Method and device for simulating mechanical properties of zirconium-niobium alloy under irradiation condition

Abstract

The invention discloses a method and a device for simulating the mechanical property of a zirconium-niobium alloy under an irradiation condition, relates to the technical field of data processing, and mainly aims to solve the problems of lack of microstructure simulation of the zirconium-niobium alloy after irradiation and high cost, long period and low safety coefficient of mechanical property inspection of the zirconium-niobium alloy. Comprising the following steps: establishing a microstructure model of the zirconium-niobium alloy by adopting a phase field method, and introducing a rate theoretical model of irradiation defect evolution into the model to obtain a microstructure evolution model of the zirconium-niobium alloy under the irradiation condition; determining the defect concentration under the irradiation condition based on the microstructure evolution model of the zirconium-niobium alloy; obtaining the zirconium element concentration in the zirconium-niobium alloy under the irradiation condition, and determining the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium element concentration; determining a total free energy density function of the zirconium-niobium alloy based on the non-linear elastic energy density, the defect concentration and the zirconium element concentration of the zirconium-niobium alloy under the irradiation condition; and deriving the total free energy density function to obtain a target stress tensor component.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions. Background Technology

[0002] Currently, zirconium alloys are widely used as cladding materials for pressurized water reactor fuel elements due to their small neutron absorption cross section, good corrosion resistance, and good radiation resistance. Zr-4 alloy, belonging to the Zr-Sn alloy series, is currently the most widely used in commercial pressurized water reactors. To further improve the corrosion resistance of zirconium alloys, Canada, Russia, the United States, France, and other countries have successively developed Zr-Nb alloys. Under irradiation conditions, the mechanical properties of zirconium-niobium alloys directly affect the material's service life and safety.

[0003] To explore zirconium-niobium alloys with superior radiation resistance, it is necessary to determine their mechanical properties under neutron irradiation conditions, thereby evaluating their performance in reactor operations. However, current numerical simulation techniques for nuclear materials have not yet been applied to zirconium-niobium alloys. The mechanical properties of these alloys are currently obtained through post-irradiation testing, which is not only costly and time-consuming, but also carries the risk of harm to testing personnel due to the radioactive nature of the materials. Summary of the Invention

[0004] In view of this, the present invention provides a method and apparatus for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions. The main purpose is to solve the problems of lack of simulation of the microstructure of zirconium-niobium alloys after irradiation, as well as the high cost, long inspection cycle and low safety factor of mechanical property testing of zirconium-niobium alloys after irradiation.

[0005] According to one aspect of the present invention, a method for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions is provided, comprising:

[0006] A microstructure model of zirconium-niobium alloy was established using the phase-field method, and a rate theory model of irradiation defect evolution was introduced into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions.

[0007] The defect concentration under irradiation conditions was determined based on the microstructure evolution model of the zirconium-niobium alloy.

[0008] The zirconium concentration in the zirconium-niobium alloy under irradiation conditions is obtained, and the nonlinear elastic energy density of the zirconium-niobium alloy is determined based on the zirconium concentration.

[0009] The total free energy density function of the zirconium-niobium alloy is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration.

[0010] The total free energy density function is differentiated to obtain the target stress tensor components.

[0011] Furthermore, the microstructure evolution model of the zirconium-niobium alloy under irradiation conditions is as follows:

[0012]

[0013] Where c is the zirconium concentration, c v Let φ represent the concentration of vacancy defects, and φ represent the order parameter of the second phase. The kinetic coefficients representing zirconium atoms. Here, Γ represents the Gibbs energy, and Γ represents the atomic migration frequency. <c> w This represents the average concentration of zirconium. The Gaussian thermal noise of zirconium; M φ For the kinetic coefficients of the second phase, This represents the Gaussian thermal noise of the second phase. ε represents the occurrence rate of point defects. v D represents the clustering ratio of vacancy sites. v D represents the diffusivity of vacancies. i λ represents the interstitial atom diffusivity. g μ(ρ) is the mean free path of the vacancy. i, ρ v ) indicates the lack of trap strength, α r ρ represents the recombination rate of point defects. i ρ represents the interstitial ring density. v c represents the vacancy ring density. v0 L represents the equilibrium vacancy concentration. v The kinetic coefficient for vacancies is represented by ν, which represents Poisson's ratio. It represents the product of bulk modulus and atomic volume. Indicates the volume of expansion. Let r represent the gradient operator. d0 This represents the distance between the defect and the matrix atoms. The Gaussian thermal noise representing the defect, r i The average size of the gap ring is represented by r. v This indicates the average size of the vacancy ring. c represents the magnitude of the Burgers vector. vL Represents the concentration of vacancies absorbed by the interstitial loop, ∈ i ε represents the proportion of interstitial atoms. i This indicates the clustering ratio of interstitial atoms.

[0014] Furthermore, the determination of defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy includes:

[0015] The relevant parameters of the irradiation conditions and the relevant parameters of the zirconium-niobium alloy are used as inputs to the microstructure evolution model, and the defect concentration is used as the output of the microstructure evolution model.

[0016] The defect concentration under the irradiation conditions is obtained through evolution simulation processing of the microstructure evolution model.

[0017] Further, determining the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium element concentration includes:

[0018] Obtain the bulk modulus of zirconium and niobium, and determine the bulk modulus of the zirconium-niobium alloy based on the bulk modulus of zirconium, the bulk modulus of niobium, and the zirconium element concentration.

[0019] A simulated elastic displacement vector is applied to the zirconium-niobium alloy; and the corresponding expansion strain, tetragonal strain, and shear strain are determined based on the simulated elastic displacement vector.

[0020] The corresponding shear strain energy is determined based on the zirconium element concentration, the tetragonal strain, and the shear strain.

[0021] The nonlinear elastic energy density is determined based on the bulk modulus of the zirconium-niobium alloy, the expansion strain, and the shear strain.

[0022] Further, determining the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration includes:

[0023] The elastic contribution caused by elastic mismatch is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration.

[0024] The free energy density of the alloy system is determined based on the zircon concentration and the defect concentration under irradiation conditions.

[0025] The total free energy density function of the zirconium-niobium alloy is determined based on the elastic contribution, the free energy density of the alloy system, the zirconium element concentration, and the defect concentration.

[0026] Further, the determination of the elastic contribution caused by elastic mismatch based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration includes:

[0027] Obtain the coupled strain ratio caused by alloy composition, the coupled strain ratio caused by vacancy defects, and the expansion strain corresponding to the simulated elastic displacement.

[0028] The elastic contribution of the alloy composition is obtained by multiplying the coupling strain ratio caused by the alloy composition, the expansion strain and the zirconium concentration.

[0029] The elastic contribution of the defect is obtained by multiplying the coupling strain ratio caused by the vacancy defect, the expansion strain, and the defect concentration.

[0030] The elastic contribution caused by elastic mismatch is obtained by summing the elastic contribution of the alloy composition, the elastic contribution of the defect, and the nonlinear elastic energy density of the zirconium-niobium alloy.

[0031] Furthermore, the target stress tensor components obtained in the stress determination module include:

[0032]

[0033] Where K is the bulk modulus of the zirconium-niobium alloy, e1 is the expansion strain corresponding to the elastic displacement vector, e2 is the tetragonal strain corresponding to the elastic displacement vector, e3 is the shear strain corresponding to the elastic displacement vector, and c is the alloy composition concentration. v Let α be the concentration of vacancy defects, α be the proportion of coupled strain introduced by the alloy composition, β be the proportion of coupled strain introduced by vacancy defects, and μ be the concentration of vacancy defects. α μ is the shear modulus of zirconium. β This represents the shear modulus of niobium.

[0034] According to another aspect of the present invention, a device for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions is provided, comprising:

[0035] The modeling module is used to establish a microstructure model of zirconium-niobium alloy using the phase field method, and to introduce a rate theory model of irradiation defect evolution into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions.

[0036] An evolution simulation module is used to determine the defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy.

[0037] The mechanical simulation module is used to obtain the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and to determine the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration.

[0038] The free energy determination module is used to determine the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration;

[0039] The stress determination module is used to differentiate the total free energy density function to obtain the target stress tensor components.

[0040] Furthermore, the microstructure evolution model of zirconium-niobium alloy under irradiation conditions in the modeling module is as follows:

[0041]

[0042] Where c is the zirconium concentration, c v Let φ represent the concentration of vacancy defects, and φ represent the order parameter of the second phase. The kinetic coefficients representing zirconium atoms. Here, Γ represents the Gibbs energy, and Γ represents the atomic migration frequency. <c> w This represents the average concentration of zirconium. The Gaussian thermal noise of zirconium; M φ For the kinetic coefficients of the second phase, This represents the Gaussian thermal noise of the second phase. ε represents the occurrence rate of point defects. v D represents the clustering ratio of vacancy sites. v D represents the diffusivity of vacancies. i λ represents the interstitial atom diffusivity. g μ(ρ) is the mean free path of the vacancy. i, ρ v ) indicates the lack of trap strength, α r ρ represents the recombination rate of point defects. i ρ represents the interstitial ring density. v c represents the vacancy ring density. v0 L represents the equilibrium vacancy concentration. v The kinetic coefficient for vacancies is represented by ν, which represents Poisson's ratio. It represents the product of bulk modulus and atomic volume. Indicates the volume of expansion. Let r represent the gradient operator. d0 This represents the distance between the defect and the matrix atoms. The Gaussian thermal noise representing the defect, r i The average size of the gap ring is represented by r. v This indicates the average size of the vacancy ring. c represents the magnitude of the Burgers vector. vL Represents the concentration of vacancies absorbed by the interstitial loop, ∈ i ε represents the proportion of interstitial atoms. i This indicates the clustering ratio of interstitial atoms.

[0043] Furthermore, the evolution simulation module is also used for:

[0044] The relevant parameters of the irradiation conditions and the relevant parameters of the zirconium-niobium alloy are used as inputs to the microstructure evolution model, and the defect concentration is used as the output of the microstructure evolution model.

[0045] The defect concentration under the irradiation conditions is obtained through evolution simulation processing of the microstructure evolution model.

[0046] Furthermore, the mechanical simulation module is also used for:

[0047] Obtain the bulk modulus of zirconium and niobium, and determine the bulk modulus of the zirconium-niobium alloy based on the bulk modulus of zirconium, the bulk modulus of niobium, and the zirconium element concentration.

[0048] A simulated elastic displacement vector is applied to the zirconium-niobium alloy; and the corresponding expansion strain, tetragonal strain, and shear strain are determined based on the simulated elastic displacement vector.

[0049] The corresponding shear strain energy is determined based on the zirconium element concentration, the tetragonal strain, and the shear strain.

[0050] The nonlinear elastic energy density is determined based on the bulk modulus of the zirconium-niobium alloy, the expansion strain, and the shear strain.

[0051] Furthermore, the free energy determination module is also used for:

[0052] The elastic contribution caused by elastic mismatch is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration.

[0053] The free energy density of the alloy system is determined based on the zircon concentration and the defect concentration under irradiation conditions.

[0054] The total free energy density function of the zirconium-niobium alloy is determined based on the elastic contribution, the free energy density of the alloy system, the zirconium element concentration, and the defect concentration.

[0055] Furthermore, the free energy determination module is also used for:

[0056] Obtain the coupled strain ratio caused by alloy composition, the coupled strain ratio caused by vacancy defects, and the expansion strain corresponding to the simulated elastic displacement.

[0057] The elastic contribution of the alloy composition is obtained by multiplying the coupling strain ratio caused by the alloy composition, the expansion strain and the zirconium concentration.

[0058] The elastic contribution of the defect is obtained by multiplying the coupling strain ratio caused by the vacancy defect, the expansion strain, and the defect concentration.

[0059] The elastic contribution caused by elastic mismatch is obtained by summing the elastic contribution of the alloy composition, the elastic contribution of the defect, and the nonlinear elastic energy density of the zirconium-niobium alloy.

[0060] Further, the step of differentiating the total free energy density function to obtain the target stress tensor components includes:

[0061]

[0062] Where K is the bulk modulus of the zirconium-niobium alloy, e1 is the expansion strain corresponding to the elastic displacement vector, e2 is the tetragonal strain corresponding to the elastic displacement vector, e3 is the shear strain corresponding to the elastic displacement vector, and c is the alloy composition concentration. v Let α be the concentration of vacancy defects, α be the proportion of coupled strain introduced by the alloy composition, β be the proportion of coupled strain introduced by vacancy defects, and μ be the concentration of vacancy defects. α μ is the shear modulus of zirconium. β This represents the shear modulus of niobium.

[0063] According to another aspect of the present invention, a storage medium is provided, wherein at least one executable instruction is stored therein, the executable instruction causing a processor to perform an operation corresponding to the above-described simulation method for the mechanical properties of zirconium-niobium alloys under irradiation conditions.

[0064] According to another aspect of the present invention, a computer device is provided, including a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus;

[0065] The memory is used to store at least one executable instruction that causes the processor to perform an operation corresponding to the simulation method of the mechanical properties of zirconium-niobium alloys under irradiation conditions described above.

[0066] By employing the above-described technical solutions, the technical solutions provided by the embodiments of the present invention have at least the following advantages:

[0067] This invention provides a method and apparatus for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions. Compared with existing technologies, this invention establishes a microstructure model of the zirconium-niobium alloy using the phase-field method and introduces a rate theory model of irradiation defect evolution into this microstructure model, thereby obtaining a microstructure evolution model of the zirconium-niobium alloy under irradiation conditions. This enables the simulation of the microstructure of the zirconium-niobium alloy after irradiation, providing a strong foundation for mechanical property simulation and analysis. Furthermore, this invention determines the defect concentration under irradiation conditions using the microstructure evolution model of the zirconium-niobium alloy; obtains the zirconium concentration in the zirconium-niobium alloy under irradiation conditions and determines the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration; determines the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density, the defect concentration, and the zirconium concentration under irradiation conditions; and obtains the target stress tensor component by differentiating the total free energy density function, thus realizing computer simulation of the mechanical parameters of the zirconium-niobium alloy under neutron irradiation and obtaining the influence of irradiation conditions and alloy composition on the zirconium-niobium alloy. Unlike existing reactor neutron irradiation and microscopic characterization techniques, numerical simulation can significantly reduce experimental time and costs, eliminate the need for personnel to be exposed to radioactivity, and improve the safety of analysis.

[0068] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0069] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0070] Figure 1 A schematic flowchart of a method for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions, provided in an embodiment of the present invention, is shown.

[0071] Figure 2 The figure shows the stress-strain curves of a Zr-Nb alloy before and after irradiation under simulated conditions, according to an embodiment of the present invention.

[0072] Figure 3 A schematic diagram of a device for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions, provided in an embodiment of the present invention, is shown.

[0073] Figure 4 A schematic diagram of the structure of a computer device provided in an embodiment of the present invention is shown. Detailed Implementation

[0074] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0075] This invention provides a method for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions, such as... Figure 1 As shown, the method includes:

[0076] 101. A microstructure model of zirconium-niobium alloy is established using the phase-field method, and a rate theory model of irradiation defect evolution is introduced into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions.

[0077] In this embodiment of the invention, the current execution terminal uses the phase-field method to establish a microstructure model of the zirconium-niobium alloy, and introduces a rate theory model of irradiation defect evolution into the microstructure model to obtain a microstructure evolution model of the zirconium-niobium alloy under irradiation conditions, expressed by the following formula:

[0078]

[0079] Where c is the zirconium concentration, c v Let φ represent the concentration of vacancy defects, and φ represent the order parameter of the second phase. The kinetic coefficients representing zirconium atoms. Here, Γ represents the Gibbs energy, and Γ represents the atomic migration frequency. <c> w This represents the average concentration of zirconium. The Gaussian thermal noise of zirconium; M φ For the kinetic coefficients of the second phase, This represents the Gaussian thermal noise of the second phase. ε represents the occurrence rate of point defects. v D represents the clustering ratio of vacancy sites. v D represents the diffusivity of vacancies. i λ represents the interstitial atom diffusivity. g μ(ρ) is the mean free path of the vacancy. i, ρ v ) indicates the lack of trap strength, α r ρ represents the recombination rate of point defects. i ρ represents the interstitial ring density. v c represents the vacancy ring density. v0 L represents the equilibrium vacancy concentration. v The kinetic coefficient for vacancies is represented by ν, which represents Poisson's ratio. It represents the product of bulk modulus and atomic volume. Indicates the volume of expansion. Let r represent the gradient operator. d0 This represents the distance between the defect and the matrix atoms. The Gaussian thermal noise representing the defect, r i The average size of the gap ring is represented by r. v This indicates the average size of the vacancy ring. c represents the magnitude of the Burgers vector. vL Represents the concentration of vacancies absorbed by the interstitial loop, ∈ i ε represents the proportion of interstitial atoms. i This indicates the clustering ratio of interstitial atoms.

[0080] To obtain the aforementioned model parameters, the defect concentration needs to be calculated using rate theory. Under in-pile neutron irradiation, a large number of point defects are generated in the zirconium-niobium alloy. The defects in the system are described by rate theory formulas, and the interstitial atom concentrations of zirconium and niobium are... Represented as:

[0081]

[0082] in, ε represents the occurrence rate of point defects. i The clustering ratio of interstitial atoms, x Zr,Nb D represents the ratio of zirconium atoms to niobium atoms. i λ represents the interstitial atom diffusivity. g μ(ρ) is the mean free path of the vacancy. i,v ) indicates the lack of trap strength, α r c represents the recombination rate of point defects. v c represents the concentration of vacancy defects. v0 Indicates the equilibrium vacancy concentration. Represents the gradient operator. This represents the interstitial atomic flux of zirconium and niobium.

[0083] Among them, the vacancy concentration c v The evolution equation over time is:

[0084]

[0085] Where, ε v D represents the clustering ratio of vacancy sites. v This represents the diffusion rate of vacancies. This indicates the interstitial atom concentration of zirconium. J represents the interstitial atom concentration of niobium. v This represents the flux of vacant spaces.

[0086] Among them, the ratio of zirconium atoms to niobium atoms is x Zr，Nb for:

[0087]

[0088] Among them, J Zr，Nb This indicates the flux of zirconium and niobium atoms.

[0089] The density of gap rings and vacancy rings can be given by the average size of the rings and the number density of the rings, as shown in the following formula:

[0090]

[0091] Where, ρ i ρ represents the interstitial ring density. v Represents the vacancy ring density, r i The average size of the gap ring is represented by r. v This indicates the average size of the vacancy ring. c represents the magnitude of the Burgers vector. vL This indicates the concentration of vacancies absorbed by the interstitial ring. This indicates the interstitial atom concentration of zirconium. This indicates the interstitial atom concentration of niobium.

[0092] In zirconium-niobium alloys, the diffusivity of interstitial atoms is much greater than that of vacancies, and the vacancy lifetime is much greater than that of interstitial atoms. Therefore, the concentration of interstitial atoms can be assumed to be constant in the model. Based on the law of conservation of mass, the concentration of interstitial atoms can be calculated using the following formula:

[0093]

[0094] Where, ∈ i The proportion of interstitial atoms, x Nb This indicates the proportion of niobium atoms.

[0095] The potential energy of the elastic interaction between the defects is:

[0096] U d =U dd +U da

[0097] Among them, U d U represents the elastic interaction potential energy of the defect. ad U represents the potential energy of the interaction between defects. da This represents the interaction potential energy between the defect and the matrix atoms.

[0098] The potential energy of the interaction between defects is:

[0099]

[0100] Where ν represents Poisson's ratio, It represents the product of bulk modulus and atomic volume. c represents the volume of expansion. d Indicates the concentration of defects.

[0101] The interaction potential energy between the defect and the matrix atoms is:

[0102] U da =-∫Λ(|rr′||)∈(r′)ΔΩ d dr′

[0103] Where Λ is the elastic modulus operator, r represents the distance between the defect and the matrix atom, and ΔΩ d It represents the change in volume.

[0104] Assume the force acting on the defect causes the defect to move at a velocity v d sports:

[0105]

[0106] Among them, D d T represents the diffusion rate of the defect, and T represents the temperature.

[0107] At this point, the system is a defective elastic continuum, and its free energy density F is:

[0108]

[0109] Where K represents the bulk modulus, u ll u ik Represents the deformation tensor.

[0110] Since defects can cause deformation of the material medium, the displacement vector can be calculated by solving the equations as follows:

[0111]

[0112] Where ρ represents the material density, σ ik This represents the stress tensor.

[0113]

[0114] Substituting this into the dynamic equation of the displacement vector u, we get:

[0115]

[0116] Among them, c l For longitudinal sound speed, c τ It is the transverse speed of sound.

[0117] The relationship between deformation and defect concentration is as follows:

[0118]

[0119] Therefore, the elastic flux of the defect is:

[0120]

[0121] In summary, a phase field and rate theory kinetic model for simulating the microstructure evolution of zirconium-niobium alloys under irradiation conditions can be obtained.

[0122] 102. Determine the defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy;

[0123] In this embodiment of the invention, the current execution terminal uses relevant parameters of irradiation conditions and relevant parameters of zirconium-niobium alloy as inputs to the microstructure evolution model, and uses the defect concentration as the output of the microstructure evolution model; after evolution simulation processing by the microstructure evolution model, the defect concentration under the irradiation conditions is obtained, denoted as c. v .

[0124] 103. Obtain the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and determine the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration;

[0125] In this embodiment of the invention, the current execution terminal first obtains the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and then determines the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration, denoted as f. el (u, c), where c is the zirconium concentration in the zirconium-niobium alloy, and u is the elastic displacement vector. The specific process includes:

[0126] (1) Obtain the bulk modulus of zirconium and niobium, and determine the bulk modulus of the zirconium-niobium alloy based on the bulk modulus of zirconium, the bulk modulus of niobium, and the zirconium element concentration, using the following specific formula:

[0127] K = K Zr c+K Nb (1-c)

[0128] Where K represents the bulk modulus of the zirconium-niobium alloy, K Zr K represents the bulk modulus of zirconium. Nb This represents the bulk modulus of niobium.

[0129] (2) Apply a simulated quantity u of the elastic displacement vector to the zirconium-niobium alloy; and determine the corresponding expansion strain e1, tetragonal strain e2 and shear strain e3 based on the simulated quantity u of the elastic displacement vector.

[0130] (3) Based on the zirconium element concentration c, the tetragonal strain e2, and the shear strain e3, the corresponding shear strain energy Φ(c, e2, e3) is determined, and the specific formula is as follows:

[0131] Φ(c,e2,e3)=Φ α (e2, e3)(1-c)+Φ β (e2,e3)

[0132]

[0133] Where, Φ α (e2, e3) represent the shear strain energy of the α-Zr hexagonal lattice, Φ β (e2, e3) represent the shear strain energy of the β-Nb cubic lattice, μ α and μ β These represent the shear modulus of zirconium and niobium, respectively.

[0134] (4) Determine the nonlinear elastic energy density f based on the bulk modulus K of the zirconium-niobium alloy, the expansion strain e1, and the shear strain energy Φ(c, e2, e3). el (u, c), the specific formula is as follows:

[0135]

[0136] 104. Determine the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration;

[0137] In this embodiment of the invention, the current execution terminal first determines the elastic contribution caused by elastic mismatch based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration, specifically:

[0138] (1) Obtain the coupling strain ratio α caused by the alloy composition, the coupling strain ratio β caused by the vacancy defect, and the expansion strain e1 corresponding to the simulated elastic displacement.

[0139] (2) Multiply the coupling strain ratio α brought about by the alloy composition, the expansion strain e1 and the zirconium element concentration c to obtain the elastic contribution αe1c of the alloy composition;

[0140] (3) The coupling strain ratio β caused by the vacancy defect, the expansion strain e1, and the defect concentration c are used to determine the coupling strain ratio β, the expansion strain e1, and the defect concentration c. v Multiplying these components yields the elastic contribution βe1c of the defect. v ;

[0141] (4) The elastic contribution αe1c to the alloy composition and the elastic contribution βe1c to the defect. v and the nonlinear elastic energy density f of the zirconium-niobium alloy el Summing (u, c) yields the elastic contribution caused by elastic mismatch, as shown in the following formula:

[0142] g el (u,c,c v )=αe1c+βe1c v +f ell (u,c)

[0143] Next, the current execution end is based on the zirconium element concentration c and the defect concentration c under the irradiation conditions. v The free energy density of the alloy system is determined and denoted as G(c, c). v , φ; T), where φ represents the sequence parameter of the second phase and T represents the irradiation temperature.

[0144] Based on the aforementioned elastic contribution g el (u, c, c) v The free energy density G(c,c) of the alloy system v , φ; T), the zirconium element concentration c and the defect concentration c v The total free energy density function f of the zirconium-niobium alloy is determined by the following formula:

[0145]

[0146] in, V represents the gradient operator. m Represents the volume of a mole, ∈ c Indicates the proportion of zirconium, ∈ v Represents the proportion of vacancy defects, ∈ φ This represents the proportion of the sequence parameters of the second phase.

[0147] 105. Differentiate the total free energy density function to obtain the target stress tensor components.

[0148] In this embodiment of the invention, the current execution terminal performs differentiation on the total free energy density function f to obtain the target stress tensor components, including:

[0149]

[0150] Where K is the bulk modulus of the zirconium-niobium alloy, e1 is the expansion strain corresponding to the elastic displacement vector, e2 is the tetragonal strain corresponding to the elastic displacement vector, e3 is the shear strain corresponding to the elastic displacement vector, and c is the alloy composition concentration. v Let α be the concentration of vacancy defects, α be the proportion of coupled strain introduced by the alloy composition, β be the proportion of coupled strain introduced by vacancy defects, and μ be the concentration of vacancy defects. α μ is the shear modulus of zirconium. β This represents the shear modulus of niobium.

[0151] It should be noted that the stress tensor is a three-dimensional matrix that contains the stress components of an object along three coordinate axes. In three-dimensional space, the stress tensor of a point can be described by six stress components, including the xx component (σ) in the embodiments of this invention. xx ), yy component (σ yy ) and xy components (σ xy The embodiments of the present invention are not specifically limited to these parameters. In this embodiment, it is assumed that the Nb element concentration in the Zr-Nb alloy is 10%, the irradiation temperature is 500K and 550K, and the irradiation dose is 10. -6 The tensile and compressive stress-strain curves of zirconium-niobium alloy before and after irradiation were simulated using the modeling method of this invention, and the results are as follows: dpa / s. Figure 2 As shown.

[0152] This invention provides a method for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions. Compared with existing technologies, this invention establishes a microstructure model of the zirconium-niobium alloy using the phase-field method and introduces a rate theory model of irradiation defect evolution into this microstructure model, thereby obtaining a microstructure evolution model of the zirconium-niobium alloy under irradiation conditions. This achieves the simulation of the microstructure of the zirconium-niobium alloy after irradiation, providing a strong foundation for mechanical property simulation and analysis. This invention also determines the defect concentration under irradiation conditions using the microstructure evolution model of the zirconium-niobium alloy; obtains the zirconium concentration in the zirconium-niobium alloy under irradiation conditions and determines the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration; determines the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density, the defect concentration, and the zirconium concentration under irradiation conditions; and obtains the target stress tensor component by differentiating the total free energy density function, thus realizing computer simulation of the mechanical parameters of the zirconium-niobium alloy under neutron irradiation and obtaining the influence of irradiation conditions and alloy composition on the zirconium-niobium alloy. Unlike existing reactor neutron irradiation and microscopic characterization techniques, numerical simulation can significantly reduce experimental time and costs, eliminate the need for personnel to be exposed to radioactivity, and improve the safety of analysis.

[0153] As a response to the above Figure 1 The implementation of the method shown in this invention provides a simulation device for the mechanical properties of zirconium-niobium alloys under irradiation conditions, such as... Figure 3 As shown, the device includes:

[0154] Modeling module 21 is used to establish a microstructure model of zirconium-niobium alloy using the phase field method, and to introduce a rate theory model of irradiation defect evolution into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions.

[0155] Evolution simulation module 22 is used to determine the defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy;

[0156] The mechanical simulation module 23 is used to obtain the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and to determine the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration.

[0157] The free energy determination module 24 is used to determine the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration;

[0158] The stress determination module 25 is used to perform derivative processing on the total free energy density function to obtain the target stress tensor components.

[0159] Furthermore, the microstructure evolution model of zirconium-niobium alloy under irradiation conditions in the modeling module 21 is as follows:

[0160]

[0161] Where c is the zirconium concentration, c v Let φ represent the concentration of vacancy defects, and φ represent the order parameter of the second phase. The kinetic coefficients representing zirconium atoms. Here, Γ represents the Gibbs energy, and Γ represents the atomic migration frequency. <c> w represents the average value of the concentration of zirconium element, represents the Gaussian thermal noise of zirconium element; M φ represents the kinetic coefficient of the second phase, represents the Gaussian thermal noise of the second phase, represents the generation rate of point defects, ε v represents the clustering ratio of vacancies, D v represents the diffusion rate of vacancies, D i represents the diffusion rate of interstitial atoms, λ g represents the mean free path of vacancies, μ(ρ i, ρ v represents the defect trap strength, ɑ r represents the point defect recombination rate, ρ i represents the interstitial loop density, ρ v represents the vacancy loop density, c v0 represents the equilibrium vacancy concentration, L v represents the kinetic coefficient of vacancies, ν represents the Poisson ratio, represents the product of bulk modulus and atomic volume, represents the expansion volume, represents the gradient operator, r d0 represents the distance between defects and matrix atoms, represents the Gaussian thermal noise of defects, r i represents the average size of interstitial loops, r v represents the average size of vacancy loops, represents the modulus of the Burgers vector, c vL represents the vacancy concentration absorbed by interstitial loops, ∈ i represents the proportion of interstitial atoms, ε i represents the clustering ratio of interstitial atoms.

[0162] Further, the evolution simulation module 22 is further used for:

[0163] taking the related parameters of the irradiation condition and the related parameters of the zirconium-niobium alloy as inputs of the microstructure evolution model, and taking the defect concentration as an output of the microstructure evolution model;

[0164] obtaining the defect concentration under the irradiation condition through the evolution simulation processing of the microstructure evolution model.

[0165] Further, the mechanical simulation module 23 is further used for:

[0166] obtaining the bulk modulus of zirconium and the bulk modulus of niobium, and determining the bulk modulus of the zirconium-niobium alloy based on the bulk modulus of zirconium, the bulk modulus of niobium and the concentration of zirconium element;

[0167] A simulated elastic displacement vector is applied to the zirconium-niobium alloy; and the corresponding expansion strain, tetragonal strain, and shear strain are determined based on the simulated elastic displacement vector.

[0168] The corresponding shear strain energy is determined based on the zirconium element concentration, the tetragonal strain, and the shear strain.

[0169] The nonlinear elastic energy density is determined based on the bulk modulus of the zirconium-niobium alloy, the expansion strain, and the shear strain.

[0170] Furthermore, the free energy determination module 24 is also used for:

[0171] The elastic contribution caused by elastic mismatch is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration.

[0172] The free energy density of the alloy system is determined based on the zircon concentration and the defect concentration under irradiation conditions.

[0173] The total free energy density function of the zirconium-niobium alloy is determined based on the elastic contribution, the free energy density of the alloy system, the zirconium element concentration, and the defect concentration.

[0174] Furthermore, the free energy determination module 24 is also used for:

[0175] Obtain the coupled strain ratio caused by alloy composition, the coupled strain ratio caused by vacancy defects, and the expansion strain corresponding to the simulated elastic displacement.

[0176] The elastic contribution of the alloy composition is obtained by multiplying the coupling strain ratio caused by the alloy composition, the expansion strain and the zirconium concentration.

[0177] The elastic contribution of the defect is obtained by multiplying the coupling strain ratio caused by the vacancy defect, the expansion strain, and the defect concentration.

[0178] The elastic contribution caused by elastic mismatch is obtained by summing the elastic contribution of the alloy composition, the elastic contribution of the defect, and the nonlinear elastic energy density of the zirconium-niobium alloy.

[0179] Furthermore, the target stress tensor components obtained in the stress determination module 25 include:

[0180]

[0181] Where K is the bulk modulus of the zirconium-niobium alloy, e1 is the expansion strain corresponding to the elastic displacement vector, e2 is the tetragonal strain corresponding to the elastic displacement vector, e3 is the shear strain corresponding to the elastic displacement vector, and c is the alloy composition concentration. v Let α be the concentration of vacancy defects, α be the proportion of coupled strain introduced by the alloy composition, β be the proportion of coupled strain introduced by vacancy defects, and μ be the concentration of vacancy defects. α μ is the shear modulus of zirconium. β This represents the shear modulus of niobium.

[0182] This invention provides a simulation device for the mechanical properties of zirconium-niobium alloys under irradiation conditions. Compared with existing technologies, this invention establishes a microstructure model of the zirconium-niobium alloy using the phase-field method and introduces a rate theory model of irradiation defect evolution into this microstructure model, thereby obtaining a microstructure evolution model of the zirconium-niobium alloy under irradiation conditions. This achieves the simulation of the microstructure of the zirconium-niobium alloy after irradiation, providing a strong foundation for mechanical property simulation and analysis. This invention also determines the defect concentration under irradiation conditions using the microstructure evolution model of the zirconium-niobium alloy; obtains the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and determines the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration; determines the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density, the defect concentration, and the zirconium concentration under irradiation conditions; and obtains the target stress tensor component by differentiating the total free energy density function, thus realizing computer simulation of the mechanical parameters of the zirconium-niobium alloy under neutron irradiation and obtaining the influence of irradiation conditions and alloy composition on the zirconium-niobium alloy. Unlike existing reactor neutron irradiation and microscopic characterization techniques, numerical simulation can significantly reduce experimental time and costs, eliminate the need for personnel to be exposed to radioactivity, and improve the safety of analysis.

[0183] According to one embodiment of the present invention, a storage medium is provided, the storage medium storing at least one executable instruction, the computer-executable instruction being capable of executing the simulation method for the mechanical properties of zirconium-niobium alloys under irradiation conditions in any of the above method embodiments.

[0184] Figure 4 The diagram illustrates a structural schematic of a computer device according to an embodiment of the present invention. The specific embodiments of the present invention do not limit the specific implementation of the computer device.

[0185] like Figure 4 As shown, the computer device may include: a processor 302, a communications interface 304, a memory 306, and a communications bus 308.

[0186] The processor 302, communication interface 304, and memory 306 communicate with each other via communication bus 308.

[0187] Communication interface 304 is used to communicate with other network elements such as clients or other servers.

[0188] The processor 302 is used to execute program 310, which can specifically perform the relevant steps of the simulation method for the mechanical properties of zirconium-niobium alloys under the above-mentioned irradiation conditions.

[0189] Specifically, program 310 may include program code that includes computer operation instructions.

[0190] Processor 302 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement embodiments of the present invention. The computer device includes one or more processors, which may be processors of the same type, such as one or more CPUs; or processors of different types, such as one or more CPUs and one or more ASICs.

[0191] Memory 306 is used to store program 310. Memory 306 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0192] Specifically, program 310 can be used to cause processor 302 to perform the following operations:

[0193] A microstructure model of zirconium-niobium alloy was established using the phase-field method, and a rate theory model of irradiation defect evolution was introduced into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions.

[0194] The defect concentration under irradiation conditions was determined based on the microstructure evolution model of the zirconium-niobium alloy.

[0195] The zirconium concentration in the zirconium-niobium alloy under irradiation conditions is obtained, and the nonlinear elastic energy density of the zirconium-niobium alloy is determined based on the zirconium concentration.

[0196] The total free energy density function of the zirconium-niobium alloy is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration.

[0197] The total free energy density function is differentiated to obtain the target stress tensor components.

[0198] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. Optionally, they can be implemented using computer-executable program code, thereby storing them in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0199] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.< / c> < / c> < / c> < / c>

Claims

1. A method for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions, characterized in that, include: A microstructure model of zirconium-niobium alloy was established using the phase-field method, and a rate theory model of irradiation defect evolution was introduced into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions. The defect concentration under irradiation conditions was determined based on the microstructure evolution model of the zirconium-niobium alloy. The zirconium concentration in the zirconium-niobium alloy under irradiation conditions is obtained, and the nonlinear elastic energy density of the zirconium-niobium alloy is determined based on the zirconium concentration. The total free energy density function of the zirconium-niobium alloy is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration. The total free energy density function is differentiated to obtain the target stress tensor components.

2. The method according to claim 1, characterized in that, The microstructure evolution model of the zirconium-niobium alloy under irradiation conditions is as follows: Where c is the zirconium concentration, c v Let φ represent the concentration of vacancy defects, and φ represent the order parameter of the second phase. The kinetic coefficients representing zirconium atoms. Here, Γ represents the Gibbs energy, and Γ represents the atomic migration frequency. <c>w represents the average concentration of zirconium. The Gaussian thermal noise of zirconium; M φ For the kinetic coefficients of the second phase, This represents the Gaussian thermal noise of the second phase. ε represents the occurrence rate of point defects. v D represents the clustering ratio of vacancy sites. v D represents the diffusivity of vacancies. i λ represents the interstitial atom diffusivity. g μ(ρ) is the mean free path of the vacancy. i, ρ v ) indicates the lack of trap strength, α r ρ represents the recombination rate of point defects. i ρ represents the interstitial ring density. v c represents the vacancy ring density. v0 L represents the equilibrium vacancy concentration. v The kinetic coefficient for vacancies is represented by ν, which represents Poisson's ratio. It represents the product of bulk modulus and atomic volume. Indicates the volume of expansion. Let r represent the gradient operator. d0 This represents the distance between the defect and the matrix atoms. The Gaussian thermal noise representing the defect, r i The average size of the gap ring is represented by r. v This indicates the average size of the vacancy ring. c represents the magnitude of the Burgers vector. vL Represents the concentration of vacancies absorbed by the interstitial loop, ∈ i ε represents the proportion of interstitial atoms. i This indicates the clustering ratio of interstitial atoms.< / c> 3. The method according to claim 1, characterized in that, The determination of defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy includes: The relevant parameters of the irradiation conditions and the relevant parameters of the zirconium-niobium alloy are used as inputs to the microstructure evolution model, and the defect concentration is used as the output of the microstructure evolution model. The defect concentration under the irradiation conditions is obtained through evolution simulation processing of the microstructure evolution model.

4. The method according to claim 1, characterized in that, The determination of the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium element concentration includes: Obtain the bulk modulus of zirconium and niobium, and determine the bulk modulus of the zirconium-niobium alloy based on the bulk modulus of zirconium, the bulk modulus of niobium, and the zirconium element concentration. A simulated elastic displacement vector is applied to the zirconium-niobium alloy; and the corresponding expansion strain, tetragonal strain, and shear strain are determined based on the simulated elastic displacement vector. The corresponding shear strain energy is determined based on the zirconium element concentration, the tetragonal strain, and the shear strain. The nonlinear elastic energy density is determined based on the bulk modulus of the zirconium-niobium alloy, the expansion strain, and the shear strain.

5. The method according to claim 1, characterized in that, The determination of the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration includes: The elastic contribution caused by elastic mismatch is determined based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration. The free energy density of the alloy system is determined based on the zircon concentration and the defect concentration under irradiation conditions. The total free energy density function of the zirconium-niobium alloy is determined based on the elastic contribution, the free energy density of the alloy system, the zirconium element concentration, and the defect concentration.

6. The method according to claim 5, characterized in that, The determination of the elastic contribution caused by elastic mismatch based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions and the defect concentration includes: Obtain the coupled strain ratio caused by alloy composition, the coupled strain ratio caused by vacancy defects, and the expansion strain corresponding to the simulated elastic displacement. The elastic contribution of the alloy composition is obtained by multiplying the coupling strain ratio caused by the alloy composition, the expansion strain and the zirconium concentration. The elastic contribution of the defect is obtained by multiplying the coupling strain ratio caused by the vacancy defect, the expansion strain, and the defect concentration. The elastic contribution caused by elastic mismatch is obtained by summing the elastic contribution of the alloy composition, the elastic contribution of the defect, and the nonlinear elastic energy density of the zirconium-niobium alloy.

7. The method according to any one of claims 1 to 6, characterized in that, The step of differentiating the total free energy density function to obtain the target stress tensor components includes: Where K is the bulk modulus of the zirconium-niobium alloy, e1 is the expansion strain corresponding to the elastic displacement vector, e2 is the tetragonal strain corresponding to the elastic displacement vector, e3 is the shear strain corresponding to the elastic displacement vector, and c is the alloy composition concentration. v Let α be the concentration of vacancy defects, α be the proportion of coupled strain introduced by the alloy composition, β be the proportion of coupled strain introduced by vacancy defects, and μ be the concentration of vacancy defects. α μ is the shear modulus of zirconium. β This represents the shear modulus of niobium.

8. A device for simulating the mechanical properties of zirconium-niobium alloys under irradiation conditions, characterized in that, include: The modeling module is used to establish a microstructure model of zirconium-niobium alloy using the phase field method, and to introduce a rate theory model of irradiation defect evolution into the microstructure model to obtain a microstructure evolution model of zirconium-niobium alloy under irradiation conditions. An evolution simulation module is used to determine the defect concentration under irradiation conditions based on the microstructure evolution model of the zirconium-niobium alloy. The mechanical simulation module is used to obtain the zirconium concentration in the zirconium-niobium alloy under irradiation conditions, and to determine the nonlinear elastic energy density of the zirconium-niobium alloy based on the zirconium concentration. The free energy determination module is used to determine the total free energy density function of the zirconium-niobium alloy based on the nonlinear elastic energy density of the zirconium-niobium alloy under irradiation conditions, the defect concentration, and the zirconium element concentration; The stress determination module is used to differentiate the total free energy density function to obtain the target stress tensor components.

9. A storage medium, characterized in that, The storage medium stores at least one executable instruction that performs the operation corresponding to the simulation method of the mechanical properties of zirconium-niobium alloy under irradiation conditions as described in any one of claims 1-7.

10. A computer device, characterized in that, It includes a processor, a memory, a communication interface, and a communication bus, wherein the processor, the memory, and the communication interface communicate with each other through the communication bus; The memory is used to store at least one executable instruction that causes the processor to perform an operation corresponding to the simulation method of the mechanical properties of zirconium-niobium alloy under irradiation conditions as described in any one of claims 1-7.

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