{{R_{\mathrm{a}}}^2}}\right),$$

(5)

$$g\left(t\right)={\displaystyle \frac{t}{t_0}}\exp \left(-{\displaystyle \frac{t}{t_0}}\right),$$

(6)

where $x_0$ is the position of the laser light source, $R_{\mathrm{a}}$ its spot radius of the pulse laser, and $t_0$ is the rise time of the pulse laser.

The incident pulsed laser peak power is set to 1000 MW/cm², and this value exceeds the threshold intensity required for ablation―576 MW/cm², which is calculated through Formula (1). The laser source pulse width and light source radius are set to 10 ns and 500 μm, respectively. And the temporal and spatial distribution of the excitation laser can be obtained from it, as shown in Figure 2.

The ablation process is accompanied by the removal of the material surface, which produces a net reaction force caused by the change of surface momentum. And the net reaction force that produces ultrasonic waves can be used as the boundary force $F_{\mathrm{A}}$ [31]:

$${\sigma }_{net}•n=F_A,$$

(7)

where $n$ is the unit normal vector of the boundary.

Then, the net reaction force of the conversion $F_A\left(x,t\right)$ can be expressed in the following form:

$$F_A(x,t)={\displaystyle \frac{{[I_{0}f(x)g(t)]}^2}{\rho {[L+(T_v-T_0)]}^2}},$$

(8)

The elastic wave time domain explicit interface is used for the physical field. In order to avoid the influence of boundary echo, the left and right boundaries and the lower surface boundary are set as low reflection boundaries.

2.2.1. Mesh Division

Mesh is one of the elements of the accuracy of the finite element model, and in general, the denser the meshing, the more correct the results of the full-field displacement field will be obtained; however, when the mesh is too dense, it will result in a significant increase in the amount of computation and reduce the computational efficiency. On the contrary, when the mesh is sparse, it will cause problems such as large numerical solution errors and distortion of the full-field displacement map. Therefore, it is necessary to determine the appropriate meshing method and find the balance point between the solution accuracy and the computation time in order to solve the problem better.

In the mesh division, it is necessary to select the appropriate grid size to ensure that energy can be effectively transferred between two consecutive nodes. Generally, the grid size [31] should be less than 1/4 of the elastic wavelength to meet the accuracy requirements for elastic wave propagation after laser action. For the spatial distribution of the Gaussian function, the time distribution of the Dirac function representing the pulsed laser excitation of the ultrasonic center frequency is approximately

$$f_{\max }={\displaystyle \frac{\sqrt{2}{c}_R}{\pi R_a}},$$

(9)

where $c_R$ is the surface wave velocity, $R_{\mathrm{a}}$ is the spot radius of the laser, and its corresponding wavelength is

$${\lambda }_{\min }={\displaystyle \frac{\pi R_{\mathrm{a}}}{\sqrt{2}}},$$

(10)

Therefore, the grid size should be less than 277 μm.

Under the same model established in this paper, different grid sizes are set respectively, and the echo signals of ultrasound are received by the probe. Since the amplitude of the excited ultrasound and the arrival time of the waveform are closely related to each other, this paper carries out verification of the ultrasonic waveforms by observing the effects of different grid sizes.

The grid size is set to 0.277 mm, 0.1 mm, 0.03 mm, 0.002 mm, and 0.001 mm for the simulation of the model. In the reflection method, the ultrasonic echo signals at the positions of 2 mm and 5 mm from the excitation point are measured, as shown in Figure 3.

As can be seen from the Figure, the shape of the ultrasonic waveform in the reflection method does not change significantly when the grid size is smaller than 0.277 mm, but the arrival time and amplitude of the surface wave do vary. After calculation, at the reception point 2 mm from the excitation point, the arrival time of the longitudinal wave under different grid sizes is [1.658, 1.652, 1.656, 1.641, 1.641], and the amplitudes of the echo wave are [17.67, 18.77, 20.25, 26.43, 26.43]; at 5 mm from the reception point, the longitudinal wave arrives at times [1.817, 1.816, 1.812, 1.812, 1.812] with different grid sizes, and the return amplitudes are [53.67, 54.22, 55.72, 58.80, 58.80] respectively. That is, as the grid size decreases, the arrival time of the surface wave tends to decrease while the surface wave amplitude tends to increase. When the grid size is below 0.002 mm, there is no discernible difference in the arrival time and amplitude of the surface waves, which is consistent with theoretical analysis.

In the transmission method, the longitudinal distances from the excitation point were selected as 5 mm, 10 mm, 15 mm, and 20 mm for signal acquisition. The ultrasonic echo signal at the position of 20 mm is shown in Figure 4 below. The longitudinal wave arrival time and longitudinal wave amplitude variation with the grid size are plotted in Figure 5.

From the Figure, it can be seen that when the mesh size is smaller than 0.277 µm, the longitudinal wave arrival time decreases slightly, and the amplitude increases as the mesh becomes finer. However, when the mesh size is smaller than 0.002 µm, the longitudinal wave arrival time and amplitude do not change significantly. It can be observed that when the mesh size is smaller than the minimum required for an accurate solution, the size and sparsity of the mesh have less impact on the model solution, especially for nodes farther away from the excitation point, where the change in the waveform is almost negligible.

In summary, the mesh discretization is illustrated in Figure 6. Based on the considerations of computational accuracy and computational volume, a finer mesh is adopted in the surface region where the pulsed laser acts, while the mesh is sparser in the region far away from the laser action. To avoid over-sparseness of the mesh, the intermediate approach of profiling with a variable mesh technique is utilized. The minimum cell size of the mesh is 2 µm, the maximum cell size is 30 µm, and an overall free triangular mesh is chosen.

2.2.2. Selection of Time Step

In the calculation of the solution, the smaller the time step, the higher the solution accuracy, and the better able to distinguish the high-frequency components of the ultrasonic wave, but too small a time step requires a very long computation time, which affects the detection efficiency. In order to improve the computational efficiency under the condition of guaranteeing the solving accuracy, it is necessary to select an appropriate time step [41] $\Delta t$. The time step is generally selected:

$$\Delta t={\displaystyle \frac{1}{20f_{\max }}},$$

(11)

As long as the time step is chosen to be smaller than the value given by the above equation, the accuracy requirement of the calculation can be satisfied. However, if the pulse rise time is on the order of nanoseconds, the above equation may not provide sufficient spatial resolution for capturing the laser pulse rise time, which is also on the order of nanoseconds. In this case, the step size cannot meet the requirements, and it can be scaled down by a factor of 9 from the original basis [41]. Assuming that the surface wave velocity is 2909 m/s, and after several model simulations, the time step size is set to 0.003 μs, and the running time is 9 μs, as reported in the paper.

2.3. Numerical Simulation Results

Figure 7 shows the distribution of the laser ultrasonic sound field at 0.375 μs, 0.75 μs, 1.125 μs and 1.5 μs after simulation. The brightness of the color reflects the level of ultrasonic amplitude but also reflects the strength of different modes of ultrasonic signal. It can be seen from the Figure that the reaction force perpendicular to the surface of the specimen leads to the simultaneous generation of ultrasonic waves of various modes such as longitudinal wave (L wave), shear wave (S wave), surface wave (R wave) and head wave (H wave). The generation of a longitudinal wave is stronger than that of a transverse wave, and its propagation speed is the fastest.

The red arc in Figure 7 represents the wavefront of an ultrasonic longitudinal wave propagating in the specimen at different times. In order to detect the energy distribution of the body wave, the probe points are placed in front of the same wave as far as possible to reduce the influence of the diffusion effect in the process of ultrasonic propagation. A series of probes are set at 0.25 mm intervals along the x-axis direction, and the front of the wave closest to the bottom of the specimen is taken. The variation of the typical laser ultrasonic Y-displacement component with time is shown in Figure 8.

Through observing the ultrasonic signal waveform received in Figure 8, it can be found that the arrival time of the longitudinal wave and the transverse wave at the position of 0 mm, that is, the position of the center, is 3.26 μs and 6.30 μs, which is basically consistent with the theoretical arrival time. It can be observed from the local longitudinal wave amplification map in the lower left corner that the amplitude of the laser ultrasonic longitudinal wave is the strongest at the incident point of the laser (0 mm), and with the increase of the angle deviating from the incident direction, the amplitude gradually decreases. However, the amplitude of the shear wave does not show a simple monotonically increasing or decreasing relationship. By extracting the amplitude of the primary longitudinal wave and the primary transverse wave in the numerical simulation results, the ultrasonic body wave directivity diagram is drawn, as shown in Figure 9c,d.

The longitudinal wave energy distribution of the simulation results is consistent with the theoretical results. The energy is mainly concentrated in the normal direction and decreases slowly outward in an oval shape. However, the longitudinal wave sound field width of the simulation results is significantly smaller than the theoretical results. This phenomenon can be attributed to the fact that the researchers regard the excitation light source as an ideal point light source without considering the influence of the size of the excitation source on the results. Laser ultrasonic body waves will be set in the normal direction with the increase of the size of the excitation source, which means the beam width of the longitudinal wave will appear to decrease gradually [42].

The transverse wave sound field of the simulation results presents two symmetrical lobes, and the central angle is about ±45°. The energy of the theoretical transverse wave is concentrated near the normal line 35° perpendicular to the surface, and there is a slight difference of about 10° between the simulation results and the theory. This is because the theoretical directivity formula does not consider the influence of the spot radius and the center frequency of the receiving sensor on the directivity, which has been confirmed by the numerical simulation results in Reference [31] and the experimental results in Reference [43].

To further illustrate the correctness of the model, as shown in Figure 10 for the model reflection experiment of a 70 × 20 mm aluminum plate, the signal acquisition of the surface wave is carried out at the same side of the excitation point at 2 mm and 5 mm. After calculation, it can be seen that the surface wave arrival time at 2 mm is 0.78 μs, the surface wave arrival time at 5 mm is 1.81 μs, then the simulated surface wave can be calculated to be 2913.6 m/s, and the theoretical surface wave to be 2909 m/s, with an error of about 0.15%.

The simulated waveforms of the model transmission are shown in Figure 11, and the signals of the longitudinal and transverse waves are acquired at the excitation points 5 mm, 10 mm, 15 mm and 20 mm from the center of the excitation point. For accuracy, the ratio of distance interval to time interval is used to solve the velocity. After calculating the arrival time of transverse and longitudinal waves, combined with the theoretical transverse and longitudinal wave speeds of 6198 m/s and 3122 m/s, respectively, the transverse and longitudinal wave speed estimation errors are shown in

Table 2. Estimation errors of transverse and longitudinal wave speeds at different positions.

Receive Location	Longitudinal Wave Arrival Time	Transverse Wave Arrival Time	Longitudinal Wave Error Rate	Transverse Wave Error Rate
5 mm	0.829	1.592	0.66%	0.189%
10 mm	1.641	3.164	0.77%	0.45%
15 mm	2.454	4.773	0.58%	0.48%
20 mm	3.256	6.367	0.29%	0.64%

.

Based on the above analysis, the validity of the ablation model is preliminarily verified by the displacement curve of the ultrasonic wave and the directivity of the body wave.

3. Defect Detecting

3.1. Defect Detection Model

In order to further explore the interaction process between ultrasonic waves generated by ablation excitation and internal defects, a defect detection model is established, as shown in Figure 12. The laser parameters, sample material properties, mesh size, calculation steps and duration are consistent with the previous section. In order to realize the judgment of the lateral position and depth information of the defect, the detection method combining the transmission method and the reflection method is adopted. The excitation point and the detection point are fixed and scanned synchronously from −30 mm to 30 mm with a step of 1 mm to obtain the B-scan result. When the transmission method is used to detect, the detection laser beam B is always located at the center of the excitation point. And when the reflection method is used to detect the internal defects, the detection laser beam C and the pulse laser beam are on the same side, and the distance M between the fixed excitation point and the receiving point C is 5 mm.

In the transmission mode, when scanning the position of −8 mm, the sound field distribution at different times is shown in Figure 13a. With the passage of time, the longitudinal wave first encountered defects, and the displacement became a vortex spread around the center of the defect. The existence of defects hindered the propagation of the longitudinal wave. Therefore, the longitudinal wave energy that continues to propagate to the bottom is attenuated, and the color band becomes shallow. In the reflection mode, when scanning the 11 mm position, the sound field distribution cloud map at different times is shown in Figure 13b. It can be seen that the longitudinal wave will reflect when it encounters internal defects of different depths, and when the longitudinal wave continues to propagate in the distance, it will form a bottom reflection echo when it propagates to the bottom of the specimen, and then it will pass through the defect again in the process of returning.

3.2. Experimental Installation

In order to verify the correctness and effectiveness of the numerical model, a laser ultrasonic defect detection system is built in Figure 14. The Nd: YAG laser emitter emits a pulsed laser with a wavelength of 1064 nm and a pulse width of 11 ns, which is irradiated to the surface of the specimen after passing through a point-focusing lens with a focal length of 10 mm. The repetition frequency and pulse energy are adjusted by the laser controller to ensure obvious ablation when irradiated to the surface of the specimen. Under the clamping of the two-dimensional scanning frame, the test piece is scanned from −30 mm to 30 mm in a step of 1 mm based on the same coordinate system as Figure 12. The ultrasonic wave is received by a QUARTET laser interferometer with a wavelength of 532 nm and a power of 500 mW. It emits a continuous laser to receive the signal echo carrying the characteristic information, and finally, the optical signal is converted into an electrical signal and transmitted to the data acquisition card and displayed on the computer. The received detection signal is recorded after an average of 64 times so as to improve the signal-to-noise ratio of the ultrasonic signal.

When the synchronous scanning method is used, the two-dimensional scanning frame clamps the workpiece to move, and the laser transmitter and receiver remain immobile to facilitate the movement. When the transmission method is used, the interferometer is always kept at the center of the pulse laser. In the pulse-echo mode, the interferometer is always located on the same side of the pulsed laser beam. It should be noted that the light excited by the pulsed laser needs to be kept at a certain distance from the detection beam of the interferometer to avoid the interference or aliasing of the received signal by the shock wave.

3.3. Analysis of Effect

Figure 15 shows the comparison results of the experimental and simulated echo signals obtained at different detection points when using the transmission method to detect defects. It can be seen that the experimental results are consistent with the numerical simulation results. The longitudinal wave is clearly visible at the defect-free 0 mm position, and its arrival time is about 3.4 μs. In addition, there is a system delay time in the experimental system, that is, the time of the laser excitation to the specimen surface plus the time of the interferometer receiving the ultrasonic wave. Therefore, the arrival time of the longitudinal wave in the experiment is slightly later than that in the simulation. At the defect position (−22 mm, −7 mm, 7 mm and 22 mm), the received longitudinal wave signal is very small and almost annihilated in the noise due to the obstruction of the defect.

Further observing the experimental and simulated B-scan results obtained by scanning the specimen using the transmission method, as shown in Figure 16. The figure uses the amplitude value of the signal as the basis for color mapping to show the differences between different amplitude signals. In order to enhance the readability of the image, the values of the mapped data have been normalized so that the echoes of different amplitudes show a more obvious distinction in color. It can be seen from the experimental results that the light green appears in the figure when the arrival time of the transmitted longitudinal wave is about 3.4 μs, while the amplitude received at the defect-free position is stronger, showing blue–violet. In the simulation results, the defect position is bright yellow, and the defect-free position is blue–violet. This is because the longitudinal wave is attenuated by the reflected energy after encountering the defect so that the received amplitude becomes smaller. The white dotted line position in the diagram is the center position of the defect, which is −22.5 mm, −7.5 mm, 7.5 mm, and 22.5 mm, respectively, which is basically consistent with the center position of the actual defect, and the experimental results are in good agreement with the simulation results. The above phenomena show that the transverse position of the defect can be determined by the transmission method by utilizing the obstruction effect of the defect on the ultrasonic longitudinal wave.

The experimental A-scan signal obtained at different detection points is shown in Figure 17a, using the reflection method to detect defects. It can be seen that the first received wave by the detection point is the grazing surface longitudinal wave (Sp) and the surface wave (R). Then, the defect echoes from four different depth defect positions appear one after another, and finally, the echo signal at the bottom is received. Because the depth of the defect is different, the echo arrival time of each defect position shows a significant difference. The simulation results in Figure 17b are consistent with the experimental results.

The simulation of defect detection B-scan signal diagram obtained by the longitudinal wave combined with the reflection method is shown in Figure 18. The internal defect echo is obvious in the figure, and the deeper the defect, the later the arrival time of the defect echo. In addition, the secondary defect echo from the 10 mm and 12 mm depth defect positions can be clearly observed, as shown in the red coil.

The B-scan experimental results obtained by scanning the specimen with the reflection method are shown in Figure 14, and it is basically consistent with the simulation results of Figure 19. Through observation, it can be found that due to the strong surface wave signal, the presentation of the defect echo is not very obvious. In order to observe the echo characteristics more clearly, it is important to intercept the defect echo and the bottom echo part in the red-dotted rectangular frame. The defect echoes from four different depths are clearly visible, and the amplitude of the bottom echo is weak at the position where the defect echo exists. Moreover, the secondary echo from the defect reflection at 10 mm depth can also be seen. Based on the above analysis, it is feasible to determine the depth of the defect by measuring the arrival time of the reflected echo in the pulse-echo mode.

The defect echo arrival time can be obtained from the B-scan experiment. Using the theoretical longitudinal wave velocity, the error in estimating the defect depth can be calculated, as shown in

Table 3. Defect depth and error of simulation measurement.

Defect Depth	Defective Echo Arrival Time (μs)	Actual Arrival Time of Defective Echo (μs)	Measured Defect Depth (Mm)	Error/%
10 mm	3.23	10.010	0.10	3.23
12 mm	3.90	12.086	0.72	3.90
14 mm	4.63	14.348	2.48	4.63
16 mm	5.28	16.363	2.26	5.28

. Table 3 demonstrates that the model can accurately estimate the error within the material body, with the estimation error falling within 5%.

In summary, the high signal-to-noise ratio longitudinal wave excited by the ablation mechanism shows significant advantages and broad application prospects in the detection of deep defects in large-thickness materials. The high consistency between the experimental results and the simulation results of this study fully verifies the accuracy of the numerical model of laser ablation excited ultrasonic wave.

3.4. Discussion

In the thesis, the accuracy of the model is proven in two aspects. Firstly, in the basic model, the pointing of ultrasonic transverse and longitudinal waves is analyzed using the simulation data, which is consistent with the theoretical pointing. Simultaneously, the A-scan signals of the ultrasonic wave are analyzed to obtain the arrival times of the surface, transverse, and longitudinal waves at different positions. From this, the surface, transverse, and longitudinal wave speeds are derived, and the errors between the analyzed and theoretical wave speed values are all less than 1%. Secondly, in the internal defect detection model for an aluminum plate, the echo signals of defects at different positions are analyzed. The defect positions are calculated based on the echo arrival times and the theoretical longitudinal wave speed, and the error rate in estimating the defect positions is less than 5%. Additionally, the A-scan and B-scan signals obtained from the simulation of the model are compared with those from actual defect experiments, and the results show high consistency. Therefore, the model proposed in this paper can serve as a reference for the laser ablation mechanism model, providing a theoretical basis for the simulation and practical application of the subsequent ablation mechanism.

Longitudinal wave defect detection technology, as an important method of laser ultrasonic flaw detection, has the advantages of strong penetration, poor sensitivity to reflection or scattering at grain boundaries, and does not involve radioactive substances compared with other techniques (e.g., gamma ray detection), and can be used to detect components of various shapes, sizes and materials. Based on the findings of references [20,22], this paper further extends the applications of laser ultrasound technology. In literature [21], Quintero et al. realized a laser ultrasound study of ceramic matrix composite (CMC) plates under high-temperature conditions, enabling ultrasonic imaging of interlayer defects in SiC/SiC matrix materials. In literature [22], A proposed a zero hysteresis inter-correlation imaging method to achieve the detection of delamination inside composite materials, and the interaction between laser ultrasound and delamination inside graphite fiber composite plates was investigated using the finite element method. Laser ultrasonic inspection technology has important applications in the detection of internal defects in mixed-phase crystals. Mixed-phase crystals make the detection of internal defects more complex and challenging due to their complex structure and multiphase coexistence. In the model of this thesis, only the propagation of laser ultrasound and defect detection inside the metal are briefly discussed. To accurately distinguish different phases and defects in mixed-phase materials, it is necessary to take into full consideration the phase structure and physical properties of the materials as well as the propagation characteristics of the physical fields, such as ultrasound at the phase interface and defects in the modeling. The model is further improved by reasonably setting the parameters of the model, such as geometry, material properties and boundary conditions. Meanwhile, in the paper, the laser energy absorbed by the aluminum plate is converted into the net reaction force exerted by the plasma on the surface of the workpiece, and the ablation mechanism model of laser ultrasound is simplified and proposed. Therefore, the model still has many shortcomings; for example, the model does not consider the thermoelastic mechanism that exists simultaneously with the ablation mechanism, nor does it consider the gasification time and gasification effect on the surface of the object in the ablation mechanism, which needs to be further optimized in the subsequent research process.

4. Conclusions

In this paper, the ablation mechanism of laser ultrasound is modeled and simulated to realize the high signal-to-noise ratio longitudinal wave excited by it is applied to the detection of internal defects, and the accuracy and validity of the model are verified by experiments. In the transmission mode, the transverse center position of the defect can be detected according to the blocking effect of the defect on the longitudinal wave. In the pulse-echo mode, the depth information of the defects can be judged according to the different arrival times of the defect echo. From the imaging results, the internal defects are obvious, and the positioning defects are accurate. The consistency of experimental results and simulation results verifies the correctness and reliability of the numerical model. This study provides strong theoretical support and practical guidance for the in-depth study of laser ultrasonic ablation mechanism and also lays a solid foundation for the subsequent research on quantitative detection of defect location.