Finite element simulation calculation method for Rayleigh wave acoustic elastic effect in prestress semi-infinite domain medium

Abstract

The invention discloses a finite element simulation calculation method for a Rayleigh wave acoustic elastic effect in a prestress semi-infinite domain medium, which can realize prestress Rayleigh wave simulation in any waveguide section, and has the advantages of high simulation speed, random expansion of a simulation object and the like. The method comprises the following steps of: writing a VUMAT subprogram with a nonlinear characteristic to realize the introduction of a Murnaghan hyperelastic constitutive model; loading of prestress and acoustic disturbance is achieved through a quasi-static superposition dynamic analysis method; and pure Rayleigh wave feature extraction is realized through Rayleigh wave signal post-processing. The method fills up the vacancy of a simulation method in the field of ultrasonic nondestructive testing, especially in the chromatographic testing research of residual stress, and has great potential.

Description

Technical Field

[0001] The invention relates to a finite element simulation calculation method for Rayleigh wave acoustic elastic effect in a prestressed semi-infinite domain medium, and belongs to the field of non-destructive 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] Surface waves, also known as Rayleigh waves, are a special type of guided wave that can propagate along the surface of a component with a penetration depth of about 1 wavelength. In the field of engineering, due to its unique propagation characteristics, stress information detection on the surface of components and within a certain depth range has great advantages and development potential. Zhang et al. developed a theoretical calculation model for acoustic elastic Rayleigh waves in the non-patent literature [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.] and theoretically calculated and solved the Rayleigh wave propagation characteristics under stress state.

[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 semi-infinite domain 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 Rayleigh wave acoustic elastic effect in prestressed semi-infinite domain media in ABAQUS simulation software, and successfully realizes the introduction of Rayleigh wave acoustic elastic effect in prestressed semi-infinite domain 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 a prestressed semi-infinite domain medium in ABAQUS simulation software, using the VUMAT subroutine interface of ABAQUS itself to define the nonlinear constitutive law of the material, and based on the Murnaghan acoustic elastic effect as a theory, through multi-analysis step loading, the study of the propagation characteristics of Rayleigh waves under prestressed state is realized 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 semi-infinite domain 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 the action of Rayleigh wave acoustic disturbance;

[0011] Step 3: Set up quasi-static and transient analysis steps to simulate prestress and Rayleigh wave acoustic disturbance loading respectively;

[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 Rayleigh 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, according to the actual geometric dimensions of the specimen, an absorbing boundary is added to the lower surface of the specimen. The thickness of each absorbing boundary layer is 0.1 mm, and the length is consistent with the side length of the specimen. A total of 16 layers are set to simulate the medium environment of a semi-infinite domain to meet the conditions for Rayleigh wave propagation.

[0016] Furthermore, Rayleigh acoustic wave point load excitation points and Rayleigh wave signal collection points are set in the simulation model, and boundary conditions for providing displacement constraints are provided, 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. 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 acoustic-elastic Rayleigh waves 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 Rayleigh acoustic wave disturbance process is simulated by a transient analysis method to achieve the simulation of the acoustic elastic Rayleigh wave under the prestressed state.

[0018] Furthermore, the Rayleigh 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 Rayleigh wave signals is plotted. The transit time difference is calculated by the time corresponding to the peak value of the Rayleigh 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 Rayleigh waves under prestressed state.

[0019] The second aspect of the present invention provides a simulation analysis system for Rayleigh 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 Rayleigh 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. 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 collection points at different positions are set. The left side of the model uses a completely fixed constraint, and the right side constrains the displacement in the normal direction. The grid size is determined according to the geometric size of the test piece and the center frequency of the excitation sensor;

[0022] The acoustic-elastic Rayleigh 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 the quasi-static analysis method, and simulate the Rayleigh acoustic wave disturbance process through the transient analysis method to obtain the signal waveform of the Rayleigh wave;

[0023] The Rayleigh wave propagation characteristics analysis module under prestressed state is configured to post-process the Rayleigh wave signal obtained by simulation calculation to obtain a pure Rayleigh wave signal, and draw Rayleigh wave waveforms under different stresses. The transit time difference is calculated by the time corresponding to the peak value of the Rayleigh 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 Rayleigh 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 a prestressed semi-infinite domain medium, thus making up for the limitation that a 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 Rayleigh wave signal by subtracting the Rayleigh acoustic wave signal under the prestressed field from the pure prestressed field signal. The simulated Rayleigh wave signal result can be accurately obtained to further study the propagation characteristics of Rayleigh waves in prestressed semi-infinite domain media, and obtain the changes in the propagation characteristics of Rayleigh waves such as waveform and wave velocity under different stress levels, 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 50 mm away from the excitation point. The two signal collection points are 40 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 Rayleigh 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 Rayleigh wave signal under different stresses obtained by simulation and the filtered Rayleigh wave signal.

[0031] Figure 5 This is a comparison of Rayleigh 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 This is the overall flow chart of the finite element simulation calculation method for the Rayleigh wave acoustic elastic effect in prestressed semi-infinite domain media. Modeling was performed 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 structure of the simulation model of the present invention. In the modeling process, the model takes a plate as an example to establish a semi-infinite domain medium environment; the model size is 80×10mm ( Figure 2 ), a point load is used in the middle as the excitation source, the excitation signal is a three-cycle sine signal modulated by a Hanning window, the center frequency is 5MHz, and points are set from left to right at 10mm (set as point 1) and 50mm (set as point 2) as receiving sources ( Figure 2 ).

[0045] Add material properties to the model based on the material properties of aluminum. The added properties include density (2704kg*m -3 ) are directly defined by the software, and 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 analysis step 1, the load is slowly increased from zero to 100 MPa in 0.001 s, and in analysis step 2, the load of 100 MPa is maintained constant in 0.00002 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 in the form of point load excitation, 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] In order to simulate the propagation of Rayleigh waves on the specimen, a semi-infinite domain model needs to be built. The specific method is to add absorbing boundaries on the left, right and bottom surfaces of the specimen according to the actual geometric dimensions of the specimen. The thickness of each absorbing boundary layer is 0.1 mm, and the length is consistent with the length of the side of the specimen. There are 16 layers in total. According to the damping increasing method of absorbing boundaries, the relationship between the Rayleigh damping coefficient and the number of absorbing boundary layers is as follows:

[0048]

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

[0050] 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.

[0051] 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.

[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. 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 Rayleigh 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 Rayleigh wave signal under different prestress states can be filtered to obtain Figure 5The Rayleigh wave time domain waveforms under different stresses are shown in the figure. 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 Rayleigh waves 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 0.6%, which meets the error requirements of the simulation, indicating the correctness and reliability of the established finite element simulation model of acoustic elastic Rayleigh waves in prestressed media.

Claims

1. A finite element simulation calculation method for Rayleigh wave acoustic elastic 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 acoustic-elastic nonlinear constitutive equation and write the acoustic-elastic VUMAT subroutine; Step 2: Establish a finite element model of the prestressed structure under the action of Rayleigh wave acoustic disturbance; Step 3: "Two-step method" loading, setting quasi-static and transient analysis steps to simulate prestressing and Rayleigh wave acoustic disturbance loading respectively; 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 Rayleigh wave signal; According to the post-processed Rayleigh wave signal, the Rayleigh wave waveform signal curve under different stresses can be plotted, and the transit time difference is calculated by the time corresponding to the peak values ​​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 in this way. Furthermore, the changing law of the Rayleigh wave velocity under different stress states can be studied.

2. The finite element simulation calculation method for Rayleigh wave acoustic elastic effect in a prestressed semi-infinite domain medium according to claim 1, characterized in that: By writing an acoustic-elastic VUMAT subroutine with nonlinear characteristics and inserting it into ABAQUS software, the Murnaghan hyperelastic constitutive model is introduced, solving the problem that ABAQUS software cannot directly add a nonlinear acoustic-elastic constitutive model.

3. The finite element simulation calculation method for Rayleigh wave acoustic elastic effect in a prestressed semi-infinite domain medium according to claim 1, characterized in that: By setting an absorbing boundary on the lower surface of the structure, the environment of a semi-infinite domain medium is simulated to meet the conditions for Rayleigh wave propagation in the medium.

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

5. The finite element simulation calculation method for Rayleigh wave acoustic elastic effect in a prestressed semi-infinite domain 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.

6. A simulation analysis system for Rayleigh wave propagation characteristics under prestress based on the acoustic-elastic nonlinear VUMAT constitutive model, 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 Rayleigh 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; 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 collection points at different positions are set, the left side of the model adopts a completely fixed constraint, and the right side constrains the displacement in the normal direction, and the grid size is determined according to the excitation frequency of the Rayleigh 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 Rayleigh acoustic wave disturbance process through a transient analysis method. Finally, the calculation is submitted to output the signal waveform of the Rayleigh wave, and the propagation characteristics of the Rayleigh wave under the action of prestress are obtained. The simulation result post-processing module is configured to post-process the Rayleigh wave signal obtained by simulation calculation to obtain a pure Rayleigh wave signal, and draw Rayleigh wave waveforms under different stresses; calculate the transit time difference through the time corresponding to the peak 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 while considering the elastic strain, so as to calculate the wave velocity, and then study the propagation characteristics of Rayleigh waves under prestressed state.

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