A method for measuring coating interface stiffness by first derivative spectrum of ultrasonic echo phase

Abstract

The application relates to a method for measuring coating interface stiffness by using ultrasonic echo phase first derivative spectrum, belonging to the technical field of ultrasonic nondestructive testing. The method detects a coating sample by vertical incidence of ultrasonic waves, collects aliasing echoes of a coupling medium / coating and a coating / substrate interface P R , carries out fast Fourier transform to obtain an unwound phase P R , carries out fast Fourier transform to obtain an unwound phase R , carries out fast Fourier transform to obtain an unwound phase R , carries out fast Fourier transform to obtain an unwound phase f , carries out fast Fourier transform to obtain an unwound phase K , carries out fast Fourier transform to obtain an unwound phase n , carries out fast Fourier transform to obtain an unwound phase The method reduces the influence of material sound attenuation, interface roughness and other factors on the detection result, has high quantitative precision, wide application range, large detection depth range, easy operation and other advantages, and is free from the dependence on a high-quality reference signal in traditional construction of URCAS or URCPS.

Description

Technical Field

[0001] A method for determining the interface stiffness of a coating using the first derivative spectrum of ultrasonic echo phase is disclosed, which belongs to the field of ultrasonic nondestructive testing technology. Background Technology

[0002] Developing simple, reliable, and easily engineering-applied quantitative testing methods for coating interfacial bond strength is crucial for ensuring the service performance of coatings in high-temperature, high-pressure, and high-wear environments. Currently, destructive methods are predominantly used to measure the interfacial bond strength of coatings / substrate materials, including tensile, scratch, indentation, and bending methods. While non-destructive testing methods such as laser speckle interferometry, infrared thermography, and X-ray testing have made good progress, these methods suffer from limitations such as limited applicability, low testing efficiency, and high equipment costs.

[0003] Ultrasonic nondestructive testing (NDT) is a detection technique based on mechanical vibration displacement. It is highly sensitive to localized stress and displacement at interfaces and is well-suited for characterizing the bonding strength between coatings and substrates. Currently, using ultrasonic NDT to characterize interfacial bonding strength has become a research hotspot. Existing ultrasonic methods for testing interfacial bonding strength include laser-ultrasonic dissection, ultrasonic microscopy, and ultrasonic surface wave (SSW) techniques. These methods measure acoustic mode transformation / surface displacement differences, the V(z,t) curve formed by the interference effect between vertical reflected waves and leaking surface waves, and the scattering law of surface wave frequencies in the coating structure, respectively, indirectly characterizing the coating / substrate bonding strength. However, these methods have significant limitations. Laser-ultrasonic dissection can cause micro-damage to the material, and laser-ultrasonic equipment is complex and expensive, making it difficult to apply in practical industrial settings. Ultrasonic microscopy, due to its high detection frequency and large attenuation, can typically only detect coatings with micrometer-level thickness. Ultrasonic microscopes also suffer from complexity and high cost, making them more suitable for laboratory research. Ultrasonic SSW techniques can only measure within a single wavelength range, resulting in low detection efficiency and insufficient lateral resolution. They are often combined with laser-ultrasonic techniques to improve resolution, which increases the cost and complexity of the equipment.

[0004] Ultrasonic bulk wave technology is widely used in practical engineering due to its advantages such as large detection range, wide applicability, and inexpensive and portable equipment. Combined with automated equipment, it can also achieve high detection efficiency. Interface stiffness and bonding strength are both affected by the elastic modulus of the media on both sides of the interface, the distribution and orientation of micro-defects, and the interface roughness. These two factors are clearly correlated; therefore, existing methods for detecting interface bonding strength using ultrasonic bulk waves mostly indirectly characterize the bonding strength by measuring interface stiffness. Lavrentyev et al. measured the interface stiffness of diffusion welds in thick-walled S7 tool steel structures based on ultrasonic pulse echo amplitude and measured the bonding strength of the welds through tensile failure tests, showing a good linear relationship between the two. The primary condition for implementing the above methods is extracting high-quality, independent interface reflection echo signals containing interface information. However, in the interface stiffness detection of thin-layer structures such as thin-walled welds, sprayed coatings, and adhesive bonding, interface echoes overlap with surface or bottom echoes, making it impossible to extract the interface echoes independently. In such cases, the aliased echoes are usually extracted together, and an ultrasonic reflection coefficient amplitude spectrum (URCAS) or an ultrasonic reflection coefficient phase spectrum (URCPS) is constructed using signal analysis methods to extract the characteristics of the spectrum and quantify the interface stiffness. Rokhlin et al. proposed a method based on URCAS to characterize interface stiffness and measured the interface stiffness of an aluminum plate / 0.5mm aluminum thin layer / aluminum plate structure under different external loads. However, URCAS is affected by many factors such as interface roughness and material attenuation. In actual engineering, many coatings have high roughness and high attenuation characteristics, which leads to large errors in the measurement results of the URCAS method. Haldren et al. measured the interface stiffness of the bonding interface of plexiglass / epoxy resin adhesive layer / plexiglass structure based on URCPS. This method can well characterize the bonding quality of the adhesive layer / plexiglass interface. However, before preparing the acrylic sheet / epoxy resin adhesive layer / acrylic sheet structure bonding sample, it is necessary to measure the in-situ signal of the acrylic sheet as a reference signal to eliminate the influence of factors such as sound wave propagation time, initial phase of the signal, system phase, and material attenuation on URCPS, which is difficult to achieve in actual work.

[0005] This paper proposes a method for determining the interfacial stiffness of coatings using ultrasonic echo phase derivative spectrum (UEPDS). A single ultrasonic bulk wave probe is used to perpendicularly incident on the coating sample, and the echo signal P is measured in a single measurement. R For signal P RThe expanded phase of the aliased signal is obtained by performing a Fourier transform on the surface wave and multiple echoes from the interface of the aliased coating. Then, by calculating the first-order partial derivative of the expanded phase with respect to frequency, a UEPDS of the aliased signal is constructed, and the interface stiffness coefficient K is extracted from the UEPDS. n Extremal frequencies f with a clear relationship n This method achieves quantitative detection of coating / substrate interface stiffness through inversion. Compared to traditional ultrasonic volume wave methods, this method reduces the influence of material acoustic attenuation and interface roughness on the detection results, maintaining high quantitative accuracy while eliminating the dependence on high-quality reference signals when constructing URCAS or URCPS using traditional ultrasonic volume wave methods. Compared to techniques such as laser ultrasound, ultrasonic surface waves, and ultrasonic microscopy, this method also has advantages such as wide applicability, large detection depth range, inexpensive and portable equipment, and simple operation, meeting the needs of engineering applications. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the interface stiffness of coatings using ultrasonic echo phase first derivative spectra. This method directly calculates the phase-frequency first-order partial derivative of the aliased ultrasonic echoes to construct a UEPDS, and then quantitatively inverts the interface stiffness by extracting the extreme frequencies of the UEPDS. This method reduces the influence of material acoustic attenuation and interface roughness on the detection results, achieving high quantitative accuracy while eliminating the dependence on high-quality reference signals in traditional URCAS or URCPS construction. This method is simple and easy to implement in engineering applications and can be extended to C-scan imaging of coating interface bonding quality, offering significant economic and social benefits.

[0007] A method for determining the interface stiffness of a coating using ultrasonic echo phase first derivative spectrum, comprising the following measurement steps:

[0008] (1) Measure the density ρ of each layer of the coating / substrate structure of the test sample. i Longitudinal wave speed of sound v li And the thickness h of the coating, the acoustic impedance Z of each layer of material is calculated by equation (1). i Where i is the layer number, i=1 represents the coupling medium layer, i=2 represents the coating layer, and i=3 represents the substrate layer;

[0009] Z i =v li ρ i (1)

[0010] (2) Substitute the acoustic parameters measured in step (1) into the derived UEPDS extreme frequency f n With interface stiffness K n In the constitutive relation, as shown in equation (2), the theoretical extreme frequency f under different interface stiffnesses is calculated by iterative method. n theWhere n is the order of the extreme frequency and f is the frequency. As the interface stiffness increases, the extreme frequency shifts towards higher frequencies. Based on the range of extreme frequency variation, the frequency of the ultrasonic probe is selected so that its effective frequency band can cover the range of extreme frequency variation.

[0011]

[0012] (3) The ultrasonic probe is coupled to the sample surface, and the ultrasonic wave is incident on the coupling medium / coating interface and the coating / substrate interface. The A-scan waveform P containing multiple echoes from the coupling medium / coating and the coating / substrate interface is acquired. R ;

[0013] (4) Extract the signal P collected in step (3). R The reflected echo data from the coupling medium / coating interface were obtained and subjected to Fast Fourier Transform to construct the power spectrum X0(f). The frequency range in the power spectrum X0(f) with an amplitude greater than the maximum amplitude threshold of -12dB was defined as the effective frequency band [f]. b ,f e ]; and then analyze the multiple echo signals P containing the coupling medium / coating and coating / substrate interface. R A fast Fourier transform is performed on the whole sample, and the ultrasonic echo unfolded phase Φ at the corresponding position of the test sample is obtained by formula (3). R Calculate the effective frequency band [f] b ,f e ] Φ R The first-order partial derivative with respect to frequency f yields the ultrasonic echo phase derivative spectrum (UEPDS).

[0014]

[0015]

[0016] Among them, Real(FFT(P) R )) and Img(FFT(P R )) respectively represent P R The real and imaginary parts after Fast Fourier Transform;

[0017] (5) After constructing the UEPDS, identify the effective frequency band of the experimental UEPDS [f] b ,f e The extreme frequency f within ] n exp Determine the order n of the extreme frequency and record them one by one;

[0018] (6) Based on the theoretical extreme frequency f n the and the extreme frequency f collected in the experiment n expConstruct an objective function, as shown in Equation (5), and use a genetic algorithm to search for the minimum value of the objective function. Use the interface stiffness corresponding to the minimum value of the objective function as the measurement result to achieve accurate inversion of interface stiffness.

[0019]

[0020] The testing system consists of an ultrasonic probe, an ultrasonic pulse transceiver, an oscilloscope, a coating sample, a fixture, and a load device. The fixture clamps the sample to be tested, the ultrasonic probe is placed on the surface of the sample and connected to the fixture by a spring, the load device is located above the fixture, and the oscilloscope is connected to the ultrasonic probe through the ultrasonic pulse transceiver.

[0021] The effects and benefits of this invention are as follows: It directly calculates the first-order partial derivative of the phase with respect to frequency of the expanded ultrasonic echoes to construct the UEPDS, and extracts the extreme frequencies of the UEPDS to quantify the interface stiffness. This reduces the influence of factors such as material acoustic attenuation and interface roughness on the detection results, achieving high quantitative accuracy while eliminating the dependence on high-quality reference signals when constructing traditional URCAS or URCPS. Furthermore, compared to techniques such as laser ultrasound, ultrasonic surface waves, and ultrasonic microscopy, this method also has advantages such as wide applicability, large detection depth range, inexpensive and portable equipment, and simple operation, meeting the needs of engineering applications. The proposed method is simple and easy to implement in engineering applications and can be extended to C-scan imaging of coating interface bonding quality, resulting in significant economic and social benefits. Attached Figure Description

[0022] Figure 1 This is a structural diagram of an ultrasonic testing system for the interface stiffness of thin-layer structures.

[0023] The components include: 1. Carbon steel substrate; 2. 0.48mm aluminum thin layer; 3. Acrylic wedge; 4. Ultrasonic probe; 5. Tooling fixture; 6. Pressure loading system; 7. Pulse transceiver; and 8. Oscilloscope.

[0024] Figure 2 This is a graph showing the variation of UEPDS extreme frequency and sensitivity with interface stiffness.

[0025] Among them, (a) is the graph showing the variation of extreme frequency with interface stiffness; and (b) is the graph showing the variation of sensitivity.

[0026] Figure 3 It is the time-domain echo signal of the sample under no-load conditions.

[0027] (a) is the time-domain waveform; (b) is the power spectrum.

[0028] Figure 4 These are the echo time-domain signals of aluminum thin film / carbon steel substrate samples under different loads.

[0029] Wherein, (a) is the time-domain waveform, and (b) is the ultrasonic echo phase derivative spectrum (UEPDS).

[0030] Figure 5 This is a screenshot of the test results.

[0031] Wherein, (a) represents the experimental and theoretical extreme frequencies under different loads, and (b) represents the interface stiffness measurement results. Detailed Implementation

[0032] Figure 1 The structural diagram of the ultrasonic testing system for the interface stiffness of thin-layer structures is shown. The testing system of this method includes a carbon steel substrate 1, a 0.48 mm aluminum thin layer 2, an acrylic wedge 3, an ultrasonic probe 4, a tooling fixture 5, a loading system 6, a pulse transceiver 7, and an oscilloscope 8. The measurement steps are as follows:

[0033] (1) Before testing, the thickness h of each layer of material was measured by eddy current thickness measurement, Archimedes' displacement method, and ultrasonic pulse echo method. i density ρ i Longitudinal wave speed of sound v li Finally, the acoustic impedance Z of each layer of material is calculated based on equation (1). i The sample used in this experiment was a three-layer, double-interface structure consisting of plexiglass, a 0.48mm aluminum thin layer, and a carbon steel substrate. The stiffness of the aluminum thin layer / carbon steel substrate interface was changed by altering the applied load in the vertical direction. The acoustic parameters of the three-layer materials were measured as follows: the sound velocity of the plexiglass was V1 = 2336 m / s, and the density was ρ1 = 1051 kg / m³. 3 Acoustic impedance Z1 = 2455136 kg / m 2 •s; the speed of sound in the aluminum thin film V l2 =6360m / s, density is ρ2 =2706kg / m³ 3 Acoustic impedance Z2 = 17210160 kg / m 2 •s; the speed of sound in the carbon steel matrix is ​​V l3 =5863m / s, density is ρ3 =7789kg / m³ 3 Acoustic impedance Z2 = 45666907 kg / m 2 ·s.

[0034] (2) Based on the extreme frequency f of UEPDS in formula (2) n With interface stiffness K n The constitutive relation is used to substitute the acoustic parameters from step (1) and the theoretical extreme frequencies f under different interface stiffnesses are calculated using an iterative method. n the The range of extreme frequencies as interface stiffness changes is as follows: Figure 2As shown in (a), the extreme frequency f3 of the aliased coupling medium / coating interface and the coating / substrate echo UEPDS varies from 6MHz to 10MHz. Therefore, a 7.5MHz center frequency probe is selected for detection.

[0035] (3) Place the selected ultrasonic probe above the three-layer sample, clamp the sample with the tooling fixture, and connect the top of the ultrasonic probe with a spring to ensure that the coupling state between the probe and the sample surface remains unchanged during the subsequent loading process; the ultrasonic wave is incident on the sample and reflected, and the A-scan time-domain waveform P of the reflected echo signal is collected. R ,like Figure 3 (a), where t is time in microseconds, for P R The power spectrum X0(f) of the reflected echo data is obtained by performing a fast Fourier transform, as shown below. Figure 3 (b) f is the frequency in megahertz. The effective frequency band corresponding to the amplitude range of the maximum value of the power spectrum X0(f) of -12dB is [1.03MHz, 14.09MHz].

[0036] (4) Following the data acquisition method in step (3), adjust the external load and acquire ultrasonic echo A-scan waveform data P at 8MPa, 24MPa, 40MPa, and 56MPa respectively. R ,like Figure 3 As shown in (a), a fast Fourier transform is performed, and the ultrasonic echo unfolding phase Φ at the corresponding position of the sample is obtained based on equation (3). R Phase data within the effective frequency band is extracted and expanded. First-order partial derivatives with respect to frequency are used to construct a UEPDS, such as... Figure 4 As shown in (b), the extreme frequencies f under different loads are recorded. n exp The corresponding frequencies are 6.99MHz, 7.14MHz, 7.42MHz, and 7.58MHz.

[0037] (5) Extreme frequencies f3 of aliased coupling medium / coating interface and coating / substrate echo UEPDS based on experimental records exp The extreme frequency f3 of the aliased coupling medium / coating interface and coating / substrate echo UEPDS calculated by theory. the Construct the objective function F(K) n The objective function is searched for by a genetic algorithm, and the theoretical interface stiffness K at this point is then determined. n As the inversion stiffness result, the correspondence between the experimental extreme frequencies and the theoretical extreme frequencies under different pressures is as follows: Figure 5 As shown in (a), the interface stiffness measurement results are as follows: Figure 4 As shown in (b), the interface stiffness is 1.25 × 10⁻⁶ when the applied load is 8 MPa, 24 MPa, 40 MPa, and 56 MPa.14 N / m 3 ,1.85×10 14 N / m 3 ,3.16×10 14 N / m 3 ,4.04×10 14 N / m 3 。

Claims

1. A method for measuring the interfacial bonding strength of a coating by ultrasonic echo phase first derivative spectrum, the measuring steps being as follows: (1) measuring the density of each layer of material of the sample to be tested ρ i , the longitudinal wave speed v li and the thickness of the coating h , the acoustic impedance of each layer of material is calculated by equation (1) Z i wherein i The layer number, i =1, representing the coupling medium layer. i =2, representing a coating. i =3 represents the matrix layer; (1) (2) The acoustic parameter measured in step (1) is substituted into the derived UEPDS extreme frequency f n The constitutive relation of the interface stiffness K n The theoretical extreme frequency under different interface stiffness is calculated by the iterative method, as shown in formula (2) f n the , wherein n is the order of the extreme frequency, f is the frequency, and the frequency of the ultrasonic probe is selected so that the effective frequency band covers the variation range of the extreme frequency; (2) (3) The ultrasonic probe is coupled to the surface of the sample to be tested, and ultrasonic waves are incident to the coupling medium / coating interface and the coating / substrate interface, and an A-scan waveform containing multiple echoes of the coupling medium / coating and the coating / substrate interfaces is collected P R ; (4) intercepting the signal collected in step (3) P R coupling medium / coating interface echo data, and do fast Fourier transform to construct power spectrum X 0( f ), the frequency range with amplitude greater than the maximum amplitude-12dB threshold in the power spectrum X 0( f ) is defined as the effective frequency band[ f b , f e ]; again, the multiple echo signals of the coupling medium / coating and the coating / substrate interface P R are subjected to fast Fourier transform as a whole, and the ultrasonic echo phase Φ corresponding to the position of the test sample is obtained by formula (3) R ; the Φ b in the effective frequency band[ f e , f R ] is calculated f ; the first-order partial derivative of the frequency is obtained to obtain the ultrasonic echo phase derivative spectrum UEPDS; (3) (4) wherein Real ( FFT ( P R )) represents Img ( FFT ( P R )) respectively represents P R the real and imaginary parts after fast Fourier transform; (5) After constructing the UEPDS, identify the effective frequency band of the experimental UEPDS. f b , f e Extreme frequencies within ] f n exp Determine the order of the extreme frequency. n And record them one by one; (6) Based on the theoretical extreme frequency f n the and the extreme frequency of the test acquisition f n exp The objective function is constructed as shown in equation (5), and the minimum value of the objective function is searched by a genetic algorithm, and the interface stiffness corresponding to the minimum value of the objective function is taken as the measurement result, so as to realize accurate inversion of the interface stiffness. ； (5)。 2. The method of claim 1, wherein: The ultrasonic detection system used in the method comprises an ultrasonic probe, an ultrasonic pulse transceiver, an oscilloscope, a tool clamp and a load device, the tool clamp is used to press the sample to be tested, the ultrasonic probe is placed on the surface of the sample to be tested and is connected to the tool clamp through a spring to ensure that the probe contacts the surface of the sample at a fixed pressure, the load device is arranged above the tool clamp, and the oscilloscope is connected to the ultrasonic probe through the ultrasonic pulse transceiver.

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