Method for predicting high-temperature rheological behavior of amorphous alloy

Abstract

The invention relates to the technical field of material science and engineering, in particular to an amorphous alloy high-temperature rheological behavior prediction method, which comprises the following steps: acquiring multi-scale characteristic parameters of an amorphous alloy under a high-temperature condition, and constructing a viscoelastic constitutive model coupled with beta relaxation intensity and free volume evolution based on the multi-scale characteristic parameters; obtaining structure evolution data under different energy states, and correcting the viscoelastic constitutive model based on the structure evolution data; combining the corrected viscoelastic constitutive model with a machine learning algorithm, and generating a high-temperature rheological behavior prediction model through training; and based on the high-temperature rheological behavior prediction model, outputting a rheological stress value of the amorphous alloy under target temperature and stress conditions, and when the target temperature is higher than the glass transition temperature, introducing a viscous flow correction term into the viscoelastic constitutive model. According to the method, accurate and widely-applicable amorphous alloy high-temperature rheology prediction is realized by obtaining multi-scale parameters, constructing a coupling model, combining experimental correction and a neural network and verifying covered double-temperature zones.

Description

Technical Field

[0001] This invention relates to the fields of materials science and engineering technology, and in particular to a method for predicting the high-temperature rheological behavior of amorphous alloys. Background Technology

[0002] Amorphous alloys, possessing the superior properties of both metals and glasses, have broad application prospects in many high-end fields. Accurate prediction of their high-temperature rheological behavior is crucial for expanding their application as structural materials. Early research mainly relied on single theoretical frameworks such as free volume models and shear transition zone models to analyze the deformation mechanisms of amorphous alloys. With the development of testing technologies, molecular dynamics simulations have been increasingly used to study atomic-scale diffusion and rearrangement mechanisms, while nanoindentation technology has become an important means of characterizing the inhomogeneity of nanoscale microstructures and the evolution of shear bands. Dynamic mechanical analysis has also been used to explore the correlation between relaxation behavior and rheological properties. Research directions are gradually developing towards the integration of multiple technologies and the coupling of multiple mechanisms.

[0003] Despite some progress in existing technologies, significant shortcomings remain in predicting high-temperature rheological behavior. Single theoretical models struggle to comprehensively encompass the synergistic effects of multiple factors, including temperature, stress, microstructure, and energy state evolution. Some models fail to adequately consider the coupling effect between β-relaxation strength and free volume evolution, limiting prediction accuracy. Furthermore, a systematic approach is lacking for extracting and integrating multi-scale characteristic parameters; the quantitative correlation between microstructural inhomogeneity and macroscopic rheological properties is unclear; and the integration of experimental data with theoretical models is not robust enough to adapt to the dynamic changes in the mechanical state of amorphous alloys across different temperature ranges, particularly around the glass transition temperature, thus hindering the accurate output of high-temperature rheological stress values. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned problems and provide a method for predicting the high-temperature rheological behavior of amorphous alloys. To achieve the above objective, this invention adopts the following technical solution:

[0005] A method for predicting the high-temperature rheological behavior of amorphous alloys includes the following steps:

[0006] Step S1: Obtain multi-scale characteristic parameters of amorphous alloys under high temperature conditions. The multi-scale characteristic parameters include atomic-scale diffusion coefficient, nanoscale microstructure inhomogeneity parameters, and macro-scale mechanical property data.

[0007] Step S2: Construct a viscoelastic constitutive model that couples the evolution of β-relaxation intensity and free volume based on multi-scale characteristic parameters;

[0008] Step S3: Obtain structural evolution data under different energy states through thermodynamic excitation and control experiments, and revise the viscoelastic constitutive model based on the structural evolution data;

[0009] Step S4: Combine the modified viscoelastic constitutive model with a machine learning algorithm to generate a high-temperature rheological behavior prediction model through training;

[0010] Step S5: Output the rheological stress value of the amorphous alloy under the target temperature and stress conditions based on the high-temperature rheological behavior prediction model. The target temperature range includes the supercooled liquid phase region below the glass transition temperature and the viscous flow region above the glass transition temperature. When the target temperature is higher than the glass transition temperature, a viscous flow correction term is introduced into the viscoelastic constitutive model.

[0011] Further, in step S1, the atomic-scale diffusion coefficient is obtained through molecular dynamics simulation. The molecular dynamics simulation process includes initial configuration construction, potential function selection, simulation ensemble setting, quenching and relaxation, and diffusion coefficient calculation. The diffusion coefficient calculation is based on Einstein relations and is specifically determined by the following formula:

[0012]

[0013] Where D is the diffusion coefficient, N is the total number of atoms, and r i (t) is the position vector of atom i at time t, r i (0) is the initial position vector of atom i, and <·> represents the time average value. The calculation interval is the time period after the system relaxes and stabilizes.

[0014] Further, in step S1, the nanoscale microstructure inhomogeneity parameters are obtained through nanoindentation experiments. The nanoindentation experiment process includes sample preparation, indentation array design, indenter parameter setting, loading curve setting, and parameter extraction. The parameter extraction uses the Oliver-Pharr method to obtain the hardness and elastic modulus from the loading-unloading curve. The microstructure inhomogeneity parameters are calculated and determined using the following formula:

[0015] ψ=w1σ H +w2σ E ;

[0016] Where ψ is the microstructure inhomogeneity parameter, σ H σ represents the standard deviation of the hardness distribution. E The standard deviation of the elastic modulus distribution is given by w1 and w2, which are weighting coefficients that satisfy w1 + w2 = 1 and are determined according to the weights of the influence of hardness and elastic modulus on the non-uniformity of the microstructure.

[0017] Furthermore, in step S2, the viscoelastic constitutive model is used to quantitatively characterize the correlation between stress and temperature, β-relaxation strength, and free volume concentration, with stress as the dependent variable and temperature, β-relaxation strength, and free volume concentration as independent variables. Its expression is:

[0018]

[0019] Where σ is the rheological stress, σ0 is the reference stress, Q is the activation energy, R is the gas constant, T is the absolute temperature, α and β are fitting coefficients, φ is the free volume concentration, and S is the β relaxation strength.

[0020] The β-relaxation strength is determined by dynamic mechanical analysis of the ratio of the peak loss factor in the β-relaxation temperature range to the energy storage modulus at the corresponding temperature.

[0021] Furthermore, in step S2, the evolution equation of free volume concentration is used to dynamically describe the change of free volume concentration with time, temperature, and stress. The rate of change of free volume concentration is the dependent variable, and time, temperature, and stress are the independent variables. Its expression is:

[0022]

[0023] Where t is time, k1 and k2 are rate constants, U1 and U2 are activation energies for free volume formation and annihilation, and m is the stress sensitivity index; when the amorphous alloy undergoes a crystallization phase transition and the degree of crystallization reaches the threshold determined based on the statistical significance of experimental data, the free volume evolution calculation is terminated, and the degree of crystallization is determined by X-ray diffraction or transmission electron microscopy.

[0024] Furthermore, in step S3, the thermodynamic excitation control experiment includes constant temperature excitation, alternating periodic excitation, and dynamic-static coupling excitation. The structural evolution data is acquired by a dynamic mechanical analyzer in tensile mode, and the data acquisition time is not less than the structural evolution characteristic time.

[0025] Further, in step S4, the machine learning algorithm is a backpropagation neural network, which includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is consistent with the dimension of the multi-scale feature parameters. The number of hidden layers and the number of neurons in each layer are determined through model complexity optimization. The coupling between the viscoelastic constitutive model and the backpropagation neural network is achieved by using the model residual as an input feature. The model residual is the difference between the theoretical calculation value of the viscoelastic constitutive model and the experimentally measured value of the thermodynamic excitation control. The output correction coefficient is used to adjust the parameters of the viscoelastic constitutive model.

[0026] Furthermore, the preset temperature for molecular dynamics simulations was determined by the glass transition temperature measured by differential scanning calorimetry, and the stress loading rate was selected based on the strain rate sensitivity of the amorphous alloy.

[0027] Furthermore, the number of effective indentation points in the nanoindentation experiment meets the statistical significance requirement, and the number of test areas for each sample is not less than the number of parallel experimental groups determined based on the statistical reliability requirement.

[0028] Furthermore, in step S5, the rheological stress value output by the high-temperature rheological behavior prediction model is verified by comparing it with high-temperature tensile experimental data. The verification dataset contains a combination of multiple temperature levels and stress levels. The prediction error is calculated using the root mean square error. When the prediction error exceeds the threshold determined based on the statistical significance of the experimental data, the process returns to step S3 to increase the excitation type or sample size of the thermodynamic excitation control experiment.

[0029] The advantages of this invention are:

[0030] 1. This invention achieves a comprehensive capture of the influencing factors on the high-temperature rheological behavior of amorphous alloys by acquiring multi-scale characteristic parameters of amorphous alloys at high temperatures and constructing a viscoelastic constitutive model that couples β-relaxation strength with the evolution of free volume. The multi-scale parameters cover atomic, nanoscale, and macroscopic dimensions, avoiding the limitation of single-scale parameters failing to reflect the structure-property relationship. The coupling of β-relaxation and free volume overcomes the shortcomings of traditional models that only focus on a single physical mechanism, making the model more closely aligned with the actual high-temperature deformation laws of amorphous alloys. This provides more suitable mechanistic support for prediction under actual working conditions, significantly improving the physical rationality of the prediction model and its adaptability to different structural states.

[0031] 2. This invention obtains structural evolution data through thermodynamic excitation and control experiments to correct the viscoelastic constitutive model, and combines the corrected model with a backpropagation neural network, achieving a significant improvement in the prediction accuracy of high-temperature rheological behavior. The thermodynamic excitation experiments cover various types, including constant temperature, alternating period, and dynamic-static coupling, and ensure that the data acquisition time is not less than the structural evolution characteristic time, fully acquiring information on different energy states to reduce the deviation between the model's theoretical assumptions and reality. The neural network uses the model residuals as input to optimize parameters, compensating for the shortcomings of pure physical models in dealing with nonlinear problems. This allows the prediction results to rely on physical mechanisms and correct errors through data-driven correction, resulting in higher prediction accuracy, stronger stability, and a more precise reflection of rheological stress changes under different conditions.

[0032] 3. This invention achieves broad applicability and reliable results in high-temperature rheological prediction by covering the supercooled liquid phase and viscous flow regions above and below the glass transition temperature in the high-temperature rheological behavior prediction model, and introducing a viscous flow correction term when the target temperature is higher than the glass transition temperature. Simultaneously, it verifies the prediction using high-temperature tensile experiments with multiple temperature and stress combinations, and supplements the results with thermodynamic excitation experiments when the prediction error exceeds a threshold. This design avoids the prediction failure of traditional models when the temperature crosses the glass transition point, adapts to the deformation characteristics of different temperature ranges, and the multiple verification and error feedback mechanisms can promptly correct deviations, ensuring that the output rheological stress value closely matches the actual value, meeting the precise performance prediction requirements of amorphous alloys for high-temperature applications in fields such as microelectronics and aerospace. Attached Figure Description

[0033] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application.

[0034] In the attached diagram:

[0035] Figure 1 This is a flowchart of a method for predicting the high-temperature rheological behavior of amorphous alloys in Example 1. Detailed Implementation

[0036] The present invention will now be described in detail and specifically through specific embodiments to enable a better understanding of the invention. However, the following embodiments do not limit the scope of protection of the present invention.

[0037] Example 1

[0038] like Figure 1 As shown, a method for predicting the high-temperature rheological behavior of amorphous alloys includes the following steps:

[0039] Step S1: Obtain multi-scale characteristic parameters of amorphous alloys under high temperature conditions. The multi-scale characteristic parameters include atomic-scale diffusion coefficient, nanoscale microstructure inhomogeneity parameters, and macro-scale mechanical property data.

[0040] Step S2: Construct a viscoelastic constitutive model that couples the evolution of β-relaxation intensity and free volume based on multi-scale characteristic parameters;

[0041] Step S3: Obtain structural evolution data under different energy states through thermodynamic excitation and control experiments, and revise the viscoelastic constitutive model based on the structural evolution data;

[0042] Step S4: Combine the modified viscoelastic constitutive model with a machine learning algorithm to generate a high-temperature rheological behavior prediction model through training;

[0043] Step S5: Output the rheological stress value of the amorphous alloy under the target temperature and stress conditions based on the high-temperature rheological behavior prediction model. The target temperature range includes the supercooled liquid phase region below the glass transition temperature and the viscous flow region above the glass transition temperature. When the target temperature is higher than the glass transition temperature, a viscous flow correction term is introduced into the viscoelastic constitutive model.

[0044] In a specific embodiment, when predicting the high-temperature rheological behavior of amorphous alloys, step S1 is first executed to obtain multi-scale characteristic parameters. The selected parameters cover key influencing factors from atomic, nanoscale to macroscopic dimensions. Then, step S2 is executed to construct a viscoelastic constitutive model. The core of the model lies in coupling β relaxation strength and free volume evolution. This design allows the model to better fit the actual rheological laws of materials at high temperatures and avoids the limitations of describing a single mechanism. Subsequently, step S3 is executed to obtain structural evolution data through thermodynamic excitation control experiments. These data are used to correct the model and reduce the deviation between theoretical assumptions and reality. Then, step S4 is executed to combine the corrected model with a machine learning algorithm. After training, a prediction model is generated. The algorithm advantage is used to make up for the shortcomings of the pure physical model in nonlinear fitting. Finally, step S5 is executed to output the rheological stress value. The model covers the key range above and below the glass transition temperature, and a viscous flow correction term is introduced at high temperatures to ensure that accurate results can be output under different temperature conditions, meeting the prediction needs of practical applications.

[0045] Further, in step S1, the atomic-scale diffusion coefficient is obtained through molecular dynamics simulation. The molecular dynamics simulation process includes initial configuration construction, potential function selection, simulation ensemble setting, quenching and relaxation, and diffusion coefficient calculation. The diffusion coefficient calculation is based on Einstein relations and is specifically determined by the following formula:

[0046]

[0047] Where D is the diffusion coefficient, N is the total number of atoms, and r i (t) is the position vector of atom i at time t, r i (0) is the initial position vector of atom i, and <·> represents the time average value. The calculation interval is the time period after the system relaxes and stabilizes.

[0048] In a specific embodiment, the atomic-scale diffusion coefficient in step S1 is obtained based on molecular dynamics simulation. The simulation process proceeds sequentially according to a predetermined flow: the initial configuration construction provides a reasonable basic structure for the simulation; the selection of the potential function directly affects the accuracy of the description of interatomic interactions; the simulation ensemble settings need to match the environmental requirements of high-temperature research; and quenching and relaxation allow the system to reach a stable research state. The diffusion coefficient is calculated based on Einstein's relation and the corresponding specific formula. During the calculation, the time average interval is set after the system has relaxed and stabilized, which effectively eliminates the interference of the initial unstable stage on the results. The final diffusion coefficient can truly reflect the atomic migration ability of amorphous alloys at high temperatures, providing reliable microscopic data support for model construction and ensuring that the microscopic parameters are consistent with the actual material properties.

[0049] Further, in step S1, the nanoscale microstructure inhomogeneity parameters are obtained through nanoindentation experiments. The nanoindentation experiment process includes sample preparation, indentation array design, indenter parameter setting, loading curve setting, and parameter extraction. The parameter extraction uses the Oliver-Pharr method to obtain the hardness and elastic modulus from the loading-unloading curve. The microstructure inhomogeneity parameters are calculated and determined using the following formula:

[0050] ψ=w1σ H +w2σ E ;

[0051] Where ψ is the microstructure inhomogeneity parameter, σ H σ represents the standard deviation of the hardness distribution. E The standard deviation of the elastic modulus distribution is given by w1 and w2, which are weighting coefficients that satisfy w1 + w2 = 1 and are determined according to the weights of the influence of hardness and elastic modulus on the non-uniformity of the microstructure.

[0052] In a specific embodiment, the nanoscale microstructure inhomogeneity parameters in step S1 are obtained through nanoindentation experiments. The experimental process requires strict control at each stage: sample preparation must ensure the uniformity and representativeness of the test samples to avoid sample differences affecting the results; the indentation array design and indenter parameter settings must ensure a reasonable distribution of test points and that the interaction between the indenter and the material conforms to experimental specifications; the loading curve settings must match the deformation response characteristics of the amorphous alloy under nanoindentation. Parameter extraction uses the Oliver-Pharr method to accurately obtain the two key indicators, hardness and elastic modulus, from the loading-unloading curve. The microstructure inhomogeneity parameters are calculated using a specific weighted formula. The formula design fully considers the influence weights of hardness and elastic modulus on inhomogeneity, and coefficient constraints ensure rigorous calculation logic. The final parameters accurately characterize the structural inhomogeneity of the material at the nanoscale, providing crucial mesoscopic information for the model.

[0053] Furthermore, in step S2, the viscoelastic constitutive model is used to quantitatively characterize the correlation between stress and temperature, β-relaxation strength, and free volume concentration, with stress as the dependent variable and temperature, β-relaxation strength, and free volume concentration as independent variables. Its expression is:

[0054]

[0055] Where σ is the rheological stress, σ0 is the reference stress, Q is the activation energy, R is the gas constant, T is the absolute temperature, α and β are fitting coefficients, φ is the free volume concentration, and S is the β relaxation strength.

[0056] The β-relaxation strength is determined by dynamic mechanical analysis of the ratio of the peak loss factor in the β-relaxation temperature range to the energy storage modulus at the corresponding temperature.

[0057] In a specific embodiment, the viscoelastic constitutive model in step S2 is used to quantitatively characterize the correlation between stress and temperature, β-relaxation strength, and free volume concentration. The model uses stress as the dependent variable and other key factors as independent variables. This variable setting directly focuses on the core influencing relationships and avoids interference from irrelevant factors. The design of the model expression integrates the combined effects of thermal activation, free volume, and relaxation behavior. The β-relaxation strength is obtained through dynamic mechanical analysis: the peak value of the loss factor and the storage modulus at the corresponding temperature are measured within the β-relaxation temperature range, and then calculated through the ratio. This method can accurately capture the strength of β-relaxation, allowing the model to more comprehensively integrate the influence of multiple factors on rheological stress and significantly improve the accuracy of describing the high-temperature rheological behavior of amorphous alloys.

[0058] Furthermore, in step S2, the evolution equation of free volume concentration is used to dynamically describe the change of free volume concentration with time, temperature, and stress. The rate of change of free volume concentration is the dependent variable, and time, temperature, and stress are the independent variables. Its expression is:

[0059]

[0060] Where t is time, k1 and k2 are rate constants, U1 and U2 are activation energies for free volume formation and annihilation, and m is the stress sensitivity index; when the amorphous alloy undergoes a crystallization phase transition and the degree of crystallization reaches the threshold determined based on the statistical significance of experimental data, the free volume evolution calculation is terminated, and the degree of crystallization is determined by X-ray diffraction or transmission electron microscopy.

[0061] In a specific embodiment, the core purpose of the free volume concentration evolution equation in step S2 is to dynamically describe the changes in free volume with time, temperature, and stress. The equation uses the rate of change as the dependent variable, enabling real-time tracking of the dynamic evolution of free volume. The equation design fully considers the competitive relationship between free volume formation and annihilation, characterizing the two processes using different rate constants and activation energies, while introducing a stress sensitivity index to reflect the influence of external stress. When the amorphous alloy undergoes a crystallization phase transition, the degree of crystallinity needs to be characterized by X-ray diffraction or transmission electron microscopy. When the degree of crystallinity reaches a threshold determined based on the statistical significance of experimental data, the free volume evolution calculation is terminated. This effectively avoids interference between crystallization and the free volume evolution law, ensuring that the calculated free volume concentration truly reflects the internal structural state of the material in the amorphous state, providing dynamic and accurate structural parameter support for the viscoelastic constitutive model.

[0062] Furthermore, in step S3, the thermodynamic excitation control experiment includes constant temperature excitation, alternating periodic excitation, and dynamic-static coupling excitation. The structural evolution data is acquired by a dynamic mechanical analyzer in tensile mode, and the data acquisition time is not less than the structural evolution characteristic time.

[0063] In a specific embodiment, the thermodynamic excitation control experiment in step S3 includes three different types of excitation, each corresponding to a specific operating condition simulation: constant temperature excitation simulates the state of the material under continuous high temperature, alternating periodic excitation simulates the scenario of periodic temperature changes, and dynamic-static coupling excitation simulates the complex operating condition of dynamic and static temperature superposition. The combination of these three types can comprehensively cover the temperature excitation situations that may be encountered in practical applications. Structural evolution data is acquired through a dynamic mechanical analyzer in tensile mode. The tensile mode can simulate the actual stress and deformation state of the material at high temperatures, making the data more valuable. The data acquisition time must meet the requirement of not less than the structural evolution characteristic time. This setting ensures the complete capture of the entire structural evolution process of the material under different excitations, avoiding the loss of key information due to insufficient acquisition time. The final acquired structural evolution data can provide sufficient and reliable experimental basis for the correction of the viscoelastic constitutive model, helping the model to better fit the actual structural change law of the material.

[0064] Further, in step S4, the machine learning algorithm is a backpropagation neural network, which includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is consistent with the dimension of the multi-scale feature parameters. The number of hidden layers and the number of neurons in each layer are determined through model complexity optimization. The coupling between the viscoelastic constitutive model and the backpropagation neural network is achieved by using the model residual as an input feature. The model residual is the difference between the theoretical calculation value of the viscoelastic constitutive model and the experimentally measured value of the thermodynamic excitation control. The output correction coefficient is used to adjust the parameters of the viscoelastic constitutive model.

[0065] In a specific embodiment, step S4 selects a backpropagation neural network as the machine learning algorithm. This algorithm's mature advantages in nonlinear fitting and parameter optimization effectively address the discrepancy between the model and experimental data. The neural network's structural design must be tailored to practical needs: the number of neurons in the input layer must be consistent with the dimensionality of the multi-scale feature parameters to ensure all key parameter information is fully input into the network; the number of hidden layers and the number of neurons per layer are determined through model complexity optimization. This approach ensures computational accuracy while avoiding overfitting or inefficiency caused by an overly complex network structure. The coupling between the model and the neural network is achieved through model residuals. These residuals directly reflect the model's prediction bias. Using these residuals as input allows the neural network to specifically learn the bias patterns, and then adjust the model parameters through output correction coefficients. This achieves an effective fusion of physical mechanisms and data-driven approaches, significantly improving the accuracy and stability of the prediction model and making the prediction results more closely match reality.

[0066] Furthermore, the preset temperature for molecular dynamics simulations was determined by the glass transition temperature measured by differential scanning calorimetry, and the stress loading rate was selected based on the strain rate sensitivity of the amorphous alloy.

[0067] In a specific embodiment, the preset temperature for molecular dynamics simulation is determined using differential scanning calorimetry (DSC), a standard technique for measuring the glass transition temperature of materials. The obtained glass transition temperature accurately reflects the critical point in the transition of amorphous alloys from the glassy state to the supercooled liquid phase. Setting the preset temperature based on this temperature allows the simulation range to better align with the core scope of high-temperature rheological research, ensuring that the simulation results match the actual high-temperature characteristics of the material and avoiding deviations caused by improper temperature settings. The selection of the stress loading rate needs to consider the strain rate sensitivity of the amorphous alloy. This characteristic directly reflects the differences in the material's deformation response under different loading rates. Determining the loading rate based on this characteristic allows the stress conditions in the simulation to match the actual deformation characteristics of the material, ultimately improving the practicality of microscopic parameters such as the diffusion coefficient and providing more reliable microscopic data support for multi-scale parameter integration and model construction.

[0068] Furthermore, the number of effective indentation points in the nanoindentation experiment meets the statistical significance requirement, and the number of test areas for each sample is not less than the number of parallel experimental groups determined based on the statistical reliability requirement.

[0069] In specific embodiments, the number of effective indentation points in the nanoindentation experiment must meet the statistical significance requirement. This requirement ensures that the test data is statistically significant, avoids random errors caused by too few indentation points affecting data reliability, and makes the obtained hardness and elastic modulus data more representative, reflecting the overall characteristics of the material rather than local random states. The number of test areas for each sample must be no less than the number of parallel experimental groups determined based on statistical reliability. The setting of the number of parallel experimental groups follows the statistical principles of experimental design, ensuring the repeatability and comparability of data from different test areas and reducing the interference of local structural differences on experimental results. Through such experimental design, the hardness and elastic modulus distribution data extracted from the loading-unloading curve will be more accurate, and the calculated microstructural inhomogeneity parameters can more realistically reflect the structural state of the material at the nanoscale, providing reliable mesoscopic data support for multi-scale characteristic parameter systems.

[0070] Furthermore, in step S5, the rheological stress value output by the high-temperature rheological behavior prediction model is verified by comparing it with high-temperature tensile experimental data. The verification dataset contains a combination of multiple temperature levels and stress levels. The prediction error is calculated using the root mean square error. When the prediction error exceeds the threshold determined based on the statistical significance of the experimental data, the process returns to step S3 to increase the excitation type or sample size of the thermodynamic excitation control experiment.

[0071] In a specific embodiment, when verifying the rheological stress value output by the prediction model in step S5, high-temperature tensile experimental data is used as the comparison basis. This experiment can directly simulate the actual tensile rheological process of amorphous alloys at high temperatures, and the obtained data has high authenticity and reference value, which can effectively verify the accuracy of the model's prediction results. The verification dataset needs to include multiple combinations of temperature and stress levels. This setting can comprehensively cover the application conditions that the model may involve, avoid misjudging the model's accuracy due to a single verification condition, and ensure that the model can maintain good prediction performance under different working conditions. The prediction error is calculated using the root mean square error. This method can objectively quantify the degree of deviation between the predicted value and the measured value, providing a clear quantitative standard for model accuracy evaluation. When the error exceeds the threshold, the process returns to step S3 to supplement experimental data. This can specifically solve the error problem caused by insufficient data, continuously optimize the viscoelastic constitutive model, and ultimately ensure that the prediction results are highly consistent with the actual situation, meeting the accurate prediction requirements of different application scenarios for the high-temperature rheological properties of amorphous alloys.

[0072] The specific embodiments of the present invention have been described in detail above, but they are merely examples, and the present invention is not equivalent to the specific embodiments described above. For those skilled in the art, any equivalent modifications and substitutions to the present invention are also within the scope of the present invention. Therefore, all equivalent transformations and modifications made without departing from the spirit and scope of the present invention should be covered within the scope of the present invention.

Claims

1. A method for predicting the high-temperature rheological behavior of amorphous alloys, characterized in that, Includes the following steps: Step S1: Obtain multi-scale characteristic parameters of amorphous alloys under high temperature conditions. The multi-scale characteristic parameters include atomic-scale diffusion coefficient, nanoscale microstructure inhomogeneity parameters, and macro-scale mechanical property data. Step S2: Construct a viscoelastic constitutive model that couples the evolution of β-relaxation intensity and free volume based on multi-scale characteristic parameters; Step S3: Obtain structural evolution data under different energy states through thermodynamic excitation and control experiments, and revise the viscoelastic constitutive model based on the structural evolution data; Step S4: Combine the modified viscoelastic constitutive model with a machine learning algorithm to generate a high-temperature rheological behavior prediction model through training; Step S5: Output the rheological stress value of the amorphous alloy under the target temperature and stress conditions based on the high-temperature rheological behavior prediction model. The target temperature range includes the supercooled liquid phase region below the glass transition temperature and the viscous flow region above the glass transition temperature. When the target temperature is higher than the glass transition temperature, a viscous flow correction term is introduced into the viscoelastic constitutive model.

2. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 1, characterized in that, In step S1, the atomic-scale diffusion coefficient is obtained through molecular dynamics simulation. The molecular dynamics simulation process includes initial configuration construction, potential function selection, simulation ensemble setting, quenching and relaxation, and diffusion coefficient calculation. The diffusion coefficient calculation is based on Einstein relations and is specifically determined by the following formula: Where D is the diffusion coefficient, N is the total number of atoms, and r i (t) is the position vector of atom i at time t, r i (0) is the initial position vector of atom i, and <·> represents the time average value. The calculation interval is the time period after the system relaxes and stabilizes.

3. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 2, characterized in that, In step S1, the nanoscale microstructure inhomogeneity parameters are obtained through nanoindentation experiments. The nanoindentation experiment process includes sample preparation, indentation array design, indenter parameter setting, loading curve setting, and parameter extraction. The parameter extraction uses the Oliver-Pharr method to obtain hardness and elastic modulus from the loading-unloading curve. The microstructure inhomogeneity parameters are calculated and determined using the following formula: ψ=w1σ H +w2σ E ; Where ψ is the microstructure inhomogeneity parameter, σ H σ represents the standard deviation of the hardness distribution. E The standard deviation of the elastic modulus distribution is given by w1 and w2, which are weighting coefficients that satisfy w1 + w2 = 1 and are determined according to the weights of the influence of hardness and elastic modulus on the non-uniformity of the microstructure.

4. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 3, characterized in that, In step S2, the viscoelastic constitutive model is used to quantitatively characterize the correlation between stress and temperature, β-relaxation strength, and free volume concentration. Stress is the dependent variable, and temperature, β-relaxation strength, and free volume concentration are the independent variables. Its expression is: Where σ is the rheological stress, σ0 is the reference stress, Q is the activation energy, R is the gas constant, T is the absolute temperature, α and β are fitting coefficients, φ is the free volume concentration, and S is the β relaxation strength. The β-relaxation strength is determined by dynamic mechanical analysis of the ratio of the peak loss factor in the β-relaxation temperature range to the energy storage modulus at the corresponding temperature.

5. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 4, characterized in that, In step S2, the evolution equation of the free volume concentration is used to dynamically describe the change of free volume concentration with time, temperature, and stress. The rate of change of free volume concentration is the dependent variable, and time, temperature, and stress are the independent variables. Its expression is: Where t is time, k1 and k2 are rate constants, U1 and U2 are activation energies for free volume formation and annihilation, and m is the stress sensitivity index; when the amorphous alloy undergoes a crystallization phase transition and the degree of crystallization reaches the threshold determined based on the statistical significance of experimental data, the free volume evolution calculation is terminated, and the degree of crystallization is determined by X-ray diffraction or transmission electron microscopy.

6. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 5, characterized in that, In step S3, the thermodynamic excitation control experiment includes constant temperature excitation, alternating periodic excitation, and dynamic-static coupling excitation. The structural evolution data is acquired by a dynamic mechanical analyzer in tensile mode, and the data acquisition time is not less than the structural evolution characteristic time.

7. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 6, characterized in that, In step S4, the machine learning algorithm is a backpropagation neural network, which includes an input layer, a hidden layer, and an output layer. The number of neurons in the input layer is consistent with the dimension of the multi-scale feature parameters. The number of hidden layers and the number of neurons in each layer are determined through model complexity optimization. The coupling between the viscoelastic constitutive model and the backpropagation neural network is achieved by using the model residual as an input feature. The model residual is the difference between the theoretical calculation value of the viscoelastic constitutive model and the experimentally measured value of thermodynamic excitation control. The output correction coefficient is used to adjust the parameters of the viscoelastic constitutive model.

8. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 7, characterized in that, The preset temperature for the molecular dynamics simulation is determined by the glass transition temperature measured by differential scanning calorimetry, and the stress loading rate is selected based on the strain rate sensitivity of the amorphous alloy.

9. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 8, characterized in that, The number of effective indentation points in the nanoindentation experiment meets the statistical significance requirement, and the number of test areas for each sample is not less than the number of parallel experimental groups determined based on the statistical reliability requirement.

10. The method for predicting the high-temperature rheological behavior of amorphous alloys according to claim 9, characterized in that, In step S5, the rheological stress value output by the high-temperature rheological behavior prediction model is verified by comparing it with high-temperature tensile experimental data. The verification dataset contains a combination of multiple temperature levels and stress levels. The prediction error is calculated using the root mean square error. When the prediction error exceeds the threshold determined based on the statistical significance of the experimental data, the process returns to step S3 to increase the excitation type or sample size of the thermodynamic excitation control experiment.

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