Ultrasonic guided wave based method for circumferential positioning of a micro crack in a pipe

Abstract

This invention provides a method for circumferentially locating microcracks in pipes based on the second harmonic of ultrasonic guided waves. By using the fundamental wave of the axisymmetric mode to generate the second harmonic, and based on the mode and amplitude of the second harmonic, circumferential location of microcracks in tubular structures can be achieved. This method can detect and accurately locate microcracks in pipelines before they develop into macrocracks, thereby enabling timely and precise maintenance of pipelines, preventing further evolution of microcracks and accidents, ensuring the safe operation of pressure pipelines, and reducing the time and economic costs of manual inspection.

Description

Technical Field

[0001] This invention belongs to the field of nondestructive testing technology, specifically relating to a method for circumferentially locating microcracks in pipes based on the second harmonic of ultrasonic guided waves. Background Technology

[0002] Pipelines, as one of the five major transportation tools, are commonly used to transport gases, liquids, and slurries, such as natural gas, liquefied petroleum gas, and oil. During service, pressure pipelines are susceptible to crack initiation due to factors such as impact and corrosion. Microcracks can evolve into macrocracks, causing safety accidents such as pipeline leaks, fires, and explosions. Therefore, locating microcracks and performing timely and precise maintenance before macrocracks appear can prevent these safety accidents and ensure the safe operation of pressure pipelines.

[0003] Non-destructive testing (NDT) techniques can locate cracks in pressure pipelines without damaging them. Currently, widely used NDT techniques include ultrasonic testing, magnetic particle testing, penetrant testing, eddy current testing, and radiographic testing. Compared to magnetic particle testing, penetrant testing, and eddy current testing, ultrasonic testing can penetrate pressure pipelines to detect internal damage. Compared to radiographic testing, ultrasonic testing is radiation-free and harmless to humans, making it a safe and effective NDT method. Among these, point-by-point scanning based on volume waves is a type of ultrasonic testing method that can determine the displacement distribution of defects or damage in pressure pipelines. However, for large structures such as plates, pipes, or rails, the number of points requiring inspection and the subsequent data processing volume are large, making point-by-point scanning inefficient and costly. Ultrasonic guided waves can overcome these shortcomings, propagating over long distances in rails, plate structures, or tubular structures to efficiently determine the location of defects or damage. However, traditional ultrasonic guided waves mainly rely on physical phenomena such as reflection, transmission or refraction, and use linear acoustic parameters (such as amplitude, sound velocity and attenuation coefficient) to assess macroscopic defects or damage, but cannot detect changes in interfaces without obvious acoustic reflection, such as fatigue, creep, microcracks and plastic deformation.

[0004] Compared to traditional ultrasonic guided waves, nonlinear ultrasonic guided waves primarily study higher-order harmonics (including higher harmonics, difference frequency components, and sum frequency components) with frequencies different from the fundamental frequency. They are particularly sensitive to defects or damage much smaller than the wavelength. Microstructural changes such as dislocations, precipitates, microcracks, or micropores significantly affect the amplitude of higher-order harmonics, but have a relatively small impact on the fundamental frequency. Therefore, nonlinear ultrasonic guided waves, capable of long-distance propagation and detecting microstructural changes, have gradually attracted the interest of researchers in recent decades.

[0005] The second harmonic of ultrasonic guided waves, as a typical nonlinear acoustic effect, has been used to determine the size of microcracks in plate structures, but it is less relevant to the microstructural changes in tubes.

[0006] Excitation of the second harmonic of ultrasonic guided waves in pipelines is challenging due to its dispersion, multi-mode nature, and nonlinearity. Furthermore, the interaction mechanism between the second harmonic of ultrasonic guided waves and microcracks in pipelines remains unclear, particularly the functional relationship between the size and location of the microcrack region and the second harmonic mode and amplitude has not yet been established. Summary of the Invention

[0007] This invention addresses the aforementioned problems by providing a non-destructive testing method for characterizing and circumferentially locating microcracks in pipes before macroscopic cracks appear, utilizing the second harmonic of ultrasonic guided waves. This invention combines the advantages of ultrasonic guided waves and nonlinear ultrasound, generating a second harmonic using the fundamental wave of an axisymmetric mode. Based on the mode and amplitude of the second harmonic, circumferential location of microcracks in tubular structures is achieved, thus proposing a method for circumferential location and characterization of microcracks in tubular structures. This method can accurately locate microcracks in tubular structures, enabling timely and precise maintenance based on the location information, preventing further evolution of microcracks and accidents, and ensuring the safe operation of pressure pipelines.

[0008] Specifically, the present invention adopts the following technical solution:

[0009] This invention provides a non-destructive testing method based on the second harmonic of ultrasonic guided waves for characterizing and circumferentially locating cracks in pipelines. The method is characterized by: Step S1, establishing the dispersion equation of the ultrasonic guided waves in the pipeline based on the physical and geometric parameters of the pipeline, and obtaining the dispersion curves of the torsional mode and the longitudinal mode; Step S2, selecting the corresponding mode and excitation frequency based on the dispersion curves; Step S3, measuring the pipeline using a nonlinear ultrasonic measurement system based on the mode and the excitation frequency, wherein the nonlinear ultrasonic measurement system generates ultrasonic guided waves of a fixed frequency, the fundamental wave of which propagates in the pipeline to form a second harmonic, and the nonlinear ultrasonic measurement system receives the second harmonic along its propagation path; Step S4, calculating and analyzing the received second harmonic to obtain normalized acoustic nonlinear parameters, and obtaining the location and size information of the microcracks in the pipeline based on the normalized acoustic nonlinear parameters or the second harmonic.

[0010] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by this invention may also have the following technical features, wherein step S1 includes the following sub-steps: Step S1-1, constructing a cylindrical coordinate system based on the pipe; Step S1-2, constructing the physical equation of the pipe according to the physical parameters; Step S1-3, constructing the geometric equation of the pipe in the cylindrical coordinate system according to the geometric parameters and the Lamé coefficient of the cylindrical coordinate system; Step S1-4, substituting the physical equation and the geometric equation into the motion equation in the cylindrical coordinate system, and ignoring the body force term. Step S1-5: Based on the interface continuity and free boundary conditions of the pipeline, the boundary conditions for the second harmonic in the pipeline are formed. Step S1-6: According to the linear terms of the wave equation and the boundary conditions, the dispersion equation of the ultrasonic guided wave in the pipeline is established, and the dispersion curves of the torsional mode and the longitudinal mode are obtained. Step S1-7: Based on the nonlinear terms of the wave equation and the boundary conditions, the mathematical expression of the second harmonic in the pipeline is established using the second-order perturbation method and the orthogonal mode expansion method.

[0011] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by this invention may also have the following technical features: the nonlinear ultrasonic measurement system includes a signal generator and an excitation transducer for generating the ultrasonic guided waves; in step S1-1, the origin of the cylindrical coordinate system is located on the left end face of the excitation transducer, the r-axis is within this left end face, and the z-axis points along the axial direction of the pipe towards the right side of the excitation transducer, with the origin as the starting point. Let r be the rotation angle along the r-axis. In step S1-2, the physical equation is:

[0012]

[0013] In the formula, σ represents stress, σ rr Indicates radial normal stress. ε represents shear stress; ε represents strain. ε represents radial linear strain. zz Indicates axial linear strain. λ represents shear strain; λ and μ represent Lamé constants. In steps S1-3, the geometric equation is:

[0014]

[0015] In the formula, u is the displacement, u r Indicates radial displacement. Representing circumferential displacement, in steps S1-4, the wave equation is:

[0016]

[0017] In the formula, ρ is the density of the pipe material, t is time, and the boundary conditions in steps S1-5 are:

[0018]

[0019] In steps S1-7, the mathematical expression for the second harmonic in the pipe includes:

[0020] u = u1 + u2

[0021]

[0022] In the formula, u1 represents the displacement of the fundamental wave, u2 represents the displacement of the second harmonic, and A m (z) represents the amplitude of the second harmonic, and cc represents higher-order terms. For the m-mode with a frequency of 2ω, Indicates displacement along r and The distribution of .

[0023] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by this invention also has the following technical feature: in the mathematical expression of the second harmonic in the pipe, A... m (z) is represented as:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, σ m and σ n The stress tensor representing the m-th and n-th order modes, v m and v n Represents the velocity vectors of the m-th and n-th order modes, n x and n z k represents the unit vector in the x and z directions. n * The wave number represents the second harmonic, and k represents the wave number of the fundamental wave.

[0030] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by the present invention may also have the following technical features: In step S2, based on the phase velocity matching condition, the non-zero energy flow criterion and the dispersion curve, a suitable mode pair is screened, and a Hanning window is added according to the frequency and number of cycles of the fundamental wave to design an excitation signal, thereby obtaining the mode and the excitation frequency.

[0031] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by this invention also has the following technical features: the nonlinear ultrasonic measurement system includes a receiving transducer and an oscilloscope. The receiving transducer is used to receive the acoustic signal of the second harmonic and convert it into an electrical signal. The oscilloscope is used to record the time-domain signal of the second harmonic. In step S4, frequency domain analysis is performed on the measured time-domain signal to extract the amplitude A1 of the fundamental wave and the amplitude A2 of the second harmonic. The acoustic nonlinear parameter β is calculated based on the following formula:

[0032]

[0033] The normalized acoustic nonlinear parameter β' is obtained by normalizing the parameter. Based on the normalized acoustic nonlinear parameter β' or the second harmonic, the coordinates and dimensions of the microcrack on the pipeline are obtained.

[0034] The circumferential positioning method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by the present invention may also have the following technical features: In step S4, a series of slots of different sizes are prefabricated on multiple spare pipes of the same model as the original pipe. The microcracks are prepared on the spare pipes using a three-point bending test machine. The slots are then removed by machining to form a batch of samples with microcracks of different lengths. The multiple samples are measured using the nonlinear ultrasonic measurement system to obtain the normalized acoustic nonlinear parameter β' or the functional relationship between the second harmonic and the microcrack size.

[0035] The circumferential localization method for microcracks in pipes based on the second harmonic of ultrasonic guided waves provided by this invention may also have the following technical features: the nonlinear ultrasonic measurement system includes a piezoelectric ceramic array for receiving the second harmonic; in step S4, nonlinear ultrasonic measurement is performed, the acoustic signal of each unit in the piezoelectric ceramic array is extracted, and the distribution of the normalized acoustic nonlinear parameter β' or the second harmonic is calculated; and the relationship between the normalized acoustic nonlinear parameter β' or the second harmonic and the microcrack region is established. The relationship between coordinates and the number of microcracks is controlled by keeping other variables constant. Different numbers of slots are prefabricated along the circumference of the spare pipeline. The microcracks are prepared by using a three-point bending test machine. The slots are then removed by machining to form a batch of samples with different numbers of microcracks.

[0036] Invention Function and Effect

[0037] The present invention provides a method for circumferentially locating microcracks in pipes based on the second harmonic of ultrasonic guided waves. By using the fundamental wave of the axisymmetric mode to generate the second harmonic, and based on the mode and amplitude of the second harmonic, circumferential location of microcracks in tubular structures can be achieved. This method can detect and accurately locate microcracks in pipelines before they develop into macrocracks, thereby enabling timely and precise maintenance of pipelines, preventing further evolution of microcracks and accidents, ensuring the safe operation of pressure pipelines, and reducing the time and economic costs of manual inspection. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method for circumferential positioning of microcracks in a tube based on the second harmonic of ultrasonic guided waves in an embodiment of the present invention;

[0039] Figure 2 This is a diagram showing the excitation signal and the selected mode pair in an embodiment of the present invention;

[0040] Figure 3 This is a stress cloud diagram of the second harmonic of the ultrasonic guided wave in an embodiment of the present invention;

[0041] Figure 4 These are typical time-domain signals and spectrum diagrams of the axial displacement of reflected waves in embodiments of the present invention;

[0042] Figure 5 These are typical time-domain signals and spectrum diagrams of axial displacement of transmitted waves in embodiments of the present invention;

[0043] Figure 6 This is a circumferential distribution diagram of the axial displacement amplitude of the second harmonic of the reflected wave in an embodiment of the present invention;

[0044] Figure 7 This is a circumferential distribution diagram of the axial displacement amplitude of the fundamental wave and the second harmonic of the transmitted wave in an embodiment of the present invention. Detailed Implementation

[0045] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following describes in detail the method for circumferential positioning of microcracks in pipes based on the second harmonic of ultrasonic guided waves.

[0046] <Example>

[0047] This embodiment provides a method for circumferentially locating microcracks in pipes based on the second harmonic of ultrasonic guided waves. This method is used to locate microcracks in pipes circumferentially before macrocracks appear. Microcracks in pipes refer to cracks with a width of less than 10 μm.

[0048] In this embodiment, a nonlinear ultrasonic measurement system is used to measure the pipeline. The nonlinear ultrasonic measurement system consists of a signal generator, a pulse amplifier, an excitation transducer, a receiving transducer, a filter, and an oscilloscope. The excitation transducer and the receiving transducer can be piezoelectric ceramic arrays, piezoelectric ceramic tubes, etc.

[0049] Figure 1 This is a flowchart of the method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves in this embodiment.

[0050] like Figure 1 As shown, the method includes the following steps:

[0051] Step S1: Based on the physical and geometric parameters of the pipeline, establish the dispersion equation of the ultrasonic guided wave in the pipeline to obtain the dispersion curves of the torsional mode and the longitudinal mode.

[0052] Step S2: Based on the dispersion curve, select the corresponding mode and excitation frequency.

[0053] Step S3: Based on the selected mode and excitation frequency, the pipeline is measured using a nonlinear ultrasonic measurement system. The nonlinear ultrasonic measurement system generates ultrasonic guided waves of a fixed frequency, in which the fundamental wave propagates in the pipeline to form a second harmonic. The nonlinear ultrasonic measurement system receives the second harmonic along its propagation path.

[0054] Step S4: Based on the received second harmonic, perform calculation and analysis to obtain normalized acoustic nonlinear parameters, and based on the normalized acoustic nonlinear parameters or the second harmonic, obtain the location and size information of the microcracks in the pipeline.

[0055] The steps described above will be explained in detail below.

[0056] Step S1: Based on the physical and geometric parameters of the pipeline, establish the dispersion equation of the ultrasonic guided wave in the pipeline to obtain the dispersion curves of the torsional mode and the longitudinal mode.

[0057] Step S1 specifically includes the following sub-steps:

[0058] Step S1-1: Construct a cylindrical coordinate system in the pipeline.

[0059] The origin is located on the left end face of the excitation transducer; the r-axis is inside the left end face, with the origin as its starting point; the z-axis is along the direction of the pipe axis, pointing to the right side of the excitation transducer. The angle of rotation along the r-axis (observed from the opposite direction of the z-axis, the rotation direction is counterclockwise).

[0060] Step S1-2: Construct the physical equations of the pipeline based on its physical parameters, as follows:

[0061]

[0062] In the formula, σ represents stress, σ rr Indicates radial normal stress. ε represents shear stress; ε represents strain. ε represents radial linear strain. zz Indicates axial linear strain. λ represents shear strain; λ and μ represent Lamé constants.

[0063] Steps S1-3: Based on the pipe's geometric parameters and the Lamé coefficients in the cylindrical coordinate system, establish the pipe's geometric equations in the cylindrical coordinate system:

[0064]

[0065] In the formula, u is the displacement, u r Indicates radial displacement. This indicates circumferential displacement.

[0066] Steps S1-4: Substitute the above physical and geometric equations into the equations of motion in cylindrical coordinates, and neglect the body force terms to obtain the wave equations for nonlinear ultrasound in the pipe, as follows:

[0067]

[0068] In the formula, ρ is the density of the pipe material, and t is time.

[0069] Steps S1-5: Based on the interface continuity and free boundary conditions of the pipeline, the boundary conditions for the second harmonic of the ultrasonic guided wave in the pipeline are formed.

[0070] That is, since the inner and outer surfaces of the pipe are free, therefore:

[0071]

[0072] In the formula, 2r1 is the inner diameter of the pipe, and 2r2 is the outer diameter of the pipe.

[0073] Steps S1-6: Based on the above formulas (1), (2), (3) and (4), establish the dispersion equation of the ultrasonic guided wave in the pipeline and draw the dispersion curves of the torsional mode and the longitudinal mode.

[0074] That is, in this embodiment, considering the higher-order terms of the geometric equations in the cylindrical coordinate system, and based on the characteristics of the orthogonal coordinate system and isotropic materials, Landau and Lifshitz's third-order elastic constants are introduced to construct higher-order terms in the physical equations. With the help of Lamé coefficients, the Second Piola-Kirchhoff stress tensor and the First Piola-Kirchhoff stress tensor are established sequentially. Based on the nonlinear strain-displacement relationship, the stress-strain relationship, and the motion differential equations in the cylindrical coordinate system, and ignoring the body force terms, the wave equation of nonlinear ultrasound in the steel pipe is established. Based on the interface continuity and free boundary conditions, the boundary conditions for the second harmonic of the ultrasonic guided wave in the steel pipe are formed.

[0075] Steps S1-7: For the wave equation and boundary conditions of the second harmonic of the ultrasonic guided wave in the pipeline, the second-order perturbation method and the orthogonal mode expansion method are used to establish the mathematical expression of the second harmonic in the pipeline.

[0076] The expressions for the second-order perturbation method and the orthogonal mode expansion method are:

[0077] u=u1+u2 (5)

[0078]

[0079] In the formula, u1 represents the displacement of the fundamental wave, u2 represents the displacement of the second harmonic, and A m (z) represents the amplitude of the second harmonic, and cc represents higher-order terms. For the m-mode with a frequency of 2ω, Indicates displacement along r and The distribution of .

[0080] Among them, A m (z) can be represented as:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, σ m and σ n The stress tensor representing the m-th and n-th order modes, v m and v n Represents the velocity vectors of the m-th and n-th order modes, n x and n z k represents the unit vector in the x and z directions.n * The wave number represents the second harmonic, and k represents the wave number of the fundamental wave.

[0087] Step S2: Based on the dispersion curve, select the corresponding mode and excitation frequency.

[0088] Based on the phase velocity matching condition, the non-zero energy flow criterion, and the aforementioned dispersion curves, suitable mode pairs are selected. In the phase velocity dispersion curves, the L(0,2) mode exhibits a horizontal region, indicating the existence of suitable mode pairs that generate second harmonics with a cumulative effect. Furthermore, the fundamental frequencies of the torsional mode and the longitudinal mode can only generate the second harmonic of the longitudinal mode.

[0089] In this embodiment, a Hanning window is added based on the frequency and number of periods of the fundamental wave to design the excitation signal.

[0090] Step S3: Based on the selected mode and excitation frequency, the pipeline is measured using a nonlinear ultrasonic measurement system. The nonlinear ultrasonic measurement system generates an ultrasonic guided wave of a fixed frequency. The fundamental wave of the ultrasonic guided wave propagates in the pipeline to form a second harmonic. The nonlinear ultrasonic measurement system receives the second harmonic along its propagation path.

[0091] Specifically, the signal generator generates a corresponding excitation signal based on the selected mode pair and excitation frequency. This excitation signal is converted into a vibration signal by a pulse amplifier and an excitation transducer. This vibration signal forms a fixed-frequency ultrasonic guided wave in the pipe. The fundamental wave propagates in the tubular structure of the pipe, forming a second harmonic with a cumulative effect.

[0092] Step S4: Based on the received second harmonic, perform calculation and analysis to obtain normalized acoustic nonlinear parameters, and based on the normalized acoustic nonlinear parameters or the second harmonic, obtain the location and size information of the microcracks in the pipeline.

[0093] In this embodiment, a receiving transducer is arranged along the propagation path of the second harmonic, converting the acoustic signal of the second harmonic into an electrical signal. In this embodiment, the receiving transducer is a piezoelectric ceramic array arranged circumferentially along the pipe. During measurement, the acoustic signal of each unit in the piezoelectric ceramic array is extracted, and the normalized acoustic nonlinear parameter β' or the distribution of the second harmonic displacement is calculated.

[0094] The second harmonic signal is passed through a bandpass filter and an oscilloscope. The oscilloscope measures the time-domain signal multiple times and averages it. In this embodiment, the oscilloscope measures the time-domain signal 512 times and averages it. The time-domain signal is then stored on a USB flash drive. The excitation transducer and the receiving transducer are recoupled, and 2-4 more measurements are performed and the data is stored.

[0095] Then, frequency domain analysis is performed on the measured time-domain signal. In this embodiment, using Origin software, parameters such as signal input and sampling interval are set, and a Fast Fourier Transform (FFT) is performed on the time-domain signal to conduct frequency domain analysis. The amplitude A1 of the fundamental wave and the amplitude A2 of the second harmonic are extracted, and the acoustic nonlinear parameter β is calculated based on the following formula and then normalized:

[0096]

[0097] The normalized acoustic nonlinear parameter is denoted as β'. Based on the normalized acoustic nonlinear parameter β' and the second harmonic, the microcrack zone on the pipeline is obtained. Coordinates and dimensions.

[0098] The normalized acoustic nonlinear parameter β' or second harmonic wave and the functional relationship between crack size and location can be obtained by performing the above measurements on multiple samples.

[0099] In this embodiment, keeping other variables constant, a series of slots of different sizes are prefabricated on multiple spare pipes of the same model as the aforementioned pipes. Microcracks are prepared on the multiple spare pipes using a three-point bending test machine, and then the slots are removed by machining, thereby forming a batch of samples with microcracks of different lengths. Multiple samples are measured using a nonlinear ultrasonic measurement system to obtain the normalized acoustic nonlinear parameter β' or the second harmonic and the functional relationship between the microcrack size.

[0100] Keeping other variables constant, different numbers of slots are prefabricated along the circumference of the spare pipeline. Microcracks are prepared using a three-point bending test machine, and then the slots are machined out to form a batch of samples with different numbers of microcracks. Nonlinear ultrasonic measurements are performed to extract the acoustic signal of each unit in the piezoelectric ceramic array and calculate the distribution of the normalized acoustic nonlinear parameter β' or second harmonic. The relationship between the normalized acoustic nonlinear parameter β' or second harmonic and the microcrack region is established. The functional relationship between coordinates and the number of microcracks.

[0101] As described above, the method in this embodiment utilizes the second harmonic of ultrasonic guided waves to obtain the microcrack zone in the pipeline. Information such as coordinates, microcrack size, and number of microcracks enables the characterization and circumferential positioning of microcracks in pressure pipelines.

[0102] In this embodiment, the above method is verified through finite element simulation experiments.

[0103] The pipe is a 304 stainless steel round pipe, 1000mm long, with an outer diameter of 30mm, an inner diameter of 26mm, and a density of 7860kg / m³. 3 The Young's modulus is 1.996 × 10⁻⁶.11 Pa, Poisson's ratio is 0.29.

[0104] When constructing the cylindrical coordinate system, the pipe is placed approximately horizontally, with the center of the circle on the left end face of the pipe as the origin. The z-axis points to the right along the axial direction of the pipe, and the rotation angle of a specific radius on the left end face of the pipe is...

[0105] Microcracks were simulated on the pipe. Specifically, based on the nonlinear theory of contact acoustics, a major axis and a minor axis of 5×10⁻⁶ were selected. -3 m and 2×10 -8 An ellipse of length m is completely cut off along the pipe thickness direction. The cut-off portion is considered a microcrack on the pipe. Contact properties of the master and slave surfaces are set to construct a microcrack model. In the simulation experiment, using the above method, at z = 500 mm on the pipe, from... arrive One microcrack is constructed every 10°, for a total of 7 microcracks.

[0106] Figure 2 This is a diagram showing the excitation signal and the selected mode pair in this embodiment.

[0107] like Figure 2 As shown, in the simulation experiment, the excitation signal was a short, pure sinusoidal tone with a Hanning window at 200 kHz. A normal displacement was applied to the left end face of the pipe, with an amplitude of 1 × 10⁻⁶. -7 m.

[0108] According to the formula The time step is selected as 1×10 -8 s, the time length is selected as 5×10 -5 s. This invention divides the pipeline into Zone I (z = 0-400mm), Zone II (z = 400-600mm), and Zone III (z = 600-1000mm). According to the formula In the mesh control properties of Region I and Region III, the element shape and technique are tetrahedral and free, with a maximum element mesh size of 1 mm. In the mesh control properties of Region II, the element shape and technique are hexahedral and structured, with a maximum element size of 0.5 mm.

[0109] In addition, geometric nonlinearity is disabled in the simulation model during the simulation experiments. This helps in identifying the source of nonlinearity.

[0110] To avoid mutual interference between reflected and transmitted waves in the received signal, in the simulation experiment, at z = 250 mm and z = 750 mm, from Initially, an acoustic signal was received every 15°, with a total of 25 receiving points set up.

[0111] Figure 3This is the stress cloud diagram of the second harmonic of the ultrasonic guided wave in this embodiment.

[0112] When an ultrasonic guided wave passes through an area with microcracks in a pipeline, the stress cloud diagram is as follows: Figure 3 As shown, and Figure 3 In the image, the area with microcracks on the pipe was magnified locally.

[0113] Figure 4 This is a typical time-domain signal and spectrum of the reflected wave in this embodiment, showing the typical time-domain signal and spectrum of wave packet 3 at z = 250 mm.

[0114] like Figure 4 As shown, analysis of the group velocity reveals that wave packet 1 is in L(0,2) mode and wave packet 2 is in L(0,1) mode. Compared to L(0,2) mode, L(0,1) mode has lower energy. Therefore, the influence of L(0,1) mode is ignored in the simulation experiment. FFT processing of wave packet 1 did not reveal any second harmonics. The ultrasonic guided wave in the pipe encounters a microcrack and is reflected, thus wave packet 3 is present in the received signal. The reflected wave encounters the left end face and is reflected again, passing through the receiving point to form wave packet 4. Additionally, the transmitted wave is reflected at the right end face, passing through the receiving point to form wave packet 5, and then reflected again at the left end face to form wave packet 6. FFT processing of wave packets 3, 4, 5, and 6 all revealed second harmonics. The analysis results indicate that the microcrack is the main source of the second harmonics in the ultrasonic guided wave.

[0115] Figure 5 This embodiment shows a typical transmitted wave time-domain signal and spectrum, where a typical ultrasonic guided wave time-domain signal and spectrum of wave packet 1 at z = 750 mm are shown. Figure 5 (a) is the time-domain signal diagram. Figure 5 (b) is the spectrum of wave packet 1.

[0116] like Figure 5 As shown, the ultrasonic guided wave passes through the microcrack, forming wave packet 1 at the receiving point. It is reflected at the right end face, forming wave packet 2 at the receiving point. Additionally, the reflected wave from the microcrack is reflected by the left and right end faces, forming wave packets 3 and 4 at the receiving point. FFT processing of wave packets 1, 2, 3, and 4 reveals second, third, and even fourth harmonics. Therefore, when the ultrasonic guided wave passes through the microcrack, higher harmonics are generated.

[0117] Figure 6 This is a circumferential distribution diagram of the axial displacement of the second harmonic of the reflected wave in this embodiment.

[0118] like Figure 6As shown, in the simulation experiment, at z = 250 mm, displacement was received every 15° along the z-axis around the pipe, for a total of 24 signals. The wave packet 3 in the time-domain signal was processed by FFT to obtain the amplitude of the second harmonic. A graph showing the relationship between the angle and the amplitude of the second harmonic was plotted. Figure 6 As can be seen, the fundamental wave of the axisymmetric mode is reflected by the microcrack, generating the second harmonic of the bending mode. Furthermore, the amplitude of the second harmonic reaches its maximum when φ = 15°. This angle deviates by 15° from the center of the microcrack region.

[0119] Figure 7 This is a circumferential distribution diagram of the axial displacement of the fundamental and second harmonic waves of the transmitted wave in this embodiment, wherein... Figure 7 (a) is a circumferential distribution diagram of the axial displacement of the fundamental wave of the transmitted wave. Figure 7 (b) is a circumferential distribution diagram of the second harmonic axial displacement.

[0120] like Figure 7 As shown, in the simulation experiment, 24 signals were received using the same method at z = 750 mm. FFT processing was performed on wave packet 1 of the time-domain signal, and the relationships between the angle and the fundamental amplitude, and between the angle and the second harmonic amplitude, were plotted. Figure 7 As can be seen, when the fundamental wave of the axisymmetric mode passes through the microcrack, no mode conversion occurs, but a second harmonic of the bending mode is generated. Therefore, the fundamental wave of the axisymmetric mode is not sensitive to the microcrack, and the amplitude of the second harmonic is within... When this angle reaches its maximum, it perfectly coincides with the center of the crack zone. Additionally, when... and At that angle, the amplitude of the second harmonic is significantly higher than at other angles.

[0121] Based on the above simulation experiments and corresponding analysis, it can be seen that the method in this embodiment is based on nonlinear ultrasonic guided waves in the pipeline. According to the amplitude and mode of the second harmonic of the reflected wave and the transmitted wave, the circumferential positioning of the microcrack is realized, in which the second harmonic of the transmitted wave is more sensitive.

[0122] In this embodiment, the parts not described in detail are well-known technologies in the art.

[0123] Functions and effects of the embodiments

[0124] According to the method and device for circumferential positioning of microcracks in pipes based on ultrasonic guided wave second harmonics provided in this embodiment, second harmonics are generated by using the fundamental wave of axisymmetric mode. Based on the mode and amplitude of the second harmonics, circumferential positioning of microcracks in tubular structures can be achieved. Microcracks can be detected in time before they develop into macrocracks, thereby enabling timely and accurate maintenance of pipelines, avoiding further evolution of microcracks and accidents, ensuring the safe operation of pressure pipelines, and reducing the time and economic costs of manual inspection.

[0125] The above embodiments are only used to illustrate specific implementations of the present invention, and the present invention is not limited to the scope of the description of the above embodiments.

[0126] In the above embodiments, the method is used to characterize and locate microcracks in 304 stainless steel round pipes of a given size. In fact, the method can also be used to characterize and locate microcracks in pipes of other materials and sizes.

[0127] In the above embodiments, a series of slots of different sizes are prefabricated on multiple spare pipes of the same type using machining and three-point bending. Microcracks are prepared using a three-point bending testing machine, and then the slots are removed by machining to form a batch of samples with microcracks of different lengths and numbers. In alternative solutions, other methods in the prior art can also be used to prepare samples with microcracks of different lengths and numbers.

Claims

1. A method for circumferential localization of microcracks in pipes based on the second harmonic of ultrasonic guided waves, used for characterizing and locating microcracks in pipes, characterized in that... Includes the following steps: Step S1: Based on the physical and geometric parameters of the pipe, establish the dispersion equation of the ultrasonic guided wave in the pipe to obtain the dispersion curves of the torsional mode and the longitudinal mode. Step S2: Based on the dispersion curve, phase velocity matching condition, and non-zero energy flow criterion, select the corresponding mode, mode pair, and excitation frequency. Based on the mode pair, a second harmonic of a bending mode with a cumulative effect can be generated. Step S3: Based on the mode and the excitation frequency, the pipe is measured using a nonlinear ultrasonic measurement system. The nonlinear ultrasonic measurement system generates a fixed-frequency ultrasonic guided wave. The fundamental wave of the ultrasonic guided wave propagates in the pipe to form a second harmonic. The nonlinear ultrasonic measurement system receives the second harmonic along its propagation path. The nonlinear ultrasonic measurement system generates a corresponding excitation signal based on the selected mode pair and the excitation frequency, converting the excitation signal into a vibration signal. The vibration signal forms a fixed-frequency ultrasonic guided wave in the pipe, and its fundamental wave propagates in the tubular structure of the pipe, forming the second harmonic with a cumulative effect. Step S4: Based on the received second harmonic, a normalized acoustic nonlinear parameter is obtained through calculation and analysis. Based on the normalized acoustic nonlinear parameter, the size information of the microcrack in the pipe is obtained. Based on the second harmonic, the location information of the microcrack in the pipe is obtained. The circumferential positioning of the microcrack is achieved according to the amplitude of the second harmonic of the reflected wave and the transmitted wave and the bending mode. The second harmonic of the transmitted wave is more sensitive.

2. The method for circumferential positioning of microcracks in pipes based on the second harmonic of ultrasonic guided waves according to claim 1. Its features are: Step S1 includes the following sub-steps: Step S1-1: Construct a cylindrical coordinate system based on the pipeline; Step S1-2: Construct the physical equations of the pipeline based on the physical parameters; Steps S1-3: Based on the geometric parameters and the Lamé coefficients of the cylindrical coordinate system, construct the geometric equations of the pipe in the cylindrical coordinate system; Step S1-4: Substitute the physical equation and the geometric equation into the motion equation in the cylindrical coordinate system, and ignore the body force term to obtain the wave equation of the ultrasonic guided wave in the pipe. Steps S1-5: Based on the interface continuity and free boundary conditions of the pipeline, the boundary conditions of the second harmonic in the pipeline are formed. Steps S1-6: Based on the wave equation and the linear terms of the boundary conditions, establish the dispersion equation of the ultrasonic guided wave in the pipeline, and obtain the dispersion curves of the torsional mode and the longitudinal mode. Steps S1-7: Based on the wave equation and the nonlinear terms of the boundary conditions, the mathematical expression of the second harmonic in the pipeline is established using the second-order perturbation method and the orthogonal mode expansion method.

3. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 2, characterized in that: in, The nonlinear ultrasonic measurement system includes a signal generator and an excitation transducer for generating the ultrasonic guided waves. In step S1-1, the origin of the cylindrical coordinate system is located on the left end face of the excitation transducer. The r-axis lies within this left end face, with the origin as its starting point. The z-axis points along the axial direction of the pipe towards the right side of the excitation transducer, and φ is the rotation angle of the r-axis. In step S1-2, the physical equation is: In the formula, σ represents stress, σ rr Represents radial normal stress, σ rφ ε represents shear stress; ε represents strain. φφ ε represents radial linear strain. zz ε represents axial linear strain. rφ λ represents shear strain; μ and μ represent Lamé constants. In steps S1-3, the geometric equation is: In the formula, u is the displacement, u r Represents radial displacement, u φ Indicates circumferential displacement. In steps S1-4, the wave equation is: In the formula, ρ is the density of the pipe material, and t is time. In steps S1-5, the boundary conditions are: In steps S1-7, the mathematical expression for the second harmonic in the pipe includes: In the formula, u1 represents the displacement of the fundamental wave, u2 represents the displacement of the second harmonic, and A m (z) represents the amplitude of the second harmonic, and cc represents higher-order terms. For the m-mode with a frequency of 2ω, This represents the distribution of displacement along r and φ.

4. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 3, characterized in that: in, In the mathematical expression for the second harmonic in the pipeline, A m (z) is represented as: In the formula, σ m and σ n The stress tensor representing the m-th and n-th order modes, v m and v n Represents the velocity vectors of the m-th and n-th order modes, n x and n z k represents the unit vector in the x and z directions. n * The wave number represents the second harmonic, and k represents the wave number of the fundamental wave.

5. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 1, characterized in that: in, In step S2, based on the phase velocity matching condition, the non-zero energy flow criterion, and the dispersion curve, a suitable mode pair is selected, and a Hanning window is added according to the frequency and number of cycles of the fundamental wave to design the excitation signal, thereby obtaining the mode and the excitation frequency.

6. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 1, characterized in that: in, The nonlinear ultrasonic measurement system includes an excitation transducer, a receiving transducer, and an oscilloscope. The receiving transducer is used to receive the acoustic signal of the second harmonic and convert it into an electrical signal. The oscilloscope is used to record the time-domain signal of the second harmonic. The oscilloscope measures the time-domain signal 512 times and averages it. The excitation transducer and the receiving transducer are recoupled, and 2-4 more measurements are performed and the data is stored. In step S4, frequency domain analysis is performed on the measured time-domain signal to extract the amplitude A1 of the fundamental wave and the amplitude A2 of the second harmonic. The acoustic nonlinear parameter β is calculated based on the following formula: The normalized acoustic nonlinear parameter β' is obtained by normalizing it.

7. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 6, characterized in that: in, In step S4, the nonlinear ultrasonic measurement system is used to measure multiple samples to obtain the functional relationship between the normalized acoustic nonlinear parameter and the microcrack size. A series of slots of different sizes are prefabricated on multiple spare pipes of the same model as the original pipe. The microcracks are prepared on the spare pipes using a three-point bending test machine. The slots are then removed by machining to form a batch of samples with microcracks of different lengths.

8. The method for circumferential positioning of microcracks in a pipe based on the second harmonic of ultrasonic guided waves according to claim 7, characterized in that: in, The nonlinear ultrasonic measurement system includes a piezoelectric ceramic array for receiving the second harmonic. In step S4, nonlinear ultrasonic measurements are performed to extract the acoustic signal of each unit in the piezoelectric ceramic array and calculate the distribution of the second harmonic. The relationship between the second harmonic and the coordinates of the microcrack zone and the number of microcracks is then established. Keeping other variables constant, different numbers of slots are prefabricated along the circumference of the spare pipeline. The microcracks are prepared using a three-point bending test machine, and then the slots are removed by machining to form a batch of samples with different numbers of microcracks.

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