An ultrasonic testing method and system for residual stress using acoustic phase velocity inversion

Abstract

The application provides an ultrasonic detection method and system for residual stress by using acoustic phase velocity inversion, and belongs to the field of air-coupled ultrasonic guided wave detection. The application is based on an air-coupled ultrasonic guided wave sound field propagation finite element model to guide the optimal design of air-coupled ultrasonic transducer parameters. The air-coupled ultrasonic guided wave detection technology is used to non-contact excite and receive guided wave signals of a composite component with pre-stress through a stretching machine. The phase velocity of the air-coupled ultrasonic guided wave in the composite component is calculated based on the geometric positioning and time difference differential collaborative differential method. The corresponding relationship formula is obtained by calibrating the phase velocity and the pre-stress in the target composite material. The phase velocity of the unknown stress composite component is detected based on the calibration results of the target composite material, and the residual stress of the composite component is inverted. The application realizes the residual stress detection of the composite component by using the above method and system.

Description

Technical Field

[0001] This invention relates to the field of air-coupled ultrasonic guided wave testing, and in particular to an ultrasonic testing method and system for inverting residual stress using acoustic wave phase velocity. Background Technology

[0002] Composite material components are widely used in aerospace, rail transportation, and energy equipment, and their residual stress distribution directly affects the mechanical properties and service life of these components. Residual stress mainly originates from curing shrinkage, differences in thermal expansion coefficients, and machining processes during manufacturing, and can lead to component deformation, fatigue cracks, and even structural failure. Therefore, accurate detection of residual stress in composite material components is a crucial step in ensuring their reliability.

[0003] Traditional residual stress detection methods mainly include drilling, X-ray diffraction, and fiber optic sensing. Drilling can cause localized damage to the component, X-ray diffraction is only suitable for surface stress measurement and the equipment is expensive, and fiber optic sensing requires embedded sensors, affecting the integrity of the component. In contrast, ultrasonic guided wave testing has advantages such as low cost, full-field measurement, and no damage to the material, making it particularly suitable for stress assessment of large-sized composite material components. However, current mainstream contact ultrasonic testing requires the application of coupling agents or the use of high-energy laser excitation. These methods can cause contamination or thermal damage to the carbon fiber surface, seriously affecting material properties and limiting their application in surface-sensitive scenarios.

[0004] Air-coupled ultrasonic guided wave technology achieves non-contact excitation and reception through the air medium, avoiding the contamination problems caused by coupling agents. Existing ultrasonic residual stress detection technologies are mainly developed for metallic materials and are difficult to apply directly to anisotropic materials such as carbon fiber composites. Especially when the component thickness is less than 1 mm, the traditional vertical transmission method completely fails, while oblique incidence guided wave detection faces many technical bottlenecks. More importantly, the sound velocity change caused by residual stress in composite materials is extremely weak, and in engineering practice, the air section conditions are difficult to accurately reproduce, resulting in poor repeatability and low reliability of measurement results. Therefore, there is an urgent need to develop a novel air-coupled ultrasonic guided wave stress detection technology that directly measures the guided wave phase velocity, thereby overcoming the limitations of existing technologies for detecting residual stress in thin-walled composite components and providing a reliable detection method for engineering applications. Summary of the Invention

[0005] The purpose of this invention is to provide an ultrasonic testing method and system for inverting residual stress using acoustic wave phase velocity, which can accurately detect residual stress in composite material components.

[0006] To achieve the above objectives, the present invention provides an ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity, comprising the following steps:

[0007] Step S1: Determine the center frequency of the air-coupled transducer based on the dispersion curve of the composite material waveguide.

[0008] Step S2: Determine the incident angles of the transmitting transducer and the receiving transducer;

[0009] Step S3: Based on the finite element model of air-coupled ultrasonic guided wave propagation, obtain the guided wave propagation path and design the detection spacing between the transmitting transducer and the receiving transducer.

[0010] Step S4: Using the successive difference method that combines geometric positioning and time difference, the composite material component is prestressed by a tensile machine and the phase velocity of the ultrasonic guided wave is measured by an air-coupled ultrasonic guided wave detection system. The corresponding relationship between the phase velocity of the ultrasonic wave in the target composite material and the applied stress is established and calibrated.

[0011] Step S5: Based on the corresponding relationship in step S4, perform phase velocity detection on the composite material component with unknown stress and invert the residual stress of the composite material component.

[0012] Preferably, in step S1, the guided wave dispersion curve is calculated using the anisotropic elastic matrix and density parameters of the composite material, and a conventional air-coupled transducer with a frequency lower than the cutoff frequency of the A1 mode and the smallest attenuation is selected.

[0013] Preferably, in step S2, the phase velocity of mode A0 is determined based on the guided wave dispersion curve calculated in step S1, and the incident angle of the air-coupled transducer is calculated according to Snell's law in combination with the air speed of sound.

[0014] Preferably, in step S3, a two-dimensional finite element model is established to simulate the propagation characteristics of the guided wave acoustic field of the air-coupled transducer, and the minimum detection spacing is determined based on the standard that the guided wave signal does not alias with the direct air wave in the time domain.

[0015] Preferably, step S4 includes the following steps:

[0016] A stepped stress of 0-90 MPa was applied to the specimen on a tensile tester, with a single increment of 10 MPa.

[0017] Phase velocity was measured using the successive difference method: the transmitting transducer was fixed, and the receiving transducer was moved. Next, single displacement increment Record the transmission time ;

[0018] Calculate phase velocity:

[0019] , ;

[0020] ;

[0021] in, This represents the result calculated using the method of successive differences. The measurement location and the first Each measurement position corresponds to the phase velocity between measurement intervals. This indicates the final waveguide phase velocity; Indicates the position of the receiving probe. One measurement location, less than Integers;

[0022] The phase velocity and stress are fitted into a linear relationship.

[0023] Preferably, in step S5, the phase velocity of the unknown stress member is measured and substituted into the linear relationship established in step S4 to generate the residual stress value at the corresponding point and in the fiber direction.

[0024] The present invention also provides an ultrasonic testing system for implementing the above-described method, comprising:

[0025] The air-coupled ultrasonic guided wave testing fixture module is used to adjust the height of the air-coupled ultrasonic transducer from the test piece, the incident angle, and the detection distance between the transmitting transducer and the receiving transducer.

[0026] The stress preset and loading module includes the DDL100 electronic universal testing machine, controller, and main control computer;

[0027] The ultrasonic signal excitation and acquisition module generates a residual stress detection scheme for air-coupled ultrasonic guided waves based on the detection process parameters, performs ultrasonic signal excitation according to the scheme, and acquires and saves ultrasonic echo data.

[0028] The ultrasonic testing data processing and calibration module implements:

[0029] Importing and exporting testing plans and testing data;

[0030] Denoising of guided wave signals;

[0031] Phase velocity-stress linear fitting calibration;

[0032] The residual stress inversion and result output module detects the phase velocity of composite material components with unknown stress and inverts the internal stress to obtain it.

[0033] Therefore, the present invention employs the above-described ultrasonic detection method and system for retrieving residual stress using acoustic wave phase velocity, and the beneficial technical effects are as follows:

[0034] (1) This invention can solve the key technical bottleneck in non-contact ultrasonic measurement. In practical applications, the measurement accuracy of the air segment distance in traditional air-coupled ultrasonic technology is difficult to guarantee. An air segment error of only 2 mm can lead to a stress detection error on the order of 100 MPa. Since it is difficult to reproduce the air segment conditions during calibration in engineering practice, the existing method of directly fitting stress through acoustic time is only suitable for in-situ detection and has serious limitations.

[0035] (2) This invention abandons the traditional air section measurement method and instead adopts a new technical route of directly measuring the phase velocity of the guided wave for stress coefficient fitting, which fundamentally eliminates the measurement error caused by air section fluctuations and greatly improves the reliability and accuracy of detection.

[0036] (3) Since the present invention eliminates the influence of air segment fluctuations, it is not only suitable for laboratory environments, but also meets the testing needs of engineering sites, providing a practical solution for residual stress testing of composite material structures. Attached Figure Description

[0037] Figure 1 Here are the dispersion curves of carbon fiber composite components with different fiber orientations, where... Figure 1 In the diagram, (a) represents the 0° fiber direction. Figure 1 In (b), the fiber orientation is 30°. Figure 1 (c) in the text represents the 60° fiber orientation. Figure 1 In this context, (d) represents the 90° fiber direction;

[0038] Figure 2 Figure 1 shows the COMSOL simulation model of carbon fiber composite components and the simulation results of guided wave propagation in the laminate. Figure 2 (a) in the figure is the COMSOL simulation model of the carbon fiber composite component; Figure 2 (b) in the figure shows the simulation results of guided wave propagation in the laminate.

[0039] Figure 3 A complete signal diagram received by an air-coupled ultrasonic transducer;

[0040] Figure 4 The relationship between stress and acoustic time at different locations of a pre-stressed carbon fiber specimen. Figure 4 In the diagram, (a) represents the 0° fiber direction. Figure 4 In (b), the fiber orientation is 30°. Figure 4 (c) in the text represents the 60° fiber orientation. Figure 4 In this context, (d) represents the 90° fiber direction;

[0041] Figure 5 This describes the relationship between stress and acoustic time at the same location on a pre-stressed carbon fiber specimen. Figure 5(a) in the diagram represents the complete signal. Figure 5 (b) in the diagram represents the locally amplified signal in region A;

[0042] Figure 6 This is a schematic diagram of the air-coupled ultrasonic guided wave testing fixture module.

[0043] Figure 7 This is a flowchart of an ultrasonic testing method that uses acoustic phase velocity to invert residual stress.

[0044] Figure Labels

[0045] 1. Air-coupled ultrasonic transducer; 2. Split transducer clamping component; 3. Turntable connector; 4. Angle rotation slide; 5. Slider; 6. Dovetail groove displacement slide; 7. Support bracket; 8. Casters; 9. Support base plate. Detailed Implementation

[0046] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0048] Example 1

[0049] This embodiment describes an air-coupled ultrasonic guided wave nondestructive testing method for carbon fiber composite components. The test sample is M40J carbon fiber with a layup of [0, 90, 0]. s The system consists of six carbon fiber layers with a total thickness of 0.8 mm. The fiber orientations of the carbon fiber composite tensile specimens are selected as 0°, 30°, 60°, and 90°. The specimen size is 450 mm × 60 mm × 0.8 mm. The transmitting transducer is a focusing transducer, and the receiving transducer is a planar transducer. Figure 7 As shown, the detection method includes the following steps:

[0050] Step S1: Determine the center frequency of the air-coupled transducer based on the material properties of the composite component and the requirements for testing accuracy.

[0051] When the ultrasonic frequency is low, the guided wave propagates at a longer wavelength in the composite material, resulting in lower sensitivity to residual stress and insufficient detection resolution. Conversely, at higher ultrasonic frequencies, the attenuation of the sound wave at the air-composite material interface increases significantly, and the propagation loss of high-frequency signals in carbon fiber composites intensifies, leading to a decrease in the signal-to-noise ratio of the received signal, which also affects detection accuracy. Therefore, it is necessary to comprehensively consider material properties, detection distance, and accuracy requirements to optimize the selection of the center frequency of the air-coupled transducer.

[0052] Specifically, by analyzing the waveguide dispersion characteristics of carbon fiber composite materials, dispersion curves are plotted for different fiber directions, such as... Figure 1 As shown, in actual experiments, the guided wave modes should be kept as pure as possible, i.e., only including... and Modal analysis is used to reduce the number of acoustic modes during detection and suppress interference from multimodal signal aliasing, thereby more accurately extracting the acoustic propagation time difference of the guided wave. Therefore, the center frequency of the air-coupled ultrasonic transducer should be lower than that of the mode without aliasing. The frequency corresponding to the modal Lamb wave, and also to distinguish between direct air waves and the required... For the modal Lamb wave signal, the center frequency of the air-coupled ultrasonic transducer should also be greater than the corresponding velocity of sound in air. The frequency values ​​in the modal, i.e. the center frequency, range from 15 to 960 kHz.

[0053] 100kHz, 200kHz, and 400kHz are typical operating frequency bands for air-coupled transducers. Studies have found that 200kHz signals experience significant attenuation during propagation, have a low signal-to-noise ratio, and are more sensitive to system errors in phase measurement; while 100kHz signals, although having a longer wavelength, possess better penetration and more stable phase characteristics, ensuring detection accuracy. Therefore, 100kHz is preferred as the center frequency for the air-coupled transducer.

[0054] Step S2, as follows Figure 2 As shown in (a), a waveguide simulation model of a carbon fiber composite laminate is established in COMSOL to simulate the propagation process of sound waves in the plate, as follows. Figure 2 (b) guides the design of stress detection process parameters.

[0055] In ultrasonic guided wave testing technology, the design of the incident angle is one of the key factors in achieving effective guided wave excitation. The choice of incident angle directly affects the mode conversion, propagation characteristics, and detection efficiency of the guided wave. When ultrasound enters a carbon fiber specimen from air, refraction and reflection occur at the interface between the two media. Changing the incident angle alters the energy distribution of the sound wave within the medium; therefore, it is necessary to select the optimal incident angle to obtain the strongest guided wave signal. Due to the laws of reflection and symmetry, the angles of the transmitting and receiving transducers should be consistent.

[0056] According to Snell's principle, in order to maximize the energy transfer of the guided wave, the optimal incident angle of the transducer should satisfy the following when air is used as the coupling medium:

[0057] ;

[0058] in, The speed of sound in air is 340 m / s. Indicates the waveguide phase velocity. This indicates the incident angle of the transducer. The required incident angles for components with a fiber direction of 0°, 30°, 60°, and 90° are 19°, 22°, 24°, and 24°, respectively.

[0059] Step S3: Utilize the stress detection process parameters of ultrasonic guided waves, including transducer frequency and type, and transducer incident angle. In addition, it also includes detection distance. Simulations show that in air-coupled guided wave detection, the ultrasonic waves excited by the transmitting transducer propagate directly to the receiving transducer through the air path, causing time-domain aliasing with the guided wave signal inside the medium, resulting in the guided wave signal being submerged by the direct wave. To suppress the interference of the direct air wave on the guided wave, the distance of the air section of the air-coupled transducer is assumed to be... The distance between the two air-coupled ultrasonic transducers Should meet:

[0060] ;

[0061] To ensure that the detection of all fiber angles can distinguish between the guided wave and the direct air wave, the minimum phase velocity value in each fiber direction of the used modal guided wave is substituted into the above formula, yielding a minimum detection distance of 170mm. Furthermore, for a 60° fiber angle component corresponding to the minimum phase velocity, an experimental verification was conducted using a detection distance of 170mm between the transmitting and receiving transducers. The received complete signal is as follows: Figure 3 As shown.

[0062] Step S4: To address the challenge of measuring acoustic time in the air-coupled section, a time-of-sound analysis method based on geometric positioning and time difference coordination is proposed. First, the transmitting and receiving transducers are fixed by adjusting the long bolts on the split transducer clamp 2. The transmitting slider is fixed, and the receiving slider 5 is adjusted on the dovetail groove displacement slide 6 to move the receiving transducer. After adjusting it to the corresponding position, the spacing between the transmitting and receiving transducers is fixed. The angles of the air-coupled ultrasonic transmitting and receiving transducers are adjusted using the turntable connector 3 and the angle rotation slide 4. The total propagation time of the guided wave through the composite material component and the air-coupled section is measured. The receiving transducer was then moved a fixed distance along the direction of sound wave propagation, and the new propagation time was measured. Using time difference operation Eliminate acoustic time interference in the air coupling section, obtain the propagation time difference of the guided wave in the composite material component, and combine it with displacement increment. The waveguide phase velocity in the composite material component can then be determined.

[0063] To reduce the systematic error caused by the change in the waveguide measurement spacing due to the moving transducer, this invention employs a successive difference method to measure the phase velocity of the waveguide. Specifically, the method involves using 2...n The spacing between the transmitter and receiver transducers is adjusted in a single step, increasing the spacing by one time. Acquire acoustic time difference data at different propagation distances, through n The phase velocity is calculated by successive differences, and the expression is:

[0064] , ;

[0065] ;

[0066] in, This represents the result calculated using the method of successive differences. The measurement location and the first Each measurement position corresponds to the phase velocity between measurement intervals. This indicates the final waveguide phase velocity; Indicates the position of the receiving probe. One measurement location, less than Integers;

[0067] Excessive measurement distance between the transmitting and receiving transducers leads to significant attenuation of high-frequency components in the guided wave and a shift in the dominant frequency of the guided wave between adjacent measurement points. Conversely, excessively short distances significantly increase the relative proportion of transducer positioning errors, amplifying the impact of distance measurement errors on the results and thus reducing the accuracy of sound velocity measurements. Considering all these factors, the following determination is made: , .

[0068] A tensile testing machine was used to apply different stresses to composite material components, ranging from 0 to 90 MPa in 10 MPa increments. Simultaneously, during the tensile process, an air-coupled ultrasonic guided wave testing fixture module was used to fix transducers and perform stress calibration on carbon fiber composite laminates with four different fiber orientations. The ultrasonic waves received by the transducers were transmitted to the main control computer via an air-coupled ultrasonic board for signal display and processing, thereby obtaining... Figure 4 The stress-time relationship curve is shown, and the signal waveform with a 0° fiber direction and a transducer spacing of 190 mm is plotted. Figure 5 Two significant linear trends can be observed in the figure: At any fixed stress level, the acoustic time value of the same phase guided wave signal increases linearly with increasing detection distance. This phenomenon conforms to the physical laws of sound wave propagation, verifying the reliability of the phase velocity measurement method. Furthermore, for any specific transducer spacing, the acoustic time decreases linearly with increasing stress, indicating that the linear relationship between the phase velocity of the ultrasonic guided wave and stress is stable. These two linear results confirm that the phase velocity of the ultrasonic guided wave can be used as an effective characterization parameter for stress. The corresponding phase velocities are measured, and a linear relationship between phase velocity and stress is fitted.

[0069] Step S5: Based on the relationship between phase velocity and composite material stress established in Step S4, a non-contact air-coupled ultrasonic testing system is used to perform stress inversion on the composite material component under unknown stress state. During the testing process, the position of the transmitting transducer is first fixed, and the receiving transducer receives guided wave signals from different positions to obtain the phase velocity of the composite material component under unknown stress state. The magnitude of residual stress in the material is then obtained by inversion according to the relationship.

[0070] Example 2

[0071] An ultrasonic testing system for retrieving residual stress using acoustic wave phase velocity includes:

[0072] Air-coupled ultrasonic guided wave testing fixture module ( Figure 6 The device comprises an air-coupled ultrasonic transducer 1, a split-type transducer clamp 2, a turntable connector 3, an angled rotary slide 4, a slider 5, a dovetail displacement slide 6, a load-bearing bracket 7, casters 8, and a support base plate 9. The main body of the transducer clamp is composed as follows: the split-type clamp 2 is rigidly connected via M4×70 bolts, thereby adjusting the height of the air-coupled ultrasonic transducer 1 from the test piece; the split-type transducer clamp 2 and the angled rotary slide 4 are connected by an acrylic turntable connector 3; the angled rotary slide 4 and the dovetail displacement slide 6 are bolted together via the slider 5. A lightweight, short aluminum profile load-bearing bracket 7 is connected to the dovetail displacement slide 6 and the support base plate 9 via boat-shaped nuts, enabling stepless adjustment of the detection height. Four casters 8 are installed at the bottom of the support base plate 9, allowing for convenient multi-directional movement of the air-coupled ultrasonic guided wave testing fixture module.

[0073] The stress preset and loading module mainly includes the DDL100 electronic universal testing machine, controller, and main control computer;

[0074] Ultrasonic signal excitation and acquisition module: Generates a residual stress detection scheme for air-coupled ultrasonic guided waves based on the detection process parameters, performs ultrasonic signal excitation according to the scheme, and acquires and saves ultrasonic echo data;

[0075] The ultrasonic testing data processing and calibration module implements:

[0076] Importing and exporting testing plans and testing data;

[0077] Denoising of guided wave signals;

[0078] Phase velocity-stress linear fitting calibration;

[0079] Residual stress inversion and result output module: performs phase velocity detection on composite material components with unknown stress and inverts the internal stress to obtain it.

[0080] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0081] Therefore, the present invention employs the ultrasonic detection method and system described above, which utilizes the phase velocity of acoustic waves to invert residual stress, and can accurately detect residual stress in composite material components.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity inversion, characterized in that, Includes the following steps: Step S1: Determine the center frequency of the air-coupled transducer based on the dispersion curve of the composite material waveguide. Step S2: Determine the incident angles of the transmitting transducer and the receiving transducer; Step S3: Based on the finite element model of air-coupled ultrasonic guided wave propagation, obtain the guided wave propagation path and design the detection spacing between the transmitting transducer and the receiving transducer. Step S4: Using the successive difference method that combines geometric positioning and time difference, the composite material component is prestressed by a tensile machine and the phase velocity of the ultrasonic guided wave is measured by an air-coupled ultrasonic guided wave detection system. The corresponding relationship between the phase velocity of the ultrasonic wave in the target composite material and the applied stress is established and calibrated. Step S5: Based on the corresponding relationship in step S4, perform phase velocity detection on the composite material component with unknown stress and invert the residual stress of the composite material component.

2. The ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity according to claim 1, characterized in that, In step S1, the guided wave dispersion curve is calculated using the anisotropic elastic matrix and density parameters of the composite material, and a conventional air-coupled transducer with a frequency lower than the cutoff frequency of the A1 mode and the smallest attenuation is selected.

3. The ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity inversion according to claim 1, characterized in that, In step S2, the phase velocity of mode A0 is determined based on the guided wave dispersion curve calculated in step S1, and the incident angle of the air-coupled transducer is calculated according to Snell's law in combination with the air speed of sound.

4. The ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity according to claim 1, characterized in that, In step S3, a two-dimensional finite element model is established to simulate the propagation characteristics of the guided wave acoustic field of the air-coupled transducer. The minimum detection spacing is determined based on the standard that the guided wave signal does not overlap with the direct air wave in the time domain.

5. The ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity according to claim 1, characterized in that, Step S4 includes the following steps: A stepped stress of 0-90 MPa was applied to the specimen on a tensile tester, with a single increment of 10 MPa. Phase velocity was measured using the successive difference method: the transmitting transducer was fixed, and the receiving transducer was moved. Next, single displacement increment Record the transmission time ; Calculate phase velocity: ， ； ； in, This represents the result calculated using the method of successive differences. The measurement location and the first Each measurement position corresponds to the phase velocity between measurement intervals. This indicates the final waveguide phase velocity; Indicates the position of the receiving probe. One measurement location, less than Integers; The phase velocity and stress are fitted into a linear relationship.

6. The ultrasonic detection method for retrieving residual stress using acoustic wave phase velocity inversion according to claim 1, characterized in that, In step S5, the phase velocity of the unknown stress member is measured and substituted into the linear relationship established in step S4 to generate the residual stress value at the corresponding point and in the fiber direction.

7. An ultrasonic testing system for implementing the method of any one of claims 1-6, characterized in that, include: The air-coupled ultrasonic guided wave testing fixture module is used to adjust the height of the air-coupled ultrasonic transducer from the test piece, the incident angle, and the detection distance between the transmitting transducer and the receiving transducer. The stress preset and loading module includes the DDL100 electronic universal testing machine, controller, and main control computer; The ultrasonic signal excitation and acquisition module generates a residual stress detection scheme for air-coupled ultrasonic guided waves based on the detection process parameters, performs ultrasonic signal excitation according to the scheme, and acquires and saves ultrasonic echo data. The ultrasonic testing data processing and calibration module implements: Importing and exporting testing plans and testing data; Denoising of guided wave signals; Phase velocity-stress linear fitting calibration; The residual stress inversion and result output module detects the phase velocity of composite material components with unknown stress and inverts the internal stress to obtain it.

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