Methods for determining the relationship between the microstructure, stress, and crack characteristics of molybdenum-based refractory alloys under irradiation conditions.

Abstract

The embodiments of this application relate to the field of computer materials science and technology, specifically to a method for determining the relationship between the microstructure, stress, and crack characteristics of molybdenum-based refractory alloys under irradiation conditions. The method includes: determining the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, and the elemental diffusion coefficients of the matrix α phase and the precipitated χ phase under irradiation conditions; thereby determining the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions; thereby determining the microstructure of the precipitated χ phase; thereby determining the stress on the molybdenum-based refractory alloy; and determining the crack initiation location, geometry, and size under the applied stress. Based on the microstructure, applied stress, and crack initiation location, geometry, and size, the relationship between the three is determined. This method can accurately determine the crack initiation and evolution laws of molybdenum-based refractory alloys, achieving precise simulation of crack initiation and evolution caused by solute segregation-induced phase transformation in actual irradiation environments.

Description

Technical Field

[0001] The embodiments of this application relate to the field of computer materials science and technology, specifically to a method for determining the relationship between the microstructure of a molybdenum-based refractory alloy under irradiation conditions, the stress it is subjected to, and the crack characteristics of the molybdenum-based refractory alloy. Background Technology

[0002] The statements herein are provided merely as background information in connection with this application and do not necessarily constitute prior art.

[0003] Fourth-generation fission reactors, nuclear fusion devices, and space nuclear propulsion systems place stringent demands on structural materials. Traditional structural materials struggle to maintain structural integrity and safety under extreme conditions such as ultra-high temperatures, strong corrosion, and high-energy neutron irradiation. Therefore, molybdenum-based refractory alloys, with their high melting point, high thermal conductivity, and excellent chemical compatibility, have become candidate structural materials. However, during the service of advanced nuclear energy systems, these alloys are subjected to prolonged high-energy neutron irradiation, leading to numerous point defects within the material. This causes solute element segregation at grain boundaries, disrupting thermodynamic equilibrium and inducing phase transitions. Specifically, this manifests as the formation of brittle χ-phase precipitates at grain boundaries. The formation of χ-phase precipitates disrupts the continuity and homogeneity of the matrix α-phase. Furthermore, under externally applied stress, the interface between the χ-phase precipitates and the matrix α-phase often becomes a stress concentration point, inducing crack generation and evolution. This results in the degradation of the alloy's macroscopic mechanical properties, ultimately leading to fracture failure and impacting the operational safety and service life of advanced nuclear energy systems.

[0004] Therefore, in order to accurately assess the service life of advanced nuclear energy systems and ensure their safe operation, it is urgent to establish the correlation between alloy microstructure, externally applied stress and crack formation characteristics, and to understand the crack formation and evolution law of molybdenum-based refractory alloys, so as to predict the evolution of their mechanical properties during service based on the alloy microstructure and the stress they are subjected to. Summary of the Invention

[0005] A brief overview of this application is provided below to offer a basic understanding of certain aspects thereof. It should be understood that this overview is not an exhaustive summary of the application. It is not intended to identify key or essential parts of the application, nor is it intended to limit its scope. Its purpose is merely to present certain concepts in a simplified form as a prelude to the more detailed description that follows.

[0006] This application provides a method for determining the relationship between the microstructure, stress, and crack characteristics of a molybdenum-based refractory alloy under irradiation conditions, comprising the following steps: S10: determining the elastic modulus of the matrix α phase, the elastic modulus of the precipitated χ phase, the elemental diffusion coefficient of the matrix α phase, and the elemental diffusion coefficient of the precipitated χ phase under irradiation conditions; S20: determining the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions based on the elastic modulus and diffusion coefficient determined in S10; S30: Based on the solute segregation degree at the grain boundaries determined in S20, the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy is determined; S40: Based on the microstructure determined in S30, the stress on the molybdenum-based refractory alloy, as well as the location, geometry, and size of cracks under the stress are determined; S50: Based on the microstructure of the precipitated χ phase determined in step S30, the stress in step S40, and the location, geometry, and size of cracks determined in step S40, the relationship between the microstructure, the stress, and the location, geometry, and size of cracks is determined.

[0007] The method provided in this application for determining the relationship between the microstructure, stress, and crack characteristics of molybdenum-based refractory alloys under irradiation conditions, by determining the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, and the elemental diffusion coefficients of the matrix α phase and the precipitated χ phase under irradiation conditions, and by considering the thermodynamic and kinetic parameters of each phase affecting solute segregation and phase transformation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions, accurately determines the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions. This facilitates the reconstruction of the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy determined accordingly into its actual service condition in a nuclear energy system. Therefore, based on this... By studying the microstructure of molybdenum-based refractory alloys and obtaining the stresses they experience, as well as the crack initiation location, geometry, and size under these stresses, we can accurately establish the correlation between the microstructure of the precipitated χ phase, the stresses they experience, and crack characteristics. This will reveal the crack initiation and evolution laws of molybdenum-based refractory alloys, and further enable precise simulation of crack initiation and evolution caused by solute segregation-induced phase transformation in molybdenum-based refractory alloys under actual nuclear energy system irradiation. Based on the microstructure and stresses of molybdenum-based refractory alloys, we can accurately predict the evolution of their mechanical properties during service, providing reliable technical support for optimizing their macroscopic mechanical properties. Attached Figure Description

[0008] Other objects and advantages of this application will become apparent from the following description of embodiments of this application with reference to the accompanying drawings, and will help to provide a comprehensive understanding of this application.

[0009] Figure 1This is a schematic diagram of solute segregation at the grain boundaries of a molybdenum-based refractory alloy under irradiation conditions according to an embodiment of this application; Figure 2 This is a schematic diagram of the microstructure of the precipitated χ phase at the grain boundaries of a molybdenum-based refractory alloy according to an embodiment of this application. Figure 3 This is a schematic diagram showing the location, geometry, and size of cracks in a molybdenum-based refractory alloy under stress at a simulation time of 35 seconds, according to an embodiment of this application. Figure 4 This is a schematic diagram showing the location, geometry, and size of cracks in a molybdenum-based refractory alloy under stress at a simulation time of 125 s, according to an embodiment of this application.

[0010] It should be noted that the accompanying drawings are not necessarily drawn to scale, but are shown only in a schematic manner without affecting the reader's understanding. Detailed Implementation

[0011] Exemplary embodiments of this application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the development of any such actual embodiment to achieve the developer's specific goals, such as complying with constraints related to the system and business, and these constraints may vary depending on the implementation. Furthermore, it should be understood that while development work can be very complex and time-consuming, such development work is merely a routine task for those skilled in the art who benefit from the content of this application.

[0012] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the equipment structure and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0013] The inventors of this application have discovered that the simulation of the microstructure evolution and fracture failure of materials under irradiation conditions involves the complex coupling of multiple physical processes such as thermodynamics, kinetics, phase field, and fracture mechanics. In related technologies, it is difficult to accurately establish the relationship between the microstructure of molybdenum-based refractory alloys, the externally applied stress, and the crack characteristics of the alloy. This results in low simulation accuracy for the crack generation and evolution caused by solute segregation-induced phase transformation in molybdenum-based refractory alloys under irradiation conditions, which is not conducive to accurately predicting the evolution of the mechanical properties of molybdenum-based refractory alloys during service.

[0014] Based on this, embodiments of this application provide a method for determining the relationship between the microstructure, stress, and crack characteristics of a molybdenum-based refractory alloy under irradiation conditions, comprising the following steps: S10: Determine the elastic modulus of the matrix α phase, the elastic modulus of the precipitated χ phase of the molybdenum-based refractory alloy, the elemental diffusion coefficient of the matrix α phase under irradiation conditions, and the elemental diffusion coefficient of the precipitated χ phase.

[0015] S20: Based on the elastic modulus and diffusion coefficient determined in S10, determine the degree of solute segregation at the grain boundaries of molybdenum-based refractory alloys under irradiation conditions.

[0016] S30: Based on the degree of solute segregation at the grain boundaries determined by S20, determine the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy.

[0017] S40: Based on the microstructure determined by S30, determine the stress on the molybdenum-based refractory alloy, as well as the location, geometry, and size of cracks under the stress.

[0018] S50: Based on the microstructure of the precipitated χ phase determined in step S30, the stress determined in step S40, and the crack initiation location, geometry, and size determined in step S40, determine the relationship between the microstructure, the stress, and the crack initiation location, geometry, and size.

[0019] The method provided in this application for determining the relationship between the microstructure, stress, and crack characteristics of molybdenum-based refractory alloys under irradiation conditions, by determining the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, and the elemental diffusion coefficients of the matrix α phase and the precipitated χ phase under irradiation conditions, and by considering the thermodynamic and kinetic parameters of each phase affecting solute segregation and phase transformation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions, accurately determines the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions. This facilitates the reconstruction of the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy determined accordingly into its actual service condition in a nuclear energy system. Therefore, based on this... By studying the microstructure of molybdenum-based refractory alloys and obtaining the stresses they experience, as well as the crack initiation location, geometry, and size under these stresses, we can accurately establish the correlation between the microstructure of the precipitated χ phase, the stresses they experience, and crack characteristics. This will reveal the crack initiation and evolution laws of molybdenum-based refractory alloys, and further enable precise simulation of crack initiation and evolution caused by solute segregation-induced phase transformation in molybdenum-based refractory alloys under actual nuclear energy system irradiation. Based on the microstructure and stresses of molybdenum-based refractory alloys, we can accurately predict the evolution of their mechanical properties during service, providing reliable technical support for optimizing their macroscopic mechanical properties.

[0020] In some embodiments, step S10 may further include the following steps: S11: Determine the initial elemental diffusion coefficients of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy.

[0021] S12: Based on the initial element diffusion coefficients determined in step S11, determine the element diffusion coefficients of the matrix α phase of the molybdenum-based refractory alloy under irradiation conditions and the element diffusion coefficients of the precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions.

[0022] Under irradiation conditions, high-energy incident particles knock lattice atoms out of their equilibrium positions, creating vacancies and increasing the probability of exchange transitions between solute atoms and vacancies. Macroscopically, this manifests as an accelerated diffusion rate of solute elements. Therefore, in this embodiment, based on the initial element diffusion coefficients of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, the influence of irradiation conditions on the migration of solute elements is considered to determine the element diffusion coefficients of the matrix α phase and the precipitated χ phase under irradiation conditions. This facilitates accurate simulation of the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions.

[0023] In some embodiments, step S12 may further include the following steps: S121: Determine the enhancement factor.

[0024] S122: Based on the initial elemental diffusion coefficients and the strengthening factor, determine the elemental diffusion coefficients of the matrix α phase of the molybdenum-based refractory alloy under irradiation conditions and the elemental diffusion coefficients of the precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions.

[0025] In this embodiment, by determining the enhancement factor, the initial elemental diffusion coefficients of the matrix α phase and precipitated χ phase of the molybdenum-based refractory alloy are amplified, and the influence of irradiation conditions on the diffusion rate of solute elements is quantified. Thus, the elemental diffusion coefficients of the matrix α phase and precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions are determined, making the simulation of the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions more accurate.

[0026] Specifically, in step S122, the initial diffusion coefficients are amplified by multiplying the enhancement factor by the initial element diffusion coefficients of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, respectively, thereby determining the element diffusion coefficients of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions.

[0027] In some embodiments, in step S121, the enhancement factor may be determined as follows: determining the number of vacancies in the molybdenum-based refractory alloy under thermal equilibrium conditions; determining the number of vacancies in the molybdenum-based refractory alloy generated under irradiation conditions; determining the total number of vacancies in the molybdenum-based refractory alloy based on the number of vacancies in the molybdenum-based refractory alloy under thermal equilibrium conditions and the number of vacancies in the molybdenum-based refractory alloy generated under irradiation conditions; and determining the enhancement factor based on the total number of vacancies and the number of vacancies in the molybdenum-based refractory alloy under thermal equilibrium conditions.

[0028] When determining the elemental diffusion coefficient under irradiation conditions, the phenomenological models or empirical formulas used in related technologies typically only multiply the initial diffusion coefficient by an empirical constant related to the irradiation dose, ignoring the microscopic physical nature of diffusion, namely the exchange transition between solute atoms and vacancies. Furthermore, most diffusion models used in related technologies cannot distinguish between thermal diffusion at high temperatures and irradiation-accelerated diffusion at low temperatures, limiting the application scenarios of these diffusion models. The elemental diffusion coefficients determined only within specific temperature ranges or irradiation dose rate intervals are considered valid values. Based on these problems, this embodiment decomposes the total number of vacancies in molybdenum-based refractory alloys into thermally flattened... By considering both the number of vacancies in molybdenum-based refractory alloys under equilibrium and irradiation conditions, a dimensionless enhancement factor is determined to directly quantify the increase in the total number of vacancies relative to the pure thermodynamic state, thereby improving the accuracy of the enhancement factor. This ensures the accuracy of the elemental diffusion coefficients of the matrix α phase and precipitated χ phase of molybdenum-based refractory alloys under irradiation conditions. Furthermore, by rigorously decomposing the total number of vacancies in molybdenum-based refractory alloys, the elemental diffusion coefficients determined over a very wide temperature range and irradiation dose rate range remain self-consistent and highly applicable, which is beneficial for further improving the simulation accuracy of solute segregation at grain boundaries of molybdenum-based refractory alloys under irradiation conditions.

[0029] Specifically, in step S121, the strengthening factor, the total number of vacancies in the molybdenum-based refractory alloy, and the number of vacancies in the molybdenum-based refractory alloy under thermal equilibrium conditions conform to the following relationship: .

[0030] in, Indicates the enhancing factor. This indicates the number of vacancies in a molybdenum-based refractory alloy under thermal equilibrium conditions. This indicates the number of vacancies in molybdenum-based refractory alloys produced by irradiation conditions. This indicates the total number of vacancies in a molybdenum-based refractory alloy.

[0031] In some embodiments, step S20 may further include the following steps: S21: Determine the solute element distribution of molybdenum-based refractory alloys under irradiation conditions based on the elastic modulus and diffusion coefficient determined in S10.

[0032] S22: Based on the solute element distribution determined in step S21, determine the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions.

[0033] In this embodiment, by considering the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, as well as the elemental diffusion coefficients of the matrix α phase and the precipitated χ phase under irradiation conditions, the thermodynamic and kinetic parameters affecting solute segregation are comprehensively considered to determine the solute element distribution of the molybdenum-based refractory alloy under irradiation conditions. This facilitates a quantitative description of the process of solute element segregation and migration caused by high-energy incident particles under irradiation conditions, thereby improving the accuracy of the determined degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions. This allows the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy determined accordingly to accurately reflect its actual service performance in nuclear energy systems.

[0034] In some embodiments, step S22 may further include the following steps: S221: Determine the collision exchange frequency of high-energy incident particles under irradiation conditions.

[0035] S222: Determine the degree of homogenization of solute elements in a local region caused by high-energy incident particles under irradiation conditions based on the collision exchange frequency of high-energy incident particles under irradiation conditions.

[0036] S223: Based on the solute element distribution determined in step S21 and the degree of homogenization of solute elements in the local area caused by high-energy incident particles under irradiation conditions determined in step S222, determine the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions.

[0037] Under irradiation conditions, high-energy incident particles collide with solute atoms inside molybdenum-based refractory alloys, causing the solute atoms to detach from their lattice equilibrium positions and undergo violent random displacement and rearrangement. This results in the homogenization of solute elements in local regions. Therefore, this embodiment introduces the collision exchange frequency of high-energy incident particles under irradiation conditions to quantitatively describe the homogenization process of solute elements in local regions caused by high-energy incident particles under irradiation conditions. Based on this, by comprehensively considering the solute element distribution of molybdenum-based refractory alloys that describes the process of solute element segregation and migration caused by high-energy incident particles, it is beneficial to ensure that the determined degree of solute segregation at the grain boundaries of molybdenum-based refractory alloys under irradiation conditions is consistent with its actual service conditions in nuclear energy systems.

[0038] In some embodiments, in step S222, the degree of homogenization of solute elements in a local region caused by high-energy incident particles under irradiation conditions can be determined as follows: determining the element concentration at a predetermined point in the space where the molybdenum-based refractory alloy is located; determining the average value of the element concentration in the region near the predetermined point in the space where the molybdenum-based refractory alloy is located; determining the rate of change of the element concentration at the predetermined point in the space where the molybdenum-based refractory alloy is located based on the collision exchange frequency, element concentration, and average element concentration of the high-energy incident particles under irradiation conditions; and determining the degree of homogenization of solute elements in a local region caused by high-energy incident particles under irradiation conditions based on the rate of change.

[0039] When determining the degree of solute segregation at grain boundaries in molybdenum-based refractory alloys under irradiation conditions, traditional simulation methods often only focus on the drag effect of vacancies formed by high-energy incident particles on solute elements. This leads to a continuous increase in the simulated degree of solute segregation with increasing irradiation time, deviating from the experimental fact that solute segregation tends to saturate or even decrease under high-dose irradiation conditions. Furthermore, the macroscopic homogenization index, which characterizes the degree of homogenization of solute elements caused by high-energy incident particles under irradiation conditions, can only reflect the global average effect and cannot determine the degree of homogenization of solute elements in local regions, thus limiting the simulation accuracy. Based on the above problems, this implementation... In this example, by determining the element concentration at a predetermined point in the space where the molybdenum-based refractory alloy is located, as well as the average element concentration in the vicinity of the predetermined point, and combining this with the collision exchange frequency of high-energy incident particles, the element concentration at the predetermined point is forced to continuously approach the average level of the vicinity, thereby counteracting the element aggregation caused by thermodynamic driving. The rate of change of the element concentration at the predetermined point is accurately determined, and thus the degree of homogenization of solute elements in the local area caused by high-energy incident particles under irradiation conditions is determined. This achieves a high degree of localization and adaptability, which is beneficial to ensure that the determined degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions is consistent with its actual service conditions in the nuclear energy system.

[0040] In some embodiments, step S30 may further include the following steps: S31: Based on the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions determined in step S20, determine the phase transformation driving force for the precipitation of the χ phase at the grain boundaries of the molybdenum-based refractory alloy.

[0041] S32: Based on the phase transformation driving force determined in step S31, determine the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy.

[0042] In this embodiment, by considering the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions, the phase transformation driving force of the χ phase precipitated at the grain boundaries of the molybdenum-based refractory alloy is determined. This is to facilitate the determination of the occurrence location and nucleation probability of the χ phase precipitated at the grain boundaries of the molybdenum-based refractory alloy in the space where the molybdenum-based refractory alloy is located, and to facilitate the prediction of the growth trend after the nucleation of the χ phase. Thus, the determined microstructure of the χ phase precipitated at the grain boundaries of the molybdenum-based refractory alloy can be used to reconstruct its actual service situation in the nuclear energy system, which is beneficial for establishing an accurate correlation between the microstructure, the stress, and the crack characteristics based on the microstructure of the χ phase precipitated.

[0043] In some embodiments, step S32 may further include the following steps: S321: Determine the nucleation barrier and critical nucleation radius for the precipitated χ phase based on the phase transition driving force.

[0044] S322: Determine the statistical probability of nucleation events of the precipitated χ phase occurring at different spatial locations based on the nucleation barrier and critical nucleation radius of the precipitated χ phase.

[0045] S323: Based on the statistical probability of nucleation events of the precipitated χ phase at different spatial locations and the driving force of phase transformation, determine the microstructure of the precipitated χ phase at the grain boundaries of molybdenum-based refractory alloys.

[0046] In this embodiment, the nucleation barrier and critical nucleation radius of the precipitated χ phase are determined based on the phase transition driving force to quantify the energy threshold required for the system to overcome the phase transition barrier. Based on this, the statistical probability of the nucleation event of the precipitated χ phase at different spatial locations is determined. On this basis, combined with the driving effect of the phase transition driving force on the growth of the precipitated χ phase, a quantitative description of the relationship between the phase transition driving force and the nucleation process of the precipitated χ phase is realized. Finally, the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy is obtained, further improving the degree of conformity between this microstructure and the actual service situation of the molybdenum-based refractory alloy in the nuclear energy system.

[0047] In some embodiments, in step S322, the nucleation rate of the precipitated χ phase can be determined according to classical nucleation theory, based on the nucleation barrier and critical nucleation radius of the precipitated χ phase, and the nucleation rate of the precipitated χ phase can be converted into the statistical probability of the occurrence of nucleation events of the precipitated χ phase at different spatial locations.

[0048] In some embodiments, step 40 may further include the following steps: S41: Based on the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy determined in S30, determine the local stress and strain distribution of the precipitated χ phase and its surrounding area under the applied stress.

[0049] S42: Based on the local stress-strain distribution determined in step S41, determine the crack initiation conditions and crack propagation process of molybdenum-based refractory alloys under the applied stress.

[0050] S43: Based on the crack initiation conditions and crack propagation process of the molybdenum-based refractory alloy under stress determined in step S42, determine the stress on the molybdenum-based refractory alloy, as well as the location, geometry, and size of the crack under the stress.

[0051] In this embodiment, based on the microstructure of the precipitated χ phase, the local stress-strain distribution of the precipitated χ phase and its surrounding area under stress in molybdenum-based refractory alloys is determined. This allows for the identification of stress concentration points in the precipitated χ phase and its surrounding area, i.e., the identification of regions prone to crack induction. This facilitates accurate simulation of crack initiation conditions and crack propagation processes in molybdenum-based refractory alloys under stress. Consequently, it enables the determination of more accurate stresses on molybdenum-based refractory alloys, as well as the location, geometry, and size of cracks under stress. Thus, it establishes a correlation between the microstructure of the precipitated χ phase, the stress, and crack characteristics of molybdenum-based refractory alloys that can reproduce actual service conditions, clarifying the crack formation and evolution laws of molybdenum-based refractory alloys.

[0052] In some embodiments, step S41 may further include the following steps: S411: Based on the microstructure of the precipitated χ phase, determine the spatial distribution of the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy.

[0053] S412: Based on the microstructure of the precipitated χ phase, determine the spatial distribution of the elastic modulus at the interface between the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy.

[0054] S413: Determine the spatial distribution of the elastic modulus of the molybdenum-based refractory alloy based on the spatial distribution of the elastic modulus determined in step S411 and step S412.

[0055] S414: Based on the spatial distribution of the elastic modulus of molybdenum-based refractory alloys, determine the local stress and strain distribution of the χ phase precipitated in the molybdenum-based refractory alloy under stress and its surrounding area.

[0056] In this embodiment, based on the microstructure of the precipitated χ phase, the spatial distribution of the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy, as well as the spatial distribution of the elastic modulus at the interface between the matrix α phase and the precipitated χ phase, are determined. This determines the spatial distribution of the elastic modulus of the molybdenum-based refractory alloy, smoothly connecting the elastic moduli of the matrix α phase and the precipitated χ phase. This allows the determined elastic modulus of the molybdenum-based refractory alloy to smoothly and continuously transition from the matrix α phase to the precipitated χ phase. Consequently, it facilitates a more accurate determination of the local stress-strain distribution of the precipitated χ phase and its surrounding area under stress, thereby improving the simulation accuracy of crack initiation conditions and crack propagation processes under stress in the molybdenum-based refractory alloy. This ensures that the determined stress on the molybdenum-based refractory alloy, as well as the crack initiation location, geometry, and size under stress, conform to actual service conditions.

[0057] In some embodiments, step S412 may further include the steps of: determining the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy based on the microstructure of the precipitated χ phase; and using an interpolation function, weighting the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy according to the ratio of the matrix α phase and the precipitated χ phase to obtain the spatial distribution of the elastic modulus at the interface between the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy. The interpolation function is composed of a high-order polynomial and has an operator that can smoothly transition the elastic modulus between the matrix α phase and the precipitated χ phase. In this embodiment, by introducing an interpolation function, a continuous transition of the elastic modulus is achieved. Furthermore, the function and its first and second derivatives are both zero at the phase interface, thereby ensuring the numerical stability of the determined spatial distribution of the elastic modulus at the interface between the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy.

[0058] In some embodiments, step S50 may further include the following steps: S51: Based on the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy determined in step S30, the stress and crack initiation location, geometry and size determined in step S40, generate first image data, vector data and second image data; wherein, the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy is the first image data, the stress is the vector data, and the crack initiation location, geometry and size are the second image data.

[0059] S52: Construct a dataset that includes multiple sets of first image data, vector data, and second image data.

[0060] S53: Input the dataset constructed in step S52 into the multimodal deep learning model, use the model to extract the morphology and size feature data of the extracted χ phase in the first image data, and concatenate it with the vector data to obtain the fused feature tensor data.

[0061] S54: Using the fused feature tensor data obtained in step S53, iteratively train the multimodal deep learning model to obtain an updated multimodal deep learning model.

[0062] S55: Based on the updated multimodal deep learning model, determine the relationship between the microstructure of the precipitated χ phase, the stress it is subjected to, the crack initiation location, geometry, and size.

[0063] In this embodiment, a multimodal deep learning model is used, and the combined influence of the first image data consisting of the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy and the vector data consisting of the stress corresponds to the crack generation and evolution is considered. By stitching the data, fused feature tensor data is obtained. The modal deep learning model is trained using the fused feature tensor data to ensure that the relationship between the microstructure of the precipitated χ phase, the stress, and the crack generation location, geometry, and size determined by the model conforms to physical laws, effectively revealing the crack generation and evolution law of molybdenum-based refractory alloy.

[0064] Please see Figure 1 , Figure 1 This diagram illustrates solute segregation at grain boundaries of a molybdenum-based refractory alloy under irradiation conditions, according to an embodiment of this application. Figure 1 In the diagram, 10 represents the grain matrix, and 20 represents the grain boundary. Figure 1 It can be seen that under irradiation conditions, the solute of the molybdenum-based refractory alloy significantly segregates towards the grain boundary 20, and the solute is highly enriched in the grain boundary 20 region, with a concentration significantly higher than that inside the grain matrix 10.

[0065] Please see Figure 2 , Figure 2 This diagram illustrates the microstructure of the precipitated x-phase at the grain boundaries of a molybdenum-based refractory alloy according to an embodiment of this application. Figure 2 In the diagram, 10 represents the grain matrix, 20 represents the grain boundary, and 30 represents the χ phase. Figure 2 It can be seen that the χ phase 30 nucleates and precipitates at the grain boundary 20 where the solute concentration of the molybdenum-based refractory alloy is relatively high, while no χ phase 30 precipitation occurs inside the grain matrix 10 where the solute concentration of the molybdenum-based refractory alloy is relatively low.

[0066] Please see Figure 3 and Figure 4 , Figure 3 This diagram illustrates the location, geometry, and size of cracks in a molybdenum-based refractory alloy under stress during a simulation time of 35 seconds, according to an embodiment of this application. Figure 4 This diagram illustrates the location, geometry, and size of cracks in a molybdenum-based refractory alloy under stress at a simulation time of 125 s, according to an embodiment of this application. Figure 3 and Figure 4In the diagram, 20 represents grain boundaries and 40 represents cracks. Figure 3 and Figure 4 It can be seen that, Figure 3 In the molybdenum-based refractory alloy, crack 40, generated under stress, is in its initial development stage. Crack 40 begins to form near grain boundary 20 and exhibits behavior that crosses grain boundary 20. Figure 3 The image shows three independent cracks 40, which are generally strip-shaped and oriented differently; compared to Figure 3 , Figure 4 As the simulation time increased, the cracks 40 in the middle and bottom of the image clearly extended, the length of the cracks 40 increased significantly, and they were about to connect with each other. Figure 3 and Figure 4 The crack growth and evolution process reflected is consistent with experimental facts, proving the reliability of the method provided in this application.

[0067] Regarding the embodiments of this application, it should also be noted that, without conflict, the embodiments of this application and the features in the embodiments can be combined with each other to obtain new embodiments.

[0068] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. The scope of protection of this application shall be determined by the scope of the claims.

Claims

1. A method for determining the relationship between the microstructure, stress, and crack characteristics of a molybdenum-based refractory alloy under irradiation conditions, characterized in that, It includes the following steps: S10: Determine the elastic modulus of the matrix α phase of the molybdenum-based refractory alloy, the elastic modulus of the precipitated χ phase of the molybdenum-based refractory alloy, the elemental diffusion coefficient of the matrix α phase under the irradiation conditions, and the elemental diffusion coefficient of the precipitated χ phase. S20: Based on the elastic modulus and diffusion coefficient determined in S10, determine the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under the irradiation conditions; S30: Based on the degree of solute segregation at the grain boundaries determined in S20, determine the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy. S40: Based on the microstructure determined in S30, determine the stress on the molybdenum-based refractory alloy, as well as the location, geometry, and size of cracks under the stress. S50: Based on the microstructure of the precipitated χ phase determined in step S30, the stress determined in step S40, and the crack initiation location, geometry, and size determined in step S40, determine the relationship between the microstructure, the stress, and the crack initiation location, geometry, and size.

2. The method according to claim 1, characterized in that, Step S10 also includes the following steps: S11: Determine the matrix α phase of the molybdenum-based refractory alloy and the initial elemental diffusion coefficients of the precipitated χ phase of the molybdenum-based refractory alloy; S12: Based on the initial element diffusion coefficient determined in step S11, determine the element diffusion coefficient of the matrix α phase of the molybdenum-based refractory alloy under irradiation conditions and the element diffusion coefficient of the precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions.

3. The method according to claim 2, characterized in that, Step S12 also includes the following steps: S121: Determine the enhancement factor; S122: Based on the initial element diffusion coefficient and the enhancement factor, determine the element diffusion coefficient of the matrix α phase of the molybdenum-based refractory alloy under irradiation conditions and the element diffusion coefficient of the precipitated χ phase of the molybdenum-based refractory alloy under irradiation conditions.

4. The method according to claim 3, characterized in that, In step S121, the enhancement factor is determined in the following manner: Determine the number of vacancies in the molybdenum-based refractory alloy under thermal equilibrium conditions; Determine the number of vacancies in the molybdenum-based refractory alloy produced by the irradiation conditions; The total number of vacancies in the molybdenum-based refractory alloy is determined based on the number of vacancies in the molybdenum-based refractory alloy under the thermal equilibrium conditions and the number of vacancies in the molybdenum-based refractory alloy generated by the irradiation conditions. The enhancement factor is determined based on the total number of vacancies and the number of vacancies in the molybdenum-based refractory alloy under the thermal equilibrium conditions.

5. The method according to claim 1, characterized in that, Step S20 also includes the following steps: S21: Determine the solute element distribution of the molybdenum-based refractory alloy under irradiation conditions based on the elastic modulus and diffusion coefficient determined in S10. S22: Based on the solute element distribution determined in step S21, determine the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions.

6. The method according to claim 5, characterized in that, Step S22 also includes the following steps: S221: Determine the collision exchange frequency of high-energy incident particles under irradiation conditions; S222: Determine the degree of homogenization of solute elements in a local area caused by high-energy incident particles under irradiation conditions based on the collision exchange frequency of the high-energy incident particles under irradiation conditions. S223: Based on the solute element distribution determined in step S21 and the degree of homogenization of solute elements in the local area caused by high-energy incident particles under irradiation conditions determined in step S222, determine the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under irradiation conditions.

7. The method according to claim 6, characterized in that, In step S222, the degree of homogenization of solute elements in the local region caused by high-energy incident particles under irradiation conditions is determined as follows: Determine the element concentration at a predetermined point in the space where the molybdenum-based refractory alloy is located; Determine the average elemental concentration in the region near a predetermined point in the space containing the molybdenum-based refractory alloy; The rate of change of element concentration at a predetermined point in the space where the molybdenum-based refractory alloy is located is determined based on the collision exchange frequency of high-energy incident particles under irradiation conditions, the element concentration, and the average element concentration. Based on the rate of change, the degree of homogenization of solute elements in a local region caused by high-energy incident particles under the irradiation conditions is determined.

8. The method according to claim 1, characterized in that, Step S30 also includes the following steps: S31: Based on the degree of solute segregation at the grain boundaries of the molybdenum-based refractory alloy under the irradiation conditions determined in step S20, determine the phase transformation driving force for the precipitation of the χ phase at the grain boundaries of the molybdenum-based refractory alloy. S32: Determine the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy based on the phase transformation driving force determined in step S31.

9. The method according to claim 8, characterized in that, Step S32 also includes the following steps: S321: Determine the nucleation barrier and critical nucleation radius of the precipitated χ phase based on the phase transition driving force; S322: Determine the statistical probability of nucleation events of the precipitated χ phase occurring at different spatial locations based on the nucleation barrier and critical nucleation radius of the precipitated χ phase; S323: Based on the statistical probability of nucleation events of the precipitated χ phase at different spatial locations and the phase transformation driving force, determine the microstructure of the precipitated χ phase at the grain boundaries of the molybdenum-based refractory alloy.

10. The method according to claim 1, characterized in that, The 40 steps also include the following steps: S41: Based on the microstructure of the precipitated χ phase at the grain boundary of the molybdenum-based refractory alloy determined in S30, determine the local stress and strain distribution of the precipitated χ phase and its surrounding area under the stress applied to the molybdenum-based refractory alloy. S42: Based on the local stress-strain distribution determined in step S41, determine the crack initiation conditions and crack propagation process of the molybdenum-based refractory alloy under the applied stress. S43: Based on the crack initiation conditions and crack propagation process of the molybdenum-based refractory alloy under stress determined in step S42, determine the stress on the molybdenum-based refractory alloy, as well as the location, geometry, and size of the crack under the stress.

11. The method according to claim 10, characterized in that, Step S41 also includes the following steps: S411: Based on the microstructure of the precipitated χ phase, determine the spatial distribution of the elastic modulus of the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy. S412: Based on the microstructure of the precipitated χ phase, determine the spatial distribution of the elastic modulus at the interface between the matrix α phase and the precipitated χ phase of the molybdenum-based refractory alloy. S413: Determine the spatial distribution of the elastic modulus of the molybdenum-based refractory alloy based on the spatial distribution of the elastic modulus determined in step S411 and step S412. S414: Based on the spatial distribution of the elastic modulus of the molybdenum-based refractory alloy, determine the local stress and strain distribution of the χ phase precipitated in the molybdenum-based refractory alloy and its surrounding area under the applied stress.

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