A method for analyzing the effect of stress on ultrasound harmonics based on molecular dynamics

Abstract

This invention discloses a method for analyzing the influence of stress on ultrasonic harmonics based on molecular dynamics, belonging to the field of discrete solution technology. The method includes establishing an unloaded model that satisfies ultrasonic wave propagation. Prestressed models with different stress magnitudes and directions are prepared, and dislocation nucleation is monitored to achieve real-time diagnosis and storage of the stress state. Hanning-modulated sinusoidal ultrasonic waves are applied to atoms within each prestressed model interval to avoid disturbances caused by new energy propagating the ultrasonic waves in the NVE ensemble. The trajectory file is post-processed and analyzed to identify the ultrasonic wave propagation process under stress. The model is divided into single-layer atomic regions along the X-axis, and the acoustic signals of ultrasonic waves passing through each region are extracted. The harmonic generation process is obtained through wavelet transform, the linear accumulation interval of harmonics is determined, the cumulative slope is extracted, and the influence of stress on the ultrasonic harmonic generation efficiency is analyzed.

Description

Technical Field

[0001] This specification relates to the field of discrete solution technology for ultrasonic wave propagation in metallic materials, and in particular to a method based on molecular dynamics analysis of the influence of stress on ultrasonic harmonics. Background Technology

[0002] Aluminum and high-strength aluminum alloys are widely used in aerospace, automotive, and transportation engineering due to their lightweight, corrosion resistance, and high strength. Improper handling of parts during forming, machining, or operation can introduce residual stress. Residual stress can have detrimental effects on the operation of parts, such as reducing fatigue strength, fracture resistance, dimensional stability, and resistance to stress corrosion cracking. Therefore, effective assessment of residual stress is crucial for the safe operation of metal parts.

[0003] Non-destructive testing (NDT) methods that do not introduce additional stress or damage during the testing process have attracted much attention from scholars. Ultrasonic NDT is a commonly used method for residual stress detection. This method utilizes the changes in characteristic parameters of ultrasonic waves propagating in a medium, such as wave velocity, frequency, and energy, to detect the stress state. The measurement of residual stress based on ultrasonic wave velocity mainly utilizes the theory of acoustoelasticity. In practical testing, the change in ultrasonic wave propagation velocity caused by stress changes is very small; for example, a stress change of 100 MPa can only change the wave velocity in steel by 0.01%. The uncertainty in sound velocity measurement makes quantifying residual stress in metallic materials very difficult. Furthermore, residual stress can also cause changes in the nonlinear characteristics of ultrasonic waves. When ultrasonic waves interact with structures containing residual stress, harmonic components are generated. Therefore, acoustic nonlinear parameters can be used to characterize residual stress.

[0004] Previous studies have shown that second-order and third-order nonlinear parameters have an approximately linear relationship with stress. However, as stress increases, specimen deformation becomes significant, and the ultrasonic propagation distance and path change due to deformation. Simultaneously, the coupling quality between the probe and the specimen contact surface also changes continuously during loading. Therefore, the measurement of relative nonlinear parameters is easily affected by specimen deformation and coupling conditions, making it difficult to accurately quantify the relationship between stress magnitude and direction and ultrasonic nonlinearity. Simulation methods have unique advantages in studying single factors and the entire dynamic propagation process. Molecular dynamics simulations based on atomic potentials are widely used to study the mechanical response and deformation mechanisms of metallic materials under uniaxial, multiaxial, and cyclic loading. Therefore, this method can be used to establish models for different stress states. Introducing ultrasound into this model allows for the analysis of the entire process of harmonic generation under different stress states without being affected by coupling conditions. This avoids experimental errors caused by changes in specimen deformation and coupling state affecting ultrasonic propagation distance and path. Molecular dynamics methods can establish atomic-scale acoustic models that can intuitively reflect the interaction between stress and acoustic signals, revealing the efficiency of stress magnitude and direction in inducing ultrasonic harmonic generation. This is a key and important approach to understanding nonlinear ultrasonic testing results and improving testing accuracy.

[0005] Current research on the relationship between stress and nonlinear ultrasound is mostly based on in-situ tensile experiments, fitting the changes in stress values ​​and acoustic nonlinear parameters to determine the underlying patterns. In-situ experiments require specific measuring fixtures and procedures to minimize experimental errors, and cannot eliminate the influence of variations in propagation distance. Currently, finite element models of the contribution of different stress states to ultrasonic harmonics are lacking. Regarding microacoustic models, the focus is mainly on microscopic defects; research on the impact of stress states on ultrasonic harmonic generation is currently unavailable.

[0006] Therefore, in order to study the influence of stress state on the efficiency of ultrasonic harmonic generation, this invention proposes a method for extracting harmonics throughout the ultrasonic propagation process under different stress states based on molecular dynamics. The influence of stress magnitude and direction on harmonic generation efficiency was studied by using molecular dynamics simulation. Summary of the Invention

[0007] To address the lack of effective research methods for studying the influence of residual stress magnitude and direction on ultrasonic harmonic generation efficiency in aluminum alloy materials, this invention provides a novel molecular dynamics simulation method for studying ultrasonic harmonic generation based on different prestress states. Specifically, it involves controlling the direction and magnitude of uniaxial loading on the material, performing atomic-scale acoustic simulations on models with different stress states, extracting nonlinear information from acoustic signals during ultrasonic wave propagation in real time, and studying the ultrasonic harmonic generation efficiency and full-path conversion law under different stress states.

[0008] In some embodiments, a method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics includes the following steps:

[0009] S1: Prepare prestressed models with different stress magnitudes and directions. The preparation process includes applying multi-directional stress to the unloaded model, setting the strain rate, performing deformation once at each time step, performing strain simulation, and saving the current loading state. The unloaded model is constructed based on the conjugate gradient algorithm to minimize the energy of the aluminum single crystal. The applied multi-directional stress is one of the normal stress, negative stress, and shear stress within the elastic deformation range of the material, and the direction of the multi-directional stress is one of the X, Y, and Z directions.

[0010] S2: Apply ultrasonic waves to the prestressed model after preparation to obtain a trajectory file, wherein the stress stored in the trajectory file is uniformly distributed;

[0011] S3: Divide the model into equal regions under the direction of detection, extract the acoustic signal of the region through which the ultrasonic wave passes, solve for the time-varying amplitude, and calculate the acoustic nonlinear parameters based on multiple time-varying amplitude values;

[0012] S4: By constructing a harmonic linear accumulation region using acoustic nonlinear parameters and performing linear fitting, the harmonic generation efficiency under multi-directional stress is obtained.

[0013] Furthermore, in S1, after constructing the unloaded model of the aluminum single crystal, the unloaded model is relaxed in the NVT ensemble and NPT ensemble. Combined with the Nosé-Hoover thermostat, a structurally stable unloaded model is obtained after relaxation.

[0014] Furthermore, S1 also includes calculating the stress components and tensor components of each atom in the aluminum single crystal to obtain the von Mises stress. Extract the stress and strain data from the prestressed model, specifically:

[0015] ;

[0016] In the formula, , , All are stress components. , , All are tensor components.

[0017] Furthermore, in S1, the strategy for saving the current loading state during strain simulation is adjusted based on dislocation nucleation early warning, specifically as follows:

[0018] ;

[0019] This is the actual storage interval. As the initial save interval, when hour, Take 1; when hour, Let G be 0, and let G be the shear modulus. This is a scaling factor.

[0020] Existing calibration experiments for residual stress detection require obtaining fitting results between different stress values ​​and acoustic nonlinear parameters during the elastic stage on a tensile testing machine. However, capturing the process in the purely elastic stage is difficult, and data from the plastic stage is easily mixed in. This is generally because the distinction between the elastic and plastic stages is difficult, which may introduce contributions from microstructure changes. Therefore, the model in this application retains a prestressed model with different stress states before plastic deformation occurs, i.e., before dislocation nucleation. The model is calculated based on a specifically constructed aluminum single crystal model. This is the critical value for early warning of incorrect nuclei.

[0021] Furthermore, in S2, a Hanning-modulated sine wave is applied to the prestressed model after preparation, specifically as follows:

[0022] ;

[0023] In the formula, A is the amplitude, step is the time step, and T is the excitation frequency of the ultrasonic wave. S represents the number of excited ultrasonic waves, dt represents the time step size, and Hanning-modulated sinusoidal vibration is applied to the ultrasonic excitation layer to simulate the ultrasonic wave propagation process after excitation is complete.

[0024] In actual testing, the above-mentioned technology can only transmit wave packets of limited duration. Due to the abrupt changes in the signals at both ends, the frequency domain information is leaked, causing energy to extend from the excitation frequency to the adjacent frequency range, severely interfering with the nearby harmonic frequency components and easily submerging the high-order harmonic components generated by stress. The Hanning modulated sine wave signal greatly reduces the abrupt changes in the time domain signal, making the spectral energy of the excitation signal highly concentrated near the excitation frequency, and with very little leakage outward.

[0025] Furthermore, in S3, the model is divided into single-atom-layer regions in the X direction, and the ultrasonic displacement signal of each region is obtained. Continuous wavelet transform is performed, and the complex Morlet wavelet is selected as the mother wavelet.

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, For the mother wavelet, It is an imaginary number. For time, Frequency resolution is controlled by bandwidth parameters. Here, 'a' is the center frequency of the mother wavelet, and 'a' is the scale parameter. For frequency analysis, b is the translation parameter. Let n be the time-varying amplitude value of the nth harmonic. Given an nth-order time-frequency matrix, the excitation frequency is obtained by using the nth-order time-frequency matrix. The time-varying amplitude A1, twice the excitation frequency The time-varying amplitude A2, 3 times the excitation frequency The time-varying amplitude value A3, For secondary acoustic nonlinear parameters, For cubic acoustic nonlinear parameters, n = 1, 2, 3.

[0034] Based on the above technical features, traditional ultrasonic analysis uses Fourier transform technology for processing. The standard Fourier transform gives the frequency components over the entire time interval. However, the frequency components are constantly changing during the propagation of ultrasonic waves. This time-varying characteristic will lose accuracy after the Fourier transform is averaged over the entire domain. The wavelet transform used in this invention can provide both time and frequency information simultaneously, and intuitively show the evolution process of harmonics.

[0035] Furthermore, in S4, the acoustic nonlinear parameter varies with the propagation distance after being divided into i equal parts. The dataset is obtained as follows , Piecewise linear regression models are constructed, where there are k unknown variable points dividing the curve into k+1 segments. The quadratic acoustic nonlinear parameters satisfy a linear relationship within each segment. ,

[0036] ;

[0037] Uniform(1, );

[0038] ;

[0039] ;

[0040] ;

[0041] In the formula, Let i represent the random fluctuation noise assumed to exist in the line segment, and let i be the number of equally divided monoatomic layers. For the intercept parameter, For the slope parameter, This represents the farthest distance that ultrasound can travel. The intercept and slope are the average of the a priori guesses in a linear relationship, and the variable point is... Let the discrete uniform distribution be Uniform(1, ), where each parameter and noise variance Let the conjugate distributions be the normal distributions. and inverse-gamma distribution By using Markov chain Monte Carlo sampling to jointly sample the posterior distribution P( , , | , ), calculate the variable point Marginal posterior distribution P( | , ),in, The variable point configuration with the highest posterior probability is selected, and the linear variation range of acoustic nonlinear parameters is determined based on Bayesian variable point detection. The longest continuous interval with stable slope and small fitting residual is the harmonic linear accumulation region. The stress-induced ultrasonic harmonic generation efficiency is obtained through this slope.

[0042] By utilizing the aforementioned technical features, the acoustic nonlinear parameters at a single location under stress are not affected by changes in propagation distance. An extraction of acoustic nonlinear parameters over the entire propagation distance is proposed. However, the harmonic accumulation interval has nonlinear characteristics, requiring the identification of the linear accumulation interval of harmonics to extract the slope and then compare the effect of stress.

[0043] The beneficial effects of this invention are:

[0044] 1. The research method of molecular dynamics simulation can effectively reduce experimental costs and consumption, obtain the whole process of ultrasonic harmonic generation under stress, avoid experimental errors introduced by specimen deformation, attenuation and changes in coupling state, provide microscopic information supplement and data support for macroscopic detection results, and improve the accuracy of residual stress detection.

[0045] 2. Based on the fact that the residual stress in the parts has different magnitudes and directions, preload models with different stress magnitudes and directions are constructed. The harmonic components are efficiently extracted from the Hanning modulated ultrasonic waves excited by each model, and the influence of stress magnitude and direction on harmonic generation efficiency is studied.

[0046] 3. This invention can observe the generation relationship of harmonics with stress state during ultrasonic wave propagation, providing a theoretical basis for experimental residual stress analysis and performance evaluation. Attached Figure Description

[0047] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein:

[0048] Figure 1 This is a schematic diagram illustrating the working principle according to some embodiments of this specification;

[0049] Figure 2 It is an acoustic model for stress assessment based on some embodiments shown in this specification;

[0050] Figure 3 This describes the accumulation of quadratic nonlinear parameters when different normal stresses are applied along the X direction, as shown in some embodiments of this specification.

[0051] Figure 4 This describes the cumulative effect of three nonlinear parameters when different normal stresses are applied along the X direction, as shown in some embodiments of this specification.

[0052] Figure 5 This describes the accumulation of quadratic nonlinear parameters when different negative stresses are applied along the X direction, as shown in some embodiments of this specification.

[0053] Figure 6 This is the cumulative case of three nonlinear parameters when different negative stresses are applied along the X direction, as shown in some embodiments of this specification;

[0054] Figure 7 This describes the accumulation of quadratic nonlinear parameters when different normal stresses are applied along the Y direction, as shown in some embodiments of this specification.

[0055] Figure 8 This describes the cumulative effect of three nonlinear parameters when different normal stresses are applied along the Y direction, as shown in some embodiments of this specification.

[0056] Figure 9 This describes the accumulation of quadratic nonlinear parameters when different normal stresses are applied along the Z direction, as shown in some embodiments of this specification.

[0057] Figure 10 This is the cumulative case of three nonlinear parameters when different normal stresses are applied along the Z direction, as shown in some embodiments of this specification. Detailed Implementation

[0058] To more clearly illustrate the technical solutions of the embodiments in this specification, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples or embodiments of this specification. For those skilled in the art, these drawings can be applied to other similar scenarios without creative effort. Unless obvious from the context or otherwise specified, the same reference numerals in the drawings represent the same structures or operations.

[0059] As indicated in this specification and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of expressly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0060] Example 1:

[0061] This embodiment relates to the technology of stress magnitude and direction affecting ultrasonic harmonic generation. Specifically, it relates to a method for analyzing the cumulative generation of second and third harmonics along the ultrasonic propagation direction under different stress magnitudes and directions. The method controls the direction and magnitude of uniaxial loading on the material, performs atomic-scale acoustic simulations on models with different stress states, extracts nonlinear information from acoustic signals during ultrasonic propagation in real time, and studies the ultrasonic harmonic generation efficiency and full-path conversion law under different stress states.

[0062] Please refer to Figure 1The unloaded model of aluminum single crystal was completed in the open-source software Atomsk and LAMMPS, and was divided into two steps: model building and relaxation. The smallest unit cell of aluminum single crystal under the

[100]

[010]

[001] orientation was built using Atomsk software. Considering the stability of ultrasonic wave propagation to avoid reflected wave interference and harmonic accumulation, the size of the model in the ultrasonic wave propagation direction is greater than z+(n+1)*λ, where z is the harmonic accumulation distance, n is the number of cycles of the excitation ultrasonic wave, and λ is the ultrasonic wave wavelength. The size in the non-ultrasonic wave propagation direction is greater than 5 times the lattice constant to avoid the influence of size effect. The duplicate command was run to expand the cell in the three directions by 640 times, 21 times, and 21 times. The above model was read using the read_data command in LAMMPS software. The model atoms are in metal units and the atom type is atomic. The spatial dimension is set to three dimensions. In order to make the ultrasonic wave propagate in a single direction, the boundary condition in the ultrasonic wave propagation direction is a non-periodic boundary condition, and the boundary conditions in the other directions are periodic boundary conditions. The simulation step size is 1fs. Energy minimization was performed using the conjugate gradient algorithm. The initial atomic velocities were set using the velocity command to avoid thermal effects introducing new energy into the ultrasonic wave propagation. The system temperature was set to 0.01 K. Relaxation of the model was performed in the NVT and NPT ensembles. After relaxation, a stress-free and structurally stable unloaded model was obtained.

[0063] Metal components are subjected to complex loads during service, including multi-directional stress. Establishing a correlation between stress and acoustic parameters is difficult by applying multiple stress magnitudes and directions to a single specimen. Using multiple specimens introduces variations in microstructure. Please refer to [reference needed]. Figure 2 This application uses the same stress-free and structurally stable unloaded model, enabling the accurate preparation of prestressed samples with different stress magnitudes and directions under the same microstructure conditions. This lays the foundation for accurately determining the influence of stress direction and magnitude on harmonic generation. Stress is applied to the unloaded model using the Fix deform command in LAMMPS software. The strain rate is set, and deformation is performed once per time step to ensure uniform model deformation. Considering the diversity of loads, normal and negative stresses can be applied to the X, Y, and Z directions of the unloaded model, as well as multiaxial loads. During loading, the model is kept at a constant temperature under the NPT ensemble, and the pressure in the unloaded directions is 0 Bar.

[0064] Real-time calculation of stress components for each atom ( , , ), tensor components ( , , ), and then calculate atomic-level von Mises stress. ,

[0065] ;

[0066] when A dislocation nucleation warning is issued when the value exceeds 0.7 × G / 2π, where G is the shear modulus and the scaling factor is 0.7. The storage strategy is dynamically adjusted based on the identified status, with a basic storage interval of...

[0067] ;

[0068] in It adaptively adjusts from a state of 1.0 (elastic) to 0.1 (dislocation nucleation).

[0069] In LAMMPS software, the `compute stress / atom` and `compute reduce` commands are used to calculate the stress in the loading direction. The `Fix ave / time` command is used to average the stress and strain every 500 steps to extract the stress and strain data of the prestressed model.

[0070] In LAMMPS software, the `read_restart` command is used to read restart files of models under different prestressed states with the same stress direction. Atoms in the 0Å-X / 100Å region along the X direction are selected as the fixed layer for ultrasonic excitation, where X is the length of the model in the x-direction. Ultrasonic longitudinal waves are most sensitive to stress; therefore, vibration in the x-direction is applied at the excitation end to excite the ultrasonic longitudinal wave. During the stress application process, the model will generate corresponding strain. Using equidistant excitation and reception or fixing the positions of the excitation and reception ends makes it difficult to identify the influence of propagation distance and stress coupling on harmonic generation. Therefore, it is necessary to achieve real-time extraction of the displacement waveform during ultrasonic longitudinal wave propagation. The `compute displace / atom` command is used to calculate the real-time displacement of all atoms in the model. Since the ultrasonic longitudinal wave propagates forward along the x-direction, the `compute reduce` command is used to decompose the displacement vector into scalars, and only the displacement in the x-direction is extracted based on the propagation characteristics of the ultrasonic longitudinal wave. There are no signal characteristics in the y and z directions; therefore, a single or multiple atomic planes within the yOz plane are taken as the receiving signal unit, and the displacement component of this atomic plane in the x-direction is calculated as the ultrasonic vibration displacement. In this embodiment, the compute chunk / atom command is used to divide the model into z+(n+1) equal parts along the X direction to receive ultrasonic displacement signals from different regions. The number of parts can be reduced to decrease the computational load as needed, where z is the harmonic cumulative distance, n is the number of excitation ultrasonic cycles, and λ is the ultrasonic wavelength.

[0071] To highlight the main frequency components of the signal, a Hanning-modulated sine wave is excited to reduce spectral leakage and efficiently extract the frequency domain information of the displacement signal. The Hanning-modulated sine wave is defined using the `variable` command. Where A is the amplitude, step is the time step of the current system (the current model running in the LAMMPS command), and T is the excitation frequency of the ultrasound. , The number of ultrasonic waves to be excited. This represents the current system time step. Based on the above formula, the displacement and velocity in the X direction are set, and Hanning-modulated sinusoidal vibration is applied to the excitation end. The single-cycle excitation time for an ultrasonic wave with an excitation frequency of 5 THz is 5,000 steps, and the number of cycles and the excitation frequency can be adjusted as needed. After the ultrasonic excitation is complete, the simulation continues for 30,000 steps to simulate the ultrasonic wave propagation process. Both the ultrasonic excitation and propagation processes are run under the NVE ensemble.

[0072] The model was divided into single-atom-layer regions along the X-axis, and the ultrasonic displacement signal of each region was obtained. According to the Nyquist sampling metric, the sampling frequency of the nth harmonic amplitude needs to be extracted. The sampling frequency required to effectively extract the third harmonic is set to at least 2n times the excitation frequency. The ultrasonic displacement signal of each receiving area must not be lower than 30 THz. Perform continuous wavelet transform, and select complex Morlet wavelet as the mother wavelet. ,in Frequency resolution is controlled by bandwidth parameters. The center frequency of the mother wavelet is given. Wavelet transform is defined as... Analysis frequency With scale parameters Inversely proportional ( Translation parameters Determine the position of the wavelet function on the time axis. This is done by applying different scales. (corresponding to base frequency) Up to the third harmonic The time-frequency matrix is ​​obtained by calculating the frequency range. Extract the time-varying amplitude values ​​of each harmonic from it. (in The acoustic nonlinear parameters are calculated based on the information of each time-varying amplitude. The formula for calculating the secondary acoustic nonlinear parameters is:

[0073] ;

[0074] Where A1 is the fundamental frequency amplitude and A2 is the second harmonic frequency amplitude. The formula for calculating the third acoustic nonlinear parameter is:

[0075] ;

[0076] in For the fundamental amplitude, This represents the amplitude of the third harmonic.

[0077] The acoustic nonlinear parameters are plotted as a function of propagation distance based on the X-axis coordinates of each region. In the initial stage of ultrasonic excitation, due to incomplete waveforms and short propagation distances, the changes in acoustic nonlinear parameters are nonlinear, indicating that harmonic accumulation is non-uniform. Furthermore, harmonic generation is also affected by attenuation; at longer propagation distances, harmonic generation will be less than attenuation. Assuming the data for the second-order acoustic nonlinear parameters as a function of propagation distance are... Construct a piecewise linear regression model where there are k unknown variable points that divide the curve into k+1 segments, and each segment satisfies a linear relationship.

[0078] ;

[0079] in, This is assumed to be random fluctuation noise within the line segment. The number of equally divided monolayers, For the intercept parameter, This is the slope parameter. We are considering the location of the variable point. Set discrete uniform prior ~Uniform(1,N-1), and set parameters for each segment. The conjugate prior is set with the noise variance σ². ~ , ~Inverse-Gamma , The shape and scale parameters of the inverse-Gamma distribution are determined by selecting... and This expresses the value of the noise variance σ². For example, if we guess the noise standard deviation is approximately s, we can set... and This causes most of the probability mass of the inverse gamma distribution to fall around (0, s²). The joint posterior distribution P(...) is sampled using Markov chain Monte Carlo (MCMC) sampling. , , | , ), calculate the marginal posterior probability P( ) of the point of change. | , Finally, the configuration with the highest posterior probability is selected. The curve is divided into different regions, where the slope is stable ( And the fitting residual is small ( ,in The longest consecutive interval (the upper limit of the noise level within a line segment) is defined as the harmonic linear accumulation region. This is a commonly used parameter in this field, referring to the minimum value. The joint probability distribution of all unknown parameters given data; although the joint posterior contains all information, we are often more concerned with the location of individual change points. Statistical inference. Marginal posterior probabilities are derived from the integration of other parameters in the joint posterior distribution (i.e., excluding...). All outside , and The edge posterior probability obtained directly tells us the probability of each possible location being a change point, which facilitates determining the most likely location and quantifying uncertainty. Similarly, the linear fitting of the cubic acoustic nonlinear parameters is consistent with the above, and the cubic acoustic nonlinear parameters change with the propagation distance after being divided into i equal parts. The dataset is obtained as follows Assuming that the nonlinear parameters of the quadratic acoustic system satisfy a linear relationship within each segment, the following equations are provided. The cubic acoustic nonlinear parameters satisfy a linear relationship within each segment. , .

[0080] In simple terms, it involves linear fitting of the harmonic linear accumulation region. , ,in , All are acoustic nonlinear parameters at this distance under stress-free conditions. For slope, For the propagation distance. Based on the slope. The changes in stress direction and magnitude are used to determine the relationship between harmonic generation and stress direction. The acquisition of displacement information from a single atomic layer provides a high-precision representation of the entire harmonic generation process, avoiding other influencing factors introduced by changes in propagation distance.

[0081] Example 2:

[0082] In practical applications, this invention also includes the following:

[0083] (1) The orientation of the aluminum single crystal is

[100]

[010]

[001] , and the smallest unit cell is expanded in the X, Y and Z directions by 640 times, 21 times and 21 times respectively.

[0084] (2) The model atoms are metal units, the spatial dimension is three-dimensional, the periodic boundary conditions are applied in three directions, the simulation time step is 1fs, and the number of nearest neighbors of the atoms is set to 2.0bin.

[0085] (3) The MEAM potential function is used to describe the interaction force between aluminum atoms.

[0086] (4) Obtaining a structurally stable unloaded model through energy minimization and relaxation: Energy minimization was performed using the conjugate gradient algorithm, the initial atomic velocity was set using the velocity command, and the system temperature was set to 0.01 K. The system was initially relaxed for 200,000 steps in the NVT ensemble. Subsequently, the temperature was controlled at 0.01 K and the pressure was balanced at 0 Bar in the NPT ensemble, and the relaxation work of the model was completed after 200,000 steps of equilibration.

[0087] (5) Use the Fix deform command in LAMMPS software to load the unloaded model and prepare the prestressed model. Set the strain rate to 1×10⁻⁶. -9 S -1 Deformation is performed once at each time step. Stress is applied in the X, Y, and Z directions respectively. During loading, the model is kept at a constant temperature under the NPT ensemble, and the pressure in the non-loaded directions is 0 Bar. 50,000 steps are run on the unloaded model to apply a total strain of 5%. The restart command is used to save the current prestressed model's restart file every 10,000 steps.

[0088] (6) The therom command outputs statistical parameters once every 1000 steps. It adopts the thermo_style custom output method. The output physical quantities are step, temp, pe, ke, total, press, lx, ly, lz, and vol, which represent the number of simulation steps, system temperature, potential energy, kinetic energy, total energy, model pressure, x-direction length, y-direction length, z-direction length, and model volume, respectively. These parameters can reflect the rationality of the model in the prestressing loading and ultrasonic propagation process in real time, so as to provide subsequent adjustment and modification of model parameters.

[0089] (7) Calculate the stress in the loading direction using the compute stress / atom and compute reduce commands in LAMMPS software. Use the Fix ave / time command to average the stress and strain every 500 steps and output the results.

[0090] (8) Use the `read_restart` command in the LAMMPS software to read the restart files for different loading states. Select atoms in the 0Å-5Å region along the X direction as the fixed layer for ultrasonic excitation. Reset the current time step and use the `compute displace / atom` command to calculate the displacement of all atoms in the model. Use the `compute reduce` command to split the displacement vector into scalars and extract only the displacement in the X direction. Use the `compute chunk / atom` command to divide the model into 400 equal parts along the X direction to receive ultrasonic displacement signals from different regions.

[0091] The LAMMPS software obtains the stress parameter data in this embodiment by inputting the following specific data reading commands:

[0092] mass 1 27

[0093] pair_style meam

[0094] pair_coeff * * library-Al.meam Al Al.meam Al

[0095] compute myT move temp

[0096] thermo_style custom step temp epair pe ke etotal press lx ly lz vol

[0097] thermo_modify flush yes temp myT

[0098] neighbor 2.0 bin

[0099] neigh_modify delay 0 every 1 check yes

[0100] timestep 0.001

[0101] thermo 1000

[0102] min_style cg

[0103] min_modify dmax 0.1

[0104] minimize 1.0e-13 1.0e-13 10000 10000

[0105] reset_timestep0

[0106] compute myTT move temp / partial 0 1 1

[0107] velocity move create 0.01 3242345 dist uniform units box

[0108] dump 1 all custom 10000 a.*.lammpstrj id type xyz

[0109] dump_modify 1 element Al

[0110] unfix 1

[0111] unfix 2

[0112] fix 11all npt temp 0.01 0.01 0.1 iso 1000 0 1

[0113] run 10000

[0114] unfix 11

[0115] fix 11all nvt temp 0.01 0.01 0.1

[0116] run 10000

[0117] unfix 11

[0118] undump 1

[0119] write_restart file.restart

[0120] reset_timestep0

[0121] dump_modify 2 element Al

[0122] # fix_modify 33 temp myTT

[0123] run 30000.

[0124] (9) Excite a Hanning modulated sine wave to reduce spectral leakage and highlight the main frequency components of the signal. Use the variable command to define the Hanning modulated sine wave. Where A is the amplitude, step is the current system time step, T is the excitation ultrasonic frequency, R is T*S, S is the number of excitation ultrasonic waves, and dt is the current system time step size. The displacement and velocity of the ultrasonic excitation layer are applied in the X direction in conjunction with the fix move command to execute the sinusoidal vibration of Hanning modulation. The single-cycle excitation time of the ultrasonic wave with a frequency of 5THz is 5,000 steps, and the number of cycles and the excitation frequency can be adjusted as needed. After the ultrasonic excitation is completed, it continues to run for 30,000 steps to realize the ultrasonic propagation process. The ultrasonic excitation and propagation process are both run under the NVE ensemble. (10) The model is divided into 400 regions along the X direction, and the ultrasonic displacement information of the 400 regions is obtained to extract the frequency domain information in the ultrasonic propagation process. (11) The atomic trajectory file is visualized using OVITO software. The x-direction displacement in the model output file is selected through the color coding module, and the upper and lower limits are set to -0.1Å to 0.1Å to obtain the real-time ultrasonic propagation map. The atomic trajectory files were visualized using OVITO software. The x-direction displacement in the model output file was selected using the color coding module, with upper and lower limits set from -0.1 Å to 0.1 Å to obtain the real-time ultrasonic wave propagation map. Figure 3 As shown.

[0125] like Figure 3 As shown in the figure, this diagram illustrates the accumulation of secondary acoustic nonlinear parameters during ultrasonic wave propagation when a normal stress is applied along the X-direction. In the initial stage of ultrasonic wave propagation, the accumulation of nonlinear parameters fluctuates significantly; within the linear accumulation range, the acoustic nonlinear parameters increase linearly with increasing propagation distance. Simultaneously, the slope of the secondary acoustic nonlinear parameters continuously increases with increasing applied stress. Figure 4 As shown, the cubic acoustic nonlinear parameters also exhibit a trend of increasing slope with increasing stress. Due to the low generation efficiency, the fluctuations in the curves are more pronounced. Furthermore, the figure allows for comparison of acoustic nonlinear parameters at the same location or with the same propagation distance before and after stress application, providing more effective data support for complex practical detection requirements.

[0126] like Figure 5 As shown in the figure, this graph illustrates the accumulation of secondary acoustic nonlinear parameters during ultrasonic wave propagation when negative stress is applied along the X-direction. With increasing applied stress, the secondary acoustic nonlinear parameters initially decrease and then increase. Figure 6 As shown, the cumulative effects of the three acoustic nonlinear parameters exhibit the same trend.

[0127] like Figure 7 As shown in the figure, this graph illustrates the accumulation of secondary acoustic nonlinear parameters during ultrasonic wave propagation when a normal stress is applied along the Y direction. The slope of the secondary acoustic nonlinear parameters remains almost constant as the applied stress increases. Figure 8As shown, the cumulative effects of the three acoustic nonlinear parameters exhibit the same trend.

[0128] like Figure 9 As shown in the figure, this graph illustrates the accumulation of secondary acoustic nonlinear parameters during ultrasonic wave propagation when a normal stress is applied along the Z-direction. The slope of the secondary acoustic nonlinear parameters remains almost constant as the applied stress increases. Figure 10 As shown, the cumulative effects of the three acoustic nonlinear parameters exhibit the same trend. The results indicate that the ultrasonic nonlinear parameters are highly sensitive to stresses in the same direction as the ultrasonic wave propagation, but insensitive to stresses orthogonal to the ultrasonic wave propagation direction. The dynamic relationship between the nonlinear parameters and stress can be intuitively seen through the accompanying figures of this embodiment.

[0129] A stress-free model satisfying ultrasonic wave propagation was established. Prestressed models under different stress states with the same microstructure were prepared using the Fix deform command in LAMMPS software. Dislocation nucleation was monitored to achieve real-time diagnosis and adaptive saving of the stress state. Hanning-modulated ultrasonic longitudinal waves were applied to atoms in the X=0-X / 100Å interval of each prestressed model using the Fix move command in LAMMPS software to avoid disturbances caused by new energy during ultrasonic wave propagation in the NVE ensemble. Post-processing analysis was performed on the trajectory files to identify the ultrasonic wave propagation process under stress. The model was divided into z+(n+1) equal regions along the X direction, with the acoustic nonlinear parameters varying with i = z+(n+1) in each i-division. Each region contained only a single layer of atomic planes, enabling real-time acquisition of the ultrasonic wave propagation process. Harmonic components were obtained with high precision based on time-frequency joint analysis. Piecewise linear regression and Bayesian variable point detection were used to determine the linear variation range of the acoustic nonlinear parameters. The slope within the linear range was used to analyze the influence of stress on the ultrasonic harmonic generation efficiency.

[0130] In summary, this invention employs molecular dynamics simulation, which effectively reduces experimental costs and consumption, captures the entire process of ultrasonic harmonic generation under stress, avoids experimental errors introduced by specimen deformation, attenuation, and changes in coupling state, provides microscopic information and data support for macroscopic detection results, and improves the accuracy of residual stress detection. Based on the varying magnitudes and directions of residual stress in the parts, pre-loaded models with different stress magnitudes and directions are constructed using LAMMPS software. Harmonic components are efficiently extracted from Hanning-modulated ultrasonic waves excited by each model, and the influence of stress magnitude and direction on harmonic generation efficiency is studied. This invention can observe the generation relationship of harmonics with stress state changes during ultrasonic wave propagation, providing a theoretical basis for experimental residual stress analysis and performance evaluation.

Claims

1. A method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics, characterized in that, Includes the following steps: S1: Pre-stressed models with different stress magnitudes and directions are prepared. The preparation process includes applying multi-directional stress to the unloaded model, setting the strain rate, performing deformation once at each time step, performing strain simulation, and saving the current loading state. The unloaded model is constructed based on the conjugate gradient algorithm to minimize the energy of the aluminum single crystal. The applied multi-directional stress is one of the normal stress, negative stress, and shear stress within the elastic deformation range of the material. The direction of the multi-directional stress is one of the X, Y, and Z directions in the three-dimensional coordinate system. S1 also includes calculating the stress components and tensor components of each atom in the aluminum single crystal to obtain the von Mises stress. Extract the stress and strain data from the prestressed model, specifically: ； In the formula, , , All are stress components. , , All are tensor components. The strain simulation also includes an adjustment to the current loading state saving strategy based on dislocation nucleation early warning; specifically... ； This is the actual storage interval. As the initial save interval, when hour, Take 1, when hour, Let G be 0, and let G be the shear modulus. It is a scaling factor; S2: Apply ultrasonic waves to the prestressed model after preparation to obtain a trajectory file, wherein the stress stored in the trajectory file is uniformly distributed; S3: Divide the model into equal regions under the direction of detection, extract the acoustic signal of the region through which the ultrasonic wave passes, solve for the time-varying amplitude, and calculate the acoustic nonlinear parameters based on multiple time-varying amplitude values; S4: By constructing a harmonic linear accumulation region using acoustic nonlinear parameters and performing linear fitting, the harmonic generation efficiency under multi-directional stress is obtained.

2. The method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics as described in claim 1, characterized in that, In S1, after constructing an unloaded model of aluminum single crystal, the unloaded model is relaxed in the NVT and NPT ensembles. Combined with the Nosé-Hoover thermostat, a structurally stable unloaded model is obtained after relaxation.

3. The method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics as described in claim 2, characterized in that, In S2, a Hanning-modulated sine wave is applied to the prestressed model after preparation. Specifically, ； In the formula, A is the amplitude, step is the time step, T is the excitation frequency of the ultrasonic wave, R=T*S, S is the number of ultrasonic waves excited, dt is the size of the time step, and Hanning modulated sinusoidal vibration is applied to the ultrasonic excitation layer. After the excitation is completed, the ultrasonic wave propagation process is simulated.

4. The method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics as described in claim 3, characterized in that, In S3, the model is divided into single-atom-layer regions in the X direction, and the ultrasonic displacement signal of each region is obtained. Continuous wavelet transform is performed, and the complex Morlet wavelet is selected as the mother wavelet. ； ； ； ； ； ； ； In the formula, For the mother wavelet, It is an imaginary number. For time, Frequency resolution is controlled by bandwidth parameters. Here, 'a' is the center frequency of the mother wavelet, and 'a' is the scale parameter. For frequency analysis, b is the translation parameter. Let n be the time-varying amplitude value of the nth harmonic. Given an nth-order time-frequency matrix, the excitation frequency is obtained by using the nth-order time-frequency matrix. The time-varying amplitude A1, twice the excitation frequency The time-varying amplitude A2, 3 times the excitation frequency The time-varying amplitude value A3, For secondary acoustic nonlinear parameters, For cubic acoustic nonlinear parameters, n = 1, 2, 3.

5. The method for analyzing the effect of stress on ultrasonic harmonics based on molecular dynamics as described in claim 4, characterized in that, In S4, the acoustic nonlinear parameters vary with the propagation distance after being divided into i equal parts. The dataset is obtained as follows , Piecewise linear regression models are constructed, where k unknown variable points divide the curve into k+1 segments. The quadratic acoustic nonlinear parameters satisfy a linear relationship within each segment. , ； Uniform(1, ); ； ； ； In the formula, Let i represent the random fluctuation noise assumed to exist in the line segment, and let i be the number of equally divided monoatomic layers. For the intercept parameter, For the slope parameter, Let N be the maximum distance that an ultrasound wave can travel, and N be the normal distribution function. The intercept and slope are the a priori guesses of the average in a linear relationship. For the covariance matrix, the variable point Let the discrete uniform distribution be Uniform(1, ), where each parameter and noise variance Let the conjugate distributions be the normal distributions. and inverse-gamma distribution By using Markov chain Monte Carlo sampling to jointly sample the posterior distribution P( , , | , ), calculate the variable point Marginal posterior distribution P( | , ),in, The variable point configuration with the highest posterior probability is selected, and the linear variation range of acoustic nonlinear parameters is determined based on Bayesian variable point detection. The longest continuous interval with stable slope and small fitting residual is the harmonic linear accumulation region. The stress-induced ultrasonic harmonic generation efficiency is obtained through this slope.

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