A finite element simulation method for the acoustic-elastic effect of Rayleigh wave in a prestressed semi-infinite medium

Abstract

The application discloses a finite element simulation calculation method of Rayleigh wave acoustic-elastic effect in a prestressed semi-infinite medium, which can realize prestressed Rayleigh wave simulation in an arbitrary waveguide section, has the advantages of fast simulation speed, and the simulation object can be arbitrarily extended. By writing a VUMAT subprogram with nonlinear characteristics, the introduction of a Murnaghan hyperelastic constitutive model is realized. Through a quasi-static superposition dynamic analysis method, the prestress and acoustic wave disturbance are loaded. Through Rayleigh wave signal post-processing, pure Rayleigh wave feature extraction is realized. The method fills the gap of simulation methods in the field of ultrasonic nondestructive testing, especially in the tomographic detection of residual stress, and has great potential.

Description

TECHNICAL FIELD

[0001] The application relates to a finite element simulation calculation method of Rayleigh wave acoustic-elastic effect in a prestressed semi-infinite 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 method is the key to accurately evaluating such invisible and intangible defects.

[0003] Surface wave, also known as Rayleigh wave, is a special guided wave that can propagate along the surface of a component and has a penetration depth of about one wavelength. In the engineering field, due to its unique propagation characteristics, it has great advantages and development potential in stress information detection of the surface layer and a certain depth range of the component. Zhang et al. developed a theoretical calculation model of acoustic-elastic Rayleigh wave in a non-patent document

Zhang Y, Lyu Y, Gao J, et al. A novel method for stress measurement utilizing the Rayleigh wave virtual superimposed interference spectrum [J]. NDT & E International, 2024, 146: 103169.

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

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

[0006] In view of the shortcomings of the existing simulation technology, the application provides a finite element calculation method for realizing the acoustic-elastic effect in a prestressed semi-infinite medium in 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 Rayleigh 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 realize the above-mentioned purpose, the application is realized by the following technical scheme:

[0008] The application provides a simulation calculation method for realizing the acoustic-elastic effect in a prestressed semi-infinite 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 finite element model of a prestressed measured structure under the disturbance of a Rayleigh wave;

[0011] Step three: setting a quasi-static and transient analysis step to simulate prestress and Rayleigh wave disturbance loading respectively;

[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 Rayleigh 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, according to the actual geometric size of the test piece, an absorbing boundary is added to the lower surface of the test piece, the thickness of each layer of the absorbing boundary is 0.1mm, the length is consistent with the length of the side of the test piece, a total of 16 layers are provided, and the semi-infinite medium environment is simulated to meet the conditions of Rayleigh wave propagation.

[0016] Further, in the simulation model, Rayleigh acoustic wave point load excitation points and Rayleigh wave signal collection points are set, and boundary conditions for providing displacement constraints are set, including setting fixed constraints on the left side of the model and constraining the displacement in the normal direction on the right side of the model, determining the grid size according to the geometric size of the tested piece and the center frequency of the excitation sensor, and then completing the simulation modeling of the acoustoelastic Rayleigh wave under prestress.

[0017] Further, the Murnaghan hyperelastic 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 Rayleigh acoustic wave disturbance process is simulated by a transient analysis method to realize the simulation of the acoustoelastic Rayleigh wave under prestress.

[0018] Further, the Rayleigh 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 obtained 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 Rayleigh wave signals is drawn. The time corresponding to the peak value of the Rayleigh wave signal at different positions is used to calculate the time difference, and the spatial distance between the two receiving points after the test piece bears stress is calculated under the consideration of elastic strain, so as to calculate the wave velocity, and then the propagation characteristics of the Rayleigh wave under prestress can be studied.

[0019] The second aspect of the present application provides a simulation analysis system for the propagation characteristics of Rayleigh wave under prestress based on the acoustoelastic nonlinear VUMAT constitutive model, 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 the FORTRAN syntax to introduce the Murnaghan hyperelastic material constitutive model into ABAQUS;

[0021] The acoustoelastic Rayleigh wave modeling module is configured to determine the shape size of the Murnaghan hyperelastic material, establish the Murnaghan hyperelastic 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. An absorbing layer is set at the bottom of the hyperelastic material to simulate a semi-infinite medium environment. Point load excitation points and signal collection points at different positions are set, the left side of the model is completely fixed, the right side is constrained in the normal direction, and the grid size is determined according to the geometric size of the tested piece and the center frequency of the excitation sensor;

[0022] The acoustic-elastic Rayleigh wave simulation module under 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 Rayleigh acoustic wave disturbance process by a transient analysis method, and obtain the signal waveform of the Rayleigh wave;

[0023] The Rayleigh wave propagation characteristic analysis module under prestress state is configured to post-process the Rayleigh wave signal obtained through simulation calculation to obtain a pure Rayleigh wave signal, draw the Rayleigh wave waveform diagram under different stresses, calculate the time difference of the Rayleigh wave signal peak value at different positions, calculate the spatial distance between the two receiving points after the test piece bears stress under the consideration of elastic strain, and calculate the wave velocity, so as to study the propagation characteristics of the Rayleigh wave under the prestress state.

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

[0025] (1) The 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 prestressed semi-infinite medium, which makes up for the limitation that the traditional ABAQUS simulation cannot add a nonlinear acoustic-elastic constitutive model.

[0026] (2) The stress loading process and the acoustic wave disturbance process of the Murnaghan super-elastic material model can be accurately simulated by combining the quasi-static loading and the transient loading through multiple analysis steps, and the pure Rayleigh wave signal can be obtained by subtracting the Rayleigh acoustic wave signal under the prestress field from the pure prestress field signal, so that the simulation Rayleigh wave signal result can be accurately obtained to study the propagation characteristics of the Rayleigh wave in the prestressed semi-infinite medium, obtain the waveform, wave velocity and other propagation characteristics of the Rayleigh wave under different stress levels, provide a simulation technical reference for ultrasonic stress detection, and make 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 overall simulation modeling.

[0028] Figure 2 is a simulation model schematic diagram of ABAQUS, in which the left side adopts fixed constraints, the right side adopts fixed normal direction constraints, the signal collection point 1 is 10mm away from the excitation point, the signal collection point 2 is 50mm away from the excitation point, and the distance between the two signal collection points is 40mm.

[0029] Figure 3 is a "two-step method" quasi-static load application method proposed in the simulation process, Load1 represents the application of prestress, and Load2 represents the point load applied for exciting the Rayleigh wave.

[0030] Figure 4 are the time domain waveform results of the simulation extraction and the filtered time domain signal diagram, including the original Rayleigh wave signal and the filtered Rayleigh wave signal obtained by simulation under different stresses.

[0031] Figure 5 is a contrast diagram of Rayleigh wave time domain signals under different stresses.

[0032] Figure 6 is a contrast diagram of simulation results and theoretical calculation results. DETAILED DESCRIPTION

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

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

[0035] First, 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 hyperelastic material, so as to realize the nonlinear change of simulation.

[0036] Based on the ABAQUS own subprogram VUMAT, the nonlinear constitutive equation of acoustic-elastic effect is constructed according to the theory of Murnaghan acoustic-elastic effect, and the simulation modeling of acoustic-elastic effect in 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 velocity 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; and U is the right tensile tensor.

[0043] In subsequent simulation studies, a nonlinear elastic material model is required, but this model is not available in ABAQUS. Therefore, the VUMAT subroutine is used to add the necessary constitutive model through secondary development. The required isotropic nonlinear elastic constitutive model is the Cauchy stress tensor under the Green-Naghdi datum. The stress formula in the VUMAT subroutine must be stored in `stressNew(i)` at the end in the form of `t+Δt` to derive the recursive formula for stress increment. This formula is compiled in FORTRAN and then called in ABAQUS. The stress value in the subroutine at the end of the previous step is used as the initial value for the constitutive model calculation in the simulation. Then, the next integration step is performed to obtain the wave velocity state of the force corresponding to that feature point, thus completing 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, a semi-infinite domain medium environment is established using a plate as an example; the model size is 80×10mm. Figure 2 A point load is used as the excitation source in the middle, and the excitation signal is a three-cycle sine wave modulated by the Hanning window with a center frequency of 5MHz. Points are set at 10mm (point 1) and 50mm (point 2) from left to right as receiving sources. Figure 2 ).

[0045] Material properties were added to the model based on the material properties of aluminum, except for density (2704 kg / m³). -3 The other performance parameters (λ = 54.3 GPa, μ = 27.2 GPa, l = -281.5 GPa, m = -339.0 GPa, n = -416.0 GPa) are defined directly by the software and added by custom user materials, defined by the VUMAT subroutine.

[0046] The load is applied using a quasi-static analysis method at a low load rate and with a smooth, gradual slope, such as... Figure 3 Taking a prestress of 100 MPa as an example, in analysis step 1, the load is slowly increased from zero to 100 MPa over a time interval of 0.001 s. In analysis step 2, the load of 100 MPa is maintained constant for a time interval of 0.00002 s. The applied load is as follows: Figure 2 The excitation signal is applied to the right side of the model and exists in both analysis steps. It is applied via a reserved point as a point load excitation, such as...Figure 2 , and only exists in the second analysis step. The added receiving source is applied by the reservation point as Figure 2 , and also only exists in the second analysis step.

[0047] In order to simulate the propagation of Rayleigh wave on the test piece, a semi-infinite domain model needs to be built. The specific method is to add an absorbing boundary to the left and right and lower surface of the test piece according to the actual geometric size of the test piece. The thickness of each layer of the absorbing boundary is 0.1 mm, the length is consistent with the length of the side of the test piece, and a total of 16 layers are set. According to the damping incremental method absorbing boundary method, the relationship between the Rayleigh damping coefficient and the number of absorbing boundary layers is as follows:

[0048]

[0049] In the formula, l is the length of each layer of absorbing boundary, L is the total length of the absorbing boundary, α max is the maximum value of the damping coefficient, where α max =10f, f is the excitation frequency, and n is the power index.

[0050] According to the simulation requirements, the model needs to be modeled according to the principle of the stretching machine, such as Figure 2 The left side of the model is applied with a completely fixed boundary condition, and the normal axis displacement of the right side of the model is fixed to 0.

[0051] According to the geometric size of the test piece and the center frequency of the excitation sensor, the grid size is determined to be 0.1 mm, and the grid attribute is determined to be dynamic plane strain.

[0052] 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 point, because the quasi-static analysis method needs to simulate multiple analysis steps, and the collection is carried out 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, through quasi-static response filtering, the difference in time and the fluctuation in amplitude are eliminated to obtain a pure static Rayleigh wave as 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 Figure 4 (b). The prestressed field signal obtained by processing the prestressed field signal and the fluctuation signal under the prestressed field is reduced by the time used in the first analysis step, 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 filtering the Rayleigh wave signals under different prestress states, the Figure 5The Rayleigh wave time-domain waveform diagram under different stresses is shown. The time corresponding to the peak value of the waveform at two different positions is used to calculate the time difference. In the case of considering 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. The results are compared with the theoretical calculation results. Figure 6 As shown, the wave velocity of the Rayleigh wave has a linear correlation with the stress, and the simulation results have the same trend as the theoretical calculation results. At this time, the relative error between the simulation results and the theoretical results is 0.6%, which meets the error requirement of the simulation, and proves the correctness and reliability of the finite element simulation model of the acoustic-elastic Rayleigh wave in the prestressed medium.

Claims

1. A finite element simulation method for Rayleigh wave acoustoelastic effect in a prestressed semi-infinite domain medium, characterized in that, The specific implementation steps of this method include the following: Step 1: Derive and establish the acoustoelastic nonlinear constitutive equation, and write the acoustoelastic VUMAT subroutine; Step 2: Establish a finite element model of the prestressed structure under test under Rayleigh wave acoustic disturbance; Step 3: "Two-step" loading, setting up quasi-static and transient analysis steps to simulate prestress and Rayleigh wave acoustic disturbance loading respectively; Step 4: Call the VUMAT subroutine created in Step 1 to perform calculations and solve the problem; Step 5: Extract the sound wave propagation signal and post-process the signal to extract the pure Rayleigh wave signal; Based on the post-processed Rayleigh wave signal, Rayleigh wave waveform signal curves under different stresses can be plotted. The transit time difference can be calculated by the time corresponding to the peak values ​​of two waveforms at different positions. Considering elastic strain, the spatial distance between the two receiving points after the specimen is subjected to stress can be calculated, and the wave velocity can be obtained. In this way, the variation law of Rayleigh wave velocity under different stress states can be studied. The Murnaghan hyperelastic constitutive model was introduced by writing the acoustoelastic VUMAT subroutine with nonlinear characteristics and inserting it into the ABAQUS software; the environment of a semi-infinite domain medium was simulated by setting an absorbing boundary on the lower surface of the structure, thereby satisfying the conditions for Rayleigh wave propagation in the medium.

2. The finite element simulation calculation method for Rayleigh wave acoustoelastic effect in a prestressed semi-infinite domain medium as described in claim 1, characterized in that, The "two-step" loading method involves setting up two analysis steps. One analysis step applies stress using a quasi-static analysis method, while the other analysis step applies acoustic disturbances using a transient analysis method.

3. The finite element simulation calculation method for Rayleigh wave acoustoelastic effect in a prestressed semi-infinite domain as described in claim 1, characterized in that, By disabling acoustic disturbance loading, the signal curve of the signal receiving point under prestress is obtained; the difference between the obtained prestress field signal and the wave signal under the prestress field is processed to complete the pure filtering of the data signal and eliminate the low-frequency disturbance interference caused by acoustic loading.

4. A simulation analysis system for Rayleigh wave propagation characteristics under prestress based on the acoustoelastic nonlinear VUMAT constitutive model, characterized in that, 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 acoustoelastic Rayleigh wave modeling module is configured to determine the shape and size of the Murnaghan hyperelastic material, establish a geometric model of the Murnaghan hyperelastic material, directly define the material density through the material property setting module in ABAQUS software, and add the second and third elastic constants of the material through a custom user material and define them through the VUMAT subroutine; an absorption layer is set at the bottom of the hyperelastic material to simulate a semi-infinite domain medium environment; point load excitation points and signal acquisition points at different locations are set; the left side of the model is completely fixed, and the right side is constrained for displacement in the normal direction; the mesh size is determined according to the excitation frequency of the Rayleigh wave. The prestressing and acoustic disturbance loading module is configured to perform multi-step analysis on the Murnaghan hyperelastic material model. It simulates the stress loading process through a quasi-static analysis method and the Rayleigh acoustic disturbance process through a transient analysis method. Finally, it submits the calculation and outputs the Rayleigh wave signal waveform to obtain the Rayleigh wave propagation characteristics under prestress. The simulation result post-processing module is configured to post-process the Rayleigh wave signal obtained from the simulation calculation to obtain a pure Rayleigh wave signal and plot the Rayleigh wave waveform under different stresses; calculate the transit time difference by the time corresponding to the peak value of the Rayleigh wave signal at different positions; and calculate the spatial distance between the two receiving points after the specimen is subjected to stress, taking into account elastic strain, so as to calculate the wave velocity and further study the propagation characteristics of Rayleigh waves under prestressed state.

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