TiAl alloy Nb content design method based on molecular dynamics simulation and machine learning

Abstract

The invention relates to the field of data processing, in particular to a TiAl alloy Nb content design method based on molecular dynamics simulation and machine learning. The method comprises the following steps: constructing a pure binary model based on a gamma-TiAl single crystal structure, and adding Nb with different contents into the pure binary model to obtain a plurality of initial models; performing simulation stretching on the plurality of initial models through molecular dynamics to obtain a molecular dynamics simulation result; flow stress corresponding to the multiple initial models is calculated based on the multiple stress-strain curves obtained through simulation; based on a molecular dynamics simulation result, calculating and extracting simulation characteristic parameters of the plurality of initial models in a simulation stretching process; a flow stress prediction model is trained through the flow stress corresponding to the multiple initial models and the simulation characteristic parameters, flow stress data corresponding to different Nb contents are predicted through the flow stress prediction model, and finally the corresponding optimal Nb content is determined according to the maximum flow stress prediction value. According to the method, prediction of fluid stress data is realized through combination of molecular dynamics and a neural network, and the accuracy of model prediction is enhanced.

Description

[0001] This application claims priority to Chinese patent application number 202411904243.8, entitled “Flow stress prediction method and related device based on multiple models”, the entire contents of which are incorporated herein by reference. Technical Field

[0002] The present application relates to the field of data processing, and in particular to a method for designing the Nb content of TiAl alloys based on molecular dynamics simulation and machine learning. Background Art

[0003] The primary components of TiAl single crystals are titanium (Ti) and aluminum (Al), with their atomic percentages typically varying within a certain range, such as the common Ti-48Al-2Cr-2Nb. Small amounts of other elements, such as chromium (Cr), niobium (Nb), and rare earth elements (Re), may also be added to improve performance. TiAl possesses a specific crystallographic structure that imparts unique physical and mechanical properties. TiAl single crystals are an ideal material for manufacturing high-temperature components such as automotive powertrains, aircraft engine blades, and turbine disks.

[0004] TiAl single crystals have complex microstructures. Their crystal structures, such as the tetragonal phase, have unique atomic arrangements, leading to complex and diverse deformation mechanisms such as dislocation motion and twin formation. In related technologies, these microstructural changes under varying conditions, such as temperature and strain rate, can significantly affect flow stress, making it difficult to accurately describe and quantify, increasing the difficulty of prediction. For example, dislocations moving within a complex crystal structure are hindered and influenced by a variety of factors, making their movement difficult to accurately grasp, which in turn affects the accurate prediction of flow stress.

[0005] Therefore, there is an urgent need to design a technical solution to solve at least one of the above technical problems. Summary of the Invention

[0006] In response to the technical problems existing in the prior art, this application provides a method for designing the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning, so as to establish a more accurate flow stress prediction model, strengthen the physical basis of the model to make it more consistent with the physical nature of the material, thereby achieving accurate prediction of fluid stress data, improving the overall model performance, and enhancing the accuracy of model prediction.

[0007] In a first aspect, an embodiment of the present application provides a method for designing the Nb content of a TiAl alloy based on molecular dynamics simulation and machine learning, the method comprising:

[0008] A pure binary model based on the γ-TiAl single crystal structure was constructed. Different amounts of Nb atoms were added to the constructed pure binary model to obtain multiple initial models. The Nb content of the initial models ranged from 0.3% to 15%, with a Nb content gradient of 0.3%.

[0009] Performing stretching simulation on the multiple initial models using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models; and calculating the bulk modulus, shear modulus, Poisson's ratio, and flow stress based on the multiple stress-strain curves, wherein the flow stress is the average stress from the first peak to the end of deformation;

[0010] Based on the multiple initial models, calculating simulation characteristic parameters of the multiple initial models during the simulated stretching process, the simulation characteristic parameters at least including: stacking fault energy and lattice constant;

[0011] Using the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as the original data set for training the flow stress prediction model;

[0012] Processing the original data set to obtain a standard data set, and training a BP neural network model based on the standard data set to obtain a flow stress prediction model;

[0013] Inputting the Nb content to be predicted into the flow stress prediction model for prediction analysis to obtain a corresponding flow stress prediction value;

[0014] The corresponding optimal Nb content is determined based on the predicted value of the maximum flow stress.

[0015] In a second aspect, the present invention provides a device for predicting the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning, wherein

[0016] A construction unit is configured to construct a pure binary model based on a γ-TiAl single crystal structure, and add different contents of Nb atoms to the constructed pure binary model to obtain multiple initial models; wherein the Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%;

[0017] A simulation unit is configured to simulate stretching of the multiple initial models through molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models;

[0018] A calculation unit is configured to calculate, based on the multiple stress-strain curves, a bulk modulus, a shear modulus, a Poisson's ratio, and a flow stress, respectively, wherein the flow stress is an average stress from a first peak to an end of deformation; and based on the multiple initial models, calculate simulation characteristic parameters of the multiple initial models during the simulated stretching process, wherein the simulation characteristic parameters include at least stacking fault energy and a lattice constant;

[0019] The training unit is configured to use the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as an original data set for training the flow stress prediction model; process the original data set to obtain a standard data set, and train the BP neural network model based on the standard data set;

[0020] The prediction unit is configured to input the Nb content to be predicted into the optimal flow stress prediction model obtained by training the BP neural network model based on the standard data set, perform prediction analysis, obtain the corresponding flow stress prediction value, and determine the corresponding optimal Nb content according to the maximum flow stress prediction value.

[0021] In a third aspect, an embodiment of the present application provides a model construction method, which is used to construct the flow stress prediction model in the first aspect, and the method includes:

[0022] A pure binary model based on the γ-TiAl single crystal structure was constructed. Different amounts of Nb atoms were added to the constructed pure binary model to obtain multiple initial models. The Nb content of the initial models ranged from 0.3% to 15%, with a Nb content gradient of 0.3%.

[0023] Performing stretching simulation on the multiple initial models using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models; and calculating the bulk modulus, shear modulus, Poisson's ratio, and flow stress based on the multiple stress-strain curves, wherein the flow stress is the average stress from the first peak to the end of deformation;

[0024] Based on the multiple initial models, calculating simulation characteristic parameters of the multiple initial models during the simulated stretching process, the simulation characteristic parameters at least including: stacking fault energy and lattice constant;

[0025] Using the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as the original data set for training the flow stress prediction model;

[0026] The original data set is processed to obtain a standard data set, and a BP neural network model is trained based on the standard data set to obtain a flow stress prediction model.

[0027] In a fourth aspect, an embodiment of the present application provides an electronic device, comprising:

[0028] at least one processor and memory;

[0029] The memory is used to store a computer program, and the processor is used to call the computer program stored in the memory to execute the TiAl alloy Nb content design method based on molecular dynamics simulation and machine learning described in the first aspect.

[0030] In a fifth aspect, a computer-readable storage medium is provided, which includes instructions. When the instructions are executed on a computer, the computer executes the TiAl alloy Nb content design method based on molecular dynamics simulation and machine learning described in the first aspect.

[0031] The beneficial effect of this application is to provide a method for designing the Nb content of TiAl alloys based on molecular dynamics simulation and machine learning. The technical solution of this application constructs a pure binary model based on the γ-TiAl single crystal structure, and adds different Nb atoms to the constructed pure binary model to obtain multiple initial models. The Nb content of the initial models ranges from 0.3% to 15%, with a Nb content gradient of 0.3%. Then, the multiple initial models are simulated and stretched using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models. The molecular dynamics simulation results include at least: multiple stress-strain curves corresponding to the multiple initial models; based on the multiple stress-strain curves, the bulk modulus, shear modulus, Poisson's ratio, and flow stress are calculated respectively, where the flow stress is the average stress from the first peak to the end of the deformation stage; then, based on the multiple initial models, the simulated characteristic parameters of the multiple initial models during the simulated stretching process are calculated, and the simulated characteristic parameters include at least: stacking fault energy and lattice constant; then, the bulk modulus, shear modulus, Poisson's ratio, flow stress, and the simulated characteristic parameters corresponding to the multiple initial models are used as the original data set for training the flow stress prediction model. Next, the original data set is processed to obtain a standard data set, and a BP neural network model is trained based on the standard data set to obtain a flow stress prediction model. Finally, the Nb content to be predicted is input into the flow stress prediction model for prediction analysis to obtain the corresponding flow stress prediction value.

[0032] The technical solution of this application integrates molecular dynamics simulation with machine learning. On the one hand, it uses simulation to understand the tensile behavior of γ-TiAl single crystals at different Nb contents from a microscopic perspective. Multiple initial models are stretched using molecular dynamics to obtain flow stress data and microscopic data. On the other hand, the dataset obtained from the simulated stretching describes the mechanical properties of the material at multiple scales, from macroscopic and microscopic characteristics. This is used to establish a more accurate flow stress prediction model, strengthen the model's physical foundation, make it more consistent with the material's physical nature, improve the overall model performance, and enhance the accuracy of the model prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 1 is a flow chart of a method for designing the Nb content of a TiAl alloy based on molecular dynamics simulation and machine learning according to an embodiment of the present application;

[0034] Figures 2 to 5 Schematic diagram of the principle of a method for designing the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning according to an embodiment of the present application;

[0035] Figure 6 Schematic diagram of a device for predicting Nb content in TiAl alloy based on molecular dynamics simulation and machine learning according to an embodiment of the present application;

[0036] Figure 7 It is a structural diagram of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making creative efforts are within the scope of protection of this application.

[0038] In order to solve at least one technical problem in the related art, an embodiment of the present application provides a method for designing the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning.

[0039] In the technical solution provided by the present application, first, a pure binary model based on the γ-TiAl single crystal structure is constructed, and different contents of Nb atoms are added to the constructed pure binary model to obtain multiple initial models. The Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%. Then, the multiple initial models are simulated and stretched by molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results include at least: multiple stress-strain curves corresponding to the multiple initial models; based on the multiple stress-strain curves, the bulk modulus, shear modulus, Poisson's ratio, and flow stress are calculated respectively, wherein the flow stress is the average stress from the first peak to the end of the deformation stage.

[0040] In this way, by constructing a single crystal model through molecular dynamics and performing tensile simulation, we can gain an in-depth understanding of the tensile behavior of γ-TiAl single crystals at different Nb contents from a microscopic level, and obtain key microscopic data such as tensile yield strength. At the same time, combined with the original data set of flow stress containing a variety of macroscopic material properties (such as Poisson's ratio, bulk modulus, etc.), the microscopic simulation results are integrated with the macroscopic experimental data. This multi-scale data utilization method can more comprehensively describe the mechanical properties of the material, thereby establishing a more accurate flow stress prediction model. Molecular dynamics simulation provides information on the behavior of materials at the atomic scale, giving the prediction model a solid physical foundation. Compared with models that rely solely on macroscopic experimental data, this method can better understand the impact of interactions between atoms within the material on the flow stress, making the prediction model more consistent with the physical nature of the material, thereby improving the reliability and applicability of the model.

[0041] Furthermore, based on the multiple initial models, simulated characteristic parameters of the multiple initial models during the simulated stretching process are calculated. The simulated characteristic parameters include at least stacking fault energy and lattice constant. The bulk modulus, shear modulus, Poisson's ratio, flow stress corresponding to the multiple initial models, as well as the simulated characteristic parameters, are used as the original dataset for training the flow stress prediction model. In this way, model training using the original dataset containing data on Nb content, stacking fault energy, lattice constant, bulk modulus, shear modulus, Poisson's ratio, and flow stress considers the combined influence of multiple material properties on flow stress. These factors are interrelated and interact with each other, jointly determining the flow stress of the material. By integrating these factors, the model can learn the complex relationships between them, thereby more accurately predicting the flow stress and avoiding prediction errors caused by considering only a single factor. The original dataset is constructed based on pre-collected experimental data, which itself has high credibility and practical physical significance. Combining experimental data with simulated data can fully leverage the accuracy advantages of experimental data and the systematic advantages of simulated data, enabling the model to better fit the performance variations of actual materials during training, further improving the credibility and accuracy of the model prediction results.

[0042] Finally, the predicted Nb content is input into the flow stress prediction model for analysis, resulting in a corresponding predicted flow stress value. The optimal Nb content is then determined based on the predicted maximum flow stress value. This provides valuable guidance for optimizing material properties. For example, during material design and manufacturing, parameters such as the Nb content can be adjusted based on the predicted results to increase the material's maximum flow stress and meet the mechanical performance requirements of specific engineering applications.

[0043] In practical engineering applications such as aerospace and automotive manufacturing, accurately predicting a material's maximum flow stress is crucial for structural design and safety assessment. The predictions provided by this method can help engineers better design structures and rationally select materials and processes to ensure the safety and reliability of structures under the expected loads. This also helps optimize material usage and reduce cost and weight.

[0044] The technical solution of this application realizes a close connection between the microscopic and macroscopic levels through the deep integration of molecular dynamics simulation and macroscopic experimental data. On the one hand, from the microscopic level, with the help of molecular dynamics simulation, we can deeply understand the tensile behavior of γ-TiAl single crystals under different Nb contents, accurately obtain microscopic data such as tensile yield strength, and carefully analyze the arrangement, movement and interaction of atoms, so as to provide a microscopic basis for in-depth understanding of the mechanical properties of materials. On the other hand, combined with a variety of macroscopic characteristics in the original data set, such as various moduli, Poisson's ratio, etc., the mechanical properties of the material are comprehensively and meticulously described from multiple scales. This multi-scale analysis method not only helps to build a more accurate flow stress prediction model, but also further strengthens the physical basis of the model, makes the model more consistent with the physical nature of the material, and significantly improves the reliability and applicability of the model. This solution can comprehensively and accurately characterize the material properties. When systematically studying the effect of Nb content on tensile properties, it fully considers the tensile changes in different dimensions, accurately captures key behavioral characteristics such as dislocation movement and atomic bond changes when stretching in different directions, and plays a key role in accurately predicting flow stress. Furthermore, the rich and diverse data generated by the simulation allows the model to learn more complex behavioral patterns, significantly enhancing its generalization capabilities. This allows the model to no longer be limited to specific conditions or Nb content ranges, allowing it to flexibly respond to prediction needs under diverse operating conditions. By comprehensively considering the impact of multiple factors on flow stress, the original dataset includes characteristics such as Nb content, various moduli, and Poisson's ratio. These factors are interrelated and mutually influential, collectively determining flow stress. By learning these complex relationships, the model achieves more accurate predictions, effectively avoiding the errors caused by considering only a single factor. Furthermore, by combining experimental data to construct a dataset, the accuracy of experimental data and the systematic advantages of simulation data are fully utilized, better fitting actual performance variations and significantly improving the confidence of the prediction results. This solution provides practical and effective guidance for optimizing material properties. Based on the predicted maximum flow stress, key parameters such as Nb content can be rationally adjusted to achieve targeted improvements in material performance, meeting the stringent mechanical property requirements of aerospace, automotive, and other fields. In the field of engineering design, it provides solid and strong support for structural design, safety assessment and other work, helps to achieve reasonable material selection, optimize processes, ensure the safety and reliability of structures, and at the same time achieve optimal use of materials and effectively reduce costs and weight.

[0045] The flow stress prediction scheme based on multiple models provided in the embodiments of the present application can also be performed by an electronic device, which can be a server, a server cluster, or a cloud server. The electronic device can also be a terminal device such as a mobile phone, a computer, a tablet computer, a wearable device, or a dedicated device (such as a dedicated terminal device with a flow stress prediction method system based on multiple models). The chip introduced in the above embodiments can also be carried in these electronic devices. Alternatively, these electronic devices can also be installed with a service program for executing the flow stress prediction scheme based on multiple models.

[0046] Figure 1 A schematic diagram of a process for designing the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning is provided in an embodiment of the present application, as shown in FIG. Figure 1 As shown, the method includes the following steps:

[0047] 101. Constructing a pure binary model based on a γ-TiAl single crystal structure, and adding different amounts of Nb atoms to the constructed pure binary model to obtain multiple initial models;

[0048] 102. Performing stretch simulation on the multiple initial models using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models, wherein the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models;

[0049] 103. Based on the multiple stress-strain curves, respectively calculate the bulk modulus, shear modulus, Poisson's ratio, and flow stress, wherein the flow stress is the average stress from the first peak to the end of deformation;

[0050] 104. Calculate, based on the multiple initial models, simulation characteristic parameters of the multiple initial models during the simulated stretching process, the simulation characteristic parameters including at least stacking fault energy and lattice constant;

[0051] 105. Using the bulk modulus, shear modulus, Poisson's ratio, flow stress, and the simulation characteristic parameters corresponding to the multiple initial models as original data sets for training a flow stress prediction model, processing the original data sets to obtain a standard data set, and training a BP neural network model based on the standard data set to obtain a flow stress prediction model;

[0052] 106 , inputting the Nb content to be predicted into the flow stress prediction model for prediction analysis to obtain a corresponding flow stress prediction value, and determining the corresponding optimal Nb content according to the maximum flow stress prediction value.

[0053] In the embodiment of the present application, the pure binary model based on the γ-TiAl single crystal structure is a model constructed based on the single crystal structure of the intermetallic compound γ-TiAl, and the model contains two elements, namely titanium (Ti) and aluminum (Al). γ-TiAl has a specific crystal structure and belongs to the face-centered tetragonal (FCT) structure. In this structure, Ti and Al atoms are arranged according to a certain rule to form a periodic lattice. This crystal structure gives the γ-TiAl material unique physical and mechanical properties, such as higher hardness, good high-temperature strength and oxidation resistance. It is worth noting that the pure binary model mainly involves two elements, Ti and Al. This helps researchers focus on the interaction between Ti and Al and their basic influence on material properties. By constructing a pure binary model, the intrinsic properties of γ-TiAl, such as electronic structure, chemical bonding, crystal growth, etc., can be studied in a relatively simple system, providing a basis for further studying complex alloy systems.

[0054] Based on the principle of molecular dynamics, computer simulation software can be used to construct it. During the construction process, it is necessary to determine the coordinates of the Ti and Al atoms, lattice parameters and other information to accurately describe the crystal structure of γ-TiAl. For example, the first-principles calculation method can be used to determine the optimal arrangement of atoms and lattice constants based on density functional theory. Molecular dynamics methods can also be used to simulate the equilibrium structure of atoms at a certain temperature and pressure by giving the interaction potential function between atoms, thereby constructing a pure binary model that conforms to the γ-TiAl single crystal structure.

[0055] The pure binary model is an important foundational tool for studying γ-TiAl materials. On the one hand, it can be used for theoretical research, such as understanding the bonding characteristics and electronic state distribution of materials through electronic structure calculations, thereby predicting the material's physical properties. On the other hand, it can serve as a starting point for studying more complex alloy systems. For example, when studying the effect of adding other alloying elements (such as niobium (Nb)) on the properties of γ-TiAl, a pure binary model can be established first, and then Nb atoms can be introduced on this basis. Comparative analysis of the changes in material properties at different Nb contents can help to gain a deeper understanding of the alloying mechanism and the principles of material performance regulation.

[0056] As an optional embodiment, in 101, multiple initial models corresponding to the pure binary model at different Nb contents are constructed; the Nb content is set using a gradient increase; and then, tensile simulation is performed based on the multiple initial models to obtain tensile simulation data corresponding to the multiple initial models.

[0057] Here, multidimensional tensile simulations are performed based on a pure binary model at different Nb contents. First, multiple initial models corresponding to the pure binary model at different Nb contents are constructed. Here, the Nb content is set to a gradient increment, for example, increasing gradually from a lower content to a higher content in a certain small increment. That is, as the Nb content changes, the specific distribution and arrangement of atoms within the model also changes accordingly. Further tensile simulations are then performed based on these multiple initial models, thereby obtaining tensile simulation data corresponding to each initial model during the tensile process. The entire process comprehensively and systematically demonstrates all aspects of the material's performance from its initial state to the tensile process under the influence of different Nb contents, covering relevant changes at the atomic level as well as tensile simulation data such as stress and strain during the tensile process. This helps to gain a deeper understanding of the changes in the mechanical properties of the material under different Nb content conditions, providing rich and valuable data support for subsequent operations such as training flow stress prediction models based on these data, better exploring the intrinsic relationship between material properties and Nb content, and thus improving the accuracy and scientific nature of flow stress prediction.

[0058] Based on the above principles, further optionally, in the embodiment of the present application, the Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%.

[0059] As an optional embodiment, in 101, a pure binary model based on a γ-TiAl single crystal structure is constructed, and different contents of Nb atoms are added to the constructed pure binary model to obtain multiple initial models, which can be implemented as follows:

[0060] Molecular dynamics was used to simulate and model the pure γ-TiAl single crystal to construct the corresponding pure binary model. Among them, the different crystal directions in the pure binary model were aligned with different directional axes in the simulation space. The pure binary model was filled with different amounts of Nb to construct 50 initial models with different Nb contents. The Nb content of the first initial model was 0.3%, and the Nb content of the 50th initial model was 15%. The Nb content of each initial model increased gradually by 0.3%.

[0061] It is worth noting that in the examples of this application, when constructing a pure binary model using molecular dynamics, the atomic composition and arrangement of the γ-TiAl single crystal were precisely set. For example, the positions and proportions of Ti, Al, and Nb atoms, as well as their interactions, were considered in detail. For complex crystal structures of γ-TiAl single crystals (such as the L10 structure), modeling was performed according to their actual lattice parameters and atomic distribution, reproducing the microstructure as realistically as possible.

[0062] In the embodiment of the present application, a constitutive model based on crystal plasticity theory is also used. This model can directly consider the influence of microscopic mechanisms such as crystal structure and dislocation movement on material deformation. In the model, the crystal structure parameters of the γ-TiAl single crystal (such as lattice orientation, slip system, etc.) are used as input, and the plastic deformation and flow stress of the material are calculated by describing the movement and interaction of dislocations in different slip systems. The parameters in the constitutive model are updated according to the microstructural change information (such as dislocation density, slip system activation, etc.) obtained by molecular dynamics simulation, so that the model can accurately reflect the influence of complex changes in microstructure on flow stress.

[0063] If a multiphase structure exists in a γ-TiAl single crystal, the phase-field model can effectively describe the migration of phase interfaces, phase transitions, and their effects on flow stress. By introducing order parameters to describe the distribution and evolution of different phases, the phase-field model can account for the influence of microstructural changes during phase transitions (such as phase volume fraction, shape and curvature of phase interfaces, etc.) on the mechanical properties of the material. By combining molecular dynamics simulations with experimental data, the parameters of the phase-field model were determined, enabling accurate prediction of the flow stress of γ-TiAl single crystals with complex microstructures.

[0064] For example, in 101, a pure binary model is constructed by molecular dynamics, and the pure binary model is constructed based on the characteristics of γ-TiAl single crystal. The pure binary model can be referred to Figure 2 The model structure is shown.

[0065] Specifically, the first step is to determine the dimensions of the simulation box. For a purely binary model, the dimensions of the simulation box in the x, y, and z directions are appropriately set based on the research objectives and the dimensional characteristics of the actual material. For example, based on the typical size range of the material in practical applications or the size of the experimental sample, the simulation box dimensions can be set to the nanometer level, such as 10-20 nm in the x-direction, 15-30 nm in the y-direction, and 8-15 nm in the z-direction. This size range allows for a sufficient number of atoms to reflect the material's microstructural characteristics while also allowing for efficient simulation within the limits of computational resources. Secondly, the number and composition of atoms in the simulation system must be clearly defined. The number of Ti and Al atoms is determined based on the stoichiometric ratio of a γ-TiAl single crystal. For example, in ideal γ-TiAl (a phase structure of TiAl), the ratio of Ti to Al atoms is close to 1:1. In actual simulations, the specific number of Ti and Al atoms is calculated based on the size of the simulation box and the required atomic density. Furthermore, if doping elements (such as Nb) are considered, the appropriate number of dopant atoms should be determined based on the desired doping concentration range.

[0066] Furthermore, the atomic arrangement is constructed based on the known crystal structure of γ-TiAl single crystal. γ-TiAl usually has a tetragonal L10 structure, and its lattice constant is a key parameter for building the model. By consulting the literature or the lattice constant data obtained by experimental measurement, the initial lattice structure is set in the simulation software (such as LAMMPS). For example, according to the atomic arrangement of the L10 structure, the Ti and Al atoms are placed in the corresponding lattice positions to ensure that the relative positions between the atoms meet the symmetry and periodicity requirements of the crystal structure.

[0067] Considering the alignment of crystal directions with coordinate axes is very important for studying the mechanical properties of materials in different directions. For example, specific crystal directions of γ-TiAl single crystals (such as

[001] ,

[100] ,

[010] , etc.) are aligned with the coordinate axes (x, y, z axes) of the simulation box so that the direction-dependent mechanical behavior can be clearly defined in subsequent operations such as tensile simulation. At the same time, in terms of boundary condition setting, periodic boundary conditions are usually used to avoid boundary effects. Periodic boundary conditions assume that the simulation box is infinitely repeated in space, so that the behavior of atoms at the boundary of the simulation box is consistent with the behavior of atoms inside, and the bulk properties of the material are more realistically simulated.

[0068] Furthermore, in an embodiment of the present application, a suitable interatomic interaction potential can be selected to describe the interaction between atoms in the γ-TiAl single crystal. For this intermetallic compound, commonly used potential functions include the embedded atom method (EAM) potential function or the improved embedded atom method (MEAM) potential function. These potential functions can take into account factors such as the electronic structure and chemical bonding of atoms, and more accurately describe the interaction between Ti, Al and possible doping atoms (such as Nb). The parameters of the potential function are determined according to the properties of the material and existing experimental data. For example, the parameters in the potential function are determined by fitting the physical properties such as the elastic modulus and lattice constant of the material measured in the experiment. At the same time, it can be compared and verified with some simple experimental results or other reliable simulation results to ensure that the selected potential function and the set parameters can reasonably describe the interaction between the atoms of the γ-TiAl single crystal, laying the foundation for subsequent accurate simulation.

[0069] For example, first, in 101, with the help of molecular dynamics simulation software (such as LAMMPS), an initial model is constructed based on the characteristics of γ-TiAl single crystal. During the construction process, the dimensions of the simulation box in the x, y, and z directions are set to 10.2nm, 15.7nm, and 8.3nm, respectively, and about 82,944 atoms are generated in the simulation box, which constitute the basic atomic set of the pure binary model. Among them, the atoms in the simulation box are distinguished by different colors, the blue icon represents Al atoms, the yellow icon represents Ti atoms, and the red icon represents Nb atoms. When modeling, in strict accordance with the crystallographic orientation requirements, the crystal direction [-110] is accurately aligned with the x-axis, the crystal direction [-1-12] is accurately aligned with the y-axis, and the crystal direction

[111] is accurately aligned with the z-axis, so as to ensure the crystallographic orientation consistency of the model. At the same time, the Nb atomic content was finely set, starting from 0.3% and gradually increasing to 15% in steps of 0.3%. Through this setting, 50 initial models with different Nb contents were constructed, which provided a diverse model basis for subsequent in-depth research on the changes in the tensile properties of γ-TiAl single crystals under different Nb contents, so as to comprehensively explore the influence mechanism and law of the Nb element on the tensile behavior of γ-TiAl single crystals, thereby providing key theoretical basis and data support for the performance optimization and engineering application of related materials.

[0070] Alternatively, in step 101, a pure binary model based on a γ-TiAl single crystal structure is constructed. Different amounts of niobium atoms (Nb) are added to the constructed pure binary model to obtain multiple initial models. A MEAM potential function can then be selected to describe the atomic interactions of each initial model. Furthermore, parameters are set for the 50 initial models to dynamically adjust the external forces, pressures, atomic types, and / or periodic boundary conditions applied to the target model. Finally, an energy minimization calculation is performed on the 50 initial models using the conjugate gradient method to adjust the relative positions of the atoms in the 50 initial models, eliminate unreasonable interactions between atoms, and make the optimized initial models more structurally stable.

[0071] In the above steps, after constructing the initial model with different Nb contents, the energy minimization method (such as the conjugate gradient method) is used to initialize the initial model. This step can make the atomic system reach a relatively stable initial state and eliminate the unreasonable high-energy state that may exist in the initial arrangement of atoms, such as overlap or unreasonable spacing between atoms. Check the structural rationality of the constructed initial model, including whether the atomic spacing conforms to the physical properties of the actual material, whether the crystal structure remains intact (such as whether the lattice symmetry meets the requirements), etc. The rationality of the model can be verified by calculating some basic physical parameters of the model (such as lattice constant, atomic coordination number, etc.) and comparing them with known experimental data or theoretical values.

[0072] In the embodiment of the present application, the potential function is used to represent the interaction force between atoms during the stretching process. Further optionally, the potential function is affected by at least one factor selected from the group consisting of electron cloud distribution, embedding energy, and attractive and repulsive forces between atoms.

[0073] After constructing multiple initial models corresponding to different Nb contents, the Nb content is set in a gradient-increasing manner, and the number of atoms and the atomic distribution structure of each initial model are determined according to the corresponding different Nb contents. Optimization work is carried out on these initial models to make them have a stable structure. For example, based on the MEAM potential function, this potential function performs well in describing the interaction force between atoms in TiAlNb single crystals and simulating the stretching process, and can provide a basis for interatomic interactions that conform to actual physics for subsequent simulations. At the same time, the atom type is set to atomic, and the metal unit is used to ensure that the calculation of physical quantities and parameter settings during the simulation process conform to the research habits of metal materials. In addition, periodic boundary conditions are set in the x, y, and z directions to avoid boundary effects and make the simulation system closer to the internal conditions of the actual material.

[0074] Through the above steps, we first determine the potential functions corresponding to multiple initial models, as potential functions can represent the interactions between atoms during the stretching process. The interactions between atoms are complex and are influenced by factors such as electron cloud distribution, embedding energy, and the attractive and repulsive forces between atoms. Therefore, a suitable potential function is key to accurate simulation. This potential function allows us to reasonably describe the interactions between atoms during the stretching process in subsequent steps.

[0075] Next, parameters were set for multiple initial models, and the conjugate gradient method was used to adjust the relative positions of atoms to obtain a minimized energy model. This model has an atomic configuration that minimizes energy, based on physical considerations: in their natural state, materials tend to be in their lowest energy stable state. This operation ensures that the model achieves a relatively stable and reasonable initial structure before the stretching simulation, providing a more realistic starting state for subsequent simulations.

[0076] Optionally, the conjugate gradient method (cg) is used to perform energy minimization, which continuously adjusts the positions of atoms to reduce the total energy of the model until the system energy reaches a minimum value, thereby obtaining the most stable model, that is, the initial model after optimization.

[0077] Among them, the conjugate gradient method is an iterative algorithm for solving unconstrained optimization problems and is used for energy minimization in molecular dynamics simulations. Its core goal is to find the minimum value of a function (in this case, the energy function of the system). It is based on the fact that for a quadratic function, starting from any initial point, by performing a one-dimensional search along a set of mutually conjugated directions, it is possible to converge to the minimum value of the function within a finite number of steps. By continuously searching for a suitable step size along the conjugate direction to update the atomic position, the conjugate gradient method gradually reduces the total energy of the system. Because each search direction is determined based on the current energy gradient and is conjugated with the previous search direction, this method can effectively avoid falling into a local optimal solution (to a certain extent), and compared to the steepest descent method, it converges faster and can more efficiently find the minimum value of the energy function, so that the atomic arrangement of the model reaches the lowest energy stable state, which is consistent with the stable structure of the material under actual physical conditions.

[0078] Then, factors such as external forces, pressures, atomic types, and / or periodic boundary conditions in the target model are dynamically adjusted, and the previously determined potential function is used to simulate the corresponding stretching change data of the target model during these adjustments. These stretching change data include atomic interaction potential, stretching force adjustment position, atomic motion state, atomic displacement changes, and other aspects. This step can simulate the various complex changes in the material during the actual stretching process, and can record and simulate in detail everything from atomic-level interactions to macroscopic displacement changes, providing a deeper and more comprehensive understanding of the material stretching process.

[0079] Finally, based on the aforementioned tensile variation data, the tensile yield strength at different Nb contents was determined. Tensile yield strength is a key indicator of a material's mechanical properties. Through the preceding series of simulations and data recording, we were able to accurately determine the value of this important parameter at different Nb contents. This provides crucial data support for studying the relationship between material properties and composition (Nb content), which is extremely important for material performance evaluation, design, and optimization.

[0080] 102. Simulate stretching of the multiple initial models through molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models.

[0081] In the embodiment of the present application, the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to multiple initial models.

[0082] 103. Based on the multiple stress-strain curves, respectively calculate the bulk modulus, shear modulus, Poisson's ratio, and flow stress, wherein the flow stress is the average stress from the first peak to the end of deformation.

[0083] It is understood that bulk modulus is a physical quantity that measures a material's ability to resist volume deformation. It represents the ratio of the relative change in a material's volume under uniform pressure to the applied pressure. Bulk modulus reflects a material's ability to resist compression or expansion in three-dimensional space. In stretching simulations, although the stretching is primarily in a certain direction, there is also a certain amount of volume change within the material. Materials with larger bulk moduli experience smaller volume changes when subjected to external forces, indicating that their atoms are tightly bonded and have a strong ability to resist volume deformation. Conversely, materials with smaller bulk moduli are more susceptible to volume changes. By extracting the bulk modulus, we can understand the overall stiffness and stability of the material during stretching, as well as its volume response characteristics under different stress states.

[0084] The shear modulus is used to describe the mechanical properties of a material under shear force. It is equal to the ratio of shear stress to shear strain. Shear stress refers to the stress caused by a force parallel to the material's cross-section, while shear strain is the angular deformation of the material under shear force. The shear modulus reflects the material's ability to resist shear deformation. During the tensile process, in addition to the stress and strain in the tensile direction, a certain amount of shear stress and strain is also generated within the material. In particular, processes such as dislocation movement and slip are closely related to the shear modulus in crystal structures. Materials with higher shear moduli have a stronger ability to resist shear deformation, making dislocation movement relatively difficult, and the material may have higher strength and hardness. Materials with lower shear modulus are more susceptible to shear deformation and may exhibit better toughness and plasticity. Extracting the shear modulus helps to gain a deeper understanding of the microscopic deformation mechanism and mechanical properties of materials during tension.

[0085] Poisson's ratio refers to the absolute value of the ratio of transverse strain to longitudinal strain when a material is stretched or compressed uniaxially. When a material is stretched in one direction, it contracts in a plane perpendicular to the direction of stretching. The Poisson's ratio describes the relationship between this transverse contraction and longitudinal extension. The Poisson's ratio reflects the degree of coupling between the transverse and longitudinal deformations of a material under stress. For most materials, the Poisson's ratio ranges from 0 to 0.5. A Poisson's ratio close to 0 indicates little to no transverse contraction when stretched, while a ratio close to 0.5 indicates significant transverse contraction. In tensile simulations, the Poisson's ratio can help analyze the coordination of material deformation in different directions and predict its behavior under complex stress states. It is closely related to the material's microstructure, chemical bond properties, and other aspects. Extracting the Poisson's ratio can provide further insights into the material's mechanical properties and deformation characteristics.

[0086] In the embodiments of the present application, a stress-strain curve is a visual representation of the relationship between stress and strain when a material is subjected to an external force. In the embodiments of the present application, the stress-strain curve is obtained by simulating the stretching of multiple initial models using molecular dynamics. It reflects how the stress (the force per unit area) of the material changes as the strain (the degree of deformation of the material) increases during the stretching process.

[0087] Specifically, when a material is subjected to tensile force, the stress will increase linearly with the strain in the initial stage. At this stage, the material is in the elastic deformation stage. When the stress reaches a certain value (the first peak, also called yield strength), the material begins to enter the plastic deformation stage. At this time, the stress no longer increases linearly with the strain, but shows complex changes until the material finally deforms.

[0088] In 103, based on multiple stress-strain curves, the average stress from the first peak to the end of deformation is calculated as the flow stress corresponding to multiple initial models. The specific principle is as follows:

[0089] During the plastic deformation stage of a material, the stress-strain relationship is complex. However, the average stress from the first peak to the end of deformation can reflect the material's stable load-bearing capacity during this stage. The stress changes during this stage are crucial for understanding the material's mechanical behavior in practical applications, as they represent the material's sustained resistance to a given deformation, rather than simply the initial yield strength. The initial yield peak can be affected by various factors, such as microstructural heterogeneity, and it does not fully represent the material's performance during subsequent deformation. Calculating the average stress from the first peak to the end of deformation avoids the transient effects of the initial yield peak and more comprehensively considers the material's mechanical response throughout the entire plastic deformation process. In engineering applications, materials are often required to maintain stable mechanical properties within a certain deformation range. Calculating the average stress during this stage as the flow stress better aligns with the material's performance requirements in actual service, providing more reliable mechanical parameters for engineering design. During plastic deformation, materials undergo work hardening, meaning that their strength and hardness gradually increase with increasing deformation. The average stress from the first peak to the end of deformation can comprehensively reflect the material's work hardening characteristics because it accounts for the stress changes throughout the deformation process. Using this method to calculate flow stress provides a unified standard for evaluating material properties across different initial models. Regardless of the material's specific microstructure, its flow stress performance can be evaluated by comparing the average stress from the first peak to the end of deformation, making it easy to compare and optimize performance between materials.

[0090] It can be understood that in 103, by calculating the average stress from the first peak to the end of deformation as the flow stress, the mechanical properties of the material in the plastic deformation stage can be more accurately reflected, providing more valuable information for material research and engineering applications.

[0091] As an optional embodiment, in step 102, multiple initial models are simulated and stretched using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models. This can be achieved by: using an NPT stretching ensemble to perform the stretching simulation, setting the stretching direction along a first axis, setting the system temperature, and setting initial velocities for atoms according to a Gaussian distribution so that each initial model reaches equilibrium at the system temperature, with a relaxation time set to 50 ps; after relaxation is completed, setting the strain rate and dependent variable, starting the simulated stretching operation, and setting a period for collecting model information and atomic information during the simulated stretching process to obtain the molecular dynamics simulation results. Furthermore, in step 103, based on the multiple stress-strain curves, the average stress from the first peak to the end of the deformation stage is calculated as the flow stress corresponding to the multiple initial models. A correlation between Nb content and flow stress can also be generated based on the flow stress corresponding to the multiple initial models.

[0092] Based on the above-mentioned optimized initial model, the pre-adopted stretching ensemble and stretching simulation parameters are further selected to construct the initial model to simulate the stretching process and obtain the corresponding stretching simulation results. The entire stretching simulation is implemented with the help of LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) software. For example, the "pair_coeff" command is used to define the interaction potential between atoms to ensure that the interatomic forces can be accurately calculated during the stretching process. Then, the "fix" command is used to perform a stretching operation on the model along the y direction to simulate the actual stretching process.

[0093] The tensile ensemble was selected as the NPT ensemble to simulate the constant pressure and temperature environment of actual tensile testing. Initial velocities were first applied to the optimized initial model to bring the system to equilibrium at the target temperature. During this process, the velocity distribution and direction were explicitly specified, setting the initial velocities for the simulated atoms and officially initiating the simulation. Temperature initialization was accomplished using the "velocitycreat" command, using an appropriate random number seed, a system temperature of 900°C, and initial velocities according to a Gaussian distribution.

[0094] The stretching simulation parameters include the simulation temperature and relaxation time. In the NPT ensemble, the model temperature was set to 900°C and the relaxation time to 50 ps. After the relaxation period was complete, the steady-state stretching simulation began, with the stretching parameters set to a strain rate of 5e8s⁻¹ and a strain of 20%. During the simulation, the initial model and atomic information were output every 10,000 steps using the dump command. The entire simulation was run for 400,000 steps. At the end of the calculation, the simulation results were obtained.

[0095] As an optional embodiment, in step 102, after simulating stretching of multiple initial models using molecular dynamics and obtaining molecular dynamics simulation results corresponding to the multiple initial models, the multiple initial models and the molecular dynamics simulation results may be visualized to obtain an image of the changes in the multiple initial models during the stretching simulation. Furthermore, based on the multiple stress-strain curves, the average stress from the first peak to the end of deformation is calculated as the flow stress corresponding to the multiple initial models. The molecular dynamics simulation results corresponding to the multiple initial models may then be analyzed using the origin function to obtain a scatter plot of the average stress corresponding to the initial models with different Nb contents.

[0096] For example, the simulated stretching process of the initial model is visualized, and the pictures and videos of the initial model and the entire stretching process can be post-processed and visualized using post-processing software (Open Visualization Tool, OVITO).

[0097] For example, the simulation results are analyzed and processed using origin to obtain a scatter plot of different Nb contents and flow stress. For example, the scatter plot in the embodiment of this application can be found in Figure 3 shown.

[0098] 104. Calculate simulation characteristic parameters of multiple initial models during the simulated stretching process based on the molecular dynamics simulation results. In the embodiment of the present application, the simulation characteristic parameters include at least stacking fault energy and lattice constant.

[0099] It can be understood that stacking fault energy refers to the energy required to form a stacking fault per unit area in a crystal. Stacking fault is a misalignment phenomenon of atomic planes in a crystal, that is, a local error occurs in the normal atomic stacking order. Stacking fault energy has an important influence on the mechanical properties and deformation mechanism of the material. Lower stacking fault energy makes it easier for dislocations to form and move in the crystal, causing the material to be more susceptible to plastic deformation, and the deformation mechanism may be dominated by stacking fault nucleation and expansion; while for materials with higher stacking fault energy, dislocation movement is relatively difficult, the strength of the material may be higher, but the toughness may be relatively low. Calculating the stacking fault energy through molecular dynamics simulation helps to understand the impact of the formation and evolution of defects at the internal atomic level on the overall performance of the material during tension.

[0100] The lattice constant is a basic parameter that describes the crystal structure. It represents the size and shape of the lattice unit in the crystal. For the cubic crystal system, the lattice constant usually refers to the side length of the unit cell; for other crystal systems, multiple parameters may be involved to describe the size and angle of the unit cell. The change in the lattice constant reflects the slight deformation of the crystal structure of the material when it is subjected to force. In the tensile simulation, the lattice constant may change with the action of external force, which means that the distance and arrangement between atoms inside the crystal have changed. By monitoring the change in the lattice constant, we can understand the deformation law of the material at the microscopic level, and then analyze the relationship between the mechanical properties of the material and the crystal structure. For example, an increase in the lattice constant may indicate the expansion of the material in the tensile direction, which is closely related to properties such as the elastic modulus of the material.

[0101] 105. Use the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to multiple initial models as the original data set for training the flow stress prediction model, process the original data set to obtain a standard data set, and train the BP neural network model based on the standard data set to obtain the flow stress prediction model.

[0102] As an optional embodiment, in step 105, the bulk modulus, shear modulus, Poisson's ratio, flow stress, and the simulation characteristic parameters corresponding to multiple initial models are used as original data sets for training the flow stress prediction model. The original data sets are processed to obtain a standard data set. The BP neural network model is trained based on the standard data set to obtain the flow stress prediction model. This can be implemented as follows:

[0103] 201. Using the bulk modulus, shear modulus, Poisson's ratio, flow stress, and the simulation characteristic parameters corresponding to multiple initial models as original data sets for training a flow stress prediction model, processing the original data sets to obtain a first standard data set and a second standard data set, respectively; wherein the first standard data set includes at least: Nb content and flow stress, and the second standard data set includes at least: Nb content, flow stress, stacking fault energy, lattice constant, bulk modulus, shear modulus, and Poisson's ratio;

[0104] 202, preprocessing the first standard data set and the second standard data set respectively and randomly dividing them into corresponding training sets and test sets, wherein 80% is the training set and 20% is the test set;

[0105] 203, using the training sets divided from the first standard data set and the second standard data set to train different BP neural network models respectively, where the different BP neural network models refer to neural network models with different structures and / or different model parameters;

[0106] 204 , using the test set divided from the first standard data set and the second standard data set to test the prediction performance of different BP neural network models; the flow stress prediction model with the best prediction performance is used as the flow stress prediction model to be finally used.

[0107] Specifically, in 201, the bulk modulus, shear modulus, Poisson's ratio, flow stress, and simulation characteristic parameters corresponding to multiple initial models were used as the original data set for training the flow stress prediction model. This data set was then processed into a first standard data set and a second standard data set containing different information, based on the data characteristics and subsequent analysis requirements. The first standard data set focused on the relationship between Nb content and flow stress and their correlation, used for preliminary exploration of the basic relationship between the two. The second standard data set was more comprehensive, including simulation characteristic parameters, to facilitate in-depth research on the combined effects of multiple factors on flow stress.

[0108] In this way, by organizing and classifying the raw data, the data becomes more structured, facilitating subsequent analysis and modeling. Different standard data sets can meet different levels of research needs and provide diverse data support for building accurate prediction models.

[0109] In 202, data preprocessing is performed to improve data quality, such as standardizing the data and removing outliers, to make the data more suitable for model training. Preprocessing can improve data reliability and consistency and reduce the impact of data noise on the model.

[0110] Furthermore, in the above steps, obtaining the original sampling data of flow stress is the basis. These data contain information obtained from various actual measurements and are the source of materials for subsequent model training. Candidate feature data related to the microstructure and performance characteristics of the material are extracted from the original sampling data. Because the microstructure of the material (such as crystal orientation distribution, dislocation density, grain size, etc.) and the actual performance (such as actual flow stress) are closely related, these feature data can reflect the essential properties of the material. The extracted candidate feature data are preprocessed and converted into a standard data set. This step is to eliminate the influence of dimensional differences in the data, so that the data can be compared and processed on the same scale, which is convenient for model training.

[0111] In 203, multiple neural network models are obtained based on different neural network model structures and / or different model parameter combination configurations, and these candidate models are trained using the divided training set. By adjusting the parameters of the model, the model can learn the rules in the data, that is, the relationship between Nb content, bulk modulus, shear modulus, Poisson's ratio, flow stress, stacking fault energy, lattice constant and flow stress, thereby realizing the prediction of flow stress. Therefore, by using a variety of different model structures and parameter combinations for training, different modeling methods can be explored to find the model that best suits the data and problem. This can fully tap the information in the data, improve the model's fitting ability and prediction accuracy, and avoid performance limitations caused by improper model selection.

[0112] For example, the training set is used to train the flow stress prediction model. This model is obtained by adaptively configuring the characteristics of the γ-TiAl single crystal. This can better fit the characteristics of the research object and enable the model to learn the intrinsic relationship between material properties and flow stress.

[0113] For example, based on the crystal structure characteristics of γ-TiAl single crystals, it often presents specific crystallographic morphologies such as the tetragonal L10 structure. When constructing the model, the relevant parameters of this crystal structure are quantified and incorporated into it. For example, the lattice constant, the arrangement of atoms in the unit cell, etc. These structural information determine the interaction paths between atoms and the deformation modes that may occur under external forces. The model will set the corresponding initial architecture based on these crystal structure data, so that it can simulate the behavior of atoms under force at the microscopic level, laying the foundation for the accurate prediction of flow stress.

[0114] Furthermore, the anisotropy of γ-TiAl single crystal is also one of its key characteristics. Its mechanical properties in different directions vary significantly. For example, it may show higher strength when stretched in certain crystal directions, while it has different elastic and plastic characteristics in other crystal directions. In response to this characteristic, the first flow stress prediction model is equipped with a module that can identify and process anisotropy. By performing differentiated learning and analysis on stress-strain data in different directions, the model can accurately predict the flow stress changes in the corresponding direction based on input information such as the force direction. This means that whether it is simulating the complex directional stresses on aircraft engine blades or the working conditions of other engineering components under multi-directional forces, the model can give realistic prediction results.

[0115] The performance stability of γ-TiAl single crystals in high-temperature environments cannot be ignored either. In actual application scenarios, high-temperature components in the aerospace field often operate at relatively high temperatures, and the material's high-temperature strength, oxidation resistance and other properties play a decisive role in its reliability. Based on this, the prediction model incorporates temperature-related variables and parameters, and adaptively adjusts the calculation logic within the model according to the flow stress variation law of γ-TiAl single crystals in different temperature ranges. For example, as the temperature rises, the material will soften. The model will dynamically update the prediction of the flow stress based on the temperature-stress variation relationship obtained from experimental data and theoretical analysis to reflect the impact of the high-temperature environment on the material properties.

[0116] Furthermore, considering the impact of compositional changes in γ-TiAl single crystals (such as the possible presence of different doping elements and their contents) on flow stress, the model has the ability to adaptively configure itself to address these changes. Taking Nb doping as an example, different Nb contents will alter the material's microstructural factors, such as the lattice constant and dislocation motion characteristics, thereby affecting the flow stress. The model can adjust the internal calculation weights and correlations of the corresponding micromechanisms based on the input composition information, accurately capturing the changes in flow stress caused by compositional changes, thereby adapting to the prediction requirements of γ-TiAl single crystals with different compositions. Furthermore, during the adaptive configuration process, a large amount of experimental and simulation data is combined for continuous optimization and calibration. Flow stress data obtained from actual mechanical property testing experiments, such as tensile and compression, as well as data on microstructural changes and stress relationships obtained through molecular dynamics simulations, are used as the basis for model learning and improvement. By repeatedly comparing and correcting the model's parameters and algorithm logic, the flow stress prediction model can more accurately fit the actual performance of γ-TiAl single crystals under various working conditions, becoming a reliable and practical flow stress prediction tool, providing strong support for many aspects such as material design, application and performance optimization.

[0117] In 204, the prediction performance of different trained BP neural network models was tested using the partitioned test set. By comparing the differences between the predictions of each model on the test set and the actual values, such as by calculating metrics such as mean squared error and mean absolute error, the predictive performance of the model was evaluated, and the best-performing model was selected as the final flow stress prediction model. Thus, by evaluating on an independent test set, the generalization ability and prediction accuracy of different BP neural network models can be objectively measured. Selecting the best-performing BP neural network model ensures accurate flow stress prediction in practical applications, providing reliable support for material performance research and engineering applications, and enhancing the practicality and application value of the model.

[0118] For example, the processed standard data set is randomly divided into a training set and a test set, for example, 80% of the data set is used as a training set and 20% as a test set.

[0119] In this way, the BP neural network model with the best prediction performance is found as the final flow stress prediction model. This process is equivalent to optimizing and screening the model so that the model can achieve the best prediction effect when facing the actual flow stress prediction task.

[0120] Exemplarily, the parameter combination for constructing the flow stress prediction model includes but is not limited to: the number of hidden layers, the number of neurons in each hidden layer, Epochs (number of training cycles), Optimizer (type of optimizer), Learning_rate (learning rate) and Dropout_rate (dropout rate).

[0121] This training method fully leverages both actual measured and simulated data, closely linking the material's microstructure and performance characteristics with its flow stress. Preprocessing and rational data partitioning enhance the model's stability and generalization capabilities. The model, constructed and optimized based on the properties of γ-TiAl single crystals, more accurately predicts the material's flow stress, providing a reliable prediction tool for performance evaluation and design in practical applications. This helps better understand the dynamics of material properties, optimize material composition and processing techniques, and ultimately improve the material's reliability and performance in practical engineering applications.

[0122] Alternatively, a flow stress prediction model based on the properties of γ-TiAl single crystals is an advanced model specifically designed to accurately estimate the flow stress of this material under various operating conditions. In terms of crystal structure, it fully considers the tetragonal L10 structure of γ-TiAl single crystals, incorporating parameters such as lattice constants and atomic arrangement into the model architecture. This enables the model to understand interatomic interactions at a microscopic level. During stress simulations, this structural information accurately tracks the relationship between atomic displacements and stress changes, providing an atomic-scale physical basis for flow stress prediction. To address the anisotropy of γ-TiAl single crystals, the model incorporates a dedicated direction recognition and processing mechanism. By learning from mechanical property data in different crystal directions, it can adaptively adjust the calculation strategy based on the input force direction, accurately predicting flow stress differences in various directions. This is particularly critical for evaluating the material properties of complex load-bearing components. Regarding temperature characteristics, the model incorporates temperature as a variable, given the significant performance changes of γ-TiAl single crystals at high temperatures. Based on the material's softening and phase transformation behavior in different temperature ranges, a temperature-stress correlation module is constructed, combining experimental and theoretical data. When high-temperature operating conditions are input, the model dynamically modifies predictions to reflect the effects of high temperatures on flow stress. Taking into account compositional variations, such as the doping of elements like Nb, the model adjusts parameters related to microstructural changes based on the input compositional information. Different elemental contents alter lattice distortion, dislocation motion, and other conditions. By learning the inherent relationship between composition, microstructure, and stress, the model accurately predicts flow stress changes caused by compositional changes. This meets the prediction needs of γ-TiAl single crystals with varying compositions, providing powerful flow stress prediction support for their efficient application in aerospace, automotive, and other fields.

[0123] For example, in order to obtain the optimal flow stress prediction model, different parameter combinations need to be tested and the regression coefficient R 2 The regression coefficient and the root mean square error (RMSE) are used as indicators for evaluating the accuracy of the model. That is, in the above step 204, the prediction performance value of the BP neural network model can be evaluated using the regression coefficient and the root mean square error (RMSE).

[0124] The regression coefficient is expressed as The root mean square error RMSE is: Where n is the number of data groups in the test set, y j is the flow stress test value of atom j in the test set, is the predicted value of flow stress of atom j obtained by BP neural network model using test set, is the average value of all flow stresses of atom j predicted by the BP neural network model using the test set.

[0125] In 106 , the Nb content to be predicted is input into the flow stress prediction model for prediction analysis to obtain a corresponding flow stress prediction value, and the corresponding optimal Nb content is determined according to the maximum flow stress prediction value.

[0126] For example, see Figure 4 and Figure 5 By inputting the Nb content to be predicted, the flow stress prediction model will output the corresponding flow stress prediction value. When the input Nb content is 9.10%, the predicted maximum flow stress is 2.178 GPa. In other words, when the maximum flow stress is 2.178 GPa, the optimal Nb content is 9.10%.

[0127] This embodiment of the application integrates molecular dynamics simulation with a flow stress prediction model. On the one hand, the tensile behavior of γ-TiAl single crystals at different Nb contents is simulated from a microscopic perspective. Multiple initial models are stretched using molecular dynamics to obtain flow stress data and microscopic data. Furthermore, the datasets obtained from the simulated stretching describe the material's mechanical properties at multiple scales, from both macroscopic and microscopic perspectives. This is used to establish a more accurate flow stress prediction model, strengthen the model's physical foundation, make it more consistent with the material's physical nature, improve overall model performance, and enhance the accuracy of model predictions.

[0128] In another embodiment of the present application, a device for predicting the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning is provided. Figure 6 Said device comprises the following units:

[0129] A construction unit is configured to construct a pure binary model based on a γ-TiAl single crystal structure, and add different contents of niobium atoms Nb to the constructed pure binary model to obtain multiple initial models; wherein the Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%;

[0130] A simulation unit is configured to simulate stretching of the multiple initial models through molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models;

[0131] A calculation unit is configured to calculate, based on the multiple stress-strain curves, a bulk modulus, a shear modulus, a Poisson's ratio, and a flow stress, respectively, wherein the flow stress is an average stress from a first peak to an end of deformation; and based on the multiple initial models, calculate simulation characteristic parameters of the multiple initial models during the simulated stretching process, wherein the simulation characteristic parameters include at least stacking fault energy and a lattice constant;

[0132] The training unit is configured to use the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as an original data set for training the flow stress prediction model; process the original data set to obtain a standard data set, and train the BP neural network model based on the standard data set;

[0133] The prediction unit is configured to input the Nb content to be predicted into the optimal flow stress prediction model obtained by training the BP neural network model based on the standard data set, perform prediction analysis, obtain the corresponding flow stress prediction value, and determine the corresponding optimal Nb content according to the maximum flow stress prediction value.

[0134] The device can implement various steps in the above method embodiment, which will not be expanded here.

[0135] In the embodiment of the present application, a multi-model based flow stress prediction device is adopted. By establishing a more accurate flow stress prediction model, the physical basis of the model is strengthened to make it more in line with the physical nature of the material, thereby achieving accurate prediction of fluid stress data, improving the overall model performance, and enhancing the accuracy of model prediction.

[0136] See also Figure 7 , Figure 7 This is a schematic diagram of an embodiment of an electronic device provided in an embodiment of the present application. Figure 7 As shown, an embodiment of the present application provides an electronic device 500, including a memory 510, a processor 520, and a computer program 511 stored in the memory 510 and executable on the processor 520. When the processor 520 executes the computer program 511, each step of the multi-model-based flow stress prediction method in the above embodiment is implemented.

[0137] The present invention provides a computer-readable storage medium having a software program stored thereon, which, when executed by a processor, implements the steps of the multi-model-based flow stress prediction method in the above-mentioned embodiment.

[0138] It should be noted that, in the above embodiments, the description of each embodiment has its own focus. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0139] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0140] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0141] Obviously, those skilled in the art may make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if such changes and modifications of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such changes and modifications.

Claims

1. A method for designing the Nb content of TiAl alloy based on molecular dynamics simulation and machine learning, characterized in that: The method comprises: A pure binary model based on a γ-TiAl single crystal structure is constructed, and different contents of Nb atoms are added to the pure binary model to obtain multiple initial models; wherein the Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%; Performing stretching simulation on the multiple initial models using molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models; and calculating the bulk modulus, shear modulus, Poisson's ratio, and flow stress based on the multiple stress-strain curves, wherein the flow stress is the average stress from the first peak to the end of deformation; Based on the multiple initial models, calculating simulation characteristic parameters of the multiple initial models during the simulated stretching process, the simulation characteristic parameters at least including: stacking fault energy and lattice constant; Using the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as the original data set for training the flow stress prediction model; Processing the original data set to obtain a standard data set, and training a BP neural network model based on the standard data set to obtain a flow stress prediction model; Inputting the Nb content to be predicted into the flow stress prediction model for prediction analysis to obtain a corresponding flow stress prediction value; The corresponding optimal Nb content is determined based on the predicted value of the maximum flow stress.

2. The design method according to claim 1, characterized in that: The method of constructing a pure binary model based on a γ-TiAl single crystal structure, adding Nb atoms of different contents to the constructed pure binary model to obtain multiple initial models, comprises the following steps: Molecular dynamics was used to simulate and model a pure γ-TiAl single crystal to construct a corresponding pure binary model. In this pure binary model, different crystal orientations were aligned with different directional axes in the simulation space. By filling different Nb contents into the pure binary model, 50 initial models with different Nb contents were constructed. The Nb content of the first initial model was 0.3%, and the Nb content of the 50th initial model was 15%. The Nb content of each initial model increased in a gradient of 0.3%.

3. The design method according to claim 1 or 2, characterized in that: The method comprises constructing a pure binary model based on a γ-TiAl single crystal structure, adding different contents of niobium atoms Nb to the constructed pure binary model to obtain multiple initial models, and optimizing the multiple initial models. The optimization process comprises: A MEAM potential function is selected to describe the interatomic interactions of each initial model; the potential function is used to represent the interaction force between atoms during the stretching process; the potential function is affected by at least one factor selected from the group consisting of electron cloud distribution, embedding energy, and attractive and repulsive forces between atoms; Setting parameters for the multiple initial models and dynamically adjusting the external forces, pressures, atomic types, and / or periodic boundary conditions in the target model; The conjugate gradient method is used to perform energy minimization calculations on multiple initial models to adjust the relative positions of atoms in multiple initial models, eliminate unreasonable interactions between atoms, and make the structure of the optimized initial model more stable.

4. The design method according to claim 1, characterized in that: The method of performing molecular dynamics simulation stretching on the multiple initial models to obtain molecular dynamics simulation results corresponding to the multiple initial models includes the following steps: The NPT stretching ensemble was used for stretching simulation. The stretching direction was set along the y-axis, the system temperature was set, and the initial velocity of the atoms was set according to the Gaussian distribution. Each initial model reached equilibrium at the system temperature, and the relaxation time was set to 50 ps. After the relaxation is completed, the strain rate and the dependent variable are set, the simulated stretching operation is started, and the cycle of collecting model information and atomic information during the simulated stretching process is set to obtain the molecular dynamics simulation results.

5. The design method according to claim 1, characterized in that: The original data set is processed to obtain a standard data set, and a BP neural network model is trained based on the standard data set to obtain a flow stress prediction model, including: The bulk modulus, shear modulus, Poisson's ratio, flow stress corresponding to the plurality of initial models and the simulation characteristic parameters are used as original data sets for training the flow stress prediction model, and the original data sets are standardized to obtain a first standard data set and a second standard data set, respectively; wherein the first standard data set includes at least: Nb content and flow stress, and the second standard data set includes at least: Nb content, flow stress, stacking fault energy, lattice constant, bulk modulus, shear modulus, and Poisson's ratio; The first standard data set and the second standard data set are preprocessed and randomly divided into their respective training sets and test sets, of which 80% are training sets and 20% are test sets; Use the training sets divided from the first standard data set and the second standard data set to train different BP neural network models respectively; The prediction performance of different BP neural network models was tested using the test set divided from the first standard data set and the second standard data set; the prediction model with the best prediction performance was used as the final flow stress prediction model.

6. The design method according to claim 1 or 5, characterized in that: Different BP neural network models refer to neural network models with different structures and / or different model parameters.

7. The design method according to claim 5, characterized in that: The test set obtained by dividing the first standard data set and the second standard data set is used to test the prediction performance of different BP neural network models, including: The regression coefficient and root mean square error were used to evaluate the prediction performance of the BP neural network model; The regression coefficient is expressed as The root mean square error RMSE is: Where n is the number of data groups in the test set, y j is the flow stress test value of atom j in the test set, is the predicted value of flow stress of atom j obtained by BP neural network model using test set, is the average value of all flow stresses of atom j predicted by the BP neural network model using the test set.

8. A device for predicting Nb content in TiAl alloy based on molecular dynamics simulation and machine learning, characterized in that: The device comprises the following units, wherein: A construction unit is configured to construct a pure binary model based on a γ-TiAl single crystal structure, and add different contents of niobium atoms Nb to the constructed pure binary model to obtain multiple initial models; wherein the Nb content of the initial model ranges from 0.3% to 15%, and the Nb content gradient is 0.3%; A simulation unit is configured to simulate stretching of the multiple initial models through molecular dynamics to obtain molecular dynamics simulation results corresponding to the multiple initial models; the molecular dynamics simulation results at least include: multiple stress-strain curves corresponding to the multiple initial models; A calculation unit is configured to calculate, based on the multiple stress-strain curves, a bulk modulus, a shear modulus, a Poisson's ratio, and a flow stress, respectively, wherein the flow stress is an average stress from a first peak to an end of deformation; and based on the multiple initial models, calculate simulation characteristic parameters of the multiple initial models during the simulated stretching process, wherein the simulation characteristic parameters include at least stacking fault energy and a lattice constant; The training unit is configured to use the bulk modulus, shear modulus, Poisson's ratio, flow stress and the simulation characteristic parameters corresponding to the multiple initial models as an original data set for training the flow stress prediction model; process the original data set to obtain a standard data set, and train the BP neural network model based on the standard data set; The prediction unit is configured to input the Nb content to be predicted into the optimal flow stress prediction model obtained by training the BP neural network model based on the standard data set, perform prediction analysis, obtain the corresponding flow stress prediction value, and determine the corresponding optimal Nb content according to the maximum flow stress prediction value.

9. An electronic device, characterized in that: include: Memory for storing computer software programs; A processor is used to read and execute the computer software program, thereby implementing the TiAl alloy Nb content design method based on molecular dynamics simulation and machine learning as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The method comprises instructions, which, when executed on a computer, enable the computer to execute the method for designing the Nb content of a TiAl alloy based on molecular dynamics simulation and machine learning according to any one of claims 1 to 7.

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