Method for measuring single crystal elastic constants of polycrystalline alloy material based on ultrasonic complex wave number

Abstract

This invention belongs to the field of ultrasonic nondestructive testing technology, specifically relating to a method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement. The method includes: S1, determining the physical relationship between the ultrasonic longitudinal wave parameters and the theoretical values ​​of the single-crystal elastic constant of the polycrystalline alloy material; S2, performing multi-frequency ultrasonic testing on the polycrystalline alloy material to obtain ultrasonic longitudinal wave signals, and acquiring the phase velocity spectrum and longitudinal wave attenuation coefficient; S3, based on the phase velocity spectrum and longitudinal wave attenuation coefficient obtained in S2, constructing a joint error objective function to determine the correction value of the single-crystal elastic constant of the polycrystalline alloy material. This invention establishes a unified propagation model considering grain scattering effects, utilizes multi-frequency information on phase velocity and wave attenuation, extends the traditional sound velocity method to a joint inversion of complex wavenumbers, derives the effects of dispersion and wave attenuation, improving the accuracy and applicability of single-crystal elastic constant measurement of polycrystalline alloy materials, and is suitable for rapid nondestructive testing of alloy materials.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic nondestructive testing technology, specifically to a method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement. Background Technology

[0002] The single-crystal elastic constant is a fundamental parameter characterizing the elastic mechanical behavior of crystalline materials. It directly determines the stress-strain response of the material within a small strain range and further affects the calculation results of macroscopic mechanical parameters such as elastic modulus, shear modulus, and Poisson's ratio. The single-crystal elastic constant is not only crucial for understanding the intrinsic mechanical properties of single-crystal materials but also plays a vital supporting role in constitutive modeling of polycrystalline alloys, micro-macroscopic mechanical correlation, fatigue and fracture mechanism explanation, plastic deformation and microstructure evolution analysis, and service performance evaluation. Therefore, accurately obtaining the single-crystal elastic constant of a material has long been an important research and engineering requirement in the field of materials testing and nondestructive testing.

[0003] Existing methods for testing the elastic constants of single crystals are generally divided into two categories depending on the material morphology: direct measurement methods for single-crystal samples and inversion measurement methods for polycrystalline samples. For single-crystal samples, under conditions unaffected by polycrystalline factors such as grain boundaries and textures, the elastic constants can be directly obtained using methods such as resonance spectroscopy, Brillouin scattering, and ultrasonic velocity methods. The theoretical model is clear, and the measurement chain is relatively straightforward. However, single-crystal preparation, especially for engineering alloys such as high-temperature alloys, is difficult, time-consuming, and costly. Furthermore, it is often difficult to provide single-crystal samples that meet the testing requirements in a timely manner for new material systems. With the continuous emergence of new alloys and additive manufacturing materials, the traditional approach of "preparing single crystals first and then measuring" faces significant limitations in engineering applications. This has prompted academia and industry to continuously explore single-crystal elastic constant measurement and inversion techniques based on polycrystalline alloy materials to achieve faster, non-destructive, and engineering-oriented parameter acquisition.

[0004] In the measurement of single-crystal elastic constants of polycrystalline alloys, ultrasonic methods have attracted widespread attention due to their advantages such as non-contact / contact operation, online application, minimal material damage, and applicability to complex environments. The common approach involves establishing a relationship between wave velocity and equivalent elastic parameters using a polycrystalline averaging model and the intrinsic Christoffel equation for plane waves in anisotropic elastic media. The single-crystal elastic constants are then inverted using one or more measured ultrasonic velocity parameters. However, because polycrystalline alloys consist of numerous grains, the grain size is often on the same order of magnitude as the ultrasonic wave length used, inevitably leading to grain scattering during ultrasonic propagation. Scattering not only causes energy wave attenuation, manifested as a frequency-dependent longitudinal wave attenuation coefficient, but also results in sound velocity dispersion, meaning different phase velocities at different frequencies. In this situation, if the "ideal homogeneous medium wave velocity," which ignores scattering effects, is still used as the inversion input, it will be difficult to reflect the actual propagation physics, thus leading to systematic bias or increased uncertainty in the correction value of the single-crystal elastic constants.

[0005] To address the aforementioned issues, a unified complex wavenumber scattering model proposes a theoretical framework to describe the influence of polycrystalline scattering on propagation. This framework introduces the perturbation term caused by the local anisotropy of individual grains into the Christoffel equation, transforming the wavenumber of a homogeneous medium into an "effective complex wavenumber." This invention enables the acquisition of observations containing both phase velocity and wave attenuation, along with frequency dimension information, based on engineering-implemented ultrasonic testing methods, without relying on the preparation of single-crystal samples. Furthermore, within the framework of a unified complex wavenumber scattering model addressing the effects of dispersion and wave attenuation caused by grain scattering, a quantitative relationship between the complex wavenumber and the single-crystal elastic constant is established. This allows for stable and accurate inversion of the single-crystal elastic constant even under conditions of insufficient observation dimensions or significant errors in traditional wave velocity methods. These requirements constitute the technical background and practical application drivers for this invention. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention aims to provide a method for detecting the single-crystal elastic constants of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement. By establishing a unified propagation model considering grain scattering effects, and within the framework of unified scattering theory, the method utilizes multi-frequency phase velocity and multi-frequency longitudinal wave attenuation coefficient information to achieve the inversion determination of the single-crystal elastic constants of polycrystalline alloy materials. Through a complex wavenumber joint inversion mechanism of "multi-frequency phase velocity spectrum + multi-frequency wave attenuation spectrum," and simultaneously introducing the dispersion and wave attenuation effects caused by material grain scattering, compared to traditional inversion methods based solely on sound velocity, this method can improve the dimensionality of observational information and reduce the influence of underdetermined and systematic errors. The experimentally obtained sound velocity spectrum and attenuation spectrum are simultaneously used as constraints, along with the theoretical sound velocity spectrum and theoretical attenuation spectrum output from the first-layer model. Joint matching is performed to improve the accuracy and stability of single-crystal elastic constant measurement of polycrystalline alloy materials. Complex wavenumber is used as a unified characterization quantity, and multi-frequency measurement results of phase velocity and longitudinal wave attenuation coefficient are fused within the same inversion framework. This forms a multi-dimensional constraint relationship on the single-crystal elastic constant of polycrystalline alloy materials over a wide frequency band, thereby improving the sensitivity and noise resistance of parameter identification. By introducing microstructural statistical information such as grain size as model input or constraint, good consistency and repeatability of results are maintained at different grain scales and under different material conditions. Simultaneously, quality evaluation indicators such as residuals and convergence are obtained, enabling rapid, non-destructive, and engineering-grade determination of the single-crystal elastic constant of polycrystalline engineering materials. This provides reliable basic data support for material selection, service evaluation, and multi-scale mechanical modeling.

[0007] Specifically, the present invention provides a method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement, which includes the following steps: S1: Determine the physical relationship between the ultrasonic longitudinal wave parameters of polycrystalline alloy materials and the theoretical values ​​of the single-crystal elastic constants, obtain the theoretical values ​​of the phase velocity spectrum and wave attenuation spectrum within the effective bandwidth of the ultrasonic probe, and determine the effective complex wave number of the longitudinal wave through complex nonlinear equations. A complex nonlinear equation after scattering correction was established with the effective complex wavenumber of longitudinal waves as the core quantity; a unified complex wavenumber scattering model that satisfies the grain scattering effect of polycrystalline alloy materials was determined. S2: Multi-frequency ultrasonic testing of polycrystalline alloy materials yields ultrasonic longitudinal wave signals, providing the phase velocity spectrum and attenuation coefficient of the longitudinal waves. Specifically, this includes: S21: Establish the spectral expressions for the first and second bottom surface echoes to obtain the first bottom surface echo. Second bottom surface echo ; S22: The phase velocity spectrum is measured by the phase difference between the first and second bottom surface echoes of the longitudinal wave to determine the first bottom surface echo. Corresponding phase spectrum and the second bottom surface echo Corresponding phase spectrum The phase difference between the first and second bottom surface echoes of the longitudinal wave is obtained, thus yielding the phase velocity spectrum of the longitudinal wave. ; S23: Determine the wave attenuation spectrum from the amplitude frequency spectrum, and combine it with the first bottom surface echo from step S21. Second bottom surface echo Obtain the longitudinal wave attenuation coefficient ; S3: Based on the phase velocity spectrum and attenuation coefficient of the longitudinal wave obtained in S2, and combined with the unified complex wavenumber scattering model in step S1, construct a joint error objective function to determine the correction value of the single-crystal elastic constant of the polycrystalline alloy material, including: the positive tensile and compressive stiffness of the polycrystalline alloy material. Coupling stiffness of polycrystalline alloy materials and the shear stiffness of polycrystalline alloy materials This allows us to obtain the key parameters for controlling the mechanical response of metals.

[0008] Preferably, the theoretical values ​​of the single-crystal elastic constants in step S1 include the positive tensile and compressive stiffness. Coupling stiffness and shear stiffness The expression for the physical relationship is: ; in, For the first The estimated effective complex wave number of the P-wave in the next iteration; This represents the number of iterations. For updating the iterative mapping function; For the iterative parameter terms of the complex nonlinear transcendental equation; For the longitudinal wave number characteristic parameter of a homogeneous medium; For a homogeneous medium, the longitudinal wave number is [value missing]. is the macroscopic average elastic constant of the polycrystalline alloy material.

[0009] Preferably, step S1 specifically includes: S11: Based on the unified complex wavenumber scattering theory of ultrasound, establish the governing equation for the effective complex wavenumber of longitudinal waves; S12: Determine the physical relationship between the grain structure parameters, ultrasonic properties, and single-crystal elastic constants of polycrystalline alloy materials; S13: Determining the effective complex wave number of the P-wave using complex nonlinear equations Establish the effective complex wave number of the longitudinal wave. Phase velocity in longitudinal wave theory and longitudinal wave attenuation coefficient The conversion relationship between them; S14: The governing equations are solved using an iterative numerical method to obtain the theoretical phase velocity spectrum and theoretical attenuation spectrum of the longitudinal wave within the effective bandwidth of the ultrasonic probe, and to determine the effective complex wave number of the longitudinal wave. A unified complex wavenumber scattering model relating the theoretical values ​​of single-crystal elastic constants and grain structure parameters.

[0010] Preferably, the effective complex wave number of the longitudinal wave in step S11 satisfies the following relationship: ; in, This is an estimate of the effective complex wave number of the P-wave. This is the perturbation term caused by grain scattering.

[0011] Preferably, the relationship between the macroscopic average elastic constant of the polycrystalline alloy material and the single-crystal elastic constant in step S12 is as follows: ; ; in, For the elastic anisotropy parameters of cubic crystals; For material coupling stiffness; For material shear stiffness; This refers to the material's positive tensile and compressive stiffness.

[0012] Preferably, the expressions for the first bottom surface echo and the second bottom surface echo in step S21 are as follows: ; ; ; in, The first bottom surface echo; The incident wave spectrum; The angular frequency of the ultrasonic testing system in frequency domain analysis; This is the first bottom surface transmission coefficient term; This is the reflection coefficient term for the first bottom surface; For the first bottom surface diffraction correlation terms; The longitudinal wave attenuation coefficient; The thickness of the material sample; The phase velocity in longitudinal wave theory; For the first bottom surface system delay term; It is a natural base constant; The second bottom surface echo; This is the second bottom surface transmission coefficient term; This is the reflection coefficient term for the second bottom surface; For the second bottom surface diffraction correlation terms; For the second bottom surface system delay term; It is a complex number.

[0013] Preferably, the phase difference between the first bottom surface echo and the second bottom surface echo of the longitudinal wave in step S22 is: ; ; in, The phase difference between the two bottom surface echoes of the longitudinal wave; The phase spectrum of the first bottom surface echo; The phase spectrum of the second bottom surface echo; It represents the equivalent time shift between the first bottom surface echo and the second bottom surface echo.

[0014] Preferably, the phase velocity spectrum of the longitudinal wave in step S22 for: ; ; in, The phase velocity spectrum of the longitudinal wave; The thickness of the material sample; The phase difference between the two bottom surface echoes of the longitudinal wave; To evaluate the parameters of a function; for The first bottom surface echo at that moment; for The second bottom surface echo at time; The time sampling interval is denoted as .

[0015] Preferably, the longitudinal wave attenuation coefficient in step S23 for: ; in, The longitudinal wave attenuation coefficient; It is the natural logarithm function; The first bottom surface echo; The second bottom surface echo; The first bottom surface echo of the reference polycrystalline alloy material sample; The second bottom surface echo is for reference to the polycrystalline alloy material sample.

[0016] Preferably, step S3 specifically includes: S31: Obtain the grain size of polycrystalline alloy materials As input parameters; grain size Substituting the unified complex wavenumber scattering model established in step S1, the effective complex wavenumber of the P-wave is obtained. Thus, the phase velocity of the longitudinal wave theory is obtained. With the theoretical attenuation coefficient of longitudinal waves ; S32: Construct a joint error objective function and perform numerical optimization to invert the correction value of the single-crystal elastic constants; adjust the positive tensile and compressive stiffness in step S1. Coupling stiffness and shear stiffness As initial parameters, a joint error objective function is constructed using multi-frequency phase velocity and multi-frequency wave attenuation. And a numerical optimization method is used to optimize the joint error objective function. Perform iterative updates; S33: Use the optimal solution obtained by iterative update as the correction value of the single crystal elastic constant of the polycrystalline alloy material.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention proposes an ultrasonic complex wavenumber method for polycrystalline alloy materials. By establishing a unified propagation model that considers grain scattering effect, under the unified scattering theory framework, and using the information of multi-frequency phase velocity and multi-frequency longitudinal wave attenuation coefficient, ultrasonic propagation is regarded as a process that simultaneously includes "propagation phase change" and "energy loss". Thus, it is possible to describe the changes in sound velocity and attenuation at different frequencies under the same framework, and realize the inversion determination of the single crystal elastic constant of polycrystalline alloy materials, thereby improving the measurement accuracy and engineering applicability.

[0018] (2) This invention uses a complex wavenumber joint inversion mechanism of “multi-frequency phase velocity spectrum + multi-frequency wave attenuation spectrum”, and introduces the dispersion and wave attenuation effects caused by material grain scattering. Compared with the traditional inversion method based only on sound velocity, it can improve the dimension of observation information and reduce the influence of underdetermined and systematic errors. The experimentally obtained sound velocity spectrum and attenuation spectrum are used as constraints and are jointly matched with the theoretical sound velocity spectrum and theoretical attenuation spectrum output by the first layer model, thereby improving the accuracy and stability of the measurement of the single crystal elastic constant of polycrystalline alloy materials. It is suitable for engineering polycrystalline alloy materials that are difficult to prepare single crystals.

[0019] (3) This invention uses the complex wavenumber as a unified characterization quantity and integrates the multi-frequency measurement results of phase velocity and longitudinal wave attenuation coefficient within the same inversion framework. This forms a multi-dimensional constraint relationship on the single-crystal elastic constants of polycrystalline alloy materials over a wide frequency band, thereby improving the sensitivity and noise resistance of parameter identification. By introducing microstructural statistical information such as grain size as model input or constraint, this invention can maintain good consistency and repeatability of results at different grain scales and under different material conditions, and simultaneously obtain quality evaluation indicators such as residuals and convergence. Therefore, this invention is beneficial for realizing rapid, non-destructive, and engineering-oriented determination of the single-crystal elastic constants of polycrystalline engineering materials, providing reliable basic data support for material selection, service evaluation, and multi-scale mechanical modeling. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for measuring and evaluating the single-crystal elastic constants of polycrystalline alloy materials based on ultrasonic complex wavenumber inversion, according to the present invention. Figure 2 This is a schematic diagram of ultrasonic testing in an embodiment of the present invention; Figure 3 This is a curve fitting diagram of the experimental longitudinal wave attenuation coefficient and the theoretical curve in an embodiment of the present invention; Figure 4 This is a curve fitting diagram of the experimental phase velocity versus the theoretical curve in an embodiment of the present invention; Figure 5 This is a detailed flowchart of the ultrasonic complex wavenumber inversion method in this embodiment of the invention; Figure 6 This is a graph showing the phase velocity data obtained in the ultrasonic frequency band during actual detection in an embodiment of the present invention; Figure 7 This is a graph showing the attenuation data obtained in the ultrasonic frequency band during actual testing, according to an embodiment of the present invention.

[0021] Key reference numerals: 1. Coupling agent; 2. Phased array probe; 3. Detection sample. Detailed Implementation

[0022] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0023] This invention provides a method for detecting the single-crystal elastic constants of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement, such as... Figure 1 As shown, a unified complex wavenumber scattering model satisfying the grain scattering effect of polycrystalline alloy materials is established to obtain the relationship between the complex wavenumber and the single-crystal elastic constant and grain structure parameters. Multi-frequency ultrasonic testing is performed on the polycrystalline alloy material, and the two bottom echoes are analyzed to obtain the phase velocity spectrum and longitudinal wave attenuation coefficient. A joint error objective function is constructed, and the single-crystal elastic constant of the polycrystalline alloy material is determined for quality assessment. This invention addresses the common problem of polycrystalline alloy materials but the difficulty in directly measuring the single-crystal elastic constant by proposing a practical non-destructive testing process: when ultrasound propagates in a sample, the wave not only "travels fast or slow" (represented by sound speed) but also "weakens as it travels" (represented by attenuation) due to grain scattering, and both phenomena change with frequency. Therefore, this invention proposes a method using "ultrasonic complex wavenumber inversion" to measure the single-crystal elastic constant of polycrystalline alloys. , , The purpose of this detection method is to deduce the elastic parameters of the single-crystal layer from common polycrystalline samples without damaging the material or requiring oriented single-crystal samples. The technical term "inversion" in this invention refers to the process of using experimentally measured phase velocity and attenuation spectra to perform error matching and optimization iteration with the theoretical results output by the forward model, thereby deriving the corrected value of the single-crystal elastic constant that best matches the experimental results. Forward modeling refers to the process of substituting known material parameters such as single-crystal elastic constants and grain size into a unified complex wavenumber scattering model to calculate the corresponding effective complex wavenumber of longitudinal waves, as well as the theoretical phase velocity spectrum and theoretical attenuation spectrum. Traditional ultrasonic methods often only use the ultrasonic arrival time to obtain an average sound velocity, or only measure attenuation to obtain an empirical index, making it difficult to simultaneously explain the grain scattering effect that is prevalent in polycrystalline materials, and thus difficult to reliably deduce the single-crystal elastic constants. The core idea of ​​this invention is as follows: First, a unified model is established that can simultaneously describe "sound velocity changing with frequency" and "energy attenuation during propagation," treating these two phenomena as two manifestations of the same propagation process, and linking them to structural parameters such as single-crystal elastic constants and grain size. Then, multi-frequency ultrasonic testing is performed on the sample to extract the sound velocity spectrum and attenuation spectrum of the longitudinal wave at different frequencies, obtaining experimental data reflecting the true propagation characteristics of the material. Finally, the experimentally obtained sound velocity spectrum and attenuation spectrum are jointly matched with the model prediction results, and the parameter combination that best explains both types of data is obtained through iterative optimization, thereby acquiring the single-crystal elastic constants. Because this method integrates sound velocity and attenuation information into the same model and performs joint inversion, compared to using only a single sound velocity or a single attenuation index, it can significantly reduce errors caused by factors such as grain scattering and system frequency response, improving the stability and reliability of the inversion results. It is suitable for non-destructive elastic parameter characterization and quality consistency assessment of polycrystalline alloy materials. Specifically, the steps include: Step S1: Establish a unified complex wavenumber scattering model that satisfies the grain scattering effect of polycrystalline alloy materials, and obtain the relationship between the complex wavenumber and the single-crystal elastic constant and grain structure parameters. This invention first establishes a unified propagation model considering the grain scattering effect. This model does not simply provide an "average sound velocity," but rather treats ultrasonic propagation as a process that simultaneously includes "propagation phase change" and "energy loss," thus enabling the description of sound velocity changes and attenuation changes at different frequencies within the same framework. More importantly, the model explicitly introduces the single-crystal elastic constant. , , Furthermore, by using structural information such as the orientation average and grain size of the polycrystalline material, these single-crystal constants are correlated with the macroscopic propagation response of the polycrystalline material. In other words, the model obtains "what kind of sound velocity spectrum and attenuation spectrum should be observed within the effective frequency band of the ultrasonic probe if the single-crystal constants of the material are a certain set of values ​​and the grain structure is a certain state." The unified complex wavenumber scattering model refers to the effective complex wavenumber theoretical model established through steps S11-S15, used to describe the influence of polycrystalline alloy grain scattering on ultrasonic complex wave propagation; taking longitudinal waves as an example, the unified complex wavenumber scattering model incorporates the disturbance term caused by grain scattering. Introducing the wavenumber relationship of a homogeneous medium, the effective complex wavenumber of the longitudinal wave is... See step S11 for the complex nonlinear equations. The unified complex wavenumber scattering model simultaneously characterizes phase velocity dispersion in the same complex wavenumber variable, expressed by the real part of the complex wavenumber. The amplitude attenuation is determined by the imaginary part of the complex wave number. This decision allows for unified modeling and joint inversion of the phase velocity spectrum and wave attenuation spectrum. For example... Figure 2 The diagram illustrates ultrasonic testing in an embodiment of the present invention. Ultrasonic testing of the sample 3 is performed using a phased array probe 2. The coupling agent 1 efficiently transmits the ultrasonic energy from the probe to the workpiece and efficiently transmits the echo back to the probe, eliminating / reducing the influence of the air layer, improving transmission efficiency, improving the contact interface, stabilizing the echo amplitude and phase, reducing interface-related losses and coupling fluctuation errors, protecting the probe and workpiece surfaces, and facilitating scanning. The unified complex wavenumber scattering model is established at the overall level in step S1. The basic control relationships of the model are given in step S11, and the numerical solution of the model in the experiment is completed in step S14.

[0024] Step S11: Based on the unified complex wavenumber scattering theory of ultrasound, establish the governing equation for the effective complex wavenumber of the longitudinal wave; based on the control relationship between the disturbance of the ultrasonic complex wave and the unified complex wavenumber scattering model, taking the longitudinal wave as an example, the effective complex wavenumber of the longitudinal wave is obtained as follows: ; in, The effective complex wave number of the longitudinal wave; For a homogeneous medium, the longitudinal wave number is [value missing]. This is the perturbation term caused by grain scattering.

[0025] For polycrystalline alloys with cubic crystal system, no texture, and equiaxed grain characteristics, a unified complex wavenumber scattering model is used to obtain the specific solution form of the effective complex wavenumber of longitudinal waves, which is a complex nonlinear equation. The input parameters of the complex nonlinear equation include: the average grain size of the material. Longitudinal wave number in homogeneous medium Shear wave number in a homogeneous medium And anisotropy coefficients related to the elastic constants of a single crystal, specifically in the form of: ; in, The average grain size of the material; For a homogeneous medium, the transverse wave number is [value missing]. The macroscopic average elastic constant of polycrystalline alloy materials; For the elastic anisotropy parameters of cubic crystals; It is the arctangent function; The wavenumber was determined in the experiment; These are the characteristic parameters of the longitudinal and transverse wavenumbers of a homogeneous medium.

[0026] In step S11, the effective complex wave number of the longitudinal wave The solution employs complex nonlinear equations and Joint determination: The square of the effective complex wave number of the P-wave was obtained from the complex nonlinear equation. relative to the square of the reference P-wave wavenumber offset A quantitative relationship between the offset and the material scattering / perturbation intensity parameter, wherein the offset is determined by a constant coefficient and several parameters related to... , , The complex function terms together constitute the expression used to characterize the dispersion and attenuation effects caused by the microstructure of the medium; the formula is used... Further regulations It is in complex form, that is The real part corresponds to the phase propagation term The imaginary part corresponds to the attenuation term. Thus making the same It simultaneously carries both "propagation speed information" and "energy attenuation information." Specifically, in complex nonlinear equations, Represents the anisotropy coefficient. Represents the elastic constant components, For equivalent grain size, and These are the reference wave numbers for longitudinal and transverse waves, respectively. The imaginary unit; the numbers appearing in the formula Let be the arctangent function of a complex variable, whose independent variable is of the form: and This is used to characterize the different contributions of the P-wave and S-wave channels to the scattering response; the subsequent polynomial-fractional combination terms within the parentheses, for example, contain... , , , Items and related , Different combinations of coefficients are used to express frequency-related corrections of different orders; at the same time, the complex nonlinear equations also contain several rational terms, such as those in the denominator. or The structure and explicit complex linear / higher-order terms, for example, with , , These related terms collectively reflect the combined influence of P-wave and S-wave coupling, near-field terms, and higher-order scattering terms on the complex wavenumber. In actual calculations, [the following terms are used]. , , , , , Using these as initial values, the formula is first applied. get The parameterized form, containing unknowns and Or, an equivalent unknown complex wavenumber can be substituted into a complex nonlinear equation to construct a function relating to... The complex nonlinear equations are solved by iterative numerical methods to obtain... Ultimately by Separation phase velocity With attenuation coefficient This enables the unified inversion of the longitudinal wave dispersive spectrum and the attenuation spectrum.

[0027] effective complex wave number of longitudinal waves To establish the scattering-corrected complex nonlinear equations for the core quantities: First, the offset of the square of the effective complex wavenumber of the P-wave relative to the square of the background P-wave number is defined using complex nonlinear equations. This offset is determined by the coefficient. Standardize the scattering intensity and reference stiffness, and specify the values ​​in parentheses regarding... , , The complex function term obtains frequency-related corrections; where the parentheses first contain two sets of terms... and The terms with the core characterize the difference in scattering contributions from background P-waves and background S-waves, respectively, and are subsequently expanded with polynomials / fractions, containing... , , , Equal terms and , Coupling with different coefficients characterizes dispersion and attenuation corrections of different orders; simultaneously, several rational terms are introduced into the formula, the denominator of which contains or The structure and explicit complex linear and higher-order terms, such as with and Related terms are used to comprehensively reflect the effects of P-wave and S-wave coupling, near-field effects, and higher-order scattering terms on... The impact; secondly, the use of formulas Regulation ,Right now real part Corresponding phase propagation and determining the phase velocity of the longitudinal wave imaginary part The corresponding amplitude decays exponentially and determines the longitudinal wave attenuation coefficient, thus enabling the solution of the complex nonlinear equation to obtain... Simultaneously obtaining the dispersion and attenuation characteristics of materials within the same framework; in practical calculations, , , , , and As input, construct complex nonlinear equations And obtained by iterative numerical method Then based on and The longitudinal wave phase velocity and attenuation parameters are separated, thus providing a basis for the unified prediction and parameter inversion of subsequent multi-frequency sound velocity spectrum and attenuation spectrum.

[0028] The core improvement of this invention is primarily reflected in the unified complex wavenumber scattering model; compared to the known longitudinal wavenumber of homogeneous media... To obtain only single-phase velocity information, this invention application uses grain scattering as a perturbation term. By explicitly incorporating the wavenumber equation, the effective complex wavenumber relation is obtained. And obtain the computational expansion under cubic crystal, untextured, and equiaxed grain conditions; the technical meaning of this "deformation" is: to change the real wavenumber, which was originally determined only by the macroscopic homogeneous medium, to be simultaneously determined by the average grain size of the material. The elastic anisotropy parameter of cubic crystal Macroscopic average elastic constant of polycrystalline alloy materials The complex solution with equal control makes the elastic constant of the single crystal to be inverted not only affect the baseline sound velocity, but also affect dispersion and attenuation through the scattering term.

[0029] This invention provides an embodiment that obtains a set of actual inputs and forms an equation to be solved. A polycrystalline alloy sample is used for calculation at a certain frequency point. A single frequency point is demonstrated, and the frequency band is analyzed point by point in practice. , Average grain size The wave velocity in a homogeneous medium is estimated from density and macroscopic elastic parameters, specifically as follows: but Bundle Substituting the obtained expansion of "cubic crystal, untextured, equiaxed grains" yields a complex number about the unknown. Complex nonlinear equations: ,in It refers to the right-hand side of the expansion, which includes terms of arctan, fractions, and polynomials.

[0030] Note: The above is for example only. c11, c12, and c44 are unknowns and need to be substituted into the subsequent calculations. , , .

[0031] Step S12: Determine the physical relationship between the grain structure parameters, ultrasonic parameters, and single-crystal elastic constants of the polycrystalline alloy material; for the cubic crystal of the polycrystalline alloy material, the macroscopic average elastic constant of the polycrystalline alloy material is expressed using the Voigt average elastic constant as follows: ; in, The macroscopic average elastic constant of polycrystalline alloy materials; For the elastic anisotropy parameters of cubic crystals; For material coupling stiffness; This refers to the material's shear stiffness.

[0032] For cubic symmetric crystals, the commonly referred to elastic anisotropy parameter (the anisotropy constant for cubic symmetry) usually refers to the anisotropy parameter composed of the elastic constants of a single crystal, and it has units of GPa. for: ; in, This refers to the material's positive tensile and compressive stiffness.

[0033] Therefore, it can be concluded that under the condition of decoupling between the statistical quantity of grain morphology and the elastic property parameter of polycrystalline alloy material, the effective complex wave number is determined by both the statistical characteristics of grain size of polycrystalline alloy material and the single crystal elastic constant. Thus, when using ultrasonic parameters to determine the single crystal elastic constant of polycrystalline alloy material, the influence of grain size of polycrystalline alloy material cannot be ignored.

[0034] The embodiments of the present invention are calculated from the initial value of the single crystal constant. and Used for back-substitution step S11; take an initial engineering value, from the literature of the same alloy grade / previous batch inversion, specifically: but ; Note: The above is for illustrative purposes only. c11, c12, and c44 are unknowns and need to be substituted into the subsequent calculations.

[0035] Step S13: Establish the effective complex wave number of the P-wave Phase velocity in longitudinal wave theory and longitudinal wave attenuation coefficient The conversion relationship between them; the effective complex wave number of the longitudinal wave obtained by solving in step S11 within the frequency band is determined by the longitudinal wave attenuation coefficient. They are respectively: ; ; in, The angular frequency of the ultrasonic testing system in frequency domain analysis; The real part of the complex wave number corresponds to the phase accumulation rate when the longitudinal wave propagates in the polycrystalline alloy material being tested, and is the phase change per unit length, which determines the phase velocity spectrum in engineering. is the imaginary part of the complex wave number, which corresponds to the amplitude exponential wave attenuation rate when the longitudinal wave propagates in the polycrystalline alloy material under test, and in engineering it corresponds to the longitudinal wave attenuation coefficient spectrum. The phase velocity in longitudinal wave theory; This is the longitudinal wave attenuation coefficient.

[0036] This step uses the well-known complex wavenumber decomposition relation to split the same propagation variable into two types of observation spectra. The improvement here is not in the mathematical identity itself, but in the processing method. The phase velocity dispersion and scattering attenuation are consistently characterized in the same model output, thereby avoiding the neglect of scattering or empirical separation when only sound velocity is used for inversion in the traditional way. This is equivalent to expanding the observation information from a single sound velocity to a joint constraint of "multi-frequency phase velocity spectrum + multi-frequency attenuation spectrum" without increasing the number of propagation directions / modes.

[0037] Step S14: Solve the governing equations using an iterative numerical method to obtain the theoretical phase velocity spectrum and theoretical attenuation spectrum of the longitudinal wave within the effective bandwidth of the ultrasonic probe. Since the unified complex wavenumber scattering model is a complex nonlinear transcendental equation, it typically lacks an analytical solution. Therefore, this invention employs an iterative numerical method to solve for the complex wavenumber. In this embodiment, Steffensen's accelerated iteration method is used to obtain the theoretical values ​​of the phase velocity spectrum and wave attenuation spectrum within the effective bandwidth of the ultrasonic probe. For the complex nonlinear equations in step S11, the density of the polycrystalline alloy material being measured is first determined... And the range of macroscopic elastic moduli that can be obtained in engineering, such as Young's modulus values ​​from tensile tests or handbooks. Poisson's ratio Estimating wave velocity in a homogeneous medium Thus, the initial value of the wavenumber of the homogeneous medium is obtained. Then, the initial values ​​of the single-crystal elastic constants are... Substitute the literature value of the same alloy grade or the inversion value of the previous batch into step S12 for calculation. and As the numerical iterative solution in this step The initial parameter set. In this invention, the effective complex wave number of the longitudinal wave. It satisfies the complex nonlinear transcendental equation established by the unified scattering theory. The unified scattering theory refers to characterizing the comprehensive influence of polycrystalline grain scattering on ultrasonic propagation using the effective complex wavenumber: the real part of the complex wavenumber simultaneously determines phase accumulation and phase velocity dispersion, while the imaginary part simultaneously determines amplitude exponential wave attenuation and wave attenuation spectrum. Thus, dispersion and wave attenuation are modeled uniformly within the same mathematical framework and used to invert the elastic constants of single crystals. To facilitate numerical solutions, the complex nonlinear transcendental equation is rewritten in fixed-point form, and an iterative update operator for the effective complex wavenumber of longitudinal waves is introduced, which is the iterative mapping. Specifically: ; in, For the first The estimated effective complex wave number of the P-wave in the next iteration; This represents the number of iterations. For updating the iterative mapping function; For the iterative parameter terms of the complex nonlinear transcendental equation; For the longitudinal wave number characteristic parameter of a homogeneous medium; Let be the longitudinal wave number of the homogeneous medium; where, This represents the number of iterations. For the first The estimated effective complex wave number of the P-wave in the next iteration; To update the iterative mapping function, It is not a new physical parameter, but rather an update rule iterative function composed of the entire right-hand side expression of the above model, used to update the current estimate. Mapping to the next estimate ; The iterative parameter terms of the complex nonlinear transcendental equations represent the scattering perturbation terms, integral terms, and directional averaging terms obtained from steps S11 to S13. The equations show that in practical applications… At least explicitly dependent on the current iteration value Furthermore, it also depends on model parameters such as frequency, grain size, and equivalent dielectric constant; This is a characteristic parameter of the longitudinal wave number in a homogeneous medium.

[0038] This invention is based on the update iterative mapping function of fixed-point iteration. Construct an accelerated sequence; for each frequency point In the The calculation is performed in the next iteration, specifically as follows: At each frequency point effective complex wave number of longitudinal waves The unified complex wavenumber equation is determined by the equation derived in step S11. This is because the unified complex wavenumber equation is simultaneously related to the grain size of the polycrystalline alloy material being tested. Density of polycrystalline alloy materials And the single-crystal elastic constants to be inverted. , and This correlation, in turn, determines the elastic anisotropy parameters of the cubic crystal. Macroscopic average elastic constant of polycrystalline alloy materials Therefore, this invention obtains a set of material physical quantity parameters. Substitute into the update iterative mapping function For each frequency point, output the current iteration value. Specifically: ; ; in, This is an estimate of the effective complex wave number of the first longitudinal wave; This is an estimate of the effective complex wave number of the second longitudinal wave; It is a set of physical quantity parameters of materials.

[0039] Using Steffensen acceleration to obtain the first The effective complex wave number estimate of the P-wave in the next iteration Thus, given the polycrystalline alloy material parameters and frequency conditions, the effective complex wavenumber of the longitudinal wave can be obtained rapidly through convergence. Ultimately, the theoretical phase velocity and wave attenuation spectrum of longitudinal waves are formed for subsequent inversion.

[0040] The embodiments of the present invention are based on Parameter set Get initial value Example of how to write project records, demonstrating "complex solution + convergence": 0th iteration: ;calculate have to: ;calculate have to: Steffensen accelerated the update: If the convergence criterion is satisfied... like If the frequency is converged, then the convergence point is considered to be converged. Note: The above is for illustrative purposes only. , , As an unknown, it needs to be substituted into subsequent calculations. The final output of step S1 is: effective complex wave number of the P-wave. The solution relationship; the theoretical phase velocity spectrum obtained based on the complex wavenumber within the effective bandwidth of the probe; the theoretical wave attenuation spectrum obtained based on the complex wavenumber within the effective bandwidth of the probe; and the quantitative relationship between the above theoretical quantities and the single crystal elastic constant and grain structure parameters.

[0041] Step S2: Perform multi-frequency ultrasonic testing on the polycrystalline alloy material using a single propagation mode, measuring and calculating the phase velocity and longitudinal wave attenuation coefficient at each frequency point, and experimentally measuring the phase velocity spectrum and wave attenuation spectrum. The second layer is the measurement and data extraction layer: In actual testing, this invention uses longitudinal waves for multi-frequency ultrasonic testing and collects the echo signal from the bottom surface of the sample. By processing the phase and amplitude of the two bottom surface echoes in the frequency domain, two frequency-related experimental curves are obtained: one is the sound velocity spectrum, reflecting how fast the wave "propagates" at different frequencies; the other is the attenuation spectrum, reflecting how much the wave "loses" at different frequencies. To reduce the influence of system factors such as instrument frequency response, coupling state, and probe characteristics on the amplitude, this invention introduces a reference sample / reference echo for correction, making the obtained attenuation results closer to the intrinsic characteristics of the material rather than the characteristics of the equipment. At this stage, what is obtained is a set of experimental input data that can be repeated, compared, and covers the frequency band, rather than single-point sound velocity or single-point attenuation. This embodiment of the invention employs a pulse-echo contact measurement configuration; the pulse-echo contact measurement configuration refers to an ultrasonic transducer or phased array probe contacting the surface of the alloy sample through a coupling agent. The probe emits short pulse longitudinal waves and receives the echo signals reflected back from the bottom surface of the alloy sample. The first bottom surface echo and the second bottom surface echo are respectively intercepted through gating, utilizing the constant path difference between two adjacent bottom echoes. This invention features the ability to simultaneously extract phase velocity and wave attenuation spectra without changing the probe position, reducing geometric path uncertainty. It also extracts multi-frequency phase velocity and wave attenuation spectra by analyzing the amplitude and phase changes of two adjacent bottom surface echoes. In this embodiment, the first bottom surface echo is selected. With the second bottom surface echo Take measurements.

[0042] Step S21: Establish the spectral expressions for the first and second bottom surface echoes, specifically as follows: Obtain the first bottom surface echo for: ; ; in, The first bottom surface echo; The incident wave spectrum; The angular frequency of the ultrasonic testing system in the frequency domain analysis. The unit is , usually according to deal with; This is the first bottom surface transmission coefficient term; This is the reflection coefficient term for the first bottom surface; For the first bottom surface diffraction correlation terms; The thickness of the material sample; For the first bottom surface system delay term; It is a natural base constant; It is a complex number.

[0043] Obtain the second bottom surface echo for: ; in, The second bottom surface echo; This is the second bottom surface transmission coefficient term; This is the reflection coefficient term for the second bottom surface; For the second bottom surface diffraction correlation terms; This is the time delay term for the second bottom surface system.

[0044] Step S22: Measure the phase velocity spectrum based on the phase difference between the first and second bottom surface echoes of the longitudinal wave to determine the first bottom surface echo. Second bottom surface echo The corresponding phase spectra are respectively , Specifically: ; in, The phase spectrum of the first bottom surface echo; This is the phase spectrum of the second bottom surface echo.

[0045] The phase difference between the first bottom surface echo and the second bottom surface echo of the longitudinal wave is: ; in, This represents the phase difference between the two bottom surface echoes of the longitudinal wave.

[0046] Thus, the phase velocity spectrum of the longitudinal wave is obtained as follows: ; in, The phase velocity spectrum of the longitudinal wave; This is the equivalent time shift between the first bottom surface echo and the second bottom surface echo.

[0047] In the above formula, the molecule The units are length / time, and the denominator is... Since it is dimensionless, the result is speed.

[0048] The equivalent time shift between the first bottom surface echo and the second bottom surface echo Determined by the maximum cross-correlation value, specifically: ; in, To evaluate the parameters of a function; for The first bottom surface echo at that moment; for The second bottom surface echo at time; The time sampling interval is denoted as .

[0049] The maximum cross-correlation value is used to determine the optimal alignment of the two bottom surface echoes in the time domain. This is the equivalent time shift between the first and second bottom surface echoes. Specifically, the intercepted first bottom wave time domain signal With the second bottom wave time domain signal The cross-correlation parameters are calculated as follows:

[0050] in, These are the cross-correlation parameters of the bottom wave time-domain signal; These are time-domain parameters; for The first bottom wave time-domain signal at time; for The second bottom wave time-domain signal at time t.

[0051] Take the absolute value of the cross-correlation parameter of the bottom wave time domain signal Time-domain parameters with maximum value As the equivalent time shift between the first bottom surface echo and the second bottom surface echo. The equivalent time shift between the first bottom surface echo and the second bottom surface echo. It represents the time difference between the arrival of two echoes, including the path difference and the system time delay difference, and is used to compensate for the system delay term in the phase difference expression.

[0052] This invention provides an embodiment for calculating the speed of sound using "phase difference + time compensation"; still taking... frequency ,but Cross-correlation alignment yields: Frequency domain phase difference measurement: 99; Substitute: Note: The above data is for illustrative purposes only. Actual data obtained in the ultrasonic frequency band during testing may vary. Figure 6 As shown, the phase velocity varies with frequency.

[0053] Step S23: Measure the wave attenuation spectrum by amplitude ratio, ignore the phase difference, and combine it with the first bottom surface echo from step S21. Second bottom surface echo The longitudinal wave attenuation coefficient is obtained. for: ; in, It is the natural logarithm function.

[0054] like Figure 3 The figure shows the fitting graph of the experimental longitudinal wave attenuation coefficient and the theoretical curve in an embodiment of the present invention. This figure shows the result of the variation of the longitudinal wave attenuation coefficient spectrum of the sample with frequency within the effective frequency band of the 5MHz main frequency probe: the horizontal axis is the frequency (MHz), and the vertical axis is the attenuation coefficient (Np / m); the circular scatter points represent the experimental attenuation data obtained by combining the ratio of the amplitudes of two adjacent bottom surface echoes in steps S21 and S23 with the reference block method to cancel out systematic terms such as transmission, reflection, diffraction, and probe frequency response; the dashed line is the theoretical curve calculated and fitted by the unified complex wavenumber scattering model in steps S11-S15. It can be seen that the attenuation coefficient shows a significant upward trend with increasing frequency, reflecting the typical law of grain scattering increasing with frequency; the theoretical curve is consistent with the overall upward trend of the experimental data, indicating that the unified complex wavenumber model can effectively reduce the attenuation coefficient. This invention provides a unified description of scattering attenuation and constrains for subsequent joint inversion of single-crystal elastic constants with phase velocity spectra. Meanwhile, at high-frequency points, experimental curves deviate somewhat from theoretical curves. In engineering practice, this is typically related to factors such as decreased high-frequency signal-to-noise ratio, gating errors, residual system terms in the reference block, and multi-mechanism attenuation, such as the superposition of intrinsic absorptions in the material. This highlights the necessity of introducing weights or limiting the effective frequency band during joint fitting. Since experimentally measured wave attenuation includes transmission, reflection, and diffraction effects in addition to grain scattering, this invention employs the reference block method to eliminate non-scattering factors, obtaining the longitudinal wave attenuation coefficient. for: ; in, The first bottom surface echo of the reference polycrystalline alloy material sample; The second bottom surface echo is for reference to the polycrystalline alloy material sample.

[0055] Measuring wave attenuation spectrum by amplitude ratio refers to taking the ratio of the amplitudes of the echo spectra of adjacent bottom surfaces in the frequency domain, and utilizing the difference in propagation distance. This known quantity allows us to separate the exponential wave attenuation term from the amplitude ratio, thus yielding the longitudinal wave attenuation coefficient that varies with frequency. To eliminate the influence of transmission, reflection, diffraction, and probe frequency response on the amplitude, this invention further employs the reference block method, using the amplitude ratio of adjacent bottom waves of the reference alloy sample to cancel out the systematic terms, so that the obtained wave attenuation spectrum mainly reflects the scattering contribution of the polycrystalline alloy material grains. In this embodiment of the invention, the reference polycrystalline alloy material is selected as a fine-grained material, making its scattered wave attenuation negligible, thereby achieving systematic term cancellation; through steps S22 and S23, the experimental phase velocity spectrum of the polycrystalline alloy material sample within the effective frequency band of the acoustic wave is obtained. Compared with the experimental wave attenuation spectrum .

[0056] The embodiments of the present invention directly calculate using the amplitude ratio. ;Pick .exist At this point, the frequency domain amplitude, already gated + FFT amplitude, was measured. Note: The above data is for illustrative purposes only. Actual data obtained in the ultrasonic frequency band during testing may vary. Figure 7 As shown, this illustrates how the attenuation parameter changes with frequency.

[0057] like Figure 4 The figure shows the experimental phase velocity versus theoretical curve fitting diagram in an embodiment of the present invention. This figure shows the result of the longitudinal wave phase velocity spectrum of the sample changing with frequency within the effective frequency band of the 5MHz main frequency probe: the horizontal axis represents frequency (MHz), and the vertical axis represents phase velocity (m / s); the square scatter points represent the experimental phase velocity data extracted from the phase difference between two adjacent bottom surface echoes according to steps S21-S22; the dashed line represents the theoretical fitting curve calculated based on the unified complex wavenumber scattering model in steps S11-S15 and obtained through parameter inversion. It can be seen that the phase velocity shows a slow decreasing trend with increasing frequency, reflecting the dispersion characteristics of polycrystalline materials under grain scattering perturbation; the fitting curve has good consistency with the overall trend of the experimental data, indicating that the established unified complex wavenumber model can reasonably characterize the dispersion behavior of the phase velocity within the same framework, and provides a valid basis for subsequent joint constraint inversion of single-crystal elastic constants with attenuation spectrum. Measurement and Inversion Innovative Expressions and Engineering Explanation: Through steps S21-S23, adjacent bottom surface echoes are written as unified propagation factors containing complex wavenumbers, for example, the first bottom surface echo. The experimental phase velocity spectrum was obtained by using the phase difference. The experimental wave attenuation spectrum was obtained by using the amplitude ratio and canceling the system terms through the reference block. Thus, the experimental complex wavenumber is constructed and in step S32, the complex wavenumber is used to construct the experimental complex wavenumber. A joint inversion is performed. Compared to the well-known inversion that "only performs least squares on the speed of sound," this improvement lies in directly fitting phase and amplitude information simultaneously in the complex wavenumber domain, allowing the inversion to utilize both dispersion and attenuation as physical links to constrain the single-crystal elastic constants. This reduces understability and lowers system bias caused by neglecting scattering.

[0058] Step S3: Based on the ultrasonic longitudinal wave signal data and the unified complex wavenumber scattering model and its numerical solution process in Step S1, a joint error objective function is constructed, and an optimized inversion algorithm is used to solve and determine the single-crystal elastic constants of the polycrystalline alloy material. This invention uses the experimentally obtained sound velocity spectrum and attenuation spectrum as constraints, and performs joint matching with the theoretical sound velocity spectrum and theoretical attenuation spectrum output from the first-layer model. The matching process employs iterative optimization: continuously adjusting the parameters to be determined... , , The invention, along with the grain structure parameters as needed, allows the two curves predicted by the model to simultaneously match the experimental curves across the entire frequency band. The significance of this is that using only the speed of sound leads to the problem of multiple sets of parameters being able to explain the speed of sound, and using only attenuation can misinterpret equipment effects or other mechanisms as material scattering. This invention uses both speed of sound and attenuation information to constrain the same set of unknown parameters, essentially using two "rulers" to measure the same object simultaneously, thus significantly improving the uniqueness, stability, and reliability of the inversion results, ultimately outputting the single-crystal elastic constants. Grain size of polycrystalline alloy materials... The metallographic measurements from step S31 are used in the inversion calculation as: input parameters for the grain size of the polycrystalline alloy material. The average grain size measured by metallography is fixed, and it is directly substituted into the complex wave number equation in step S11 for forward modeling to determine the single crystal elastic constant of the polycrystalline alloy material.

[0059] Step S31: Obtain the grain size of the polycrystalline alloy material The embodiments of this invention use metallographic microscopy and other methods to measure the statistical results of grain size in polycrystalline alloy material samples, such as the grain size of polycrystalline alloy materials. And its distribution information, including grain size Substituting the unified complex wavenumber scattering model established in step S1, the grain size of the polycrystalline alloy material under test is obtained. In this embodiment, a metallographic microscope, electron backscatter diffraction (EBSD) or image analysis software are used to statistically analyze the microstructure of the polycrystalline alloy material sample to obtain the grain size. In particular, the unified complex wavenumber scattering model established in step S1 is based on grain size. With single-crystal elastic constant As input, the output is the effective complex wave number of the longitudinal wave at each frequency point within the specified frequency band. And further, in step S13, the effective complex wave number of the longitudinal wave is determined. The theoretical phase velocity of the longitudinal wave was calculated. With P-wave attenuation coefficient Grain size In inversion calculations, the following parameters are used as input parameters: when the metallographic statistical results are reliable and the sample microstructure is relatively homogeneous: The measured average grain size value is fixed, and directly substituted into the unified complex wavenumber scattering model in the forward calculations of steps S11 and S14 to obtain the effective complex wavenumber of the longitudinal wave. Thus, the phase velocity of the longitudinal wave theory is obtained. With P-wave attenuation coefficient This is used in step S32 to construct the joint error objective function and invert the single-crystal elastic constants.

[0060] Step S32: Construct the joint error objective function and perform numerical optimization inversion; convert the single-crystal elastic constants and positive tensile / compressive stiffness from step S1 into... Coupling stiffness and shear stiffness As initial parameters, a joint error objective function is constructed using multi-frequency phase velocity and multi-frequency wave attenuation, within the effective frequency band of the acoustic wave. The built-in joint error objective function is: ; in, The smaller the value of the joint error objective function, the more consistent the theoretical and experimental values ​​of the single-crystal elastic constants are. For frequency sampling points; This is the lower limit of the effective frequency band of sound waves; This represents the upper limit of the effective frequency band of sound waves. The theoretical complex wavenumber is obtained by forward modeling of the unified complex wavenumber scattering model. The experimental complex wave number is derived from the experimental phase velocity spectrum. Compared with the experimental wave attenuation spectrum It is constructed.

[0061] Numerical optimization is used to optimize the joint error objective function. Iterative updates are performed; in this embodiment of the invention, numerical optimization is carried out using a gradient-type or derivative-free optimization algorithm to minimize the joint error objective function and perform inverse calculation. The methods employed include the Levenberg-Marquardt method, the quasi-Newton method BFGS / L-BFGS-B, the Nelder-Mead simplex search with boundaries, particle swarm optimization, or genetic algorithms. Among these, the Nelder-Mead algorithm directly applies the physical extent, for example... , Equal stability constraints are imposed to improve convergence stability and result interpretability; a general iterative form and stopping output condition are defined, specifically as follows: ; in, Number of iterations The single-crystal elastic constant at that time; This is the first convergence threshold; This is the second convergence threshold.

[0062] The iteration stops and the inversion result is output when any of the above conditions are met: ; in, This represents the number of outer layer inversion iterations. To iteratively optimize the step size; The normalized residuals are used as indicators for evaluating convergence and reliability and are output along with the results.

[0063] The single-crystal elastic constant that the iteration finally converges The output is: ; This is a set of correction values ​​for the single-crystal elastic constants of polycrystalline alloy materials. For polycrystalline alloy materials, this refers to the positive tensile and compressive stiffness. The coupling stiffness of the polycrystalline alloy material; This refers to the shear stiffness of polycrystalline alloy materials.

[0064] Step S33: Use the optimal solution obtained through iterative update as the correction value for the single-crystal elastic constants of the measured polycrystalline alloy material; use the optimal solution as the single-crystal elastic constants of the measured polycrystalline alloy material, and obtain residual or convergence evaluation to determine the reliability of the measured polycrystalline alloy material. The residual or convergence evaluation includes at least one of the following: the final joint error objective function value. The three factors are: 1) its normalized form, such as dividing by the number of frequency points or by the energy of the experimental data; 2) the root mean square (RMS) or maximum deviation of the theoretical and experimental complex wavenumber difference within the frequency band; and 3) the number of optimization iterations and whether the convergence threshold is met. When the residual is below the preset threshold and the iteration converges stably, the measurement inversion result is considered reliable. If the residual is significantly large or does not converge, it indicates problems such as unstable coupling, insufficient echo signal-to-noise ratio, improper frequency band selection, or mismatch of grain statistical parameters, requiring retesting or parameter adjustment. A normalized residual less than 0.05 is considered passing; if it is greater than 0.1, it indicates reference block mismatch or abnormal coupling.

[0065] The positive tensile and compressive stiffness of polycrystalline alloy materials Coupling stiffness of polycrystalline alloy materials and the shear stiffness of polycrystalline alloy materials Elastic performance indicators directly used in engineering practice are used for the evaluation of polycrystalline alloy materials, process control, or service integrity assessment, thereby achieving the quality assessment of polycrystalline alloy materials.

[0066] This invention enables the application of anisotropy and equivalent elasticity indices to the consistency determination and batch sorting of polycrystalline alloy materials; based on the positive tensile and compressive stiffness of polycrystalline alloy materials... Coupling stiffness of polycrystalline alloy materials and the shear stiffness of polycrystalline alloy materials Calculate the anisotropy factor, equivalent modulus and other indicators of polycrystalline alloy materials, and compare them with the acceptance threshold to achieve rapid sorting and consistency evaluation of polycrystalline alloy materials with different heat treatments and different furnace batches.

[0067] This invention can be used for quality control of polycrystalline alloy materials in heat treatment, rolling, and additive manufacturing processes; by using the inverted single-crystal elastic constant as a characterization quantity related to microstructure and texture, the relationship between "process parameters-elastic constant-ultrasonic response" is established to achieve online or offline process window optimization.

[0068] This invention is used as a material parameter input in the structural health monitoring and life assessment of polycrystalline alloy materials; the measured single-crystal elastic constants are used as material inputs for multi-scale simulation, crystal plasticity, wave propagation simulation and damage evolution model, etc., to improve the prediction accuracy of remaining life, defect assessment and propagation characteristics.

[0069] For ease of explanation, the following examples use the same set of calculation data, in GPa: Batch A is used as a reference / acceptance standard: Batch B suspected deviation: .

[0070] 1. Used for consistency determination and batch sorting, and rapid screening of heat treatment / furnace batches.

[0071] 1) From Calculate the "anisotropy + equivalent elasticity index".

[0072] (a) Zener anisotropy factor, most commonly used in cubic crystal engineering, specifically: Batch A: Batch B: .

[0073] (b) Equivalent bulk modulus Voigt: ; ; .

[0074] (c) Equivalent shear modulus Voigt: ; ; .

[0075] Further, the equivalent Young's modulus and Poisson's ratio are obtained, making the acceptance criteria more intuitive: Batch A: Batch B: .

[0076] 2) Compare with acceptance threshold → Quick sorting as an example rule; assuming the company's internal control threshold, determined based on historical qualified batch statistics: lower limit of shear bearing capacity. Overall stiffness lower limit Anisotropic stability region Therefore: Batch A: →Passed; Batch B: →Failed / Requires re-verification or downgrade. Even if The changes are minor, and the volume compressibility remains similar. The significant decrease usually corresponds to changes in the microstructure related to crystal shearing, heat treatment deviations, differences in texture / dislocation / precipitate phases, etc., thus enabling rapid sorting and consistency assessment of different furnace batches and heat treatment states.

[0077] II. For quality control in heat treatment / rolling / additive manufacturing, establish a "process-elastic constant-ultrasonic response" model; here, it is not necessary to forcibly obtain a complex mechanism model, but a data closed loop for engineering execution can still be obtained: using As a "structure-sensitive characterization quantity" of process quality, it is used for window monitoring and trend identification. Engineering case: using... or To monitor process drift; assuming the same part is printed at different times / in different batches, or inverted from different heat treatment furnaces: Monday: ; Tuesday: ; Wednesday: ; Set process control lines: Warning: ; Call the police: ; An alarm is triggered on Wednesday. The engineering procedure is to: verify the heat treatment temperature / holding time, rolling reduction rate, additive energy density, powder oxygen content, etc., and transfer the batch to the re-inspection or process adjustment window. The inverted results will be used to... Or calculated by it As a quality characteristic, it enables online / offline process drift identification and process window optimization.

[0078] Third, it is used for structural health monitoring and life assessment, serving as material parameter input for simulation and evaluation models. The key point here is that S3's output can directly provide a consistent elastic input for multi-scale / wave propagation simulations, thereby improving prediction reliability. Even without unfolding the complete damage model, engineering examples demonstrating how parameter inputs change the magnitude of simulation results can be obtained.

[0079] 1) Put Converting to wave velocity input is the most common method in engineering; for isotropic equivalent bodies, the above method is used. P-wave / S-wave velocity: Density example : Batch A: ; ; Batch B: ; ; Engineering significance: The difference in transverse wave velocity is approximately Approximately 6.4%, which significantly affects the arrival time, positioning accuracy, and scattering response of guided / shear waves, therefore, using "measured inversion elastic input" in life assessment can significantly reduce systematic errors.

[0080] 2) Input to the remaining life / damage model; In fatigue crack propagation or damage evolution simulations, many models require elastic modulus or shear modulus as input. Calculated using S3 output: And it serves as a material parameter in finite element, crystal plasticity, or damage models. In the example above: vs Differences in modulus can alter the stress / strain distribution and crack tip field under the same load, thereby affecting the consistency of life prediction.

[0081] This invention uses a GH4742 polycrystalline sample as the verification object. GH4742 is one of the nickel-based high-temperature alloy grades, and it is often used in high-temperature service components in polycrystalline form in engineering. The aim is to demonstrate that this invention can obtain the corresponding cubic single-crystal elastic constants without preparing single-crystal or polycrystalline alloy material samples. And used for verification of equivalent macroeconomic elasticity indicators, such as Figure 5 The diagram shows a detailed flowchart of the ultrasonic complex wavenumber inversion method in an embodiment of the present invention. Analysis of the nickel-based superalloy GH4742 in the embodiment yields its single-crystal constants as follows: positive tensile / compressive stiffness... GPa, coupling stiffness GPa, shear stiffness For GPa verification, in the embodiments of this invention, VRH averaging is used to convert the inverted single-crystal elastic constants into equivalent Young's modulus for cross-verification with tensile test results. VRH averaging is a general term for Voigt averaging, Reuss averaging and Hill averaging, which is used to estimate the equivalent isotropic elastic modulus of randomly oriented polycrystalline materials from single-crystal elastic constants.

[0082] To evaluate the effectiveness and accuracy of the proposed method for measuring the elastic constants of single crystals, static tensile tests were conducted to determine the elastic constants of polycrystalline alloys. Two standard tensile specimens were prepared, and the experimentally measured Young's moduli were 210 GPa and 204 GPa, respectively. Using the single-crystal elastic constants obtained through ultrasonic evaluation, the theoretical Young's modulus was calculated using the Voigt-Reuss-Hill averaging method, and its value was 221 GPa. Compared with the Young's moduli measured in the two tensile tests, the relative errors were 5.24% and 8.10%, respectively.

[0083] The beneficial effects of this invention are as follows: This invention proposes a method for detecting the single-crystal elastic constants of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement. Compared to the traditional inversion method that only uses multi-directional single-frequency sound velocities, this invention utilizes multi-frequency phase velocity spectra and multi-frequency wave attenuation spectra for joint complex wavenumber inversion, thereby improving measurement accuracy and engineering applicability. This invention explicitly uses dispersion and wave attenuation caused by grain scattering, thereby reducing system bias, improving parameter identification stability, and is applicable to engineering polycrystalline alloy materials where single crystals are difficult to prepare. The errors in the equivalent modulus and tensile modulus obtained in the embodiments are within an acceptable engineering range and can reflect the changing trends of material batch / structure differences. Therefore, this invention is beneficial for achieving rapid, non-destructive, and engineering-grade determination of the single-crystal elastic constants of polycrystalline engineering materials, proving its engineering applicability and providing reliable basic data support for material selection, service evaluation, and multi-scale mechanical modeling.

[0084] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for detecting the single-crystal elastic constants of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement, characterized in that, It includes: S1: Determine the physical relationship between the ultrasonic longitudinal wave parameters of polycrystalline alloy materials and the theoretical values ​​of the single-crystal elastic constants, obtain the theoretical values ​​of the phase velocity spectrum and wave attenuation spectrum within the effective bandwidth of the ultrasonic probe, and determine the effective complex wave number of the longitudinal wave through complex nonlinear equations. The complex nonlinear equation after scattering correction is established with the effective complex wave number of the longitudinal wave as the core quantity; A unified complex wavenumber scattering model that satisfies the grain scattering effect of polycrystalline alloy materials was determined; S2: Multi-frequency ultrasonic testing of polycrystalline alloy materials yields ultrasonic longitudinal wave signals, providing the phase velocity spectrum and attenuation coefficient of the longitudinal waves. Specifically, this includes: S21: Establish the spectral expressions for the first and second bottom surface echoes to obtain the first bottom surface echo. Second bottom surface echo ; S22: The phase velocity spectrum is measured by the phase difference between the first and second bottom surface echoes of the longitudinal wave to determine the first bottom surface echo. Corresponding phase spectrum and the second bottom surface echo Corresponding phase spectrum The phase difference between the first and second bottom surface echoes of the longitudinal wave is obtained, thus yielding the phase velocity spectrum of the longitudinal wave. ; S23: Determine the wave attenuation spectrum from the amplitude frequency spectrum, and combine it with the first bottom surface echo from step S21. Second bottom surface echo Obtain the longitudinal wave attenuation coefficient ; S3: Based on the phase velocity spectrum and attenuation coefficient of the longitudinal wave obtained in S2, and combined with the unified complex wavenumber scattering model in step S1, construct a joint error objective function to determine the correction value of the single-crystal elastic constant of the polycrystalline alloy material, including: the positive tensile and compressive stiffness of the polycrystalline alloy material. Coupling stiffness of polycrystalline alloy materials and the shear stiffness of polycrystalline alloy materials This allows us to obtain the key parameters for controlling the mechanical response of metals.

2. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: The theoretical values ​​of the single-crystal elastic constants in step S1 include the positive tensile and compressive stiffness. Coupling stiffness and shear stiffness The expression for the physical relationship is: ； in, For the first The estimated effective complex wave number of the P-wave in the next iteration; This represents the number of iterations. For updating the iterative mapping function; For the iterative parameter terms of the complex nonlinear transcendental equation; For the characteristic parameter of longitudinal wave number in a homogeneous medium; For a homogeneous medium, the longitudinal wave number is [value missing]. is the macroscopic average elastic constant of the polycrystalline alloy material.

3. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: Step S1 is as follows: S11: Based on the unified complex wavenumber scattering theory of ultrasound, establish the governing equation for the effective complex wavenumber of longitudinal waves; S12: Determine the physical relationship between the grain structure parameters, ultrasonic properties, and single-crystal elastic constants of polycrystalline alloy materials; S13: Determining the effective complex wave number of the P-wave using complex nonlinear equations Establish the effective complex wave number of the longitudinal wave. Phase velocity in longitudinal wave theory and longitudinal wave attenuation coefficient The conversion relationship between them; S14: The governing equations are solved using an iterative numerical method to obtain the theoretical phase velocity spectrum and theoretical attenuation spectrum of the longitudinal wave within the effective bandwidth of the ultrasonic probe, and the effective complex wave number of the longitudinal wave is determined. A unified complex wavenumber scattering model relating the theoretical values ​​of single-crystal elastic constants and grain structure parameters.

4. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 3, characterized in that: The effective complex wave number of the P-wave in step S11 satisfies the following relationship: ； in, This is an estimate of the effective complex wave number of the P-wave. This is the perturbation term caused by grain scattering.

5. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 3, characterized in that: The specific relationship between the macroscopic average elastic constant of the polycrystalline alloy material and the single-crystal elastic constant in step S12 is as follows: ； ； in, For the elastic anisotropy parameters of cubic crystals; For material coupling stiffness; For material shear stiffness; This refers to the material's positive tensile and compressive stiffness.

6. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: The expressions for the first bottom surface echo and the second bottom surface echo in step S21 are as follows: ； ； ； in, The first bottom surface echo; The incident wave spectrum; The angular frequency of the ultrasonic testing system in frequency domain analysis; This is the first bottom surface transmission coefficient term; This is the reflection coefficient term for the first bottom surface; For the first bottom surface diffraction correlation terms; The longitudinal wave attenuation coefficient; The thickness of the material sample; The phase velocity in longitudinal wave theory; For the first bottom surface system delay term; It is a natural base constant; The second bottom surface echo; This is the second bottom surface transmission coefficient term; This is the reflection coefficient term for the second bottom surface; For the second bottom surface diffraction correlation terms; For the second bottom surface system delay term; It is a complex number.

7. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: The phase difference between the first bottom surface echo and the second bottom surface echo of the longitudinal wave in step S22 is: ； ； in, The phase difference between the two bottom surface echoes of the longitudinal wave; The phase spectrum of the first bottom surface echo; The phase spectrum of the second bottom surface echo; It represents the equivalent time shift between the first bottom surface echo and the second bottom surface echo.

8. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: Phase velocity spectrum of the longitudinal wave in step S22 for: ； ； in, The phase velocity spectrum of the longitudinal wave; The thickness of the material sample; The phase difference between the two bottom surface echoes of the longitudinal wave; To evaluate the parameters of a function; for The first bottom surface echo at that moment; for The second bottom surface echo at time; The time sampling interval is denoted as .

9. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: Longitudinal wave attenuation coefficient in step S23 for: ； in, The longitudinal wave attenuation coefficient; It is the natural logarithm function; The first bottom surface echo; The second bottom surface echo; The first bottom surface echo of the reference polycrystalline alloy material sample; The second bottom surface echo is for reference to the polycrystalline alloy material sample.

10. The method for detecting the single-crystal elastic constant of polycrystalline alloy materials based on ultrasonic complex wavenumber measurement according to claim 1, characterized in that: Step S3 is as follows: S31: Obtain the grain size of polycrystalline alloy materials As input parameters; grain size Substituting the unified complex wavenumber scattering model established in step S1, the effective complex wavenumber of the P-wave is obtained. Thus, the phase velocity of the longitudinal wave theory is obtained. With the theoretical attenuation coefficient of longitudinal waves ; S32: Construct a joint error objective function and perform numerical optimization to invert the correction value of the single-crystal elastic constants; adjust the positive tensile and compressive stiffness in step S1. Coupling stiffness and shear stiffness As initial parameters, a joint error objective function is constructed using multi-frequency phase velocity and multi-frequency wave attenuation. And a numerical optimization method is used to optimize the joint error objective function. Perform iterative updates; S33: Use the optimal solution obtained by iterative update as the correction value of the single crystal elastic constant of the polycrystalline alloy material.

Images