Method for measuring thickness of adhesive layer of bonded stiffened structure on the basis of attenuation characteristics of feature guided wave

Abstract

A method for measuring the thickness of an adhesive layer of a bonded stiffened structure on the basis of attenuation characteristics of a feature guided wave, comprising the following steps: 1, establishing a two-dimensional model of the cross section of a bonded stiffened structure, and carrying out grid division, the two-dimensional model comprising stiffeners, a skin, an adhesive layer and a perfectly matched layer; 2, calculating complex wavenumbers of multiple modals at each frequency and adhesive layer thickness; 3, singling out modals having high average energy flux density and low attenuation to obtain theoretical attenuation characteristics; 4, exciting a feature guided wave of a specific frequency and modal combination, and measuring actual attenuation characteristics; and 5, using a match error to select the closest candidate adhesive layer thickness as a measured thickness of the adhesive layer of the bonded stiffened structure under test. Exciting the feature guided wave on the bonded stiffened structure under test and measuring the attenuation characteristics allow for non-destructive measurement of the thickness of the adhesive layer of the bonded stiffened structure under test.

Description

Thickness detection method of adhesive layer in adhesive-bonded reinforced structures based on characteristic guided wave attenuation characteristics Technical Field

[0001] The present invention belongs to the technical field of nondestructive testing and structural health monitoring, and particularly relates to a method for detecting the thickness of an adhesive layer of an adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics. Background Art

[0002] Adhesively reinforced structures offer advantages such as light weight, lack of stress concentration, and flexible design. They can be used to connect homogeneous or dissimilar materials. However, during manufacturing and service, problems such as interface debonding and weakened cohesive strength may arise. Characteristic guided waves, whose energy is concentrated in characteristic locations (reinforcements, welds, etc.) and propagates axially, are a potential viable solution for inspecting adhesively reinforced structures. The propagation characteristics of characteristic guided waves in adhesively reinforced structures are not only related to the material and cross-sectional geometry of the reinforcements and skin, but are also affected by the mechanical properties of the adhesive interface. Current methods for inverting structural geometry or mechanical parameters mostly achieve this through matching dispersion characteristics, and few consider attenuation characteristics. Summary of the Invention

[0003] The object of the present invention is to provide a method for estimating the thickness of the adhesive layer of an adhesively bonded reinforced structure based on matching of characteristic guided wave attenuation characteristics.

[0004] The present invention provides a method for detecting the thickness of an adhesive layer of an adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics, comprising the following steps:

[0005] Step 1: Create a 2D model of the cross section of the adhesive-bonded reinforced structure and perform meshing. The 2D model includes the reinforcement, skin, adhesive layer, and perfect matching layer. The reinforcement and skin are connected by the adhesive layer. Perfect matching layers are set on the opposite edges of the skin. Set multiple different characteristic guided wave analysis frequencies f i , and multiple alternative adhesive layer thicknesses d n The thickness of the adhesive layer in the tested adhesive reinforced structure is between the thickness of each alternative adhesive layer d n According to the materials of the reinforcement, skin and adhesive layer in the tested adhesive-bonded reinforced structure, the corresponding material parameters are set for the 2D model.

[0006] Step 2: Calculate each analysis frequency f i and the thickness of the alternative adhesive layer d n The complex wave number, displacement components, and stress components of the first M modes under . M is the extracted modal order.

[0007] Step 3: Calculate the average energy flux density ratio η(i, m, n) and attenuation α(i, m, n) corresponding to the first M modes; select the complex wave number k(i, m, n) corresponding to the mode that meets the following conditions:

[0008]

[0009] Among them, η threshold Indicates the threshold of the average energy flux density ratio. threshold Indicates the attenuation threshold.

[0010] Each analysis frequency f i and alternative adhesive layer thickness d n The combination of all filters out multiple modes as a screening set; the union of all the screening sets is taken as the preferred mode set T.

[0011] Step 4: Excite characteristic guided waves of a specific frequency range in the adhesively reinforced structure under test; the excited characteristic guided waves have multiple modes m'; the specific frequency range is selected from the analysis frequencies f determined in step 1 i The interval between the maximum and minimum values ​​of the ribs is arranged along the axial direction of the reinforcement. According to the characteristic guided wave amplitude measured at each measuring point, the different frequencies are obtained. , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesive reinforced structure α'(i',m'). All frequencies All are selected from each analysis frequency f i .

[0012] Step 5: For different frequencies , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesive reinforced structure α'(i',m'); calculate the thickness d of each alternative adhesive layer respectively n Matching error Err(d n ):

[0013]

[0014] Traverse all alternative glue layer thicknesses d1, d2, ..., d N , take the matching error Err(d n ) is taken as the measured adhesive layer thickness of the tested adhesively reinforced structure.

[0015] Preferably, the threshold value η of the average energy flux density ratio threshold The value of is greater than 1 and less than S tot / S guide ;S guide Indicates the reinforcement and glue layer area; S tot Represents the entire cross-section area; the attenuation threshold α threshold The value is 10Np / m.

[0016] Preferably, in step 3, the attenuation α(i, m, n) is the absolute value of the imaginary part of the complex wave number k(i, m, n); the expression of the average energy flux density ratio η(i, m, n) is as follows:

[0017]

[0018] in, It represents the average energy flux density of the mth mode in the reinforcement and adhesive layer area; represents the average energy flux density of the mth mode along the axial direction in the entire stiffener, adhesive layer, skin and perfectly matched layer area; j represents the imaginary unit; u x (i, m, n), u y (i, m, n), u z (i, m, n) is the displacement component obtained in step 2; σ xz (i, m, n), σ yz (i, m, n), σ zz (i, m, n) are the stress components obtained in step 2; the superscript * indicates the complex conjugate operation; Re[·] is the real part operation; f i is the analysis frequency of the characteristic guided wave; i = 1, 2, …, I; n = 1, 2, …, N; m = 1, 2, …, M; I is the number of analysis frequencies; N is the number of alternative adhesive layer thicknesses.

[0019] Preferably, the width of the perfectly matched layer is greater than or equal to each analysis frequency f i The corresponding characteristic waveguide wavelength is 1 / 2 of the maximum value.

[0020] As a preference, the size of the grid obtained by meshing the two-dimensional model is less than or equal to the size of each analysis frequency f i The corresponding characteristic waveguide wavelength is 1 / 10 of the minimum value.

[0021] Preferably, the modal order M is greater than 80.

[0022] Preferably, multiple analysis frequencies f i The value of is: from 50kHz to 200kHz, the analysis frequency f is selected at intervals of 10kHz i .

[0023] Preferably, in step 1, the width of the skin is greater than or equal to five times the width of the adhesive layer.

[0024] Preferably, the material parameters include elastic modulus and density.

[0025] Preferably, the cross-sectional shape and size of the reinforcement ribs and skin are the same as the shape and size of the reinforcement ribs and skin of the adhesively reinforced structure being tested.

[0026] Preferably, the two-dimensional model in step 1 is established in COMSOL Multiphysics finite element software.

[0027] The present invention has the following beneficial effects:

[0028] 1. The present invention can solve the characteristic guided wave propagation characteristics in metal or composite material adhesive structures using commercial finite element software. On this basis, the present invention can realize non-destructive testing of the thickness of the adhesive layer in the adhesively reinforced structure being tested by exciting the characteristic guided waves on the adhesively reinforced structure being tested and measuring the attenuation characteristics, which is helpful for quality inspection of the adhesively reinforced structure.

[0029] 2. The present invention conveniently and quickly screens out the frequency and mode combination of characteristic guided waves that are sensitive to the thickness of the adhesive layer of the adhesively bonded reinforced structure based on the cross-sectional energy flow distribution and axial attenuation characteristics.

[0030] 3. The present invention achieves estimation of glue layer thickness and evaluation of bonding quality by matching the attenuation characteristics of characteristic guided waves that are sensitive to glue layer thickness. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] FIG1 is a flow chart of the present invention;

[0032] FIG2 is a schematic cross-sectional view of an adhesively bonded reinforcement structure according to an embodiment of the present invention;

[0033] FIG3 is an embodiment of the present invention at the characteristic waveguide frequency f i = Mode shape diagrams of two characteristic guided wave modes at 100 kHz;

[0034] FIG4 is a schematic diagram of the dispersion characteristics of characteristic guided waves at different adhesive layer thicknesses in an embodiment of the present invention;

[0035] FIG5 is a schematic diagram of the attenuation characteristics of characteristic guided waves at different adhesive layer thicknesses in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] As shown in FIG1 , a method for detecting the thickness of the adhesive layer of an adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics is provided. In this embodiment, the adhesively bonded reinforced structure is specifically a structure of aluminum reinforcement and carbon fiber reinforced composite material skin bonded together as an example. The method includes the following steps:

[0038] S1: As shown in Figure 2, a two-dimensional model of the cross-section of the adhesively bonded reinforced structure is established, including the reinforcement 1, the skin 2, the adhesive layer 3, and the perfectly matched layer 4. A series of characteristic guided wave analysis frequencies f are set. i (i = 1, 2, …, I) and the thickness of the adhesive layer 3 d n (n = 1, 2, …, N). In this embodiment, the two-dimensional model is established in COMSOL Multiphysics finite element software.

[0039] S11: The cross-sectional dimensions of the reinforcement 1 are consistent with the actual dimensions of the tested adhesive reinforcement structure. The width of the skin 2 is much larger than the width of the adhesive layer 3. The thickness of the adhesive layer 3 is set to d n In this embodiment, the reinforcement rib 1 is specifically a T-shaped reinforcement rib 1; the thickness of the T-shaped reinforcement rib 1 is 2 mm, and the transverse width and longitudinal height are both 20 mm; the thickness of the skin 2 is 2 mm and the width is 100 mm; the width of the adhesive layer 3 is consistent with the transverse width of the T-shaped reinforcement rib 1, which is 20 mm.

[0040] S12: Set the analysis frequency f i , and the material parameters of the reinforcement 1, skin 2, and adhesive layer 3; the material parameters include elastic modulus and density. In this embodiment, the analysis frequency f i The values ​​of are as follows: From 50kHz to 200kHz, the analysis frequency f is selected at intervals of 10kHz. i , that is, I=16; f1 to f 16 They are 50kHz, 60kHz,..., 200kHz respectively.

[0041] In this embodiment, the material parameters of the reinforcement rib 1, the skin 2, and the adhesive layer 3 are as follows: the reinforcement rib 1 is made of aluminum, and its elastic modulus C 11 = C 22 = C 33 = 107.84GPa, C 12 = C 13 = C 23 = 54.76GPa, C 44 = C 55 = C 66 = 26.54GPa, density 2700kg / m 3 ; Complex elastic modulus C of adhesive layer 3 11 = C 22 = C 33 = 5.6+0.5j GPa, C 12 = C 13 = C 23 = 4.5+0.4j GPa, C 44 = C55 = C 66 = 0.5 + 0.05j GPa, density 1050 kg / m 3 ; Complex elastic modulus C of skin 2 11 = 13.1+0.4j GPa, C 12 = C 13 = 6.97+0.11j GPa, C 22 = C 33 = 63.7+3.1j GPa, C 23 = 20.4+0.82j GPa, C 44 = 21.6+0.86j GPa, C 55 = C 66 = 3.9 + 0.11j GPa, density 1580 kg / m 3 .

[0042] S13: A perfect matching layer 4 is provided at both sides of the skin 2. The width of the perfect matching layer 4 is greater than or equal to 1 / 2 of the longest wavelength of each characteristic waveguide used. In this embodiment, the width of the perfect matching layer 4 is 20 mm.

[0043] S14: Meshing the two-dimensional model of the adhesively bonded reinforced structure section, wherein the mesh size is less than or equal to 1 / 10 of the shortest wavelength of each characteristic guided wave used. In this embodiment, the mesh size is 1 mm.

[0044] S2: Use the modal analysis tool in the finite element software to calculate the modal analysis of the two-dimensional model at different frequencies f i , adhesive layer thickness d n The first M modes under different frequencies f i 、Thickness of adhesive layer 3 d n The corresponding complex wave number k(i, m, n), and the corresponding displacement component u x (i, m, n), u y (i, m, n), u z (i, m, n), stress component σ xz (i, m, n), σ yz (i, m, n), σ zz (i, m, n); i = 1, 2, …, I; n = 1, 2, …, N; m = 1, 2, …, M. In this embodiment, the value of M is 100.

[0045] S3: Calculate the average energy flux density ratio η(i, m, n) and attenuation α(i, m, n) corresponding to the first M modes.

[0046] The expression of the average energy flux density ratio η(i, m, n) is as follows:

[0047]

[0048] in, represents the average energy flux density of the mth mode in the area of ​​stiffener 1 and adhesive layer 3; It represents the average energy flux density of the mth mode along the axial direction in the entire cross-sectional area; S guide Indicates the area of ​​reinforcement rib 1 and adhesive layer 3; S tot represents the entire cross-sectional area; j represents the imaginary unit; the superscript * represents the complex conjugate operation; Re[·] represents the real part operation; f i is the analysis frequency of the characteristic guided wave; is the displacement component u x (i, m, n) or u y (i, m, n) or u z The conjugate complex number of (i, m, n); S represents the position on the cross-sectional area.

[0049] A larger average energy flux density ratio η(i, m, n) indicates that the energy of the m-th mode is more concentrated in the region of stiffener 1 and adhesive layer 3. The attenuation α(i, m, n) is the absolute value of the imaginary part of the complex wave number k(i, m, n). A smaller value indicates less energy dissipation during axial propagation of the m-th mode.

[0050] From each frequency f i , thickness of adhesive layer 3 d n Among the corresponding first M order modes, the modes with a larger average energy flux density ratio η(i, m, n) and a smaller attenuation α(i, m, n) are selected; the screening conditions are:

[0051]

[0052] Among them, η threshold It represents the threshold value of the artificially set average energy flux density ratio, which is generally a positive value greater than 1. In this embodiment, it is preferably 3. threshold It represents the artificially set attenuation threshold, which is a positive value. In this embodiment, it is preferably 10Np / m. The frequency f is finally screened and obtained. i 、Thickness of adhesive layer 3 d n The modes that meet the conditions are as follows; the complex wave number k(i, m, n) of the screened modes, where the real part represents the dispersion characteristics and the imaginary part represents the attenuation characteristics.

[0053] Each analysis frequency f i and alternative adhesive layer thickness d nThe combinations of are filtered out to obtain multiple modes, which are regarded as a screening set; the union of all the screening sets is taken as the preferred mode set T. The preferred mode set T contains multiple preferred modes.

[0054] In this embodiment, the frequency f i = 100 kHz, the complex wave number k(i, m, n) is 74.19+4.78jm -1 、313.31+4.81jm -1 The vibration modes of the two characteristic guided wave modes are shown in Figure 3; the color value represents the displacement amplitude; the darker the color, the larger the displacement amplitude. It can be seen that the vibration of the two characteristic guided wave modes is mainly concentrated in the reinforcement rib 1 and the adhesive layer 3, while the vibration of the skin 2 is relatively weak. Figures 4 and 5 show the dispersion and attenuation characteristics of the characteristic guided waves for different adhesive layer 3 thicknesses. It can be seen that the dispersion characteristics are less affected by the thickness of the adhesive layer 3, while the attenuation characteristics are more affected by the thickness of the adhesive layer 3. Therefore, in this embodiment, the attenuation characteristics are selected to determine the thickness of the adhesive layer 3 of the adhesively reinforced structure.

[0055] S4: Excite characteristic guided waves of a specific frequency range in the adhesively bonded reinforced structure under test with unknown adhesive layer 3 thickness; and arrange a series of measuring points along the axial direction (i.e., length direction) of the reinforcement 1. The excited characteristic guided waves have multiple modes m'; the specific frequency range is selected from the analysis frequencies f determined in step S1. i According to the characteristic guided wave amplitude measured at each measuring point, the exponential curve is used to fit the amplitude-distance attenuation law to obtain the different frequency , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesive reinforced structure α'(i',m'). All frequencies All are selected from each analysis frequency f i .

[0056] S5: For different frequencies , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesive reinforced structure α'(i',m'); for each alternative adhesive layer thickness d n , search for the same frequency Under the optimal mode set T, the theoretical attenuation characteristics α(i',m,n) corresponding to all the optimal modes m are calculated, and the minimum square error corresponding to the measured actual attenuation characteristics α'(i',m') is calculated. Considering all the measured values ​​of the actual attenuation characteristics, the overall matching error Err(d n ):

[0057]

[0058] in, is the norm operation;

[0059] Traverse all glue layer 3 thickness d1, d2, ..., d N When the matching error is minimized, that is, when the measured attenuation characteristics are closest to the theoretical attenuation characteristics, the corresponding adhesive layer 3 thickness d n Estimated thickness :

[0060] .

Claims

1. A method for detecting the thickness of adhesive layer of adhesively bonded reinforced structures based on characteristic guided wave attenuation characteristics, characterized in that: The following steps are involved: Step 1: Establish a two-dimensional model of the cross section of the adhesive-bonded reinforced structure and perform meshing; the two-dimensional model includes a reinforcing rib (1), a skin (2), an adhesive layer (3) and a perfect matching layer (4); the reinforcing rib (1) and the skin (2) are connected through the adhesive layer (3); the perfect matching layer (4) is set on the opposite side edges of the skin (2); set a plurality of different characteristic guided wave analysis frequencies f i , and multiple alternative adhesive layer thicknesses d n ; The thickness of the adhesive layer in the tested adhesive reinforced structure is between the thickness of each alternative adhesive layer d n between the maximum value and the minimum value of; setting corresponding material parameters for the two-dimensional model according to the materials of the reinforcing ribs (1), the skin (2), and the adhesive layer (3) in the tested adhesively reinforced structure; Step 2: Calculate each analysis frequency f i And the alternative glue layer thickness d n The complex wave number, displacement component and stress component of the first M modes under the condition; M is the extracted mode order; Step 3: Calculate the average energy flux density ratio η(i, m, n) and attenuation α(i, m, n) corresponding to the first M modes; select the complex wave number k(i, m, n) corresponding to the mode that meets the following conditions: ； Among them, η threshold Represents the threshold of the average energy flux density ratio; α threshold represents the threshold value of attenuation; Each analysis frequency f i and the alternative adhesive layer thickness d n The combinations of all filter out multiple modes as a filter set; the union of all filter sets is taken as the preferred mode set T; Step 4: Excite characteristic guided waves in a specific frequency range in the tested adhesively reinforced structure; the excited characteristic guided waves have multiple modes m'; the specific frequency range is selected from the analysis frequencies f determined in step 1 i The interval formed by the maximum value and the minimum value of the reinforcing rib (1); a plurality of measuring points are arranged along the axial direction of the reinforcing rib (1); and the characteristic guided wave amplitudes measured at each measuring point are obtained at different frequencies. , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesively reinforced structure α'(i',m'); Step 5: For different frequencies , the actual attenuation characteristics of the characteristic guided wave of mode m' in the tested adhesive reinforced structure α'(i',m'); calculate the thickness d of each alternative adhesive layer respectively n The matching error Err(d n ): ； Traverse all the alternative glue layer thicknesses d1, d2, ..., d N , take the matching error Err(d n ) is taken as the measured glue layer thickness of the tested adhesively reinforced structure.

2. According to claim 1, a method for detecting the thickness of adhesive layer of adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics is characterized by: The threshold value η of the average energy flux density ratio threshold The value of is greater than 1 and less than S tot / S guide ; S guide Indicates the reinforcement and glue layer area; S tot Represents the entire cross-sectional area.

3. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: In step 3, the attenuation α(i, m, n) is taken as the absolute value of the imaginary part of the complex wave number k(i, m, n); the expression of the average energy flux density ratio η(i, m, n) is as follows: ； in, It represents the average energy flux density of the mth mode in the stiffener and glue layer area; represents the average energy flux density of the mth mode along the axial direction in the entire stiffener, glue layer, skin and perfect matching layer area; j represents the imaginary unit; u x (i, m, n), u y (i, m, n), u z (i, m, n) is the displacement component obtained in step 2; σ xz (i, m, n), σ yz (i, m, n), σ zz (i, m, n) are the stress components obtained in step 2; the superscript * indicates the complex conjugate operation; Re[·] is the real part operation; f i is the analysis frequency of characteristic guided wave; i = 1, 2, …, I; n = 1, 2, …, N; m = 1, 2, …, M; I is the number of analysis frequencies; N is the number of alternative adhesive layer thicknesses.

4. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: The width of the perfectly matched layer (4) is greater than or equal to each analysis frequency f i The corresponding characteristic waveguide wavelength is 1 / 2 of the maximum value.

5. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: The size of the mesh obtained by meshing the two-dimensional model is less than or equal to the analysis frequency f i The corresponding characteristic waveguide wavelength is 1 / 10 of the minimum value.

6. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structures based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: The value of the modal order M is greater than 80.

7. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structures based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: Multiple analysis frequencies f i The value of is: from 50kHz to 200kHz, the analysis frequency f is selected at intervals of 10kHz i .

8. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structures based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: In step 1, the width of the skin (2) is greater than or equal to five times the width of the adhesive layer (3).

9. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structures based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: The material parameters include elastic modulus and density.

10. The method for detecting the thickness of adhesive layer of adhesively bonded reinforced structure based on characteristic guided wave attenuation characteristics according to claim 1, characterized in that: The cross-sectional shape and size of the reinforcing ribs (1) and the skin (2) are the same as the shape and size of the reinforcing ribs and the skin (2) of the adhesively reinforced structure being tested.

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