Finite element simulation calculation method for acoustic elastic effect of Lamb wave in prestressed medium

Abstract

The invention discloses a finite element simulation calculation method for the acoustic elastic effect of a lamb wave in a prestressed medium, which can realize the simulation of the prestressed lamb wave in any waveguide section, and has the advantages of high simulation speed, random expansion of a simulation object and the like. In the implementation process of the method, the introduction of the Murnaghan hyperelastic constitutive model is realized by writing a VUMAT subprogram with a nonlinear characteristic; loading of prestress and acoustic disturbance is achieved through a quasi-static superposition dynamic analysis method; and pure Lamb wave feature extraction is realized through Lamb wave signal post-processing. The method fills the vacancy of a simulation method in the field of ultrasonic non-destructive testing, especially in guided wave detection research of residual stress, and has great potential.

Description

Technical Field

[0001] The invention relates to a finite element simulation calculation method for Lamb wave acoustic elastic effect in a prestressed medium, and belongs to the field of nondestructive testing. Background Art

[0002] Residual stress (working stress and residual stress) is one of the main causes of failure behaviors such as material cracking, fatigue, and deformation, and has a significant impact on the integrity of the material structure and service safety. Accurate and reliable residual stress state detection methods are the key to accurately evaluate this "invisible and intangible" defect.

[0003] Lamb wave is one of the guided waves. Ultrasonic Lamb wave is a stress wave formed by the coupling of longitudinal wave and transverse wave in a solid plate whose thickness is of the same order of magnitude as the wavelength of the excitation sound wave. As a typical acoustic guided wave mode propagating in plate structures, Lamb wave can realize stress detection of solid plates. Its penetration depth is about 1 wavelength. In the engineering field, due to its unique propagation characteristics, it has great advantages and development potential in stress information detection on the surface of components and within a certain depth range. In the non-patent literature [Zhang Yizheng, Lu Yan, Gao Jie, et al. Theoretical study on the propagation characteristics of acoustic elastic guided waves based on the series method [C] / / Beijing Mechanics Society. Proceedings of the 29th Academic Annual Conference of Beijing Mechanics Society. Beijing University of Technology;, 2023: 3. DOI: 10.26914 / c.cnkihy.2023.016943.], Zhang Yizheng et al. established a theoretical analysis model of acoustic elastic guided waves in prestressed media based on the acoustic elasticity theory and the Legendre series method (LOPE-Prestress Method), and studied the effect of prestress on basic modal guided waves.

[0004] Currently, there is a strong demand for residual stress detection in the engineering field. Considering the lack of finite element calculation methods for realizing the acoustic elastic effect in prestressed media in the current non-destructive testing field, the development of finite element simulation methods will help solve the current stress detection needs in non-destructive testing.

[0005] In response to the current demand for stress detection, the present invention innovatively proposes a finite element calculation method for realizing the Lamb wave acoustic elastic effect in prestressed media in ABAQUS simulation software, and successfully realizes the introduction of Lamb wave acoustic elastic effect in prestressed media, which fills the gap in the current stress detection in simulation modeling and has great potential for engineering application. Summary of the invention

[0006] In view of the shortcomings of existing simulation technology, the present invention proposes a finite element calculation method for realizing the acoustic elastic effect in prestressed media in ABAQUS simulation software, using ABAQUS's own VUMAT subroutine interface to define the nonlinear constitutive model of the material, and based on the Murnaghan acoustic elastic effect as a theory, through multi-analysis step loading, to realize the study of the propagation characteristics of Lamb waves under prestressed state in the simulation software. The present invention makes up for the gap in current stress detection in simulation modeling, helps to solve the problem of constantly changing stress conditions in defect detection in current non-destructive testing, and helps to compare and verify with experimental data, and has great potential for engineering application.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] The first aspect of the present invention provides a simulation calculation method for realizing the acoustic elastic effect in a prestressed medium, and the specific implementation steps of the method include the following:

[0009] Step 1: Establish the acoustic-elastic nonlinear constitutive equation and write the acoustic-elastic VUMAT subroutine;

[0010] Step 2: Establish a finite element model of the prestressed structure under Lamb wave disturbance;

[0011] Step 3: Set up quasi-static and transient analysis steps to simulate prestress and Lamb wave acoustic disturbance loading respectively, where the acoustic disturbance loading adopts symmetrical loading along the thickness direction;

[0012] Step 4: Call the VUMAT subroutine established in step 1 to perform calculation and solution;

[0013] Step 5: Extract the sound wave propagation signal and perform signal post-processing methods to extract the pure Lamb wave signal.

[0014] Furthermore, according to the established VUMAT subroutine of the acoustic-elastic nonlinear constitutive equation, the second-order and third-order elastic constants of the hyperelastic material are defined, and then the material density is defined through ABAQUS software to complete the addition of material properties to the simulation model.

[0015] Furthermore, symmetrical point load excitation points are set on the upper and lower surfaces of the material in the simulation model, and then the collection points of the Lamb wave signals are set and boundary conditions for displacement constraints are provided, including setting a fixed constraint on the left side of the model and constraining the displacement in the normal direction on the right side of the model.

[0016] Furthermore, the grid size is determined according to the geometric dimensions of the test piece and the center frequency of the excitation sensor, thereby completing the simulation modeling of the acoustic-elastic Lamb wave under prestress.

[0017] Furthermore, the Murnaghan hyperelastic material model is solved in multiple analysis steps, and the stress loading process is simulated by a quasi-static analysis method to reduce the interference of stress on the fluctuation. The Lamb acoustic wave disturbance process is simulated by a transient analysis method to achieve the simulation of the acoustic elastic Lamb wave under the prestressed state.

[0018] Furthermore, the Lamb wave signal obtained by simulation calculation is post-processed. By disabling the acoustic wave disturbance loading, the signal curve of the signal receiving point under the action of prestress is obtained. The obtained prestressed field signal is processed by difference with the fluctuation signal under the prestressed field, so as to complete the pure filtering of the data signal and eliminate the low-frequency disturbance interference caused by acoustic wave loading. Finally, the relationship between different stresses and Lamb wave signals is plotted. The transit time difference is calculated by the time corresponding to the peak value of the Lamb wave signal at different positions. Considering the elastic strain, the spatial distance between the two receiving points after the specimen is subjected to stress is calculated, and the wave velocity is calculated to study the propagation characteristics of Lamb waves under prestressed state.

[0019] The second aspect of the present invention provides a simulation analysis system for Lamb wave propagation characteristics under prestress based on the acoustic-elastic nonlinear VUMAT constitutive method, comprising:

[0020] The nonlinear acoustoelastic VUMAT subroutine module is configured to introduce the Murnaghan hyperelastic material constitutive model, establish the acoustoelastic nonlinear constitutive equation based on the Cauchy stress tensor, and write the acoustoelastic VUMAT subroutine through FORTRAN syntax to introduce the Murnaghan hyperelastic material constitutive model into ABAQUS;

[0021] The acoustic elastic Lamb wave modeling module is configured to determine the shape and size of the Murnaghan hyperelastic material, establish the geometric model of the Murnaghan hyperelastic material, and directly define the material density through the material property setting module in the ABAQUS software, while the second-order and third-order elastic constants of the material are added by custom user materials and defined by subroutines. Symmetrical point load excitation points are set in the material thickness direction and signal collection points at different positions on the upper surface of the material. The left side of the model adopts a completely fixed constraint, and the right side constrains the displacement in the normal direction. The grid size is determined according to the excitation frequency of the Lamb wave;

[0022] The acoustic-elastic Lamb wave simulation module under prestressed state is configured to solve the Murnaghan hyperelastic material model in multiple analysis steps, simulate the stress loading process through a quasi-static analysis method, and simulate the Lamb acoustic wave disturbance process through a transient analysis method to obtain the signal waveform of the Lamb wave;

[0023] The Lamb wave propagation characteristic analysis module under prestressed state is configured to post-process the Lamb wave signal obtained by simulation calculation to obtain a pure Lamb wave signal, and draw Lamb wave waveforms under different stresses. The transit time difference is calculated by the time corresponding to the peak value of the Lamb wave signal at different positions. Considering the elastic strain, the spatial distance between the two receiving points after the specimen is subjected to stress is calculated, and the wave velocity is calculated in this way, so as to study the propagation characteristics of Lamb waves under prestressed state.

[0024] One or more of the above technical solutions have the following beneficial results:

[0025] (1) The present invention embeds the acoustic-elastic nonlinear constitutive VUMAT subroutine into the ABAQUS simulation software to implement a finite element calculation method for the acoustic-elastic effect in prestressed media, thus making up for the limitation that the nonlinear acoustic-elastic constitutive model cannot be added in the traditional ABAQUS simulation.

[0026] (2) The present invention can accurately simulate the stress loading process and acoustic wave disturbance process of the Murnaghan hyperelastic material model through a multi-step analysis step combined with quasi-static loading and transient loading, and obtain a pure Lamb wave signal by subtracting the Lamb acoustic wave signal under the prestressed field from the pure prestressed field signal. The simulated Lamb wave signal result can be accurately obtained to study the propagation characteristics of the Lamb wave in the prestressed medium, and the changes in the propagation characteristics of the Lamb wave such as waveform and wave velocity under different stress levels can be obtained, which provides a simulation technology reference for ultrasonic stress detection and fills the gap in the current ultrasonic stress detection in simulation modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is the flow chart of the overall simulation modeling.

[0028] Figure 2 This is a schematic diagram of the simulation model of ABAQUS. A fixed constraint is used on the left side of the figure, and a fixed normal direction constraint is used on the right side. The signal collection point 1 is 10 mm away from the excitation point, and the signal collection point 2 is 20 mm away from the excitation point. The two signal collection points are 10 mm apart.

[0029] Figure 3 It is a "two-step" quasi-static load application method proposed in the simulation process. Load1 represents the application of prestress, and Load2 represents the point load applied to excite Lamb waves.

[0030] Figure 4 It is the time domain waveform result extracted by simulation and the time domain signal diagram after filtering, including the original Lamb wave signal under different stresses obtained by simulation and the filtered Lamb wave signal.

[0031] Figure 5This is a comparison of the peak positions of Lamb wave time domain signals under different stresses.

[0032] Figure 6 This is a comparison chart between simulation calculation results and theoretical calculation results. DETAILED DESCRIPTION

[0033] The specific implementation modes of the present invention are further described below in conjunction with the accompanying drawings and examples. The following examples are only illustrative rather than restrictive and cannot be used to limit the protection scope of the present invention.

[0034] like Figure 1 The overall flow chart of the finite element simulation calculation method for Lamb wave acoustic elastic effect in prestressed media is shown in the figure. The model is built in ABAQUS simulation software.

[0035] The first step is to establish the acoustic-elastic nonlinear constitutive equation, and use the invented ABAQUS simulation software to import the simulation model and assign the material to Murnaghan hyperelastic material, so as to realize the nonlinear change of the simulation.

[0036] Based on ABAQUS's own subroutine VUMAT and the Murnaghan acoustic-elastic effect theory, a nonlinear constitutive equation that conforms to the acoustic-elastic effect is constructed to complete the simulation modeling of the acoustic-elastic effect in the prestressed plate.

[0037] By expanding the strain energy function to the third order of the strain tensor, the effect of acoustic elasticity on wave velocity can be considered. The Murnaghan model is referenced. In ABAQUS / Explicit, VUMAT can use Murnaghan's nonlinear strain energy function W(E) to define mechanical constitutive behavior. However, in ABAQUS / Explicit, the stress in VUMAT of ABAQUS / Explicit is the Cauchy stress tensor under the Green–Naghdi criterion, which can be expressed as:

[0038]

[0039] Where R is the rotation tensor and R -1 =R T .

[0040] Therefore, based on the Cauchy stress tensor, Murnaghan's nonlinear strain energy function is transformed and can be expressed as:

[0041]

[0042] Where F is the deformation gradient; J = detF; T is the second Piola–Kirchhoff stress; and U is the right tensile tensor.

[0043] In the subsequent simulation study, a nonlinear elastic material model is required, but this material model does not exist in ABAQUS. Therefore, the VUMAT subroutine is used to add the required constitutive model through secondary development. The required isotropic nonlinear elastic constitutive model is the Cauchy stress tensor under the Green–Naghdi benchmark. At the same time, the stress formula in the VUMAT subroutine must be stored in stressNew(i) in the form of t+Δt at the end, so as to derive the stress increment recursive calculation formula, compile the code in FORTRAN language, and complete the call in ABAQUS. At the end of the previous step in the simulation calculation, the stress value in the subroutine is used as the initial value for the constitutive model calculation, and then the next integration step is performed to obtain the wave velocity state of the stress at the characteristic point, and complete the stress state detection of the specimen.

[0044] Figure 2 This is a schematic diagram of the simulation model structure of the present invention. During the modeling process, the design model size is 120mm×1mm ( Figure 2 ), in order to excite the Lamb wave of S0 mode, symmetrical point load loading points are set on the upper and lower surfaces of the material. The excitation signal is a five-cycle sine signal modulated by Hanning window with a center frequency of 250kHz. From left to right, points at 10mm (set as point 1) and 20mm (set as point 2) are set as receiving sources ( Figure 2 ).

[0045] Material properties are added to the model according to the material properties of aluminum. Except for the density (2704kg*m-3), the remaining properties (λ=54.3GPa, μ=27.2GPa, l=-281.5Gpa, m=-339.0Gpa, n=-416.0GPa) are added by custom user materials and defined by the VUMAT subroutine.

[0046] According to the quasi-static analysis method, the load is applied in a low load speed and smooth and gentle slope manner, such as Figure 3 Taking the prestress of 100 MPa as an example, in the analysis step 1, the load is slowly increased from zero to 100 MPa in 0.001 s, and in the analysis step 2, the load of 100 MPa is maintained constant for 0.00004 s. The applied load is as follows: Figure 2 It is applied to the right side of the model and exists in both analysis steps. The excitation signal is applied by the reserved point, and the application method is to apply symmetrical point load excitation on the upper and lower surfaces of the material, such as Figure 2 , and only exists in the second analysis step. The added receiving source is applied by the reserved point as follows Figure 2 , and it also only exists in the second analysis step.

[0047] According to the simulation requirements, the model needs to be built based on the principle of the stretching machine, such as Figure 2 The fully fixed boundary condition is applied to the left side of the model, and the normal axis displacement is fixed to 0 on the right side of the model.

[0048] The grid size is determined according to the geometric dimensions of the test piece and the central frequency of the excitation sensor, which is defined as 0.1 mm here. The grid properties are also determined, and dynamic plane strain is defined here.

[0049] The simulation results are as follows Figure 4 (a), from the waveform results, it can be seen that the time is not collected from zero. This is because the quasi-static analysis method requires multiple analysis steps to simulate, and the collection is performed in the second analysis step, so the time is taken from the end time of the previous analysis step. The waveform fluctuates severely in amplitude. Therefore, the quasi-static response filter is used to eliminate the time difference and amplitude fluctuation to obtain a pure static Lamb wave. Figure 4 (c), the specific post-processing is to disable the three-cycle Hanning window modulated pulse signal, and only retain the prestressed field signal in the time domain. Figure 4 (b) The obtained prestressed field signal and the fluctuation signal under the prestressed field are processed and the time used in the first step of the analysis is subtracted to complete the pure filtering of the data signal. Figure 4 (c) By changing different levels of prestress and repeating the above operation, the Lamb wave signal under different prestress states can be filtered to obtain Figure 5 The Lamb wave time domain waveform under different stresses shown in the figure clearly shows that the peak position of the Lamb wave signal shifts as the stress increases. The transit time difference is calculated by the time corresponding to the peak value of the waveform at two different positions. Taking into account the elastic strain, the spatial distance between the two receiving points after the specimen is subjected to stress is calculated, and the wave velocity is calculated and compared with the theoretical calculation result. The results are shown in Figure 6 As shown in the figure, there is a linear correlation between the wave velocity of Lamb wave and stress, and the change trend of the simulation results is the same as the theoretical calculation results. At this time, the relative error between the simulation results and the theoretical results is 0.1%, which meets the error requirements of the simulation, indicating the correctness and reliability of the established finite element simulation model of acoustic-elastic Lamb waves in prestressed media.

Claims

1. A finite element simulation calculation method for Lamb wave acoustic elastic effect in a prestressed medium, the specific implementation steps of the method include the following: Step 1: Derive and establish the acoustic-elastic nonlinear constitutive equation and write the acoustic-elastic VUMAT subroutine; Step 2: Establish a finite element model of the prestressed structure under Lamb wave acoustic disturbance; Step 3: "Two-step method" loading, setting quasi-static and transient analysis steps to simulate prestressing and Lamb wave acoustic disturbance loading respectively, where the acoustic disturbance loading adopts symmetrical loading along the thickness direction; Step 4: Call the VUMAT subroutine established in step 1 to perform calculation and solution; Step 5: Extract the sound wave propagation signal and perform post-processing on the signal to extract the pure Lamb wave signal; Lamb wave waveform signal curves under different stresses are drawn based on the post-processed Lamb wave signals. The transit time difference is calculated by the time corresponding to the peak values ​​of the two waveforms at different positions. Considering the elastic strain, the spatial distance between the two receiving points after the specimen is subjected to stress is calculated, and the wave velocity is calculated in this way. The changing law of Lamb wave velocity under different stress states can then be studied.

2. The finite element simulation calculation method for Lamb wave acoustic elastic effect in a prestressed medium according to claim 1, characterized in that: The Murnaghan hyperelastic constitutive model is introduced by writing an acoustic-elastic VUMAT subroutine with nonlinear characteristics and inserting it into ABAQUS software.

3. The finite element simulation calculation method for Lamb wave acoustic elastic effect in a prestressed medium according to claim 1, characterized in that: "Two-step method" loading, set two analysis steps, one analysis step is to apply stress through quasi-static analysis method, and the other analysis step is to apply acoustic wave disturbance through transient analysis method.

4. The finite element simulation calculation method for Lamb wave acoustic elastic effect in a prestressed medium according to claim 1, characterized in that: By disabling acoustic disturbance loading, a signal curve of the signal receiving point under prestress is obtained; the obtained prestressed field signal is processed by difference with the fluctuation signal under the prestressed field to complete the pure filtering of the data signal and eliminate the low-frequency disturbance interference caused by acoustic wave loading.

5. The simulation analysis system of Lamb wave propagation characteristics under prestress based on the acoustic-elastic nonlinear VUMAT constitutive model is characterized by: include: The nonlinear acoustoelastic VUMAT subroutine module is configured to introduce the Murnaghan hyperelastic material constitutive model, establish the acoustoelastic nonlinear constitutive equation based on the Cauchy stress tensor, and write the acoustoelastic VUMAT subroutine through FORTRAN syntax to introduce the Murnaghan hyperelastic material constitutive model into ABAQUS; The acoustic-elastic Lamb wave modeling module is configured to determine the shape and size of the Murnaghan hyperelastic material, establish the geometric model of the Murnaghan hyperelastic material, and directly define the material density through the material property setting module in the ABAQUS software, while the second-order and third-order elastic constants of the material are added by custom user materials and defined through the VUMAT subroutine; symmetrical point load excitation points are set in the material thickness direction and signal collection points at different positions on the upper surface of the material. The left side of the model adopts a completely fixed constraint, and the right side constrains the displacement in the normal direction. The grid size is determined according to the excitation frequency of the Lamb wave; The prestress and acoustic wave disturbance loading module is configured to perform multi-step analysis on the Murnaghan hyperelastic material model, simulate the stress loading process through a quasi-static analysis method, and simulate the Lamb acoustic wave disturbance process through a transient analysis method. Finally, the calculation is submitted to output the signal waveform of the Lamb wave, and the propagation characteristics of the Lamb wave under prestress are obtained. The simulation result post-processing module is configured to post-process the Lamb wave signal obtained by simulation calculation to obtain a pure Lamb wave signal, and draw Lamb wave waveforms under different stresses; calculate the transit time difference through the time corresponding to the peak value of the Lamb wave signal at different positions, and calculate the spatial distance between the two receiving points after the specimen is subjected to stress while considering the elastic strain, so as to calculate the wave velocity, and then study the propagation characteristics of the Lamb wave under the prestressed state.

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