A finite element simulation calculation method for prestressed medium lamb wave acoustic-elastic effect

Abstract

The application discloses a finite element simulation calculation method of prestressed medium Lamb wave acoustic-elastic effect, which can realize prestressed Lamb wave simulation in an arbitrary waveguide section, has the advantages of fast simulation speed, and the simulation object can be arbitrarily extended and the like. In the implementation process of the application, the introduction of a Murnaghan super-elastic constitutive model is realized by compiling a VUMAT subprogram with nonlinear characteristics; the loading of prestress and acoustic wave disturbance is realized by 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 gap of simulation methods in the field of ultrasonic nondestructive testing, especially in the research of residual stress guided wave detection, and has great potential.

Description

TECHNICAL FIELD

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

[0002] Residual stress (working stress and residual stress) is one of the main reasons for causing material cracking, fatigue, deformation and other failure behaviors, and has an important influence on the integrity of material structure and service safety. An accurate and reliable residual stress state detection means is the key to accurately evaluating such invisible and intangible defects.

[0003] Lamb wave is one of guided waves, and ultrasonic Lamb wave is a stress wave formed by the mutual coupling of longitudinal waves and transverse waves in a solid plate with a thickness and an excited acoustic wave wavelength being the same order of magnitude. As a typical acoustic guided wave mode propagating in a plate structure, Lamb wave can realize stress detection of the solid plate. The penetration depth is about 1 wavelength, and in the engineering field, the stress information detection of the component surface layer and a certain depth range has great advantages and development potential due to the unique propagation characteristics. Zhang Yizheng et al. in the non-patent literature

Zhang Yizheng, Lv Yan, Gao Jie, et al. Theoretical research on acoustic-elastic guided wave propagation characteristics based on series method [C] / / Beijing Society of Mechanics. Proceedings of the 29th Academic Conference of Beijing Society of Mechanics. Beijing University of Technology; 2023:3. DOI:10.26914 / c.cnkihy.2023.016943.

[0004] At present, the detection demand of residual stress in the engineering field is strong, and considering that the current nondestructive testing field lacks a finite element calculation method for realizing acoustic-elastic effect in prestressed medium, developing a finite element simulation method is helpful to solve the demand of stress detection in the current nondestructive testing.

[0005] In view of the existing stress detection demand, the application innovatively proposes a finite element calculation method for realizing Lamb wave acoustic-elastic effect in prestressed medium in ABAQUS simulation software, successfully realizes the introduction of Lamb wave acoustic-elastic effect in prestressed medium, fills the gap of current stress detection in simulation modeling, and has great engineering application potential. SUMMARY

[0006] In view of the deficiencies of the existing simulation technology, the application provides a finite element calculation method for realizing the acoustic-elastic effect in a prestressed medium in an ABAQUS simulation software, defines the nonlinear constitutive of the material by using the VUMAT subprogram interface of ABAQUS itself, and realizes the research on the Lamb wave propagation characteristics in the prestressed state in the simulation software according to the Murnaghan acoustic-elastic effect theory through multi-analysis step loading. The application fills the gap in the simulation modeling of the current stress detection, helps to solve the problem of the changing stress conditions in the defect detection in the current nondestructive testing, and helps to compare and verify with the experimental data, and has great engineering application potential.

[0007] In order to achieve the above-mentioned purpose, the application is realized by the following technical scheme:

[0008] The first aspect of the application 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 one: establishing an acoustic-elastic nonlinear constitutive equation and writing an acoustic-elastic VUMAT subprogram;

[0010] Step two: establishing a prestressed measured structure finite element model under the disturbance of Lamb wave sound wave;

[0011] Step three: setting the quasi-static and transient analysis steps to simulate the prestress and Lamb wave disturbance loading respectively, wherein the acoustic disturbance loading is symmetrically loaded along the thickness direction;

[0012] Step four: calling the VUMAT subprogram established in step one to calculate and solve;

[0013] Step five: extracting the acoustic wave propagation signal and performing signal post-processing method to extract the pure Lamb wave signal.

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

[0015] Further, the symmetric point excitation points are set on the upper and lower surfaces of the material in the simulation model, then the Lamb wave signal collection points are set and the boundary conditions of displacement constraint are provided, including setting the 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] Further, the grid size is determined according to the geometric size of the tested piece and the center frequency of the excitation sensor, so as to complete the simulation modeling of the acoustic-elastic Lamb wave under the prestress.

[0017] Further, the Murnaghan super-elastic material model is solved by multiple analysis steps, the stress loading process is simulated by a quasi-static analysis method to reduce the interference of stress on wave, and the Lamb wave disturbance process is simulated by a transient analysis method to realize the simulation of acoustic-elastic Lamb wave under prestress state.

[0018] Further, the Lamb wave signal obtained by simulation calculation is post-processed. The signal curve of the signal receiving point subjected to the prestress effect is obtained by disabling the acoustic wave disturbance loading. The prestress field signal is subtracted from the wave signal under the prestress field to complete the pure filtering of the data signal and eliminate the low-frequency disturbance interference caused by the acoustic wave loading. Finally, a relationship diagram of different stresses and Lamb wave signals is drawn. The time corresponding to the peak value of the Lamb wave signal at different positions is calculated to obtain the transit time difference, the spatial distance between the two receiving points after the test piece bears stress is calculated under the consideration of elastic strain, and the wave velocity is calculated to study the propagation characteristics of the Lamb wave under the prestress state.

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

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

[0021] The acoustic-elastic Lamb wave modeling module is configured to determine the shape and size of the Murnaghan super-elastic material, establish the Murnaghan super-elastic material geometric model, directly define the material density through the material attribute setting module in the ABAQUS software, and add the second-order and third-order elastic constants of the material by the self-defined user material and defined by the subroutine. Symmetric point load excitation points are set in the thickness direction of the material, and signal acquisition points are set at different positions on the upper surface of the material. The left side of the model is fully fixed, and the right side is constrained 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 the prestress state is configured to solve the Murnaghan super-elastic material model by multiple analysis steps, simulate the stress loading process by a quasi-static analysis method, simulate the Lamb wave disturbance process by a transient analysis method, and obtain the signal waveform of the Lamb wave;

[0023] The prestress state Lamb wave propagation characteristic analysis module is configured to post-process the simulated Lamb wave signal to obtain a pure Lamb wave signal, and draw a Lamb wave waveform graph under different stresses, calculate the time corresponding to the peak value of the Lamb wave signal under different positions to obtain the time difference, and calculate the spatial distance between the two receiving points after the test piece bears stress under the consideration of elastic strain, so as to calculate the wave velocity, and then the propagation characteristics of the Lamb wave under the prestress state can be studied.

[0024] The above one or more technical solutions have the following beneficial results:

[0025] (1) The prestress medium acoustic-elastic nonlinear constitutive VUMAT subprogram developed twice is embedded into the ABAQUS simulation software to realize the finite element calculation method of the acoustic-elastic effect in the prestress medium, which makes up for the limitation that the traditional ABAQUS simulation cannot add the nonlinear acoustic-elastic constitutive model.

[0026] (2) The prestress field Lamb wave signal and the pure prestress field signal are subtracted to obtain a pure Lamb wave signal, and the simulated Lamb wave signal result can be accurately obtained to study the propagation characteristics of the Lamb wave in the prestress medium and obtain the changes of the waveforms, wave velocities and other propagation characteristics of the Lamb wave under different stress levels, which provides a simulation technical reference for ultrasonic stress detection and makes up for the vacancy of the current ultrasonic stress detection in simulation modeling. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a flow chart of the whole simulation modeling.

[0028] Figure 2 is a simulation model schematic diagram of ABAQUS, in which the left side adopts fixed constraints, the right side is fixed in the normal direction, the signal collection point 1 is 10mm away from the excitation point, the signal collection point 2 is 20mm away from the excitation point, and the distance between the two signal collection points is 10mm.

[0029] Figure 3 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 the Lamb wave.

[0030] Figure 4 is a time domain waveform result extracted in the simulation and a time domain signal graph after filtering, including the original Lamb wave signal obtained in the simulation under different stresses and the Lamb wave signal after filtering.

[0031] Figure 5is a contrastive drawing of the peak position of the Lamb wave time domain signal under different stresses.

[0032] Figure 6 is a contrastive drawing of the simulation result and the theoretical calculation result. DETAILED DESCRIPTION

[0033] The specific embodiments of the present application are further described below in conjunction with the accompanying drawings and examples, and the following examples are only descriptive and not restrictive, and cannot limit the protection scope of the present application.

[0034] As Figure 1 is the overall flow chart of the finite element simulation calculation method of the Lamb wave acoustic-elastic effect in the prestressed medium. Modeling is carried out in the ABAQUS simulation software.

[0035] Firstly, the acoustic-elastic nonlinear constitutive equation is established, and the ABAQUS simulation software is used to import the simulation model by setting the subprogram to give the material as Murnaghan super-elastic material, so as to realize the nonlinear change of simulation.

[0036] According to the ABAQUS own subprogram VUMAT, the nonlinear constitutive equation of the acoustic-elastic effect is constructed based on the Murnaghan acoustic-elastic effect theory, and the acoustic-elastic effect simulation modeling in the prestressed plate is completed.

[0037] By extending the strain energy function to the third order of strain tensor, the influence of acoustic-elasticity on wave speed can be considered. Murnaghan model is cited. In ABAQUS / Explicit, VUMAT can define the mechanical constitutive behavior of Murnaghan nonlinear strain energy function W(E). But in ABAQUS / Explicit, the stress in VUMAT of ABAQUS / Explicit is the Cauchy stress tensor under the Green-Naghdi standard, which can be expressed as:

[0038]

[0039] In the formula, R is a rotation tensor and R -1 = R T .

[0040] Therefore, based on the Cauchy stress tensor, the nonlinear strain energy function of Murnaghan is converted, which can be expressed as:

[0041]

[0042] In the formula, F is the deformation gradient; J = detF; T is the second Piola-Kirchhoff stress; U is the right stretch tensor.

[0043] In the subsequent simulation study, the nonlinear elastic material model needs to be used, and there is no such material model in ABAQUS, so 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 basis, and 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, and the code is compiled in FORTRAN language, and the calling is completed in ABAQUS. The stress value in the subroutine at the end of the simulation calculation in the previous step is used as the initial value of the constitutive model calculation, and then the next integration step is carried out, so as to obtain the stress wave velocity state of the feature point, and the stress state detection of the specimen is completed.

[0044] Figure 2 The simulation model structure of the application is shown in the figure, in the modeling process, the model size is designed as 120mm*1mm( Figure 2 ), in order to excite the S0 mode of Lamb wave, the symmetric point load is set on the upper and lower surfaces of the material, the excitation signal is a five-period sine signal modulated by Hanning window, the center frequency is 250kHz, and the points at 10mm (set as No. 1 point) and 20mm (set as No. 2 point) from left to right are set as receiving sources. Figure 2

[0045] According to the material performance of aluminum, the material properties of the model are added, and the properties are directly defined by the software except the density (2704kg*m-3), and the remaining performances (λ=54.3GPa, μ=27.2GPa, l=-281.5Gpa, m=-339.0Gpa, n=-416.0GPa) are added by the user-defined material, and are defined by the VUMAT subroutine.

[0046] According to the method of quasi-static analysis, the load is applied in the form of low load speed and smooth ramp, such as Figure 3 Taking prestress 100MPa as an example, in analysis step 1, the load is slowly increased from zero to 100MPa in 0.001s, and in analysis step 2, the load of 100MPa is kept unchanged in 0.00004s, and the applied load is as follows Figure 2 The excitation signal is applied by the reserved point, and the excitation is applied in the form of symmetric point load 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, such as Figure 2 , and also only exists in the second analysis step.

[0047] According to the simulation requirements, the model needs to be modeled according to the principle of the drawing machine, such as​Figure 2 The left side of the model applies a complete fixed boundary condition, and the right side of the model is fixed to 0 in the normal axis displacement.

[0048] The grid size is determined according to the geometric size of the test piece and the center frequency of the excitation sensor, which is defined as 0.1 mm, and the grid attribute is determined, which is defined as dynamic plane strain.

[0049] The simulation results are as shown in Figure 4 (a). From the waveform results, it can be seen that the time is not collected from zero point, because the quasi-static analysis method needs to simulate multiple analysis steps, and the collection is performed in the second analysis step, so the time before the end time of the previous analysis step is taken as the starting point. The waveform fluctuates seriously in amplitude. Therefore, the difference in time and the fluctuation in amplitude are eliminated by quasi-static response filtering to obtain pure static Lamb waves as shown in Figure 4 (c). The specific post-processing is to disable the three-cycle Hann window modulated pulse signal, and the time domain signal only retains the signal of the prestressed field as shown in Figure 4 (b). The obtained prestressed field signal is processed with the fluctuating signal under the prestressed field, and the time used in the analysis step is reduced, so as to complete the pure filtering of the data signal to obtain Figure 4 (c). Change the prestress of different levels and repeat the above operation, and by processing the Lamb wave signals under different prestress states by the above filtering, the Lamb wave time domain waveform diagrams under different stresses as shown in Figure 5 can be obtained. It can be seen that the peak position of the Lamb wave signal shifts with the increase of stress. The time corresponding to the peak values of the waveforms at two different positions is calculated to obtain the difference in transit time, and the spatial distance between the two receiving points after the test piece is subjected to stress is calculated under the consideration of elastic strain, so as to calculate the wave velocity and compare it with the theoretical calculation result. The results are shown in Figure 6 . The wave velocity of the Lamb wave has a linear correlation with the stress, the change trend of the simulation result is the same as that of the theoretical calculation result, at this time, the relative error between the simulation result and the theoretical result is 0.1%, which meets the error requirement of the simulation, and it proves the correctness and reliability of the established finite element simulation model of the acoustic elastic Lamb wave in the prestressed medium.

Claims

1. A finite element simulation method for Lamb wave acoustic elastic effect in prestressed media, 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 disturbance; Step 3: Two-step loading: Set up quasi-static and transient analysis steps to simulate prestressing and Lamb wave acoustic perturbation loading, respectively. The acoustic perturbation loading adopts symmetrical loading along the thickness direction. Step 4: Call the VUMAT subroutine created in step 1 to perform calculations and solutions; Step 5: Extract the sound wave propagation signal and perform post-processing on the signal to extract the pure Lamb wave signal; Based on the post-processed Lamb wave signal, the Lamb wave waveform signal curves under different stresses are drawn. The transit time difference is calculated by the time corresponding to the peaks of the two waveforms at 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 based on this. Then, the variation law of the Lamb wave velocity under different stress states can be studied. The "two-step method" loading method includes setting up two analysis steps. One analysis step is used to apply stress through the quasi-static analysis method, and the other analysis step is used to apply acoustic perturbations through the transient analysis method. By disabling acoustic disturbance loading, a signal curve of the signal receiving point subjected to prestressing is obtained; the obtained prestressed field signal is subjected to a difference process 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 loading.

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 the acoustic-elastic VUMAT subroutine with nonlinear characteristics and inserting it into ABAQUS software.

3. The simulation and 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 using 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 and establish the geometric model of the Murnaghan hyperelastic material. The material density is directly defined 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 are set at different positions on the material surface. The left side of the model adopts a fully fixed constraint, and the right side constrains the normal direction displacement. The mesh size is determined according to the excitation frequency of the Lamb wave. The prestressed and acoustic wave perturbation loading module is configured to perform a multi-step analysis of the Murnaghan hyperelastic material model. It simulates the stress loading process using a quasi-static analysis method and the Lamb acoustic wave perturbation process using a transient analysis method. Finally, the calculation is submitted and the Lamb wave signal waveform is output to obtain the Lamb wave propagation characteristics under prestressed conditions. 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 plot the Lamb wave waveform under different stresses. The transit time difference is calculated based on the time corresponding to the Lamb wave signal peak at 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 to calculate the wave velocity, which can then be used to study the propagation characteristics of the Lamb wave under prestressed state. The "two-step method" loading method includes setting up two analysis steps. One analysis step is used to apply stress through the quasi-static analysis method, and the other analysis step is used to apply acoustic perturbations through the transient analysis method. By disabling acoustic disturbance loading, a signal curve of the signal receiving point subjected to prestressing is obtained; the obtained prestressed field signal is subjected to a difference process 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 loading.

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