Nonlinear guided wave-based method for characterizing fracture toughness of aircraft composite bonded structures

Abstract

The present application relates to the technical field of non-destructive characterization of composite material interface, and provides a method for characterizing fracture toughness of aircraft composite bonding structure based on nonlinear guided waves, which comprises applying nonlinear guided wave excitation to the bonding structure of the aircraft composite skin and shell to be tested, collecting the first-arriving guided wave signals propagating along the bonding interface in each bonding sample to be tested; performing frequency domain analysis on the first-arriving guided wave signals on each propagation path, extracting the amplitudes of the fundamental frequency component, the second harmonic component and the third harmonic component, calculating the corresponding nonlinear parameters and the normalized nonlinear parameters; solving the corresponding interface evolution index by using the constructed bonding interface fracture toughness characterization model; converting the obtained interface evolution index into interface fracture toughness according to the mapping relationship between the interface evolution index and the type I interface fracture toughness established by experiments, and realizing non-destructive fracture toughness characterization of the bonding sample to be tested.

Description

Technical Field

[0001] This invention relates to the technical field of non-destructive characterization of composite material interfaces, to non-destructive quantitative evaluation of the mechanical properties of bonded structure interfaces, and in particular to a method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves. Background Technology

[0002] With the rapid development of the aviation industry, new aircraft widely adopt composite material skin-shell bonding structures in their structural design to achieve weight reduction, efficiency improvement, and overall performance enhancement. Compared to traditional mechanical connections, bonded structures can effectively reduce stress concentration and improve structural integrity, making them valuable in aircraft skin, fuselage shells, and load-bearing components. However, the mechanical properties of the bonded interface, especially its fracture toughness, directly affect the structure's load-bearing capacity and service reliability, making it a key parameter in aircraft structural design and safety assessment.

[0003] Currently, obtaining interfacial fracture toughness mainly relies on standard mechanical testing methods such as the double cantilever beam (DCB) test. These methods apply loads to prepared standard specimens and measure the energy release rate during crack propagation to obtain interfacial fracture toughness parameters. While this method has a mature theoretical foundation and high repeatability in experimental mechanics, it is essentially a destructive test, and the measured interfacial fracture toughness results are usually derived from standard specimens independent of actual service structures, making it difficult to directly reflect the true mechanical state of the interface between the composite skin and outer shell of actual aircraft. These characteristics significantly limit the application of traditional fracture toughness testing methods in engineering.

[0004] Meanwhile, existing non-destructive testing technologies, such as conventional ultrasonic testing, X-ray testing, and infrared thermography, are mainly used to identify macroscopic defects or geometric discontinuities. When interface cracks have not yet significantly propagated or the structure is still in a healthy state, it is difficult to quantitatively characterize the interface load-bearing capacity and fracture toughness level. These methods focus more on "whether defects exist" rather than "what level the interface mechanical properties are at," making it difficult to meet the high-precision requirements of aircraft composite bonded structures in design verification, quality assessment, and service status identification.

[0005] In recent years, nonlinear ultrasound and nonlinear guided wave technology have received widespread attention in the field of materials and structure characterization. Studies have shown that when ultrasound propagates in structures with microscopic contacts, closed interfaces, or non-ideal connections, it generates nonlinear responses such as higher-order harmonics. The amplitude and characteristics of these responses are highly sensitive to the interface contact state and mechanical properties. Compared to traditional linear ultrasound methods, nonlinear guided waves can respond to subtle changes in the mechanical behavior of the interface even before macroscopic damage occurs, providing a new technical approach for the non-destructive characterization of adhesive interfaces.

[0006] However, existing research based on nonlinear ultrasound or nonlinear guided waves mainly focuses on crack detection or damage identification, lacking a systematic approach to establish a physically consistent relationship between nonlinear guided wave parameters and engineering mechanical properties such as interfacial fracture toughness. Especially in aircraft composite skin and shell bonding structures, how to quantitatively characterize the fracture toughness level under different interfacial health states without introducing destructive testing remains a critical technical problem that urgently needs to be solved.

[0007] Therefore, there is an urgent need to propose a method that can combine nonlinear guided wave response with experimental mechanical reference quantities to establish a quantitative correspondence between interface nonlinear characteristics and fracture toughness, thereby realizing nondestructive characterization of fracture toughness of bonding interfaces of aircraft composite materials, and providing reliable technical support for the evaluation of interface integrity of bonded structures and engineering applications. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves, comprising: S1, apply nonlinear guided wave excitation to the bonding structure of the aircraft composite skin and shell to be tested, and collect the first wave guided wave signal propagating along the bonding interface in each bonding sample to be tested. S2, perform frequency domain analysis on the first arriving guided wave signal on each propagation path, extract the amplitude of the fundamental frequency component, second harmonic component and third harmonic component of the guided wave, and calculate the corresponding nonlinear parameters and normalized nonlinear parameters. S3. A characterization model of the fracture toughness of the bonded interface is constructed using nonlinear parameters and interface fracture toughness parameters obtained through mechanical experiments to solve for the corresponding interface evolution index. ; S4, based on the interface evolution index established experimentally. Type I interfacial fracture toughness The mapping relationship will yield the interface evolution index. Converted to interfacial fracture toughness This enables non-destructive fracture toughness characterization of the test sample.

[0009] Furthermore, in step S2, the nonlinear parameters include second harmonic nonlinear parameters. and third harmonic nonlinear parameters ; The second harmonic nonlinear parameter The formula for calculation is:

[0010] In the formula, The fundamental frequency amplitude, This represents the amplitude of the second harmonic. The third harmonic nonlinear parameter The formula for calculation is:

[0011] In the formula, The amplitude of the third harmonic; The normalized form of the nonlinear parameter is:

[0012] In the formula, For the normalized first Order nonlinear parameters; and The observed first point during the interface evolution process is respectively The minimum and maximum values ​​of the first-order nonlinear parameter; Indicates the first Order nonlinear parameters; These are harmonic orders.

[0013] Furthermore, in step S3, the specific steps for constructing the fracture toughness characterization model of the adhesive interface are as follows: S31, apply nonlinear guided wave excitation to specimens of the same material and size at different interface mode I fracture toughness levels, and collect the first arriving guided wave signal on each propagation path on the bonding interface. S32, perform frequency domain analysis on the first arriving guided wave signal on each propagation path, extract the amplitude of the fundamental frequency component, second harmonic component and third harmonic component of the guided wave, and calculate the corresponding nonlinear parameters and normalized nonlinear parameters. S33, establish a mapping relationship between the normalized nonlinear parameters of each specimen at different interface mode I fracture toughness levels and the corresponding interface fracture toughness level. S34, based on the principle of energy consistency, the evolution of interface damage must be coordinated with the decay and degradation of the interface's energy dissipation capacity, thus introducing an interface evolution index. It is used to characterize the overall trend of the adhesive interface evolving from an intact state to a degraded state, and its numerical range is [value missing]. ,in This represents an ideal, perfect interface. This indicates a completely disabled interface; S35. A unified physical phenomenological function form is selected to fit the quadratic and cubic nonlinear parameters. The physical phenomenological function form is as follows:

[0014] In the formula, For the first The growth exponent of the first-order nonlinear parameter describes the exponential evolution of the nonlinear parameter with respect to the interface. The rate of growth; The transition point represents the interface state where nonlinearity increases and decreases. S36, the physical phenomenological function is solved by globally minimizing the residuals. Growth exponent of the first-order nonlinear parameter and transition point ; By fitting the second-order nonlinear parameters, the first-order nonlinear parameter is obtained. Growth exponent of the first-order nonlinear parameter and the Transition point of first-order nonlinear parameters ; By fitting the third nonlinear parameters, the th... The growth of the first-order nonlinear parameter indicates and the Transition point of first-order nonlinear parameters ; S37 will be obtained and Substituting these values ​​into formula (4), we obtain the characterization model of fracture toughness at the bonding interface.

[0015] Furthermore, in step S34, the interface evolution index... The expression is:

[0016] In the formula, The Type I interfacial fracture toughness was obtained from a double cantilever beam test; Type I interfacial fracture toughness As a reference quantity to describe the degree of degradation of the overall crack resistance of the bonding interface, it is used to construct an interface evolution state index. This refers to the Type I fracture toughness when the interface is in a well-bonded state.

[0017] Furthermore, in step S4, the interface evolution index... Type I interfacial fracture toughness The mapping relationship is calculated by formula (5).

[0018] The present invention has the following beneficial effects: (1) This invention extracts the second and third harmonic nonlinear response characteristics generated by the bonding interface with different fracture toughness, constructs the mapping relationship between nonlinear parameters and interface fracture toughness, and introduces an interface evolution index to characterize the overall trend of the bonding interface evolving from an intact state to a degraded state. A fracture toughness characterization model for the adhesive interface is constructed, and the degradation process of the mechanical properties of the adhesive interface is quantitatively characterized non-destructively by directly calculating the fracture toughness characterization model.

[0019] (2) This invention combines nonlinear ultrasonic guided wave detection technology with mechanical test results to achieve indirect inversion and evolution assessment of the fracture toughness of the bonding interface without destroying the structural integrity, providing a new technical path for non-destructive testing and health monitoring of aircraft composite bonding structures.

[0020] (3) By introducing second and third harmonic nonlinear parameters, the present invention can maintain high sensitivity to and distinguish the bonding interface with different states and different fracture toughness. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the structure of the sample in Example 1.

[0022] Figure 2 This is the time-domain waveform of the first arriving S1 wave packet acquired in Example 1.

[0023] Figure 3 This is the frequency domain spectrum obtained by fast Fourier transform in Example 1.

[0024] Figure 4 It is the physical phenomenological function image obtained by fitting the quadratic nonlinear parameters in Example 1.

[0025] Figure 5 It is the physical phenomenological function image obtained by cubic nonlinear parameter fitting in Example 1.

[0026] Figure 6 This is a schematic diagram of the process for characterizing the fracture toughness of composite bonded structures using the fracture toughness characterization model of the bonding interface constructed in Example 1. Detailed Implementation

[0027] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. However, these embodiments are not intended to limit the present invention. Any similar structures and similar variations of the present invention should be included in the protection scope of the present invention. The commas in the present invention all indicate the relationship between and. The English letters in the present invention are case-sensitive.

[0028] Example 1 This embodiment provides a fracture toughness characterization model for adhesive interfaces, and its specific construction steps are as follows: 1. Preparation of experimental samples (1) Setting of specimen structural parameters like Figure 1 As shown, in this embodiment, a double cantilever beam (DCB) specimen is used to prepare the bonded plate for characterizing the interfacial fracture toughness. Each specimen consists of two identical t800 carbon fiber composite plates 1, each plate having dimensions of [missing information]. The thickness of the bonded board is The samples were divided into five groups, labeled A1-735 MPa, C2-660 MPa, D2-599 MPa, E1-700 MPa and F1-631 MPa, respectively. Each group corresponds to a different interface mode I fracture toughness level, and each group contains 5 samples to ensure experimental repeatability.

[0029] (2) Adhesion and curing Two T800 carbon fiber composite plates were bonded together with high-strength epoxy resin 2, and the curing process was completed under controlled temperature and time conditions. No surface treatment was performed before bonding to ensure a uniform and natural bonding state at the interface. After bonding, a complete and uniform interface layer was formed, ensuring that each specimen had a clearly defined bond interface. Subsequently, the interface mode I fracture toughness value of each group of specimens was determined by standard DCB testing. The fracture toughness value of interface mode I was obtained. As shown in Table 1, these parameters provide reference parameters and experimental verification basis for subsequent nonlinear guided wave experiments.

[0030] 2. Layout of Nonlinear Guided Wave Experimental Setup (1) Dispersion analysis and mode selection Systematic dispersion analysis was performed on the bonded plate to guide the selection of excitation frequency, waveguide mode, and wedge transducer incident angle. The bonded plate was modeled as a three-layer plate: upper and lower composite plates as the matrix, and an epoxy interface layer in the middle. The elastic modulus and density of each layer were included in the calculation, and the phase velocity and group velocity dispersion curves were obtained using the classical Rayleigh-Lamb equations. The analysis results show that within the selected frequency range, the S1 Lamb wave mode has weak dispersion characteristics, a significant displacement component in the interface thickness direction, and satisfies the approximate phase velocity matching condition between the fundamental frequency and higher harmonics, which is conducive to the generation of second and third harmonics. Therefore, the S1 mode was selected as the fundamental frequency excitation mode.

[0031] (2) Excitation signal setting To ensure mode selectivity of the excited guided signal during the experiment and effectively suppress interference from non-target modes, while maintaining spectral concentration and accurate time-domain localization to improve the reliability of higher harmonic measurements, the excitation signal uses a 1.33MHz, 5-cycle sinusoidal pulse modulated using a Hanning window. This design ensures both the narrow-band characteristics of the input signal, concentrating spectral energy within the frequency range of the target S1 Lamb wave mode and avoiding energy dispersion caused by excessively wide bandwidth, and good localization in the time domain, enabling accurate identification of the first arrival packet and minimizing interference from reflections, mode transitions, and excitation by adjacent modes. The center frequency was selected based on the theoretical dispersion analysis of the multilayer adhesive plate, falling within the weak dispersion region of the S1 mode and satisfying the approximate phase velocity matching condition between the fundamental frequency and higher harmonics, ensuring the effective generation and measurement of the second and third harmonics. This configuration enables highly sensitive and repeatable measurements of interface nonlinear effects, providing a reliable experimental basis for subsequent nonlinear parameter extraction and interface fracture toughness characterization.

[0032] (3) Ultrasonic probe placement The phase velocity of the target S1 Lamb wave mode can be obtained through multilayer plate dispersion analysis. To ensure that the excited longitudinal wave can be efficiently converted into the target S1 mode after entering the plate along the wedge transducer, the incident angle must satisfy the condition that the phase velocity of the longitudinal wave in the wedge is approximately matched with the phase velocity of the S1 mode in the bonded plate. Theoretical calculations yielded an optimal incident angle of 11.3°. In practical applications, a commercially available 11.5° wedge is used, with a center-to-center distance of 60 mm between the ultrasonic probes, ensuring the acquisition of the first arriving S1 wave packet while minimizing reflection and mode conversion interference. The received signal is acquired through a low-noise broadband amplifier and recorded on the SNAP system and an external digital oscilloscope. A uniform glycerol layer is applied between the probe, wedge, and sample to ensure stable coupling and suppress contact nonlinearity.

[0033] 3. Signal Acquisition and Processing (1) Wave packet selection During the signal analysis phase, only the first arrival packet (S1 mode) is considered to minimize reflection, mode conversion, and higher-order packet interference, ensuring that the extracted nonlinear parameters mainly reflect the interface nonlinearity.

[0034] (2) Harmonic amplitude extraction To accurately quantify the nonlinear characteristics in the guided wave signal, the first-arrival S1 wave packet signal acquired for each propagation path, such as... Figure 2 The time-domain waveform shown is analyzed in the frequency domain using Fast Fourier Transform (FFT) to obtain the following results: Figure 3 The frequency domain spectrum is shown. Using FFT, the time-domain signal can be decomposed into the fundamental frequency and its higher-order harmonic components, thereby extracting the amplitudes of the fundamental frequency, second harmonic, and third harmonic. This method effectively isolates different frequency components, avoiding interference from overlapping signals in the time-domain wave packet on the calculation of nonlinear parameters, while ensuring that the extracted amplitudes reflect the true characteristics of the interface nonlinear effects. The fundamental frequency amplitude is used for normalization calculation of higher-order nonlinear parameters, while the second and third harmonic amplitudes are directly used to characterize the enhancement and attenuation laws of interface nonlinearity, providing a precise experimental data foundation for subsequent nonlinear parameter calculations and interface evolution model fitting.

[0035] (3) Calculation of nonlinear parameters Calculate the effective nonlinear parameters based on the harmonic amplitude. and The calculation results are shown in Table 2.

[0036]

[0037] in, , , These are the fundamental frequency, second harmonic, and third harmonic amplitudes, respectively.

[0038] (4) Measurement repetition and average To minimize the impact of local material inhomogeneity, minute geometric errors, and signal acquisition noise on the measurement results, each sample was repeatedly measured along three different propagation paths. The average of the three measurements was used as a representative nonlinear parameter for a single sample. Subsequently, the parameters of multiple samples at the same interface fracture toughness level were averaged to obtain effective nonlinear parameters characterizing the interface degradation state, providing a data foundation for subsequent interface evolution studies.

[0039] 4. Nonlinear parameter normalization and interface evolution description (1) Normalization The second and third harmonic nonlinear parameters measured for each propagation path and Normalization is performed to obtain the normalized second harmonic nonlinear parameters. and third harmonic nonlinear parameters :

[0040] (2) Construction of Interface Evolution Index Define the interface evolution index It is used to quantify the interface degradation state, and the type I interface fracture toughness is obtained by conducting double cantilever beam tests on five groups of samples. The interface evolution index corresponding to each group of samples was calculated using formula (5). As shown in Table 1.

[0041] The interface evolution index Based on the principle of energy consistency, its core idea is that the evolution of interface damage must be coordinated and consistent with the decay and degradation process of the interface's energy dissipation capacity. This is due to the interface's fracture toughness... The critical energy dissipated per unit area during the crack propagation process at the interface is characterized by the degree of degradation of the interface fracture toughness. Therefore, the interface evolution index is defined as the interface evolution index. The expression is:

[0042] In the formula, The Type I interfacial fracture toughness was obtained from a double cantilever beam test; Type I interfacial fracture toughness As a reference quantity to describe the degree of degradation of the overall crack resistance of the bonding interface, it is used to construct an interface evolution state index. This refers to the Type I fracture toughness when the interface is in a well-bonded state.

[0043] This definition method enables the interface evolution index to... It is consistent with the remaining energy dissipation capacity of the interface, thus reflecting the overall process of the interface evolving from an intact state to a degraded state.

[0044] Table 1

[0045] Each group of samples (different) The normalized nonlinear parameters of the interface are mapped to the corresponding interface fracture toughness level to form a preliminary interface evolution curve. The specific values ​​are shown in Table 2, which provides a data basis for subsequent fitting.

[0046] Table 2

[0047] 5. Fitting of nonlinear evolution models (1) Experimental data fitting process Normalized nonlinear parameters for each group of samples and each path ( , With interface evolution index The data was organized to obtain the average value for each group.

[0048] A unified physical phenomenological function form is selected to fit the quadratic and cubic nonlinear parameters. The function form is as follows:

[0049] In the formula, For the first The growth exponent of the first-order nonlinear parameter describes the exponential evolution of the nonlinear parameter with respect to the interface. The rate of growth; For the first The transition point of the first-order nonlinear parameter represents the interface state from nonlinear enhancement to decay. The physical phenomenological function is solved by globally minimizing the residuals, yielding the... Growth exponent of the first-order nonlinear parameter and transition point Specifically: Substituting the values ​​from Table 1 and Table 2 into formula (4), we obtain... and ; and ; S36 will be obtained and 、 and Substituting these values ​​into formula (4), we obtain the characterization model for the fracture toughness of the bond interface, as follows: Figures 4-5 As shown:

[0050] like Figure 6 As shown, the fracture toughness characterization model of the bonding interface constructed based on Example 1 is used to characterize the fracture toughness of the bonded structure of T800 carbon fiber and high-strength epoxy resin. The specific steps are as follows: S1, apply nonlinear guided wave excitation to the bonded structure, and collect the first wave guided signal propagating along the bonded interface in each bonded sample to be tested; S2. For the first arriving guided wave signal on each propagation path, perform frequency domain analysis using Fast Fourier Transform (FFT) to extract the amplitudes of the fundamental frequency component, second harmonic component, and third harmonic component of the guided wave, and calculate their corresponding nonlinear parameters and normalized nonlinear parameters. The nonlinear parameters include second harmonic nonlinear parameters. and third harmonic nonlinear parameters ; The second harmonic nonlinear parameter The formula for calculation is:

[0051] In the formula, The fundamental frequency amplitude, This represents the amplitude of the second harmonic. The third harmonic nonlinear parameter The formula for calculation is:

[0052] In the formula, The amplitude of the third harmonic; Second harmonic nonlinear parameters measured for each propagation path and third harmonic nonlinear parameters Normalization is performed to obtain the normalized second harmonic nonlinear parameters. and third harmonic nonlinear parameters :

[0053] S3. Using the adhesive interface fracture toughness characterization model constructed in Example 1, the corresponding interface evolution index is solved. ; S4, based on the interface evolution index established experimentally. Type I interfacial fracture toughness The mapping relationship will yield the interface evolution index. Converted to interfacial fracture toughness This enables non-destructive fracture toughness characterization of the bonded structure between T800 carbon fiber and high-strength epoxy resin; specifically: Among them, the interface evolution index Type I interfacial fracture toughness The mapping relationship is calculated by formula (5); The interface evolution index obtained in step S3 From the interface evolution index Type I interfacial fracture toughness The corresponding Type I interface fracture toughness can be obtained by querying the mapping table. .

[0054] This invention extracts the second and third harmonic nonlinear response characteristics of bonded interfaces with different fracture toughnesses, constructs a mapping relationship between nonlinear parameters and interface fracture toughness, and introduces an interface evolution index to characterize the overall trend of the bonded interface evolving from an intact state to a degraded state. A fracture toughness characterization model for the adhesive interface is constructed, and non-destructive quantitative characterization of the degradation process of the mechanical properties of the adhesive interface is achieved through direct calculation of the model. Without compromising structural integrity, indirect inversion and evolution assessment of the fracture toughness of the adhesive interface are realized, providing a new technical approach for non-destructive testing and health monitoring of aircraft composite bonded structures.

[0055] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

Claims

1. A method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves, characterized in that, include: S1, apply nonlinear guided wave excitation to the bonding structure of the aircraft composite skin and shell to be tested, and collect the first wave guided wave signal propagating along the bonding interface in each bonding sample to be tested. S2, perform frequency domain analysis on the first arriving guided wave signal on each propagation path, extract the amplitude of the fundamental frequency component, second harmonic component and third harmonic component of the guided wave, and calculate the corresponding nonlinear parameters and normalized nonlinear parameters. S3. A characterization model of the fracture toughness of the bonded interface is constructed using nonlinear parameters and interface fracture toughness parameters obtained through mechanical experiments to solve for the corresponding interface evolution index. ; S4, based on the interface evolution index established experimentally. Type I interfacial fracture toughness The mapping relationship will yield the interface evolution index. Converted to interfacial fracture toughness This enables non-destructive fracture toughness characterization of the test sample.

2. The method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves according to claim 1, characterized in that, In step S2, the nonlinear parameters include second harmonic nonlinear parameters. and third harmonic nonlinear parameters ; The second harmonic nonlinear parameter The formula for calculation is: In the formula, The fundamental frequency amplitude, This represents the amplitude of the second harmonic. The third harmonic nonlinear parameter The formula for calculation is: In the formula, The amplitude of the third harmonic; The normalized form of the nonlinear parameter is: In the formula, For the normalized first Order nonlinear parameters; and The observed first point during the interface evolution process is respectively The minimum and maximum values ​​of the first-order nonlinear parameter; Indicates the first Order nonlinear parameters; These are harmonic orders.

3. The method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves according to claim 1, characterized in that, In step S3, the specific steps for constructing the fracture toughness characterization model of the adhesive interface are as follows: S31, apply ultrasonic guided wave excitation to specimens of the same material and size at different interface mode I fracture toughness levels, and collect the first arriving guided wave signal propagating in the bonding interface of each specimen. S32, perform frequency domain analysis on the first arriving guided wave signal of each sample, extract the amplitude of the fundamental frequency component, second harmonic component and third harmonic component of the guided wave, and calculate the corresponding nonlinear parameters and normalized nonlinear parameters. S33, establish a mapping relationship between the normalized nonlinear parameters of each specimen at different interface mode I fracture toughness levels and the corresponding interface fracture toughness level. S34, based on the principle of energy consistency, the evolution of interface damage must be coordinated with the decay and degradation of the interface's energy dissipation capacity, thus introducing an interface evolution index. It is used to characterize the overall trend of the adhesive interface evolving from an intact state to a degraded state, and its numerical range is [value missing]. ,in This represents an ideal, perfect interface. This indicates a completely disabled interface; S35. A unified physical phenomenological function form is selected to fit the normalized quadratic and cubic nonlinear parameters. The physical phenomenological function form is as follows: In the formula, For the first The growth exponent of the first-order nonlinear parameter describes the exponential evolution of the nonlinear parameter with respect to the interface. The rate of growth; For the first The transition point of the first-order nonlinear parameter represents the interface state from nonlinear enhancement to decay. S36, the physical phenomenological function is solved by globally minimizing the residuals to obtain the first... Growth exponent of the first-order nonlinear parameter and transition point ; By fitting the second-order nonlinear parameters, the first-order nonlinear parameter is obtained. Growth exponent of the first-order nonlinear parameter and the Transition point of first-order nonlinear parameters ; By fitting the third nonlinear parameters, the th... The growth of the first-order nonlinear parameter indicates and the Transition point of first-order nonlinear parameters ; S37 will be obtained / and / Substituting these values ​​into formula (4), we obtain the characterization model of fracture toughness at the bonding interface.

4. The method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves according to claim 3, characterized in that, In step S34, the interface evolution index The expression is: In the formula, The Type I interfacial fracture toughness was obtained from a double cantilever beam test; Type I interfacial fracture toughness As a reference quantity to describe the degree of degradation of the overall crack resistance of the bonding interface, it is used to construct an interface evolution state index. This refers to the Type I fracture toughness when the interface is in a well-bonded state.

5. The method for characterizing the fracture toughness of aircraft composite bonded structures based on nonlinear guided waves according to claim 4, characterized in that, In step S4, the interface evolution index Type I interfacial fracture toughness The mapping relationship is calculated by formula (5).

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