A Method for Inverting Elastic Constants of Carbon Fiber Composites Based on Multimodal Ultrasonic Images

Abstract

This invention discloses a method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasonic images, relating to the field of material parameter measurement technology. The method includes: placing an ultrasonic phased array device along the x-axis and y-axis of a carbon fiber composite unidirectional plate, respectively; exciting ultrasonic waves and acquiring full-matrix data of the carbon fiber composite unidirectional plate; and calculating the elastic constant C based on the full-matrix data acquired in the y-z plane. 33 And C 44 Obtain the elastic constant C 33 And C 44 Optimal value; Calculate the elastic constant C based on the full matrix data collected in the x-z plane. 11 C 13 And C 55 Obtain the elastic constant C 11 C 13 And C 55 The optimal value of elastic constants is obtained by constructing a technical framework based on ultrasonic mode transformation using full-matrix ultrasonic data and a technical strategy with the corrected and fused full-focus bottom amplitude as the inversion target. This provides a high-precision, high-robust, and high-efficiency non-destructive inversion method for elastic constants of carbon fiber composites.

Description

Technical Field

[0001] This invention relates to the field of material parameter measurement technology, and in particular to a method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasonic images. Background Technology

[0002] Carbon fiber composites are widely used in high-end technology fields such as aerospace and hydrogen energy storage and transportation. However, under the influence of environmental factors such as humidity, heat, and vibration loads, equipment made of carbon fiber composites may continuously develop internal damage, thereby affecting the mechanical properties of the equipment. Therefore, non-destructive testing (NDT) assessment of carbon fiber composites is an effective means of determining the degree of internal damage evolution. Unlike metallic materials, the prerequisite for quantitative NDT characterization of carbon fiber composites is obtaining their precise elastic constants.

[0003] In research on this problem, ultrasonic measurement is considered a promising method due to its convenience and speed. Currently, the main solution involves extracting the transit time of the bottom-reflected signal from the composite material using the bottom-echo method, establishing a corresponding mechanical model based on the relationship between the group velocity of the longitudinal wave and the material's elastic constants, establishing the connection between the group velocity and the transit time, and finally using the group velocity to invert the relevant elastic constants.

[0004] This method has high detection accuracy on composite unidirectional plates with a small thickness. However, considering the attenuation characteristics during ultrasonic propagation, the extraction of the bottom transit time in thick composite unidirectional plates is limited to a small propagation angle. In addition, the inversion method based solely on longitudinal waves is difficult to comprehensively evaluate the acoustic properties of composite materials. There will be a large error between the inversion results and the actual results, which cannot meet the requirements of accurate non-destructive testing. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology in that the evaluation of elastic constants of carbon fiber composites is not comprehensive and cannot meet the requirements of accurate non-destructive testing, this invention proposes a method for inverting the elastic constants of carbon fiber composites based on multimodal ultrasonic images.

[0006] To achieve the above objectives, the present invention employs the following technical solution: a method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images, comprising:

[0007] S1: Place the ultrasonic phased array device along the x-axis and y-axis of the carbon fiber composite unidirectional plate, respectively, to excite ultrasonic waves and acquire full matrix data in the xz plane and yz plane;

[0008] S2: Based on the full matrix data acquired in the yz plane, fully focused images in the PP mode and P-SV mode are generated respectively. The elastic constant is obtained by extracting the mean amplitude of the fully focused image at the bottom surface of the composite material. as well as The optimal value;

[0009] S3: Based on full matrix data acquired from the xz plane, combined with... The optimal values ​​are determined to generate multimodal images based on various split wavelets of quasi-longitudinal and quasi-transverse waves, and the elastic constants are obtained. , as well as The optimal values ​​include:

[0010] S31: In the xz plane, set the elastic constant. , as well as The initial value;

[0011] S32: At the current elastic constant , as well as Under the given values, generate fully focused images corresponding to various ultrasonic mode conversion processes. And determine the effective imaging range of each image. ;

[0012] S33: Effective imaging range under each mode conversion Mean amplitude of fully focused image within Perform overlay and fusion to obtain the average amplitude of the fused full-focus image. ;

[0013] S34: Use the gradient method for iterative updates to obtain the elastic constants. The optimal value.

[0014] Preferably, before step S1, a stiffness matrix C containing the elastic constants of the carbon fiber composite unidirectional plate needs to be constructed, and the elastic constants to be calculated are determined. C 11 、C 13 、C 33 、C 44 and C 55 .

[0015] Preferably, step S32 includes:

[0016] S321: At the current elastic constant , as well as Under the value of , based on the elastic constant The optimal value is determined by iterating through the range of propagation angles and calculating the group velocity corresponding to each propagation angle. The group velocity curves of quasi-transverse wave qSV and quasi-longitudinal wave qP are obtained with the propagation angle as the abscissa and the group velocity as the ordinate. The propagation angle is the angle between the ultrasonic propagation direction and the Z-axis.

[0017] S322: Based on the group velocity curves of quasi-transverse wave (qSV) and quasi-longitudinal wave (qP) and the full matrix data acquired in the xz plane, generate corresponding fully focused images of various ultrasonic mode conversion processes. Where Q represents the mode transition type, including quasi-longitudinal wave to quasi-longitudinal wave transition qP-qP, quasi-longitudinal wave to first quasi-transverse wavelet transition qP-qSV1, first quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV1-qP, quasi-longitudinal wavelet to second quasi-transverse wavelet transition qP-qSV2, second quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV2-qP, quasi-longitudinal wavelet to third quasi-transverse wavelet transition qP-qSV3, third quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV3-qP, first quasi-transverse wavelet to first quasi-transverse wavelet transition qSV1-qSV1, second quasi-transverse wavelet to second quasi-transverse wavelet transition qSV2-qSV2, and third quasi-transverse wavelet to third quasi-transverse wavelet transition qSV3-qSV3; when the quasi-transverse wave does not split, the first quasi-transverse wavelet is the quasi-transverse wavelet; in the fully focused image , , , , as well as All are 0;

[0018] S323: Calculate the effective minimum propagation angle for each mode transition. And based on the effective minimum propagation angle Determine the effective imaging range of the bottom surface in the fully focused image under each mode transition. .

[0019] Preferably, in step S323, the effective minimum propagation angle is as follows: quasi-longitudinal wave to quasi-longitudinal wave conversion qP-qP, quasi-longitudinal wave to first quasi-transverse wavelet conversion qP-qSV1, first quasi-transverse wavelet to quasi-longitudinal wave mode conversion qSV1-qP, and first quasi-transverse wavelet to first quasi-transverse wavelet conversion qSV1-qSV1. The effective imaging range is ;

[0020] in, , The minimum value of the x-coordinate of the array element. This represents the maximum value of the x-coordinate of the array element.

[0021] Preferably, in step S323, the effective minimum propagation angle under qP-qSV2 and qP-qSV3 are both equal to the propagation angle of the quasi-longitudinal wave under the corresponding mode transition. ; Propagation angles of quasi-longitudinal waves under qP-qSV2 and qP-qSV3 Calculate using the following formula:

[0022] ;

[0023] in, The minimum propagation angle of the second quasi-transverse wavelet qSV2; The group velocity of the quasi-longitudinal wave; The group velocity of the second quasi-transverse wave;

[0024] The effective minimum propagation angle under qSV2-qP and under qSV2-qSV2 is equal to the minimum propagation angle of the second quasi-transverse wavelet qSV2; the effective minimum propagation angle under qSV3-qP and under qSV3-qSV3 is equal to the minimum propagation angle of the third quasi-transverse wavelet qSV3.

[0025] Effective imaging range at qP-qSV2, qSV2-qP, qP-qSV3, qSV3-qP, qSV2-qSV2, and qSV3-qSV3 all , where each mode transition These are the products of the thickness of the carbon fiber composite material and the effective minimum propagation angle tangent under the corresponding mode transition.

[0026] Preferably, step S33 includes:

[0027] Extract the effective imaging range at depth H from the total focusing images of each modality. The image amplitude corresponding to the discrete points contained within is calculated, and the effective imaging range is determined. The mean amplitude of the corrected image corresponding to the discrete points contained therein;

[0028] Correcting the mean of image amplitude The calculation formula is:

[0029] ;

[0030] Where m is the effective imaging range in the x-direction of the fully focused image under the current mode conversion. Inner discrete point number; M is the effective imaging range in the x-direction of the fully focused image in the current modality. The number of discrete points included; Let x be the x-coordinate of the fully focused image at the m-th discrete point in the current modality;

[0031] The mean amplitudes of the corrected full-focus images under each mode transformation are superimposed and fused to obtain the mean amplitude of the fused full-focus image. The calculation formula is:

[0032] .

[0033] Preferably, step S34 includes:

[0034] Extract the mean amplitude of the fused full-focus image under the current elastic constant value. The gradient method is used to evaluate the elastic constants. The value of the elastic constant is iteratively updated, and the elastic constant is determined at the current iteration number. Whether the value of converges and whether the current iteration number is greater than the set minimum iteration number. Yes, the current elastic constant will be... The corresponding value is taken as the optimal value; otherwise, repeat steps S32-S34 until the current iteration number is greater than the set maximum iteration number. The current elastic constant The corresponding value is taken as the optimal value.

[0035] The preferred formula for the gradient method is:

[0036] ;

[0037] Where k is the number of iterations; for The learning rate; for exist The gradient at k; the elastic constant when k=1. This is the initial setting value.

[0038] Preferably, the elastic constant is calculated based on the full matrix data acquired in the yz plane. and Obtain the elastic constant as well as The optimal values ​​include:

[0039] S21: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, based on the full matrix data acquired in the yz plane, a fully focused image under the mode conversion (PP) between longitudinal waves is obtained;

[0040] S22: For the elastic constant C 33 For each value, the imaging range at depth H in the full-focus image under PP is extracted. Find the image amplitude corresponding to all discrete points within the range, and calculate the mean of the image amplitudes at these discrete points; select the elastic constant corresponding to the maximum mean of the image amplitudes at these discrete points. The value is taken as the elastic constant. The optimal value;

[0041] S23: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, the group velocity based on the longitudinal wave P The full matrix data acquired from the yz plane is used to obtain a fully focused image under P-SV mode conversion from P-wave to S-wave.

[0042] S24: For the elastic constant C 44 For each value, the imaging range at depth H in the full-focus image under P-SV is extracted. Find the image amplitude corresponding to all discrete points within the range, and calculate the mean of the image amplitudes at these discrete points; select the elastic constant corresponding to the maximum mean of the image amplitudes at these discrete points. The value is taken as the elastic constant. The optimal value;

[0043] The ultrasonic group velocity in the yz plane includes the group velocity of the longitudinal wave P. and group velocity of transverse wave SV The values ​​are elastic constants. and The principal square root of the density ratio of carbon fiber composites.

[0044] Preferably, in step S3, the physical relationship between the ultrasonic phase velocity and the elastic constant is established using the Christoffel equation:

[0045] ;

[0046] Where det(.) is the determinant of the matrix; Indicates wave number; The density of carbon fiber composite material, The frequency of the ultrasonic wave; Let r be the Christoffel matrix; r and s are the row and column indices of the Christoffel matrix, respectively. Calculated for Kronecker, ; l 1 represents the sine value of the angle between the direction of ultrasonic wave propagation and the Z-axis; l 3 represents the cosine of the angle between the direction of ultrasonic propagation and the Z-axis;

[0047] Ultrasonic group velocity The calculation formula is:

[0048] ;

[0049] in, The ultrasonic phase velocity is represented by Christoffel's equations and elastic constants. The optimal value is obtained.

[0050] The advantages of this invention are:

[0051] (1) In this invention, an ultrasonic phased array device is placed along the x-axis and y-axis of a carbon fiber composite unidirectional plate, respectively, to excite ultrasonic waves and perform full-matrix data acquisition on the carbon fiber composite unidirectional plate; the elastic constant is calculated based on the full-matrix data acquired in the yz plane. as well as Obtain the elastic constant as well as The optimal value is determined; the elastic constant is calculated based on the full matrix data collected in the yz plane. , as well as Obtain the elastic constant , as well as By fusing multimodal ultrasound full matrix data, establishing an inversion target centered on the quality of fully focused images, and employing a strategy combining hierarchical and intelligent optimization algorithms, this method successfully overcomes the shortcomings of existing technologies, such as low accuracy, poor applicability, and insufficient automation. It provides a high-precision, high-robustness, and high-efficiency non-destructive inversion method for the elastic constants of carbon fiber composite materials, which has significant practical value for the safety evaluation and life prediction of composite material structures in aerospace and other fields.

[0052] (2) By adopting a strategy of fusing full-matrix data acquisition with multimodal full-focus images, this invention achieves the effect of comprehensively utilizing multimodal acoustic information such as longitudinal waves, transverse waves, quasi-longitudinal waves, and quasi-transverse waves, overcoming the deficiency of insufficient information in traditional single longitudinal wave inversion methods, and achieving comprehensive and accurate inversion of all five independent elastic constants. , , , , ).

[0053] (3) By innovatively replacing the “transit time” index relied upon in previous inversion methods with the optimization target of “the mean amplitude of the bottom surface of the corrected full-focus image”, the present invention achieves the effect of highly consistent inversion results with physical facts (the bottom surface echo is the strongest), and makes significant progress in improving inversion accuracy and reliability.

[0054] (4) This invention employs a layered inversion strategy of "starting with the easy and then moving to the difficult" (inverting first on the yz plane). , Then, by inverting the remaining elastic constants on the xz plane, the parameter search space was significantly reduced, and the complex optimization was avoided from getting trapped in local optima. This resulted in improvements in inversion calculation efficiency and algorithm stability.

[0055] (5) By combining global parameter traversal with local gradient descent optimization algorithm, this invention achieves the effect of both locating the global optimal solution region and performing fine iteration, thus achieving progress in automated and intelligent inversion while ensuring the accuracy of the results. Attached Figure Description

[0056] Figure 1 This is a flowchart of the method steps of the present invention;

[0057] Figure 2 This is a schematic diagram of ultrasonic propagation in the xz plane.

[0058] Figure 3 The velocity curves for the xz plane group;

[0059] Figure 4 This is a schematic diagram illustrating the data collection method;

[0060] Figure 5 This is a schematic diagram of the mean amplitude of the mode conversion image of the longitudinal wave in the yz plane.

[0061] Figure 6 This is a schematic diagram of the mean amplitude of the P-wave to S-wave mode conversion image in the yz plane.

[0062] Figure 7 This is a schematic diagram of the coordinate direction of a carbon fiber composite unidirectional plate. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Specific implementation as follows Figure 7 As shown, the main directions of the carbon fiber composite unidirectional plate include the fiber direction, constructing a three-dimensional coordinate system, that is, the 0° direction or the x-axis direction, the horizontal direction perpendicular to the fiber direction, that is, the 90° direction or the y-axis direction, and the direction perpendicular to the plane of the carbon fiber composite unidirectional plate, that is, the z-axis direction.

[0065] like Figures 1-7As shown, this invention proposes a method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasonic images, including:

[0066] S1: Place the ultrasonic phased array device along the x-axis and y-axis of the carbon fiber composite unidirectional plate, respectively. Excite ultrasonic waves to perform full-matrix data acquisition on the defect-free carbon fiber composite unidirectional plate, acquiring full-matrix data in the xz and yz planes respectively; i is the transmitting element number of the ultrasonic phased array device; j is the receiving element number of the ultrasonic phased array device; the schematic diagram of ultrasonic propagation in the xz plane is shown below. Figure 2 As shown.

[0067] Full Matrix Capture (FMC) is a data acquisition method for composite materials using ultrasonic phased array equipment. For example, an ultrasonic phased array equipment has a 64-element ultrasonic probe. The first element emits an ultrasonic wave, and the bottom echo signal is received by all 64 elements. Then the second element emits an ultrasonic wave, and the bottom echo signal is received by all 64 elements. This process is repeated for the remaining elements to emit ultrasonic waves and for all elements to receive the bottom echo signals, thus forming full matrix data (FMC data) of the bottom echo.

[0068] When the ultrasonic phased array device is placed along the fiber direction of the carbon fiber composite unidirectional plate, the ultrasonic waves will generate three modes of ultrasonic data: quasi-transverse wave (qSV), quasi-longitudinal wave (qP), and pure transverse wave. Since the pure transverse wave has a negligible impact on the calculation of the elastic constant of the carbon fiber composite unidirectional plate, it is not considered in this invention. When the ultrasonic phased array device is placed along the y-axis of the carbon fiber composite unidirectional plate, the ultrasonic waves will generate two waveforms: transverse wave (SV) and longitudinal wave (P).

[0069] Carbon fiber composite unidirectional plates are macroscopically homogeneous transversely isotropic bodies, and their elastic characteristics can be characterized by a 6×6 stiffness matrix C:

[0070] ;

[0071] in, Indicates the tensile stiffness in the x-axis direction; Indicates the coupling stiffness in the xy plane; Indicates the coupling stiffness in the xz plane; Indicates the tensile stiffness in the y-axis direction; Indicates the coupling stiffness in the yz plane; Indicates the tensile stiffness in the z-axis direction; This represents the shear stiffness when rotating about the x-axis. This represents the shear stiffness when rotating about the y-axis. Represents the shear stiffness about the z-axis;

[0072] Based on the mechanical properties of transversely isotropic materials, we know that , , , Since the stiffness matrix C is a symmetric matrix, it contains only 5 unknown independent elastic constants. C 11 、C 13 、C 33 、C 44 、C 55 .

[0073] S2: Based on the full matrix data acquired in the yz plane, fully focused images in the PP mode and P-SV mode are generated respectively. The elastic constant is obtained by extracting the mean amplitude of the fully focused image at the bottom surface of the composite material. as well as The optimal values ​​include:

[0074] When an ultrasonic phased array device is positioned along the y-axis of a carbon fiber composite unidirectional plate to acquire data, the ultrasonic waves in the yz plane include longitudinal and transverse waves. The imaging plane of the linear array of the ultrasonic phased array device is isotropic, and the group velocity of the longitudinal wave P is... and group velocity of transverse wave SV It is a constant, and the calculation formulas are as follows:

[0075] ;

[0076] in, This represents the density of the carbon fiber composite material.

[0077] S21: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, based on the full matrix data acquired in the yz plane, a fully focused image under the mode conversion (PP) between longitudinal waves is obtained;

[0078] The expression for the image amplitude of a fully focused image is:

[0079] ;

[0080] Where (y,z) are the coordinates of the imaging point; The image amplitude at the imaging point (y,z); For the ultrasonic wave emitted from the i-th array element to reach the imaging point Then, the propagation time of the reflected wave to be received by the j-th array element is equal to the ratio of the total distance from the ultrasonic wave emission to the ultrasonic wave group velocity; N is the total number of array elements. This indicates that the ultrasonic wave is emitted from the i-th element and arrives at the imaging point. Then, the bottom surface echo data received by the j-th array element is reflected again.

[0081] S22: For the elastic constant C 33 For each value, the imaging range at depth H in the full-focus image under PP is extracted. Find the image amplitude corresponding to all discrete points within the range, and calculate the mean of the image amplitude at each discrete point. Select the elastic constant corresponding to the maximum mean value of the discrete point image amplitude. The value is taken as the elastic constant. The optimal value; where, the imaging range , The minimum value of the x-coordinate of the array element. This represents the maximum value of the x-coordinate of the array element.

[0082] S23: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, the group velocity based on the longitudinal wave P The full matrix data acquired from the yz plane is used to obtain a fully focused image under P-SV mode conversion from P-wave to S-wave.

[0083] S24: For the elastic constant C 44 For each value, the imaging range at depth H in the full-focus image under P-SV is extracted. Find the image amplitude corresponding to all discrete points within the range, and calculate the mean of the image amplitude at each discrete point. Select the elastic constant corresponding to the maximum mean value of the discrete point image amplitude. The value is taken as the elastic constant. The optimal value.

[0084] Obtaining ultrasonic group velocity based on Christoffel's equation v The ultrasonic group velocity in the xz plane includes the quasi-longitudinal wave group velocity. and quasi-transverse wave group velocity ;

[0085] The physical relationship between ultrasonic phase velocity and elastic constant is established using Christoffel's equation:

[0086] ;

[0087] Where det(.) is the determinant of the matrix; Indicates wave number; The density of carbon fiber composite material, The frequency of the ultrasonic wave; Let r be the Christoffel matrix; r and s are the row and column indices of the Christoffel matrix, respectively. Calculated for Kronecker, ; l 1 represents the sine value of the angle between the direction of ultrasonic wave propagation and the Z-axis; l 3 represents the cosine of the angle between the ultrasonic propagation direction and the Z-axis.

[0088] Ultrasonic group velocity v The calculation formula is:

[0089] ;

[0090] in, The ultrasonic phase velocity is represented by Christoffel's equations and elastic constants. The optimal value is obtained; l 1 represents the sine value of the angle between the direction of ultrasonic wave propagation and the z-axis; l 3 represents the cosine of the angle between the direction of ultrasonic propagation and the z-axis.

[0091] S3: Based on full matrix data acquired from the xz plane, combined with... The optimal values ​​are determined to generate multimodal images based on various split wavelets of quasi-longitudinal and quasi-transverse waves, and the elastic constants are obtained. , as well as The optimal values ​​include:

[0092] S31: In the xz plane, set the elastic constant. , as well as The initial value;

[0093] S32: At the current elastic constant , as well as Under the value of , based on the elastic constant The optimal value is determined by iterating through the propagation angle range and calculating the group velocity corresponding to each propagation angle. Then, using the propagation angle as the x-axis and the group velocity as the y-axis, the group velocities of the quasi-transverse wave and quasi-longitudinal wave are smoothly connected sequentially to obtain the group velocity curves for the quasi-transverse wave (qSV) and the quasi-longitudinal wave (qP). The propagation angle is the angle between the ultrasonic wave propagation direction and the Z-axis. The group velocities of both the quasi-transverse wave and the quasi-longitudinal wave are obtained through the ultrasonic group velocity... v The formula is used for calculation.

[0094] In the xz plane, due to the anisotropy of the composite material, the quasi-transverse wave qSV will split under certain combinations of elastic constants. The three modal wavelets generated by the splitting are defined as the first quasi-transverse wavelet qSV1, the second quasi-transverse wavelet qSV2, and the third quasi-transverse wavelet qSV3. The group velocity curves of the split quasi-transverse and quasi-longitudinal waves are shown below. Figure 3 As shown.

[0095] Based on the group velocity curves of quasi-transverse wave (qSV) and quasi-longitudinal wave (qP) and the full matrix data acquired in the xz plane, corresponding fully focused images of various ultrasonic mode conversion processes are generated. Where Q represents the mode transition type.

[0096] The amplitude calculation for a fully focused image is based on the calculation method used in the yz plane.

[0097] In the xz plane, mode transitions include quasi-longitudinal wave to quasi-longitudinal wave transition qP-qP, quasi-longitudinal wave to first quasi-transverse wavelet transition qP-qSV1, first quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV1-qP, quasi-longitudinal wavelet to second quasi-transverse wavelet transition qP-qSV2, second quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV2-qP, quasi-longitudinal wavelet to third quasi-transverse wavelet transition qP-qSV3, third quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV3-qP, first quasi-transverse wavelet to first quasi-transverse wavelet transition qSV1-qSV1, second quasi-transverse wavelet to second quasi-transverse wavelet transition qSV2-qSV2, and third quasi-transverse wavelet to third quasi-transverse wavelet transition qSV3-qSV3;

[0098] Right now ;

[0099] Corresponding all-focused image include , , , , , , , , as well as ;

[0100] Calculate the effective minimum propagation angle for each mode transition based on Snell's law. And based on the effective minimum propagation angle Determine the effective imaging range of the bottom surface in the fully focused image under each mode transition. ;

[0101] (1) Under the transformation from quasi-longitudinal wave to quasi-longitudinal wave qP-qP:

[0102] Effective minimum propagation angle Effective imaging range ;

[0103] in, , The minimum value of the x-coordinate of the array element. The maximum value of the x-coordinate of the array element;

[0104] (2) Under the transformation qP-qSV1 between the quasi-longitudinal wave and the first quasi-transverse wavelet:

[0105] Effective minimum propagation angle Effective imaging range ;

[0106] (3) Under the mode transition qSV1-qP between the first quasi-transverse wavelet and the quasi-longitudinal wavelet:

[0107] Effective minimum propagation angle Effective imaging range ;;

[0108] (4) Under the transformation qP-qSV2 between the quasi-longitudinal wave and the second quasi-transverse wavelet:

[0109] Effective minimum propagation angle The calculation formula is:

[0110] ;

[0111] in, The minimum propagation angle of the second quasi-transverse wavelet qSV2; The group velocity of the quasi-longitudinal wave; The group velocity of the second quasi-transverse wave;

[0112] Effective imaging range The calculation formula is:

[0113] ;

[0114] in, The thickness of the carbon fiber composite material;

[0115] (5) Under the mode transition qSV2-qP between the second quasi-transverse wavelet and the quasi-longitudinal wavelet:

[0116] Effective minimum propagation angle ;

[0117] Effective imaging range The calculation formula is:

[0118] ;

[0119] (6) Under the transformation qP-qSV3 between the quasi-longitudinal wave and the third quasi-transverse wavelet:

[0120] Effective minimum propagation angle The calculation formula is:

[0121] ;

[0122] in, The minimum propagation angle of the qSV3 wave; This is the group velocity of the third quasi-transverse wave.

[0123] In fact, according to Figure 3 As is known, under qP-qSV3 and under qP-qSV2 and Equal, and at the same time at the minimum propagation angle and The propagation angles of the quasi-longitudinal wave at the minimum propagation angle are equal. equal.

[0124] Effective imaging range The calculation formula is:

[0125] ;

[0126] (7) Under the mode transition qSV3-qP between the third quasi-transverse wavelet and the quasi-longitudinal wavelet:

[0127] Effective minimum propagation angle ;

[0128] Effective imaging range The calculation formula is:

[0129] ;

[0130] (8) Under the transformation qSV1-qSV1 between the first quasi-transverse wavelet and the first quasi-transverse wavelet:

[0131] Effective minimum propagation angle ;

[0132] Effective imaging range ;

[0133] (9) Under the transformation qSV2-qSV2 between the second quasi-transverse wavelet and the second quasi-transverse wavelet:

[0134] Effective minimum propagation angle ;

[0135] Effective imaging range The calculation formula is:

[0136] ;

[0137] (10) Under the mode transition qSV3-qSV3 between the third quasi-transverse wavelet and the third quasi-transverse wavelet:

[0138] Effective minimum propagation angle ;

[0139] Effective imaging range The calculation formula is:

[0140] ;

[0141] S33: Extract the effective imaging range at depth H from the total focusing images of each modality. The image amplitude corresponding to the discrete points contained within is calculated, and the effective imaging range is determined. The mean amplitude of the corrected image corresponding to the discrete points contained therein;

[0142] Correcting the mean of image amplitude The calculation formula is:

[0143] ;

[0144] Where m is the effective imaging range in the x-direction of the fully focused image under the current mode conversion. Inner discrete point number; M is the effective imaging range in the x-direction of the fully focused image in the current modality. The number of discrete points included; Let x be the x-coordinate of the fully focused image at the m-th discrete point in the current modality;

[0145] The mean amplitude of the corrected all-focused image under each mode transformation. Perform overlay and fusion to obtain the average amplitude of the fused full-focus image. The calculation formula is:

[0146] ;

[0147] When the quasi-transverse wave qSV does not split, in the fully focused image , , , , as well as All are 0.

[0148] S34: Extract the mean amplitude of the fused full-focus image under the current elastic constant value. The gradient method is used to evaluate the elastic constants. The value of is iteratively updated, and the formula for the gradient method is:

[0149] ;

[0150] Where k is the number of iterations; for The learning rate; for exist The gradient at k; the elastic constant when k=1. This is the initial setting value.

[0151] Determine the elastic constant at the current iteration number. Whether the new value converges and whether the current iteration count is greater than the set minimum iteration count. Yes, the current elastic constant will be... The corresponding value is taken as the optimal value; otherwise, repeat steps S32-S34 until the current iteration number is greater than the set maximum iteration number. The current elastic constant The corresponding value is taken as the optimal value.

[0152] Thus, all elastic constants of carbon fiber composites, including , , , as well as All were calculated.

[0153] To demonstrate the effectiveness of the present invention, the following embodiments are used to verify the method of the present invention.

[0154] In the experiment, the stiffness matrix C of the carbon fiber composite plate, which includes all elastic constants, was set as follows:

[0155] ;

[0156] Therefore, ; ; ; ; .

[0157] In this embodiment, the ultrasonic probe frequency of the ultrasonic phased array device is set to 5MHz, the number of array elements is 64, the center-to-center spacing of the array elements is 0.6mm, and the width of the array elements is 0.5mm. The density of the carbon fiber composite unidirectional plate is 1503 kg / m³, which was measured by Archimedes' displacement method. 3 The thickness H is 10mm.

[0158] First, the ultrasonic phased array device was positioned along the carbon fiber direction (x-axis) and the y-axis, and the bottom echo full matrix data in the xz plane were acquired respectively. ) and the full matrix data of bottom echoes in the yz plane ( A diagram illustrating the data collection method is shown below. Figure 4 As shown;

[0159] Then, the elastic constant C is obtained by inversion based on the full matrix data of the bottom echo in the yz plane. 33 and C 44 .

[0160] set up The value range is [5, 15] GPa, the sampling interval is 0.1 GPa, and there are a total of 101 sampling points;

[0161] According to the formula Calculate the group velocity of the longitudinal wave P at all sampling points;

[0162] Full-focus imaging was performed under a single P-wave mode conversion (PP), and the mean image amplitude at 10 mm was calculated. The result is as follows Figure 5 As shown, at the elastic constant C 33 When the index is 63, the mean image amplitude reaches its maximum value of 0.000818494, because when the index is 63, the corresponding... The value is 11.2 GPa, therefore 11.2 GPa is determined to be... This is the optimal value.

[0163] set up The value range is [2, 10] GPa, the sampling interval is 0.1 GPa, and there are a total of 81 sampling points;

[0164] According to the formula Calculate the group velocity of the shear wave SV at all sampling points;

[0165] Full-focus imaging was performed under a single P-wave to S-wave mode conversion (P-SV), and the mean image amplitude at 10 mm was calculated. The result is as follows Figure 6 As shown, at the elastic constant C 44 When the index is 13, the mean value of the image amplitude reaches its maximum value of 0.0000703836, which is 7.03836e-05 in scientific notation. This is because when the index value is 13, the corresponding... The value is 3.2 GPa. 3.2 GPa is defined as... The optimal value.

[0166] Next, the elastic constants are obtained by inversion based on the full matrix data of the bottom echo acquired in the xz plane. , and .

[0167] Set elastic constant , as well as The initial value is = , =4, =4, unit is GPa, minimum number of iterations The value is 30, and the maximum number of iterations is... It is 500;

[0168] At the current elastic constant , as well as Under the given values, the elastic constants obtained from the yz plane are... With a value of 11.2 GPa, based on the Christoffel equation and the formula for calculating ultrasonic group velocity, the corresponding group velocity curves for quasi-longitudinal and quasi-transverse waves were calculated, and the results are as follows. Figure 3 As shown.

[0169] Next, for each combination of elastic constants, a full-focus image is obtained based on the group velocity curves of quasi-longitudinal and quasi-transverse waves, the mode conversion characteristics of ultrasound, and the full-focus image amplitude formula. ,

[0170] ;

[0171] And determine the effective imaging range of the bottom surface in the fully focused images under each mode transformation. Calculate the average bottom surface amplitude of each mode within the effective imaging range. The mean amplitude of the bottom surface of the fully focused image for each modality. The images are fused and overlaid to obtain the average amplitude of the fused full-focus image. .

[0172] set up Calculate the current value according to the gradient method formula. Gradient at reference value, and update simultaneously After 67 iterations, It tends to converge, and its value is GPa, thus yielding the elastic constant , as well as The optimal values ​​are respectively = , =4.1, =4.1.

[0173] The final inverted elasticity coefficient matrix C is as follows:

[0174] ;

[0175] Compared with the actual elastic coefficient matrix, the error of most elastic constants is less than 0.1 GPa, which shows the effectiveness of this method in inverting the elastic constants of thick carbon fiber composites.

[0176] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0177] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0178] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasonic images, characterized in that, include: S1: Place the ultrasonic phased array device along the x-axis and y-axis of the carbon fiber composite unidirectional plate, respectively, to excite ultrasonic waves and collect full matrix data in the xz plane and yz plane; S2: Based on the full matrix data acquired in the yz plane, fully focused images in the PP mode and P-SV mode are generated respectively. The elastic constant is obtained by extracting the mean amplitude of the fully focused image at the bottom surface of the composite material. as well as The optimal value; S3: Based on full matrix data acquired from the xz plane, combined with... The optimal values ​​are determined to generate multimodal images based on various split wavelets of quasi-longitudinal and quasi-transverse waves, and the elastic constants are obtained. , as well as The optimal values ​​include: S31: In the xz plane, set the elastic constant. , as well as The initial value; S32: At the current elastic constant , as well as Under the given values, generate fully focused images corresponding to various ultrasonic mode conversion processes. And determine the effective imaging range of each image. ; S33: Effective imaging range under each mode conversion Mean amplitude of fully focused image within Perform overlay and fusion to obtain the average amplitude of the fused full-focus image. ; S34: Use the gradient method for iterative updates to obtain the elastic constants. The optimal value.

2. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 1, characterized in that, Before step S1, a stiffness matrix C containing the elastic constants of the carbon fiber composite unidirectional plate needs to be constructed, and the elastic constants to be calculated are determined. C 11 、C 13 、C 33 、C 44 and C 55 .

3. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 1, characterized in that, Step S32 includes: S321: At the current elastic constant , as well as Under the value of , based on the elastic constant The optimal value is determined by iterating through the range of propagation angles and calculating the group velocity corresponding to each propagation angle. The group velocity curves of quasi-transverse wave qSV and quasi-longitudinal wave qP are obtained with the propagation angle as the abscissa and the group velocity as the ordinate. The propagation angle is the angle between the ultrasonic propagation direction and the Z-axis. S322: Based on the group velocity curves of quasi-transverse wave (qSV) and quasi-longitudinal wave (qP) and the full matrix data acquired in the xz plane, generate corresponding fully focused images of various ultrasonic mode conversion processes. Where Q represents the mode transition type, including quasi-longitudinal wave to quasi-longitudinal wave transition qP-qP, quasi-longitudinal wave to first quasi-transverse wavelet transition qP-qSV1, first quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV1-qP, quasi-longitudinal wavelet to second quasi-transverse wavelet transition qP-qSV2, second quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV2-qP, quasi-longitudinal wavelet to third quasi-transverse wavelet transition qP-qSV3, third quasi-transverse wavelet to quasi-longitudinal wave mode transition qSV3-qP, first quasi-transverse wavelet to first quasi-transverse wavelet transition qSV1-qSV1, second quasi-transverse wavelet to second quasi-transverse wavelet transition qSV2-qSV2, and third quasi-transverse wavelet to third quasi-transverse wavelet transition qSV3-qSV3; when the quasi-transverse wave does not split, the first quasi-transverse wavelet is the quasi-transverse wavelet; in the fully focused image , , , , as well as All are 0; S323: Calculate the effective minimum propagation angle for each mode transition. And based on the effective minimum propagation angle Determine the effective imaging range of the bottom surface in the fully focused image under each mode transition. .

4. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 3, characterized in that, In step S323, under the following modes: quasi-longitudinal wave to quasi-longitudinal wave conversion qP-qP, quasi-longitudinal wave to first quasi-transverse wavelet conversion qP-qSV1, first quasi-transverse wavelet to quasi-longitudinal wave mode conversion qSV1-qP, and first quasi-transverse wavelet to first quasi-transverse wavelet conversion qSV1-qSV1, the effective minimum propagation angle is always... The effective imaging range is ; in, , The minimum value of the x-coordinate of the array element. This represents the maximum value of the x-coordinate of the array element.

5. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 4, characterized in that, In step S323, the effective minimum propagation angle under qP-qSV2 and qP-qSV3 are both equal to the propagation angle of the quasi-longitudinal wave under the corresponding mode transition. ; Propagation angles of quasi-longitudinal waves under qP-qSV2 and qP-qSV3 Calculate using the following formula: in, The minimum propagation angle of the second quasi-transverse wavelet qSV2; The group velocity of the quasi-longitudinal wave; The group velocity of the second quasi-transverse wave; The effective minimum propagation angle under qSV2-qP and under qSV2-qSV2 is equal to the minimum propagation angle of the second quasi-transverse wavelet qSV2; the effective minimum propagation angle under qSV3-qP and under qSV3-qSV3 is equal to the minimum propagation angle of the third quasi-transverse wavelet qSV3. Effective imaging range at qP-qSV2, qSV2-qP, qP-qSV3, qSV3-qP, qSV2-qSV2, and qSV3-qSV3 all , where each mode transition These are the products of the thickness of the carbon fiber composite material and the effective minimum propagation angle tangent under the corresponding mode transition.

6. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 3, characterized in that, Step S33 includes: Extract the effective imaging range at depth H from the total focusing images of each modality. The image amplitude corresponding to the discrete points contained within is calculated, and the effective imaging range is determined. The mean amplitude of the corrected image corresponding to the discrete points contained therein; Correcting the mean of image amplitude The calculation formula is: Where m is the effective imaging range in the x-direction of the fully focused image under the current mode conversion. Inner discrete point number; M is the effective imaging range in the x-direction of the fully focused image in the current modality. The number of discrete points included; Let x be the x-coordinate of the fully focused image at the m-th discrete point in the current modality; The mean amplitudes of the corrected full-focus images under each mode transformation are superimposed and fused to obtain the mean amplitude of the fused full-focus image. The calculation formula is: 。 7. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 6, characterized in that, Step S34 includes: Extract the mean amplitude of the fused full-focus image under the current elastic constant value. The gradient method is used to evaluate the elastic constants. The value of the elastic constant is iteratively updated, and the elastic constant is determined at the current iteration number. Whether the value of converges and whether the current iteration number is greater than the set minimum iteration number. Yes, the current elastic constant will be... The corresponding value is taken as the optimal value; otherwise, repeat steps S32-S34 until the current iteration number is greater than the set maximum iteration number. The current elastic constant The corresponding value is taken as the optimal value.

8. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 7, characterized in that, The formula for the gradient method is: Where k is the number of iterations; for The learning rate; for exist The gradient at k; the elastic constant when k=1. This is the initial setting value.

9. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 1, characterized in that, Calculation of elastic constants based on full matrix data acquired in the yz plane and Obtain the elastic constant as well as The optimal values ​​include: S21: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, based on the full matrix data acquired in the yz plane, a fully focused image under the mode conversion (PP) between longitudinal waves is obtained; S22: For the elastic constant C 33 For each value, the imaging range at depth H in the full-focus image under PP is extracted. The image amplitude corresponding to all discrete points within the range is calculated, and the mean of the discrete point image amplitude is calculated; the elastic constant corresponding to the maximum mean of the discrete point image amplitude is selected. The value is taken as the elastic constant. The optimal value; S23: Determine the elastic constant within the set range All possible values ​​of the elastic constant; For each value, the group velocity based on the longitudinal wave P The full matrix data acquired from the yz plane is used to obtain a fully focused image under P-SV mode conversion from P-wave to S-wave. S24: For the elastic constant C 44 For each value, the imaging range at depth H in the full-focus image under P-SV is extracted. The image amplitude corresponding to all discrete points within the range is calculated, and the mean of the discrete point image amplitude is calculated; the elastic constant corresponding to the maximum mean of the discrete point image amplitude is selected. The value is taken as the elastic constant. The optimal value; The ultrasonic group velocity in the yz plane includes the group velocity of the longitudinal wave P. and group velocity of transverse wave SV The values ​​are elastic constants. and The principal square root of the density ratio of carbon fiber composites.

10. The method for inverting the elastic constants of carbon fiber composite materials based on multimodal ultrasound images as described in claim 1, characterized in that, In step S3, the physical relationship between the ultrasonic phase velocity and the elastic constant is established using the Christoffel equation: Where det(.) is the determinant of the matrix; Indicates wave number; The density of carbon fiber composite material, The frequency of the ultrasonic wave; Let r be the Christoffel matrix; r and s are the row and column indices of the Christoffel matrix, respectively. Calculated for Kronecker, ; l 1 represents the sine value of the angle between the direction of ultrasonic wave propagation and the Z-axis; l 3 represents the cosine of the angle between the direction of ultrasonic propagation and the Z-axis; Ultrasonic group velocity The calculation formula is: in, The ultrasonic phase velocity is represented by Christoffel's equations and elastic constants. The optimal value is obtained.

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