Method for measuring coating thickness, roughness and interface stiffness by using ultrasonic phase derivative spectrum

Abstract

A method for measuring coating thickness, roughness and interface stiffness by using an ultrasonic phase derivative spectrum, the method belonging to the technical field of ultrasonic non-destructive testing. In the method, an ultrasonic testing system comprising a coating sample, an ultrasonic flat probe, an ultrasonic flaw detector, an XYZ three-dimensional stepping apparatus and a computer is used. In the method, a phase screen approximation spring model of ultrasonic waves acting on a rough and weakly bonded interface is provided, an ultrasonic phase derivative spectrum of ultrasonic waves being vertically incident on a three-medium two-interface structure consisting of a coupling medium, a coating and a substrate is derived, high-sensitivity ranges of the ultrasonic phase derivative spectrum in respect of coating thickness, roughness and interface stiffness are identified by means of sensitivity analysis, and deviations introduced by initial phases of reference signals and detection signals are eliminated by means of cross-correlation analysis, thereby implementing simultaneous quantitative characterization of coating thickness, roughness and interface stiffness. The method overcomes the dependence of conventional ultrasonic amplitude spectrums or phase spectrums on high-quality reference signals, and solves the problem of it being difficult to use existing non-destructive testing methods to simultaneously measure roughness and interface stiffness.

Description

Method for measuring coating thickness, roughness and interface stiffness using ultrasonic phase derivative spectroscopy Technical Field

[0001] The invention discloses a method for measuring coating thickness, roughness and interface stiffness by using ultrasonic phase derivative spectrum, which belongs to the technical field of ultrasonic non-destructive testing. Background Art

[0002] Coating technology can significantly improve the thermal insulation, wear resistance, oxidation resistance, and radar absorption properties of key functional components and has been widely used in aerospace, nuclear engineering, energy, petrochemicals, and other fields. Parameters such as coating thickness, interface roughness, and bonding strength are key indicators of the surface and interface integrity of functional components. Both coating thickness and roughness significantly affect interfacial bonding strength, ultimately determining the quality and performance of coated components. For example, as the thickness of a cold-sprayed coating increases, the stress at the coating / metal substrate interface shifts from compressive to tensile, and the interfacial bonding strength initially increases slightly before significantly decreasing. The presence of a certain degree of roughness at soft / soft, soft / hard, or hard / hard interfaces in different material combinations improves interfacial bonding strength. However, the spraying process, oxidizing environment, and other factors can alter interfacial roughness. A certain increase in roughness can cause stress concentration, weaken interfacial bonding strength, and even lead to coating spalling and failure. Therefore, developing nondestructive characterization techniques for multiple parameters of surface and interface integrity, such as coating thickness, roughness, and interface strength, to effectively control their quality is crucial for enabling coatings to achieve their superior overall performance.

[0003] Considering the thinness, layered geometry, and coupled material characteristics of coatings, such as multiphase and inhomogeneous structures, research on multi-parameter inversion of coating components based on ultrasonic propagation models has attracted widespread attention. Parameter inversion techniques offer significant advantages and flexibility in solving complex functions and problems with multiple unknown characteristic parameters. For example, Dou et al. employed the least-squares method to invert the complex spectrum of the acoustic pressure reflection system and simultaneously characterized the thickness and acoustic velocity of yttria-stabilized zirconia (YSZ) coatings with a porosity of <9%, achieving relative errors of 9.1% and 13.3%, respectively. Bustillo et al. employed a genetic algorithm based on a transmission coefficient model of the coating structure to simultaneously invert the acoustic velocity and density of porous silicon thin layers, achieving inversion errors of 0.04% and 0.8%, respectively. Messineo et al. employed a least-squares method based on a transmission coefficient amplitude function model of a multilayer structure to simultaneously invert the acoustic impedance, transit time, acoustic velocity, density, and attenuation coefficient of the multilayer structure in the frequency domain. Ma et al. constructed a URCAS (Universal Reflection Coefficient Amplitude Spectrum) for non-uniform multilayer coating structures and used the least squares coupled cross-correlation algorithm to simultaneously characterize nine parameters of the double-layer absorbing coating, including thickness, acoustic velocity, density, attenuation coefficient amplitude, and power law. The maximum measurement error was 6.1%. Technical issues

[0004] The aforementioned inverse problems in ultrasonic testing of coatings are all based on the assumption that the coating interface is smooth and perfectly bonded, thereby constructing reflection or transmission coefficient models for ultrasonic testing inversion. However, to improve the coating-substrate bonding strength, not only must the coating thickness be precisely controlled, but the interface is often pre-formed with an appropriate roughness. Corrosion and oxidation during service can cause pores and microcracks in the interface, altering the interface profile and weakening the bonding quality, resulting in a rough, weakly bonded, imperfect interface. Therefore, it is essential to develop integrated ultrasonic characterization methods or techniques for coating thickness, roughness, and interfacial bonding strength. For example, Baltazar et al. proposed a method for characterizing interface stiffness by extracting the resonant frequency of the ultrasonic pressure reflection coefficient amplitude spectrum based on a spring model of a weakly bonded interface under acoustic wave action. In their work, a 10 MHz broadband probe was used to test an aluminum plate / aluminum thin layer / aluminum plate structure. The results showed that as the interface stiffness increases, the resonant frequency shifts to the high-frequency region, and the experimental results are in good agreement with theoretical results. In the previous work of the present inventor, based on the phase screen approximation principle of sound wave scattering on a rough interface, an ultrasonic signal sound pressure reflection coefficient phase spectrum function (Ultrasonic pressure reflected coefficient phase spectrum, URCPS) was established when ultrasound waves were vertically incident on the inner interface rough coating structure, which achieved the simultaneous characterization of the roughness, sound velocity and thickness of the inner interface of the coating for the first time. Subsequent work established an ultrasonic sound pressure reflection coefficient amplitude spectrum (Ultrasonic pressure reflected coefficient amplitude spectrum, URCAS) based on a spring model to invert the interface stiffness of the coating / substrate structure. The maximum relative error between the inverted interface stiffness value and the preset value within the high sensitivity range is less than 6%. The above-mentioned methods of using URCPS or URCAS to characterize interface roughness or interface stiffness all require the collection of a reference signal in advance and then normalization of the detection signal. The reference signal amplitude fluctuation and phase deformation will bring non-negligible deviations to the detection results. Moreover, the above-mentioned methods are only separate measurements of coating thickness, roughness or interface stiffness. Technical Solutions

[0005] The purpose of the present invention is to propose a method for measuring coating thickness, roughness, and interface stiffness using ultrasonic phase derivative spectroscopy. This method solves the problem of aliasing between the coating surface echo and the coating / substrate interface echo when a single ultrasonic body wave probe is incident vertically. This method overcomes the limitation of traditional methods such as URCPS or URCAS requiring a reference signal, eliminates interference caused by the initial phase of the detection signal and the thickness of the coupling medium, and overcomes the relatively expensive, complex, and difficult engineering applications of equipment such as ultrasonic microscopes, as well as the inability of existing ultrasonic body wave technology to simultaneously characterize the coupling parameters of coating thickness, roughness, or interface stiffness. This method has a wider scope of application, is simple and easy to apply in engineering, and can be extended to C-scan imaging of coating interface quality, with significant economic and social benefits.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a method for measuring coating thickness, roughness and interface stiffness using ultrasonic phase derivative spectroscopy. The ultrasonic detection system used includes a coating sample, an ultrasonic flat probe, an ultrasonic flaw detector, an XYZ three-dimensional stepping device and a computer. The detection steps are as follows:

[0007] (1) Based on the fact that the interface stress σ is continuous (σ1=σ2) and the displacement u is discontinuous (u1-u2=K n σ) boundary conditions, proposed the phase screen approximate spring model of the rough weak bonding interface, and constructed the reflection coefficient r of the ultrasonic wave at vertical incidence. 12 and transmission coefficient t 12 , where Z1 and Z2 represent the acoustic impedance of the interface adjacent to medium 1 and medium 2, respectively, V1 and V2 represent the sound velocity of the interface adjacent to medium 1 and medium 2, respectively, i represents the imaginary part of the complex number, K n is the vertical interface stiffness coefficient, Rq is the root mean square deviation of the interface profile, and f represents the ultrasonic frequency;

[0008] (1)

[0009] (2)

[0010] (2) Reflection coefficient r based on rough weak bonding interface 12 and transmission coefficient t 12 , the reflected echo P is derived when the ultrasonic wave is vertically incident on the three-medium two-interface structure composed of coupling medium / coating / substrate. R , where φ0 is the initial phase, z0 is the distance between the probe and the coupling medium / coating interface, and k w is the wave number in the coupling medium along the incident direction of the acoustic wave, d c Indicates the coating thickness, k c represents the coating wave number, where r wc With r csdenote the reflection coefficients of the coupling medium / coating interface and the coating / substrate interface, respectively, and i denotes the imaginary part of the complex number;

[0011] (3)

[0012] (3) Reflected echo P R Perform Fourier transform to obtain P R In the frequency domain, the real part Re(P R ) and the imaginary part Im(P R ), and then derive the reflection echo phase spectrum (RPS) of the three-medium two-interface structure;

[0013] (4)

[0014] Among them: V w represents the longitudinal wave speed of the coupling medium, V c Indicates the longitudinal wave velocity of the coating;

[0015] (5)

[0016] (4) Taking the first-order derivative of the RPS obtained in step (3) with respect to the frequency variable f, and then obtaining the ultrasonic phase derivative spectrum (UPDS);

[0017] (6)

[0018] (5) The sensitivity S of UPDS to the measured parameter p is analyzed by sensitivity formula (7), where p represents the coating d c , roughness Rq and interface stiffness K n Three parameters, based on the sensitivity extreme value S extr 10% of the coating thickness d c , roughness Rq and interface stiffness K n The high sensitivity range [d c-down ~d c-up ]、[Rq down ~Rq up ] and [K n-down ~K n-up ];

[0019] (7)

[0020] (6) The ultrasonic detection system is combined with the ultrasonic transit time method and the Archimedean drainage method to obtain the sound velocity V of the coupling medium, coating, and substrate respectively. w 、Vc 、V s and density ρ w , ρ c , ρ s ;

[0021] (7) Place the ultrasonic flat probe above the coating sample to be tested, ensuring that the main sound beam axis of the probe is perpendicular to the sample surface. The ultrasonic wave passes through the coupling medium and is incident on the coupling medium / coating and coating / substrate interfaces. The reflected echo P including the coupling medium / coating and coating / substrate interfaces is collected. R (t);

[0022] (8) The reflected echo P collected in step (8) R (t) Perform Fourier transform to obtain the experimental ultrasonic phase derivative spectrum UPDS at the corresponding position of the coating sample exp (f);

[0023] (9) Use the cross-correlation formula (8) to invert the coating thickness d c , roughness Rq and interface stiffness K n , where N represents the reflected echo P R (t) The number of data points within the -6dB effective frequency band after Fourier transform. The subscript i represents the i-th data point. In the high sensitivity range [d c-down ~d c-up ]、[Rq down ~Rq up ] and [K n-down ~K n-up ], the coating thickness d is given at a certain interval c , roughness Rq and interface stiffness K n The continuous change value of the theoretical ultrasonic phase derivative spectrum UPDS is obtained cal (f), the subscript cal represents the theoretical calculation data, which is used as the matrix to transform the experimental ultrasonic phase derivative spectrum UPDS exp (f) Perform cross-correlation operation with them one by one, and the maximum correlation coefficient position η max (d c ,Rq,K n ) corresponding to d c ,Rq and K n , which is the optimal thickness, roughness and interface stiffness results of the coating sample.

[0024] (8)

[0025] Where N represents the reflected echo P R (t) is the number of data points within the -6 dB effective frequency band after Fourier transform. The j in formula (8) represents the jth data point.

[0026] Specifically, in the high sensitivity range [d c-down ~d c-up ]、[Rq down ~Rq up ] and [K n-down ~K n-up ], giving the coating thickness d c , roughness Rq and interface stiffness K n The finer the interval of the continuously changing value, the better. For example, the coating thickness d is given at an interval of one thousandth. c , roughness Rq and interface stiffness K n Continuously changing value.

[0027] Specifically, the coupling medium in the present invention is not particularly limited, and any common coupling medium may be used, such as water, glycerin, oil, organic glass, etc. Beneficial effects

[0028] The present invention proposes a method for measuring coating thickness, roughness and interface stiffness using ultrasonic phase derivative spectroscopy. It pioneered a phase screen approximate spring model for the rough weakly bonded interface acting on acoustic waves, and then constructed an ultrasonic phase derivative spectrum (UPDS) function for a three-layer two-interface structure with ultrasonic waves perpendicularly incident on a rough weakly bonded coupling medium / coating / substrate. Sensitivity analysis was used to identify the high sensitivity range of UPDS for coating thickness, roughness and interface stiffness. Cross-correlation analysis eliminated the deviation introduced by the reference signal and the initial phase of the detection signal, achieving simultaneous quantitative characterization of coating thickness, roughness and interface stiffness. The present invention only requires a single ultrasonic body wave measurement to obtain the UPDS of the aliased signal, overcoming the limitation of methods such as URCPS or URCAS requiring a reference signal, and also eliminating the interference caused by the initial phase of the detection signal and the thickness of the coupling medium. It can simultaneously measure micron-scale coating thickness, roughness or interface stiffness. It also overcomes the relatively expensive, complex operation, and inconvenient engineering application of equipment such as ultrasonic microscopes, as well as the problems of existing ultrasonic body wave technology that cannot achieve simultaneous characterization of coating thickness, roughness or interface stiffness coupling parameters. It has a wider scope of application, is simple and easy to apply in engineering, and can be extended to C-scan imaging of coating interface quality, with greater economic and social benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG1 is a connection diagram of an ultrasonic detection system.

[0030] Figure 2 is the reflected echo P of the Ni coating / epoxy resin substrate sample R (t).

[0031] Figure 3 is the ultrasonic phase derivative spectrum UPDS of the Ni coating / epoxy resin matrix sample exp(f).

[0032] Figure 4 shows the sensitivity S of the ultrasonic phase derivative spectrum UPDS(f) to the roughness Rq UPDS , Rq .

[0033] Figure 5 is the ultrasonic phase derivative spectrum UPDS (f) versus interface stiffness K n Sensitivity S UPDS , Kn .

[0034] FIG6 is a comparison diagram of the ultrasonic phase derivative spectrum UPDS(f) obtained by experiment and inversion calculation.

[0035] Figure 7 shows the thickness d of the Ni coating / epoxy resin substrate sample. c , roughness Rq and interface stiffness K n Inversion result diagram.

[0036] In Figure 1: 1. Sample, 2. Ultrasonic flat probe, 3. XYZ three-dimensional stepping device, 4. Ultrasonic flaw detector, 5. Computer. Best Mode for Carrying Out the Invention

[0037] The ultrasonic testing system used in this embodiment includes a sample 1, an ultrasonic flat probe 2, an XYZ three-dimensional stepping device 3, an ultrasonic flaw detector 4, and a computer 5. The sample 1 is placed in an aqueous medium, the ultrasonic flat probe 2 is positioned above the sample 1 and moved by the XYZ three-dimensional stepping device 3, and the computer 5 is connected to the ultrasonic flat probe 2 via the ultrasonic flaw detector 4. The specific connection method is shown in Figure 1. Sample 1 uses a Ni coating / epoxy resin matrix, and the ultrasonic flat probe 2 uses an ultrasonic flat probe with a nominal frequency of 15.0 MHz. The measurement steps used in the method of measuring coating thickness, roughness, and interface stiffness using ultrasonic phase derivative spectroscopy are as follows:

[0038] (1) The ultrasonic detection system is combined with the ultrasonic transit time method and the Archimedean drainage method to obtain the sound velocity V of the coupling medium, coating, and substrate respectively. w =1480 m / s, V c =5550 m / s, V s =2679 m / s and density ρ w =1000 kg / m 3 , ρ c =8908 kg / m 3 , ρ s =1210 kg / m 3 ;

[0039] (2) Place the ultrasonic flat probe above the coating sample to be tested, ensuring that the main sound beam axis of the probe is perpendicular to the sample surface. The ultrasonic wave is incident on the water / coating and coating / substrate interfaces through the coupling medium water, and the reflected echo P including the water / coating and coating / substrate interfaces is collected. R (t), see Figure 2;

[0040] (3) The collected reflected echo P R (t) Perform Fourier transform to obtain the experimental ultrasonic phase derivative spectrum UPDS at the corresponding position of the coating sample exp (f), see Figure 3;

[0041] (4) Analyze the UPDS to the measured parameter p (p represents the coating d) through the sensitivity formula c , roughness Rq and interface stiffness K n The sensitivity S of the three parameters is shown in Figures 4 and 5. According to the sensitivity extreme value S extr 10% of the coating thickness d c , roughness Rq and interface stiffness K n The high sensitivity ranges are [0 μm~1000 μm], [8 μm~99 μm] and [e 29.7 N / m 3 ~ e 37.8 N / m 3 ];

[0042] (5) Inverse the coating thickness d using the cross-correlation formula c , roughness Rq and interface stiffness K n , in the high sensitivity range [0 μm~1000 μm], [8μm~99μm] and [e 29.7 N / m 3 ~ e 37.8 N / m 3 ], the coating thickness is given at intervals of one thousandth.

[0043] d c , roughness Rq and interface stiffness K n A series of continuously changing values ​​to obtain the theoretical ultrasonic phase derivative spectrum UPDS cal (f) (see the ball line in Figure 6), let it be the parent, and transform the experimental ultrasonic phase derivative spectrum UPDS exp (f) Perform cross-correlation calculations with them one by one, and the maximum correlation coefficient η max =0.958, and the corresponding optimal inversion parameter is d c =308 μm, Rq=21.5 μm and K n =e 33.3 N / m 3, see Figure 7. The relative error between the inversion results of the sample thickness and the optical microscope observation thickness of 300 μm is 2.6%. The relative error between the inversion results of the interface roughness and the CLSM measurement result of Rq = 19.7 μm is -9.1%. The inversion results of the interface stiffness at different locations are positively correlated with the interface bonding strength obtained from the tensile test at the corresponding locations. Modes for Carrying Out the Invention

[0044] Same as above. Industrial Applicability

[0045] The purpose of the present invention is to propose a method for measuring coating thickness, roughness, and interface stiffness using ultrasonic phase derivative spectroscopy. This method solves the problem of aliasing between the coating surface echo and the coating / substrate interface echo when a single ultrasonic body wave probe is incident vertically. This method overcomes the limitation of traditional methods such as URCPS or URCAS requiring a reference signal, eliminates interference caused by the initial phase of the detection signal and the thickness of the coupling medium, and overcomes the relatively expensive, complex, and difficult engineering applications of equipment such as ultrasonic microscopes, as well as the inability of existing ultrasonic body wave technology to simultaneously characterize the coupling parameters of coating thickness, roughness, or interface stiffness. This method has a wider scope of application, is simple and easy to apply in engineering, and can be extended to C-scan imaging of coating interface quality, with significant economic and social benefits. Sequence Listing Free Content

[0046] none.

Claims

1. A method for measuring coating thickness, roughness and interface stiffness using ultrasonic phase derivative spectrum, characterized by: The detection steps are as follows: (1) Based on the boundary conditions of continuous interface stress σ and discontinuous displacement u, a phase screen approximate spring model of a rough weakly bonded interface is proposed to construct the reflection coefficient r of ultrasonic wave at vertical incidence. 12 and transmission coefficient t 12 : (1) (2) Where Z1 and Z2 represent the acoustic impedance of the interface adjacent to medium 1 and medium 2, respectively; V1 and V2 represent the acoustic velocity of the interface adjacent to medium 1 and medium 2, respectively; i represents the imaginary part of the complex number; K n is the vertical interface stiffness coefficient, Rq is the root mean square deviation of the interface profile, and f represents the ultrasonic frequency; (2) Reflection coefficient r based on rough weak bonding interface 12 and transmission coefficient t 12 , and obtain the reflected echo P of the ultrasonic wave vertically incident on the three-medium two-interface structure composed of coupling medium / coating / substrate R ; (3) Where φ0 is the initial phase, z0 is the distance between the probe and the coupling medium / coating interface, and k w is the wave number in the coupling medium along the incident direction of the sound wave, d c Indicates the coating thickness, k c represents the coating wave number, r wc With r cs denote the reflection coefficients of the coupling medium / coating interface and the coating / substrate interface, respectively, and i denotes the imaginary part of the complex number; (3) For the reflected echo P R Perform Fourier transform to obtain P R In the frequency domain, the real part Re(P R ) and the imaginary part Im(P R ), and then derive the reflection echo phase spectrum RPS of the three-medium two-interface structure, where V w represents the longitudinal wave speed of the coupling medium, V c Indicates the longitudinal wave velocity of the coating; (4) in: (5) (4) taking the first-order derivative of the RPS obtained in step (3) with respect to the frequency variable f, and then obtaining the ultrasonic phase derivative spectrum UPDS; (6) (5) The sensitivity S of UPDS to the measured parameter p is analyzed by sensitivity formula (7), where p represents the coating d c , roughness Rq and interface stiffness K n Three parameters, based on the sensitivity extreme value S extr 10% of the coating thickness d c , roughness Rq and interface stiffness K n The high sensitivity interval [d c-down ~d c-up ]、[Rq down ~R up ] and [K n-down ~K n-up ]; (7) (6) The ultrasonic detection system combined with the ultrasonic transit time method and Archimedes drainage method were used to obtain the sound velocity V of the coupling medium, coating, and substrate respectively. w 、V c 、V s With density ρ w , c , s ; (7) Place the ultrasonic flat probe above the coating sample to be tested. The ultrasonic wave is incident on the coupling medium coating and the coating / substrate interface through the coupling medium. The reflected echo P including the coupling medium / coating and coating / substrate interface is collected. R (t); (8) For the reflected echo P collected in step (7), R (t) Perform Fourier transform to obtain the experimental ultrasonic phase derivative spectrum UPDS at the corresponding position of the coating sample exp (f); (9) Use the cross-correlation calculation formula (8) to invert the coating thickness d c , roughness Rq and interface stiffness K n , in the high sensitivity range [d c-down ~d c-up ]、[Rq down ~R up ] and [K n-down ~K n-up ], the coating thickness is given as d c , roughness Rq and interface stiffness K n The continuous change value of the theoretical ultrasonic phase derivative spectrum UPDS is obtained cal (f) The experimental ultrasonic phase derivative spectrum UPDS exp (f) and theoretical ultrasonic phase derivative spectrum UPDS cal (f) Perform cross-correlation operations one by one, and the maximum correlation coefficient position η max (d c ,Rq,K n ) corresponds to d c , Rq and K n That is the best thickness, roughness and interface stiffness results of the coating sample; (8) Where N represents the reflected echo P R (t) is the number of data points within the -6 dB effective frequency band after Fourier transform. The j in formula (8) represents the jth data point.

2. The method for measuring coating thickness, roughness and interface stiffness using ultrasonic phase derivative spectrum according to claim 1 is characterized by: The ultrasonic testing system used includes an ultrasonic flat probe, an ultrasonic flaw detector, an XYZ three-dimensional stepping device and a computer.

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