Calculation method for creep rate of oxide dispersion strengthened steel in irradiation environment

Abstract

The invention relates to a method for calculating the creep rate of oxide dispersion strengthened steel in an irradiation environment. The method effectively combines an irradiation-induced point defect evolution theory, an Ostwald ripening theory for coarsening oxide particles under an irradiation environment, a dislocation ring hardening theory caused by irradiation, and an oxide dispersion strengthening theory for size distribution and spatial distribution of the oxide particles. Wherein the influence of specific point defect evolution, oxide particle coarsening, dislocation ring hardening and size distribution and space distribution thereof on the performance of the oxide dispersion strengthened steel in the irradiation environment is considered, and quantitative calculation and analysis of the creep rate of the oxide dispersion strengthened steel in the irradiation environment are achieved. The threshold stress obtained by the calculation method provided by the invention is well matched with an experimental result. The related strengthening mechanism analyzed in the method has important significance for researching and analyzing the mechanical property of the oxide dispersion strengthened steel at different temperatures and irradiation time in the irradiation environment. Through the analysis method provided by the invention, the temperature of the irradiation environment is changed, the numerical value of the irradiation time is regulated and controlled, and the influence of microdefect evolution and creep rate of the oxide dispersion strengthened steel under different conditions is researched, so that theoretical guidance is provided for the design of the high-performance oxide dispersion strengthened steel.

Description

Technical Field

[0001] The present invention relates to the field of creep rate calculation under irradiation environment, and specifically to the theory of evolution of point defects induced by irradiation, the Ostwald ripening theory of coarsening of oxide particles under irradiation environment, the theory of dislocation ring hardening caused by irradiation, and the theory of oxide dispersion strengthening. A theoretical model is established to consider the evolution of microscopic defects in the matrix and the coarsening of oxide particles under irradiation environment, so as to realize the analysis of the creep rate of oxide dispersion strengthened steel under irradiation environment. Background Art

[0002] Oxide dispersion strengthened (ODS) steels are among the most promising materials for building future fourth generation nuclear fission reactors and nuclear fusion devices. They exhibit superior performance when subjected to extensive neutron irradiation and high operating temperatures compared to conventional ferritic steels. Dispersed oxide nanoparticles in the matrix produce a high density of particle-matrix interfaces, small grain size, and high dislocation density. These microstructural features can act as sinks for irradiation-induced point defects, making ODS steels perform better in resisting radiation hardening and expansion. Many studies have shown that ODS steels as reactor structural materials are stable over a range of temperatures and dose rates. However, under long irradiation conditions, oxide particles are unlikely to retain their original structure, and larger particles are significantly reduced in size after irradiation. Therefore, it is necessary to gain a deeper understanding of the microstructural evolution and the extent to which point defects generated during irradiation act as sinks, thereby affecting the creep rate of the material.

[0003] Studying the effects of neutron irradiation-induced changes on microstructure and mechanical properties is key to the successful application of ODS steel in advanced fission and fusion reactor components. The current study has verified the structure and properties of ODS steel under irradiated conditions by neutron irradiation. The nanoindentation deformation behavior of heavy ion irradiation was studied, and the results showed that the irradiated material showed a lower strain rate in the loading stage, while the strain rate of the irradiated material was higher than that of the unirradiated material in the stage after reaching the maximum load. The microstructural evolution was studied from low dose to high dose. At low dose, only a small number of dislocation loops were observed, and cavities were preferentially formed at the oxide / substrate interface. With the increase of dose, the dislocation loops evolved into dislocation networks, while cavities gradually accumulated on grain boundaries and dislocation lines. The effect of fast neutron irradiation on the tensile properties of ODS steel cladding rings for fast reactors was studied. The results showed that there was no significant change in tensile strength at irradiation temperatures below 923K, while at neutron irradiation temperatures above 1023K, the tensile strength decreased by about 20% to 33dPa at most. There are many other studies on irradiation, such as the effect of irradiation dose and dose rate on the evolution of dislocation loops and voids in Fe-9%Cr oxide dispersion strengthened steel and commercial ferritic martensitic steels HCM12A and HT9. The mechanical response of the second generation ODS Eurofer97 steel after neutron irradiation at 300°C was studied. The irradiation creep and microstructural changes of two ferritic ODS steels containing 12% and 14%Cr were investigated under uniaxial tensile stresses from 40 to 300MPa. The effects of material composition, ODS particle size and bombarding particles on irradiation creep flexibility were studied.

[0004] So far, most research projects rely on experimentally verified results, and there are relatively few theoretical studies. Therefore, understanding the mechanism of defect formation is very important for understanding the impact of ODS particles on radiation resistance and the relationship between irradiated microstructure and mechanical properties. Defect clusters may have adverse effects on structural materials. Irradiation leads to the formation of nanoscale dislocation loops, cavities and other defects, which ultimately lead to increased material hardness and brittle temperature transition. As a result, the material becomes brittle and the toughness decreases. In this study, we calculated the evolution of point defects under irradiation through rate equations and studied the coarsening of oxide particles. The effect of clusters on irradiation damage was studied in depth, the effect of dislocation loops on the creep resistance of materials, and the relationship between activation energy and creep life at different temperatures were studied. Summary of the invention

[0005] The purpose of the present invention is to propose a quantitative calculation and analysis method for the creep rate of oxide dispersion strengthened steel based on experimental data combined with the theory of point defect evolution induced by radiation, the Ostwald ripening theory of oxide particle coarsening under radiation environment, the theory of dislocation ring hardening caused by radiation, and the theory of oxide dispersion strengthening. While considering the strengthening model of oxide dispersion strengthened steel under radiation environment and realizing the quantitative analysis of the creep rate of oxide dispersion strengthened steel under radiation environment, the present invention can obtain the creep rate and threshold stress of oxide dispersion strengthened steel under specific radiation conditions, and provide guidance for the design of oxide dispersion strengthened steel under radiation environment with better performance.

[0006] The technical solution of the present invention is:

[0007] Determine the material parameters of the ODS steel used, including the relevant parameters of the element physical parameters. The material used in the present invention is Fe-13Cr-2W-0.4Ti-0.6Zr (wt%), and the material parameters are shown in Table 1:

[0008] Table 1 Physical parameters of each element.

[0009]

[0010] The generation and evolution of point defects (self-interstitial atoms, vacancies) and dislocation loops caused by ion irradiation are analyzed using a rate model. The growth and contraction of dislocation loops depend on the balance of point defects entering and leaving the dislocation loop, which corresponds to the absorption and emission of point defects. We assume that point defects are generated at a constant rate and are mobile before recombination with another point defect. The rate of change of concentration of self-interstitial atoms and vacancies is described as follows:

[0011]

[0012] Among them, C V is the interstitial atomic concentration, C I is the vacancy concentration. G0 is the irradiation flux, which is used to describe the generation of point defects caused by radiation. V and D I are the diffusion coefficients of vacancies and interstitial atoms, respectively. R is a composite term and can be expressed as:

[0013]

[0014] where d rec is the Frenkel pair radius. V at is the atomic volume. The absorber strength depends on the absorber geometry and spatial distribution. For an absorber with spherical geometry, the absorber strength is given by:

[0015] k s =4πR s Cs (3)

[0016] Where Rs is the capture radius and Cs is the concentration at the convergence point. The number density and radius of the dislocation loop during irradiation are described as follows:

[0017]

[0018] C L is the number density, r L is the radius of the dislocation loop. I and Z V is the capture efficiency.

[0019] We use Ostwald ripening to explain the phenomenon that the coarsening of large nano-oxide particles during irradiation is at the expense of the dissolution of small nano-oxide particles. The average size of the nano-oxide particles can be expressed as:

[0020]

[0021] where r is the average radius of the nano-sized oxide particles, r0 is the initial radius of the nano-sized oxide particles, γ is the surface free energy of the ODS interface, D is the diffusion coefficient, and C ∞ is the limiting solubility of ODS interface, V m is the molar volume, t is the time, R is the universal gas constant, and T is the temperature. An approximation is used in the derivation of the formula, namely C P -C r ≈C P -C ∞ , here C r is the solubility at the interface of oxide particles with radius of curvature r.

[0022] Considering that the irradiation dose is proportional to the irradiation time, the average size of the oxide particles is expressed as follows:

[0023]

[0024] where k d is a constant proportional to the diffusion coefficient. d is fitted as a function of temperature k d =0.031T-23.612. φ is the total irradiation dose obtained by multiplying the irradiation rate and time, expressed as φ=G0t.

[0025] We use the FKH model to calculate the radiation-induced dislocation loop hardening. This model provides a mechanism to explain the radiation-induced material hardening phenomenon by considering the hindering effect of defects on dislocation motion. Its expression is:

[0026]

[0027] Where M is the Taylor factor, G is the shear modulus, and b is the Burgers vector of the dislocation. d and N are the defect size and defect number density, respectively.

[0028] Oxide dispersion strengthening is controlled by two mechanisms: the cross-cut strengthening mechanism τ cutting 、Orowan bypasses the reinforcement mechanism τ orowan and the climbing mechanism τ climb The critical shear stress model of oxide particles is expressed as:

[0029]

[0030] τ=min(τ climb ,τ orowan ,τ cutting ) (9)

[0031] Among them, A and B are constant parameters, D is the spatial particle diameter, L is the particle distance, r a is the dislocation core radius, assumed to be the magnitude of the Burgers vector. ε is the misfit strain, calculated as ε = b / 4r, where r is the radius of the oxide particle, which can be obtained experimentally. τ represents the minimum stress of the three interaction mechanisms.

[0032] As attached Figure 1 Given τ cutting and τ Orowan As shown in the curve, there is a critical size r for the transition of the interaction mechanism between dislocations and oxide particles. Critical When r≤r Critical When r>r Critical When the oxide dispersion strengthening is Orowan bypass strengthening mechanism. Figure 2 (a) and (b) show that the dislocation is r≤r Critical When the oxide particles are cut, the cutting strengthening mechanism is triggered; when the dislocation is r>r Critical When the oxide particles are cut, the Orowan bypass strengthening mechanism is triggered, which well explains the spatial distribution of the oxide particles. Figure 2 As shown in (a), the region AB triggers the cutting strengthening mechanism, and the region OA triggers the Orowan bypass strengthening mechanism. The triggering probability of different oxide diffusion strengthening mechanisms can be calculated by the ratio of the distance from the center of the interaction surface A to point B to the radius r of the spherical oxide particle. It can be seen that for the cutting strengthening mechanism region, the triggering probability is:

[0033]

[0034] For Orowan bypassing the reinforcement mechanism, the probability of triggering is:

[0035] p1(r)=1-p2(r) (11)

[0036] For the climb strengthening mechanism, the probability of triggering p0 is obtained by comparing the applied shear stress with the critical shear stress (CRSS).

[0037] The differential quadrature method is used to recalculate the oxide diffusion strengthening mechanism considering the spatial distribution, which can be expressed as:

[0038]

[0039] where τ climb (r), τ cutting (r) and τ orowan (r) represents the critical decomposition shear stress of the climbing mechanism, cutting mechanism and orowan mechanism.

[0040] The size distribution takes into account the different average sizes of individual oxide particles distributed in the matrix. The numerical values ​​of these average sizes show a normal distribution law, and the probability formula is:

[0041]

[0042] where μ and σ are the geometric mean and geometric standard deviation of ln(r).

[0043] In summary, by coupling the above strengthening mechanism formulas (irradiation-induced point defect strengthening, oxide particle coarsening mechanism under irradiation environment, irradiation-induced dislocation ring hardening mechanism, and oxide dispersion strengthening mechanism considering spatial distribution and size distribution), a new threshold stress model for oxide dispersion-strengthened steel under irradiation environment can be obtained:

[0044]

[0045] where r m is the maximum size of the particle, r c is the critical size of the particle, and f(r) is the normal distribution function.

[0046] The coupled threshold stress can be regarded as the coupled creep resistance of defects, dislocation loops and oxide particles in the irradiated environment. The unified creep rate equation considering the irradiation-induced point defect evolution theory, the Ostwald ripening theory of oxide particle coarsening in the irradiated environment, the irradiation-induced dislocation loop hardening theory, and the oxide dispersion strengthening theory is expressed as:

[0047]

[0048] τ L is the dislocation line tension, τL =0.5Gb 2 .c L is the strain hardening parameter, c L =10. α is the Taylor constant that depends on the lattice structure, α = 0.33. N is the dislocation mobility, which depends on the applied stress, the threshold stress, and the temperature. The dislocation mobility is described by the following formula:

[0049]

[0050] D 0sd is the pre-exponential factor, k B is the Boltzmann constant, Q sd is the self-diffusion activation energy, R g is the gas constant, R m is the tensile strength.

[0051] Finally, the calculation results are processed and analyzed to obtain a comparison between the model and the experimental data, and to predict the trend of creep rate and creep strain changing with irradiation time at different temperatures.

[0052] Beneficial Effects

[0053] The present invention proposes a method for calculating the creep rate of oxide dispersion strengthened steel under irradiation environment, which takes into account the theory of point defect evolution induced by irradiation, the Ostwald ripening theory of coarsening of oxide particles under irradiation environment, the dislocation ring hardening theory caused by irradiation, and the oxide dispersion strengthening theory of oxide particle size distribution and spatial distribution to realize the analysis of the creep rate of oxide dispersion strengthened steel under irradiation environment over time. The method is based on a solid theoretical foundation, a clear modeling process and a clear physical meaning.

[0054] The present invention takes Fe-13Cr-2W-0.4Ti-0.6Zr (wt%) oxide dispersion strengthened steel as an example, selects Y2O3 as the added oxide particles, adopts the relevant data measured in the experiment, and realizes the calculation of the qualitative and quantitative relationship of the creep rate of the alloy through the strength theory model in the calculation method. The result is in good agreement with the experiment, thereby obtaining the evolution curves of the creep rate and creep strain at different temperatures as the irradiation application time changes, providing theoretical guidance for analyzing the defect evolution and creep resistance of oxide dispersion strengthened steel under irradiation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is the corresponding oxide dispersion strengthening mechanism under different oxide particle radius.

[0056] Figure 2 Schematic diagram of dislocation bypassing oxide particles. (a) Spherical oxide particles; (b) Dislocation shearing or bypassing oxide particles.

[0057] Figure 3 is a comparison of experimental data with the current model.

[0058] Figure 4 (a) The curve of creep strain of oxide dispersion strengthened steel at different temperatures in irradiation environment as a function of irradiation time; (b) The curve of creep rate of oxide dispersion strengthened steel at different temperatures in irradiation environment as a function of irradiation time; (c) The curve of radius of oxide particles at different temperatures in irradiation environment as a function of irradiation time; (d) The curve of radius of dislocation loop in oxide dispersion strengthened steel matrix at different temperatures as a function of irradiation time. DETAILED DESCRIPTION

[0059] The following is combined with Figure 1 The corresponding oxide dispersion strengthening mechanism and attachment properties under different oxide particle radii are given. Figure 2 A schematic diagram of the interaction between dislocations and oxide particles is given, and a creep rate model for oxide dispersion strengthened steel under irradiation is provided. The theoretical model and specific examples of four effects, namely, the interaction mechanism between dislocations and oxide particles, the theory of irradiation-induced point defects, the Ostwald ripening theory of coarsening of oxide particles under irradiation environment, and the theory of irradiation-induced dislocation ring hardening, are considered. The technical scheme is further elaborated. The present invention is not limited to the following examples, and all design ideas utilizing the present invention fall within the protection scope of the present invention.

[0060] Oxide dispersion strengthening refers to adding a certain amount of thermodynamically stable oxides to high-temperature alloys, so that they are dispersed in the matrix to form an oxide dispersion phase that is insoluble in the matrix; the new phase hinders the movement of dislocations in the alloy and strengthens the mechanical properties of the material. Irradiation-induced point defect evolution is the phenomenon that atoms in the metal matrix obtain energy higher than the delocalization threshold energy during irradiation and leave the original lattice point position. These point defects migrate, aggregate, recombine, and annihilate at a certain temperature, forming a variety of mesoscopic defect clusters that affect the microstructure of the material and further affect its macroscopic properties; oxide particles will coarsen during irradiation, and Oswald ripening theory explains the phenomenon that the coarsening of large nano-oxide particles during irradiation is at the expense of the dissolution of small nano-oxide particles; dislocation loops in the matrix under irradiation will significantly hinder the movement of dislocations and thus seriously hinder the movement of dislocations, resulting in an increase in the hardness and yield strength of the material.

[0061] Specific steps: Collect experimental data of Fe-13Cr-2W-0.4Ti-0.6Zr (wt%) with Y2O3 as added oxide particles, and obtain the material parameters involved in the method of the present invention as shown in Table 2.

[0062] Table 2 Parameters of various materials

[0063]

[0064]

[0065] By fitting the relevant experimental data of oxide dispersion strengthened steel under irradiation environment, the attached Figure 3 The threshold stress experimental results and the current model are compared. Figure 3 It can be seen that after considering the various coupling enhancement theories mentioned in this paper, the calculation accuracy of the current model is relatively high.

[0066] Attached Figure 4 (a, b) is the applied stress σ APP =100MPa, the creep strain and creep rate in different temperature environments are predicted as a function of irradiation time. Figure 4 (a) It can be seen that temperature has a considerable effect on the creep strain of oxide dispersion strengthened steel in irradiated environment. At 500℃, the lowest creep strain is 1.2%, while at 800℃, the highest creep strain reaches 3.1%, which is about twice as much. As the ambient temperature increases, the creep strain increases accordingly. Figure 4 In (b), creep strain and creep rate show the same trend, both gradually increasing with the increase of irradiation time. Under different irradiation times, creep strain and creep rate have the same response trend to temperature change, but the change rate is different with the increase of irradiation time. However, at the same temperature, the creep rate and creep strain change less with the increase of irradiation time.

[0067] Attached Figure 4 (c, d) show the evolution of oxide particle radius and dislocation ring radius with irradiation time at different temperatures. Figure 4 (a) shows that for oxide particles, their radius increases linearly with time. Their coarsening rate is a function of temperature; the higher the temperature, the greater the coarsening rate. Figure 4 (d) shows that the radius of the dislocation loop increases rapidly before 200 h of irradiation and reaches a maximum value of 8.4 nm around 400 h.

[0068] Therefore, the present invention has good accuracy in analyzing the creep rate of oxide dispersion strengthened steel under irradiation environment, and can effectively predict the influence of irradiation time on the creep rate of alloy under different temperatures and applied stresses, providing a reliable theoretical model for analyzing the micro defect evolution and creep resistance of oxide dispersion strengthened steel under irradiation environment.

Claims

1. A method for calculating the creep rate of oxide dispersion strengthened steel under irradiation environment, combining the theory of point defect evolution induced by irradiation, the Ostwald ripening theory of coarsening of oxide particles under irradiation environment, the theory of dislocation loop hardening induced by irradiation, and the oxide dispersion strengthening theory of oxide particle size distribution and spatial distribution and the creep rate analysis model, characterized in that: The strengthening effects of oxide particles, defect evolution and dislocation loops in oxide dispersion strengthened steel under irradiation environment are considered. The defect evolution and dislocation rings in the material are generated when the matrix is ​​in an irradiated environment, and the oxide particles are added during the processing. By considering the strengthening model of oxide dispersion strengthened steel in an irradiated environment with multiple influencing mechanisms coupled, the creep rate of oxide dispersion strengthened steel in an irradiated environment can be quantitatively analyzed. At the same time, the application time of the irradiation environment and the irradiation dose rate can be controlled to obtain the creep rate and threshold stress of oxide dispersion strengthened steel in an irradiated environment under specific conditions, providing guidance for the design of oxide dispersion strengthened steels with better performance.

2. The method for calculating creep rate of oxide dispersion strengthened steel under irradiation environment according to claim 1, characterized in that The inherent parameters of the elements in the material and the existing experimental data are used to accurately calculate the creep rate and threshold stress changes with irradiation at different temperatures for the defect evolution and strength and creep rate models involved.

3. According to the method of use according to any one of claims 1-2, the specific steps of the processing method are as follows: Determine the basic material parameters required in the model and collect relevant physical parameters of related materials. Calculate the strength values ​​contributed by each strengthening mechanism including oxide diffusion strengthening theory, radiation-induced point defect evolution theory, Ostwald ripening theory of oxide particle coarsening under irradiation environment, and radiation-induced dislocation loop hardening theory. By coupling the above strengthening mechanisms, the threshold stress of oxide dispersion-strengthened steel in irradiated environment can be obtained: where τ cutting is the cutting strengthening mechanism, τ orowan Orowan bypasses the reinforcement mechanism, τ climb is the climbing mechanism, Δσ y is the dislocation loop hardening, and M is the Taylor constant. The coupled threshold stress can be regarded as the coupled creep resistance of defects, dislocation loops and oxide particles in the irradiated environment. The unified creep rate equation considering the irradiation-induced point defect evolution theory, the Ostwald ripening theory of oxide particle coarsening in the irradiated environment, the irradiation-induced dislocation loop hardening theory, and the oxide dispersion strengthening theory is expressed as: τ L is the dislocation line tension, τ L =0.5Gb 2 .c L is the strain hardening parameter, c L = 10. α is the Taylor constant that depends on the lattice structure, α = 0.

33. N is the dislocation mobility, described by the following formula: D 0sd is the pre-exponential factor, k B is the Boltzmann constant, Q sd is the self-diffusion activation energy, R g is the gas constant, R m is the tensile strength. Analyze and process theoretical calculation results.

4. The specific steps according to claim 3, characterized in that: Determine effective material parameters; the material used in the present invention is Fe-13Cr-2W-0.4Ti-0.6Zr (wt%) with oxide particles of Y2O3, and the material parameters are shown in Table 1. Table 1 Physical parameters of each element.

5. According to claim 3, it is characterized in that the oxide particles also have a strengthening effect on the mechanical properties of the material by hindering the movement of dislocations, and the main mechanism of oxide particle strengthening is the cutting strengthening mechanism τ cutting 、Orowan bypasses the reinforcement mechanism τ orowan and the climbing mechanism τ climb . Their expressions are: τ=min(τ climb ,t orowan ,t cutting ) in, A and B are constant parameters, D is the spatial particle diameter, L is the particle distance, r a is the dislocation core radius, assumed to be the magnitude of the Burgers vector. ε is the misfit strain, calculated as ε = b / 4r, where r is the radius of the oxide particle, which can be obtained experimentally. τ represents the minimum stress of the three interaction mechanisms. There is a critical size r for the transition of the interaction mechanism between dislocations and oxide particles. Critical When r≤r Critical When r>r Critical When the oxide diffusion strengthening is the Orowan bypass strengthening mechanism, and the dislocation is r≤r Critical When the oxide particles are cut, the cutting strengthening mechanism is triggered; when the dislocation is r>r Critical When the oxide particles are cut, the Orowan bypass strengthening mechanism is triggered; the formula considering the spatial distribution of each oxide diffusion strengthening component can be written as: For cutting through the strengthening mechanism area, the probability of triggering is: For Orowan bypassing the reinforcement mechanism, the probability of triggering is: p1(r)=1-p2(r) For the climb strengthening mechanism, the probability of triggering p0 is obtained by comparing the applied shear stress with the critical shear stress (CRSS). In oxide dispersion strengthened Fe-13Cr-2W-0.4Ti-0.6Zr (wt%) steel, the size distribution of oxide particles is normal distribution, and the probability formula is: When r≤r Critical When r>r Critical When , oxide dispersion strengthening is the Orowan bypass strengthening mechanism. Through calculus, the oxide particle size distribution radius area is divided into n parts, and the oxide dispersion strengthening formula of size distribution can be expressed as:

6. According to claim 3, the defect evolution in the irradiation environment is calculated, characterized in that: It is assumed that point defects are generated at a constant rate and are mobile before recombination with another point defect. The concentration change rate of self-interstitial atoms and vacancies is described as follows: Among them, C V is the interstitial atomic concentration, C I is the vacancy concentration. G0 is the irradiation flux, which is used to describe the generation of point defects caused by radiation. V and D I are the diffusion coefficients of vacancies and interstitial atoms, respectively. R is a composite term and can be expressed as: where d rec is the Frenkel pair radius. V at is the atomic volume. The absorber strength depends on the absorber geometry and spatial distribution. For an absorber with spherical geometry, the absorber strength is given by: k s =4πR s C s Where Rs is the capture radius and Cs is the concentration at the convergence point. The number density and radius of dislocation loops during irradiation are described as follows: C L is the number density, r L is the radius of the dislocation loop. I and Z V is the capture efficiency.

7. The method of calculating the coarsening of oxide particles in an irradiation environment according to claim 3, characterized in that the Oswald ripening is used to explain the phenomenon that the coarsening of large nano-oxide particles during irradiation is at the expense of the dissolution of small nano-oxide particles. The average size of the nano-oxide particles can be expressed as: in, r is the average radius of the nano-sized oxide particles, r0 is the initial radius of the nano-sized oxide particles, γ is the surface free energy of the ODS interface, D is the diffusion coefficient, C ∞ is the limiting solubility of ODS interface, V m is the molar volume, t is the time, R is the universal gas constant, and T is the temperature. An approximation is used in the derivation of the formula, namely C P -C r ≈C P -C ∞ , here C r is the solubility at the interface of oxide particles with radius of curvature r. Considering that the irradiation dose is proportional to the irradiation time, the average size of the oxide particles is expressed as follows: where k d is a constant proportional to the diffusion coefficient. d is fitted as a function of temperature k d =0.031T-23.

612. v is the total irradiation dose obtained by multiplying the irradiation rate and time, expressed as φ=G0t.

8. According to claim 3, the hardening value of the dislocation loop in the irradiation environment is calculated. The FKH model is used to calculate the radiation-induced dislocation loop hardening, which provides a mechanism to explain the radiation-induced material hardening phenomenon by considering the hindering effect of defects on dislocation movement. Its expression is: in, M is the Taylor factor, G is the shear modulus, and b is the Burgers vector of the dislocation. d and N are the defect size and defect number density, respectively.

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