Method and system for predicting evolution of helium bubble in irradiated metal material
The method constructs a dynamic model using phase field equations to predict helium bubble evolution in metal materials under irradiation, addressing the limitations of current methods by incorporating chemical and elastic free energy densities and stress states, thereby improving the accuracy of defect prediction in nuclear power structural materials.
Patent Information
- Application Number
- JP2024166817
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-11-01
- Filing Date
- 2024-09-26
- Publication Date
- 2025-05-15
- Estimated Expiration
- 2044-09-26
AI Technical Summary
Current methods struggle to accurately predict the evolution of helium bubbles in metal materials under irradiation, particularly due to limited experimental resolution and insufficient consideration of stress states.
A method and system that quantitatively predict the evolution of helium bubbles by constructing a dynamic model based on phase field equations, incorporating chemical and elastic free energy densities, and accounting for stress and strain states.
This approach provides a mechanistically sound foundation for predicting helium bubble evolution, enhancing the understanding of irradiation-induced defects and improving the performance evaluation and life expectancy prediction of nuclear power structural materials.
Smart Images
Figure 2025076303000001_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to the technical field of predicting the microstructure of metallic structural materials for nuclear power systems under irradiation conditions, and more particularly to a method and system for predicting the evolution of helium bubbles in metal materials under irradiation. [Background technology]
[0002] As modern society's demand for clean energy increases, nuclear energy has become an important part of the modern energy system. Material issues in advanced nuclear energy systems, mainly fast breeder reactors, are a key issue in project development. Compared with other industries, nuclear structural materials are exposed to neutron irradiation during use, and continuous displacement damage may cause saturated point defects such as vacancies and interstitial atoms. Under the joint action of diffusion, temperature, stress and inherent microstructure (e.g., grain boundaries, dislocations, interfaces), these point defects often develop into dislocation loops, voids and bubbles. Helium bubbles due to nuclear transmutation helium in irradiated materials have attracted particular attention, because irradiation hardening and high-temperature helium embrittlement cause grain boundary fracture in metals. However, the spatial and temporal resolution of experimental equipment has greatly limited the study of helium bubbles at the nano- and micron-scale. With the development of computer simulation technology, many research results have revealed the processes of nucleation, growth and coarsening of He bubbles at the atomic, nano- and micro-scales, deepening our understanding of He bubbles in irradiated materials. However, during actual use, the formation of He bubbles has a strong interaction with the stress and strain state of the material. The high pressure in the He bubble may cause plastic deformation at high temperature, which may lead to the material yielding under the conditions of use. Meanwhile, nuclear power structural materials are often used under stress, but few studies have reported the effect of the stress state on He bubbles due to irradiation. Therefore, establishing a physically meaningful He bubble evolution equation is of great importance for understanding the formation of He bubbles under irradiation and predicting irradiation defects in materials. This can provide a deep understanding of the interaction between He bubbles and the stress state due to irradiation, and provide an important theoretical basis for the performance evaluation and life prediction of nuclear power structural materials. Summary of the Invention
[0003] In order to solve the above problems, the object of the present invention is to provide a technique for quantitatively predicting the evolution of helium bubbles, thereby laying a more mechanistic theoretical basis for the evolution of helium bubbles under irradiation conditions.
[0004] In order to achieve the above object, the present invention provides a method for predicting the evolution of helium bubbles in an irradiated metallic material, comprising the steps of: Obtaining a chemical free energy density of the nuclear power structural material based on a vacancy formation energy, a helium atom formation energy, a gas constant, a molar volume fraction, and an absolute temperature of the nuclear power structural material; Obtaining an elastic free energy density of the nuclear power structural material according to the elastic constant and the elastic strain of the nuclear power structural material; According to the chemical free energy density and the elastic free energy density, the diffusion coefficients of vacancies and helium atoms of the nuclear power structural material and the generation rate of helium atoms under irradiation are collected to construct a kinetic model based on the phase field equation to predict the evolution of helium bubbles in the nuclear power structural material under irradiation; To provide a method including
[0005] Preferably, in the process of obtaining the vacancy formation energy and the helium atom formation energy of the nuclear power structural material, the total energy of the optimized vacancy-containing unit cell and the total energy of the optimized interstitial helium atom-containing unit cell are obtained, and molecular dynamics calculations are performed based on the total energy and total particle number of the optimized complete unit cell to obtain the vacancy formation energy and the helium atom formation energy, respectively.
[0006] Preferably, in the process of obtaining the chemical free energy density, the chemical free energy density is generated by setting an interpolation function based on the first free energy density of the substrate and the second free energy density of the helium bubbles, where the first free energy density and the second free energy density are obtained based on the vacancy concentration and the helium concentration.
[0007] Preferably, in the process of obtaining the first free energy density, the first free energy density is obtained based on the vacancy concentration and the helium concentration according to the molar volume fraction, the Avogadro constant, the gas constant and the absolute temperature.
[0008] Preferably, in the process of obtaining the second free energy density, the second free energy density is obtained based on the vacancy concentration and the helium concentration, according to the equilibrium concentration of helium in the helium bubbles and the maximum concentration of helium in the helium bubbles, as well as the molar volume fraction, the gas constant and the absolute temperature.
[0009] Preferably, in the process of obtaining the elastic constant and the elastic strain, the small strain in the j direction of the nuclear power plant structural material, the stress under a positive strain condition, and the stress under a negative strain condition are obtained to obtain the elastic constant of the nuclear power plant structural material; Based on the total strain of the nuclear power plant structural material, the elastic strain is obtained according to the inherent strain of the helium bubbles due to irradiation of the nuclear power plant structural material and the plastic strain of the nuclear power plant structural material.
[0010] Preferably, in the process of obtaining the inherent strain of the helium bubble due to irradiation, the components of the internal pressure and elastic constant of the helium bubble are obtained, and the inherent strain of the irradiated helium bubble is obtained according to the Kronecker delta, where the internal pressure of the helium bubble is obtained according to the helium concentration in the helium bubble, the Boltzmann constant, the absolute temperature, the atomic volume and the van der Waals constant.
[0011] Preferably, in the process of obtaining the plastic strain, the plastic strain is obtained based on the initial plastic shear rate, the dislocation shear rate, the strain sensitivity index, the Schimid tensor factor, the stress tensor, the limit shear stress, the total slip coefficient, and the current slip system.
[0012] Preferably, in the process of predicting the evolution of helium bubbles in a nuclear power plant structural material under irradiation, a thermodynamic model of the phase field equation for describing the evolution of helium bubbles in a nuclear power plant structural material under irradiation is constructed based on the chemical free energy density and the elastic free energy density, the interface mobility, the chemical mobility of helium and vacancies, and the generation rates of helium and vacancies under irradiation conditions are obtained, a kinetic model of the phase field equation is constructed, the concentration field and the order parameter field of the current time step (i.e., the current time step) are obtained and visualized, the evolution of the helium bubbles at the current time step is obtained, the density and size of the helium bubbles are quantitatively statistically calculated based on the order parameter field, and then iterative calculations are performed to obtain the evolution process of the helium bubbles under irradiation.
[0013] The present invention provides a system for predicting the evolution of helium bubbles in an irradiated metallic material, comprising: a data acquisition module for acquiring vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction, and absolute temperature of the nuclear power structural material; A chemical free energy density calculation module for obtaining a chemical free energy density of the nuclear power structural material according to the vacancy formation energy, the helium atom formation energy, the gas constant, the molar volume fraction and the absolute temperature of the nuclear power structural material; an elastic free energy density calculation module for obtaining an elastic free energy density of the nuclear power structural material according to the elastic constant and the elastic strain of the nuclear power structural material; a helium bubble evolution prediction module for predicting the evolution of helium bubbles in the nuclear power system metal structural material under irradiation based on the chemical free energy density and the elastic free energy density, constructing a thermodynamic model of the phase field equation to describe the evolution of helium bubbles in the nuclear power system metal structural material under irradiation, collecting the diffusion coefficients of vacancies and helium atoms in the nuclear power structural material and the generation rate of helium atoms under irradiation, constructing a kinetic model of the phase field equation, and predicting the evolution of helium bubbles in the nuclear power structural material under irradiation; A system is further disclosed, comprising:
[0014] The present invention has the following technical effects. In the present invention, the formation and evolution of helium bubbles under irradiation is studied by phase-field simulation, and the density and size of helium bubbles can be quantitatively obtained, thereby making up for the shortcomings of experimental research. The present invention is based on the theory of crystal plasticity, and takes into account plastic deformation that may be caused by high internal pressure in helium bubbles, while improving the accuracy of prediction of the evolution of helium bubbles by phase field simulation. The prediction method according to the present invention is simple and the necessary parameters can be determined by atomic and finite element simulations. [Brief description of the drawings]
[0015] In order to more clearly describe the embodiments of the present invention or the technical means in the prior art, the drawings used in the embodiments are briefly described below. It is obvious that the drawings described below are only some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative efforts.
[0016] [Figure 1] 1 is a flow chart of a method according to an embodiment of the present invention. [Diagram 2] 1A-1C are diagrams simulating the evolution process of a single helium bubble according to an embodiment of the present invention, where in a the simulation time step is 1, in b the simulation time step is 20, and in c the simulation time step is 30. [Diagram 3] FIG. 2 is a schematic diagram of the change in helium concentration during the simulation of the evolution of a single helium bubble according to an embodiment of the present invention. [Figure 4]FIG. 2 is a comparison diagram between simulation and experiment of the size and size distribution of helium bubbles in the 316H austenitic stainless steel described in the embodiment of the present invention under helium ion irradiation conditions at 550° C. [Diagram 5] FIG. 2 is a diagram simulating the effect of stress on He bubbles under helium ion irradiation conditions at 550° C. in the 316H austenitic stainless steel described in the embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0017] In order to make the objectives, technical means and advantages of the embodiments of the present invention clearer, the technical means in the embodiments of the present invention will be described clearly and completely below with reference to the drawings in the embodiments of the present invention. Obviously, the following embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Usually, the components of the embodiments of the present invention shown in the drawings can be arranged and designed in various different layouts. Therefore, the description of the embodiments of the present invention provided in the following drawings does not limit the scope of the claims, but only shows specific embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative efforts are included in the protection scope of the present invention.
[0018] As shown in Figures 1-5, the present invention provides a technique for predicting the evolution of helium bubbles in metallic materials under irradiation. The technique includes a prediction method and a process for constructing a prediction system based on the prediction method. Specifically, Based on the vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction and absolute temperature of the nuclear power structural material, the chemical free energy density of the material is established. Based on the elastic constants and elastic strains of the nuclear power structural material, the elastic free energy density of the material is established. Based on the chemical free energy density and elastic free energy density, a phase-field equation thermodynamic (model) module is constructed to describe the evolution of helium bubbles in irradiated nuclear power system metallic structural materials. Based on the thermodynamics (model) module, a kinetics (model) module of the phase field equation is constructed by taking the diffusion coefficients of vacancies and helium atoms in nuclear power structural materials, as well as the generation rate of helium atoms under irradiation. A data processing (model) module is constructed based on the calculation results of the phase field dynamics (model) module. Based on the data results of the data processing (model) module, calculations are performed in the thermodynamics (model) module and the kinetics (model) module for the next simulation time step, and thus a repeated loop is performed to obtain the evolution of the helium bubbles under irradiation.
[0019] The vacancy formation energies and helium atom formation energies were calculated based on molecular dynamics.
[0020] The molecular dynamics calculation is performed using LAMMPS software. The formula for calculating the vacancy formation energy is as follows:
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[0021] The formula for calculating the formation energy of a helium atom is:
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[0022] The elastic constants of the materials were calculated based on molecular dynamics.
[0023] The molecular dynamics calculation is performed using the LAMMPS software. The elastic constant is calculated using the following formula:
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[0024] The formula for calculating the elastic strain is as follows:
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[0025] The formula for calculating the inherent strain of irradiated helium bubbles is given below.
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[0026] The internal pressure of the helium bubble is calculated based on the helium concentration inside the helium bubble using the following formula:
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[0027] The formula for calculating the plastic strain is as follows:
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[0028] The critical shear stress was calculated based on the dislocation model. The formula is as follows:
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[0029] Based on the concentration field and order parameter field of the current time step calculated by the kinetics (model) module of the phase field equation, the morphology evolution of the helium bubbles is obtained by visualization with PARAVIEW software. Quantitative statistics of helium bubble density and size are calculated based on the order parameter field at the current time step calculated by the field equation dynamics (model) module.
[0030] Based on the quantitatively statistically determined helium bubble density and size, the internal pressure of the helium bubbles at the next time step is obtained, and a repeating loop is performed to obtain the evolution process of the helium bubbles under irradiation.
[0031] Example 1: In the example, the technique for predicting the evolution of helium bubbles in irradiated metallic materials provided by the present invention is taken as an example for nuclear grade 316H austenitic stainless steel, including the following steps: FIG. 1 is a flow chart of a technique for predicting the evolution of helium bubbles in irradiated metallic materials provided in the examples of the present specification.
[0032] Step 1: Calculate the vacancy formation energy and the helium atom formation energy based on molecular dynamics.
[0033] The molecular dynamics calculation is performed using LAMMPS software. The formula for calculating the vacancy formation energy is as follows:
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[0034] The formula for calculating the formation energy of a helium atom is:
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[0035] Step 2: Obtain the chemical free energy density.
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[0036] The mathematical expression for the free energy density of a substrate is:
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[0037] The mathematical expression for the free energy density of a helium bubble is:
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[0038] Step 3: Calculate the elastic constants of the material based on molecular dynamics. As a method for calculating molecular dynamics, perform molecular dynamics calculations using LAMMPS software. The formula for calculating the elastic constants is as follows:
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[0039] Step 4: Write out the formula for elastic strain.
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[0040] Step 5: Calculate the intrinsic strain of the irradiated helium bubbles.
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[0041] The internal pressure of the helium bubble is calculated based on the helium concentration inside the helium bubble using the following formula:
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[0042] Step 6: Calculate the plastic strain.
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[0043] In step 6, the calculation formula for the critical shear stress is as follows:
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[0044] In step 6, the calculation formula for dislocation density is as follows:
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[0045] Step 7: Obtain the elastic free energy density based on the calculated intrinsic strain and plastic strain of the helium bubble.
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[0046] Step 8: Construct a thermodynamic (model) module of the phase-field equations to describe the evolution of helium bubbles in irradiated nuclear power system metallic structural materials based on the calculated chemical free energy density and elastic free energy density.
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[0047] Step 9: Build the dynamics (model) module of the phase-field equations.
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[0048] Step 10: Based on the concentration field and order parameter field of the current time step calculated by the dynamics (model) module of the phase field equations, visualize by PARAVIEW software to obtain the evolution of the morphology of the helium bubbles at the current time step, and quantitatively statistically obtain the helium bubble density and size based on the order parameter field of the current time step calculated by the dynamics (model) module of the field equations.
[0049] Step 11: Based on the density and size in step 10, the internal pressure of the helium bubbles in the next time step is obtained according to the formula in step 5, and a loop is repeatedly performed to obtain the evolution process of the irradiated helium bubbles. Table 1 shows the main physical property parameters of Example 1. [Table 1]
[0050] Figures 4-5 show the comparison of the simulation and experiment of the size and size distribution of helium bubbles under helium ion irradiation conditions of 316H austenitic stainless steel at 550℃ by the prediction technology of the evolution of helium bubbles in irradiated metal materials provided by the present invention, as well as the effect of stress on He bubbles under helium ion irradiation conditions. As can be seen from Figures 4 and 5, the phase field simulation has a relatively high prediction accuracy, the action of external stress can promote the formation of He bubbles under irradiation, and the phase field simulation can make up for the lack of experimental research.
[0051] As can be seen from the results of the examples, the present invention provides a method for predicting the formation and evolution of helium bubbles under irradiation conditions and quantitatively predicting the evolution of helium bubbles, which lays a more mechanistic theoretical foundation for the evolution of helium bubbles under irradiation conditions and improves the application value of computational simulation as a theoretical basis for predicting the microstructure of nuclear power system structural materials under irradiation conditions.
[0052] The present invention will be described with reference to flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be realized by computer program instructions. These computer program instructions can instruct a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine to realize a function specified in one or more flows of the flowcharts and / or one or more blocks of the block diagrams by the instructions executed by the processor of the computer or other programmable data processing device.
[0053] In the present description, the terms "first" and "second" are for descriptive purposes only and cannot be understood as indicating or implying a relative importance or number of the indicated technical features. Thus, a "first" or "second" feature may explicitly or implicitly include one or more features. In the present description, "plurality" means two or more than two, unless otherwise specified.
[0054] Those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, the present invention is intended to include these modifications and variations as long as they fall within the scope of the claims of the present invention and their equivalents.
Claims
1. 1. A method for predicting the evolution of helium bubbles in an irradiated metallic material, comprising: Obtaining a chemical free energy density of the nuclear power structural material based on a vacancy formation energy, a helium atom formation energy, a gas constant, a molar volume fraction and an absolute temperature of the nuclear power structural material; obtaining an elastic free energy density of the nuclear power structural material according to an elastic constant and an elastic strain of the nuclear power structural material; constructing a thermodynamic model of a phase-field equation for describing the evolution of helium bubbles in the irradiated nuclear power system metal structural material based on the chemical free energy density and the elastic free energy density, and constructing a kinetic model of the phase-field equation by obtaining the interface mobility, the chemical mobility of helium and vacancies, and the generation rate of helium and vacancies under irradiation conditions, thereby predicting the evolution of helium bubbles in the irradiated nuclear power system metal structural material; Including, 1. A method for predicting the evolution of helium bubbles in a nuclear power plant structural material under irradiation, comprising: acquiring and visualizing a concentration field and an order parameter field at a current time step to acquire the evolution of helium bubbles at the current time step; calculating quantitative statistics of the density and size of the helium bubbles based on the order parameter field; and then performing iterative calculations to acquire the evolution process of the helium bubbles under irradiation.
2. 2. The method according to claim 1, characterized in that, in the process of obtaining the vacancy formation energy and the helium atom formation energy of a nuclear power structural material, the total energy of an optimized vacancy-containing unit cell and the total energy of an optimized interstitial helium atom-containing unit cell are obtained, and molecular dynamics calculations are performed based on the total energy and total particle number of the optimized complete unit cell to obtain the vacancy formation energy and the helium atom formation energy, respectively.
3. 3. The method of claim 2, wherein in the step of acquiring the chemical free energy density, the chemical free energy density is generated by setting an interpolation function based on a first free energy density of the substrate and a second free energy density of helium bubbles, and the first free energy density and the second free energy density are acquired based on a vacancy concentration and a helium concentration.
4. 4. The method according to claim 3, wherein in the step of acquiring the first free energy density, the first free energy density is acquired according to a molar volume fraction, an Avogadro constant, a gas constant and an absolute temperature based on a vacancy concentration and a helium concentration.
5. 5. The method of claim 4, wherein in the step of acquiring the second free energy density, the second free energy density is acquired based on a vacancy concentration and a helium concentration, according to an equilibrium concentration of helium in a helium bubble and a maximum concentration of helium in a helium bubble, as well as the molar volume fraction, the gas constant, and the absolute temperature.
6. In the process of obtaining the elastic constant and the elastic strain, the small strain, the stress under the positive strain condition, and the stress under the negative strain condition of the nuclear power plant structural material in the j direction are obtained to obtain the elastic constant of the nuclear power plant structural material; 6. The method according to claim 5, characterized in that the elastic strain is obtained according to the total strain of the nuclear power structural material, the inherent strain of helium bubbles due to irradiation of the nuclear power structural material, and the plastic strain of the nuclear power structural material.
7. 7. The method according to claim 6, characterized in that in the process of obtaining the inherent strain of the helium bubble due to irradiation, the internal pressure of the helium bubble and the components of the elastic constant are obtained, and the inherent strain of the irradiated helium bubble is obtained according to Kronecker's delta, where the internal pressure of the helium bubble is obtained according to the helium concentration in the helium bubble, the Boltzmann constant, the absolute temperature, the atomic volume and the van der Waals constant.
8. 8. The method according to claim 7, characterized in that in the process of obtaining the plastic strain, the plastic strain is obtained based on an initial plastic shear rate, a dislocation shear rate, a strain sensitivity index, a Schimid tensor factor, a stress tensor, a limit shear stress, a total slip coefficient, and a current slip system.
9. 1. A system for predicting the evolution of helium bubbles in an irradiated metallic material, comprising: a data acquisition module for acquiring vacancy formation energy, helium atom formation energy, gas constant, molar volume fraction, and absolute temperature of the nuclear power structural material; a chemical free energy density calculation module for obtaining a chemical free energy density of the nuclear power structural material according to a vacancy formation energy, a helium atom formation energy, a gas constant, a molar volume fraction and an absolute temperature of the nuclear power structural material; an elastic free energy density calculation module for obtaining an elastic free energy density of the nuclear power structural material according to the elastic constant and the elastic strain of the nuclear power structural material; a helium bubble evolution prediction module under irradiation, which constructs a thermodynamic model of a phase field equation for describing the evolution of helium bubbles in a nuclear power system metal structural material under irradiation based on the chemical free energy density and the elastic free energy density, and constructs a kinetic model of a phase field equation by collecting interface mobility, chemical mobility of helium and vacancies, and generation rate of helium and vacancies under irradiation conditions, and predicts the evolution of helium bubbles under irradiation of the nuclear power system structural material; Including, 1. A system for predicting the evolution of helium bubbles in a nuclear power plant structural material under irradiation, comprising: acquiring and visualizing a concentration field and an order parameter field at a current time step; acquiring the evolution of the helium bubbles at the current time step; calculating quantitative statistics of the density and size of the helium bubbles based on the order parameter field; and then performing iterative calculations to acquire the evolution process of the helium bubbles under irradiation.