A method for determining the radiation hardening of a VVER reactor pressure vessel

Abstract

The present invention provides a method for determining the radiation hardening of a VVER type reactor pressure vessel, comprising: S1, modifying a first dispersion strengthening model to a second dispersion strengthening model; wherein the first dispersion strengthening model characterizes the relationship between the yield stress increment of a material and a first parameter, the number of defects and the defect size, and the second dispersion strengthening model characterizes the relationship between the yield stress increment of the material and a second parameter and an irradiation defect structure function; the first parameter is a function of the defect size, and the second parameter is independent of the defect size; the irradiation defect structure function is a function of the number of defects and the defect size; S2, determining a second parameter of the second dispersion strengthening model; S3, obtaining the relationship between the irradiation defect structure function and the neutron injection; S4, determining the relationship between the yield stress increment of the material and the neutron injection according to the relationship between the irradiation defect structure function and the neutron injection and the second dispersion strengthening model.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear reaction technology, and more specifically, relates to a method for determining the radiation hardening of a VVER type reactor pressure vessel. Background Art

[0002] The use of nuclear energy to generate electricity is one of the main ways to solve the energy problem of mankind. The mechanical properties of commonly used metal structural materials will change after being exposed to radiation (hereinafter referred to as "irradiation"), and the materials will harden and become brittle, which is called radiation hardening and radiation embrittlement. Once the material hardens and / or becomes brittle to a certain extent, the reactor vessel subjected to high temperature and high pressure will rupture instantly, resulting in catastrophic consequences. Therefore, this field monitors the performance changes of the materials of the reactor vessel under irradiation, so as to simulate the development process of the radiation hardening of the material, and estimate the life of the reactor vessel based on the development process, so as to arrange countermeasures in advance. However, the relevant technology cannot accurately simulate the radiation hardening of metal structural materials. Summary of the invention

[0003] In view of this, the present invention provides a method for determining the radiation hardening of a VVER type reactor pressure vessel to solve the technical problem of how to accurately simulate the radiation hardening of a VVER type reactor pressure vessel.

[0004] The technical solution of the present invention is achieved in this way:

[0005] An embodiment of the present invention provides a method for determining radiation hardening of a VVER type reactor pressure vessel, comprising:

[0006] S1. Modifying the first dispersion strengthening model into a second dispersion strengthening model; wherein the first dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the first parameter, the number of defects and the defect size, and the second dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the second parameter and the irradiation defect structure function; the first parameter is a function of the defect size, and the second parameter is independent of the defect size; the irradiation defect structure function is a function of the defect number and defect size;

[0007] S2. determining the second parameter of the second dispersion enhancement model;

[0008] S3, obtaining the relationship between the irradiation defect structure function and the neutron fluence;

[0009] S4. Determine the relationship between the yield stress increment and the neutron fluence of the material according to the relationship between the irradiation defect structure function and the neutron fluence and the second dispersion strengthening model.

[0010] In some embodiments, step S1 includes:

[0011] S11, correcting the relationship between the yield stress increment and the critical shear stress increment;

[0012] S12. Determine the second dispersion strengthening model according to the relationship between the critical shear stress increment and the irradiation defect structure function.

[0013] In some embodiments, step S11 includes:

[0014] S111. Based on the Schmid law of single crystal tensile experiment, the relationship between the yield stress increment and the critical shear stress increment is obtained:

[0015] Δσ y =MΔτ (1)

[0016] Among them, Δσ y is the yield stress increment, M is the Taylor factor, and Δτ is the critical shear stress increment;

[0017] S112. According to the principle of free random distribution of defects, the relationship between the yield stress increment and the critical shear stress increment is corrected to:

[0018] Δσ y =0.85α0×MΔτ (2)

[0019] Among them, 0.85 is the defect free random distribution coefficient, and α0 is the second parameter.

[0020] In some embodiments, step S12 includes:

[0021] S121, obtaining the relationship between the critical shear stress increment, dislocation curvature, and defect spacing:

[0022]

[0023] where T(θ) is the depinning force of the dislocation fragment, <f>is the value of mixed dislocation, (L-2r) is the defect spacing, G is the shear modulus, and b is the Burgers vector;

[0024] S122. Determine the relationship between the yield stress increment, the second parameter, and the irradiation defect structure function according to the relationship between the defect spacing, the defect number, and the defect size; wherein the relationship between the defect spacing, the defect number, and the defect size is:

[0025]

[0026] L is the distance between the two defect centroids, r is the defect radius, N is the number of defects, and d is the defect size;

[0027] The relationship between the yield stress increment, the second parameter and the irradiation defect structure function is:

[0028]

[0029] Where f(N×d) is the irradiation defect structure function,

[0030] In some embodiments, the hardening term determining the irradiation defects includes dislocation loops and solute-rich clusters, and the second parameter α0 includes the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 ; After step S122, including:

[0031] S123, determining the yield stress increment Δσ y With the dislocation loop pinning factor α 01 , the solute-rich cluster pinning factor α 02 And the relationship between the irradiation defect structure function f(N×d), the second diffusion strengthening model is obtained:

[0032] Δσ y =0.517×Gb×[α 01 ×f(N1×d1)+α 02 ×f(N2×d2)] (7)

[0033] Among them, f(N1×d1) is the irradiation defect structure function of the dislocation loop, and f(N2×d2) is the irradiation defect structure function of the solute-rich cluster.

[0034] In some embodiments, step S2 includes:

[0035] The irradiation defect structure function f(N1×d1) of dislocation loops and the irradiation defect structure function f(N2×d2) of solute-rich clusters under multiple neutron fluences are compared with the yield stress increment Δσ. y Substituting into formula (7), we can obtain the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 .

[0036] In some embodiments, step S3 includes:

[0037] S31, according to the cluster dynamics method, the first relationship N(Φ A ) and the second relation d(Φ A ), where the first relation represents the relationship between the number of defects N in the material and the neutron injection Φ A The second relationship characterizes the relationship between the defect size d in the material and the neutron injection Φ A relationship;

[0038] S32, the first relational expression N(Φ A ) and the second relation d(Φ A ) is substituted into the irradiation defect structure function to obtain the irradiation defect structure function f(N(Φ A ),d(Φ A )) and the neutron fluence Φ A relationship.

[0039] In some embodiments, step S4 includes:

[0040] S41, the irradiation defect structure function f(N(Φ A ),d(Φ A )) and the neutron fluence Φ A Substitute the relationship into formula (7);

[0041] S42, the relationship between the yield stress increment and the neutron injection is obtained as follows:

[0042]

[0043] Among them, N1(Φ A ) is the number of defects in the dislocation loop, d1(Φ A ) is the defect size of the dislocation loop, N2(Φ A ) is the number of defects in the solute-rich cluster, d2(Φ A ) is the defect size of the solute-rich cluster.

[0044] In some embodiments, step S3 further includes:

[0045] Using multiple sets of first experimental data to calibrate the first relationship; wherein the first experimental data are neutron injection and corresponding defect quantity;

[0046] and / or,

[0047] The second relationship is corrected using multiple sets of second experimental data, wherein the second experimental data are neutron injection and corresponding defect size.

[0048] In some embodiments, after step S123, the method further includes:

[0049] Using multiple sets of third experimental data to calibrate the dislocation loop pinning factor α in the second dispersion strengthening model 01 and the solute-rich cluster pinning factor α 02 , wherein the third experimental data are the corresponding data of the irradiation defect structure function of the dislocation loop, the irradiation defect structure function of the solute-rich cluster and the yield stress increment.

[0050] An embodiment of the present invention provides a method for determining the radiation hardening of a VVER type reactor pressure vessel, which modifies a first dispersion strengthening model into a second dispersion strengthening model; wherein the first dispersion strengthening model characterizes the relationship between the yield stress increment of the material and a first parameter, the number of defects and the defect size, and the second dispersion strengthening model characterizes the relationship between the yield stress increment of the material and a second parameter and an irradiation defect structure function; the first parameter is a function of the defect size, and the second parameter is independent of the defect size; the irradiation defect structure function is a function of the number of defects and the defect size; determining the second parameter of the second dispersion strengthening model; obtaining the relationship between the irradiation defect structure function and the neutron injection; determining the relationship between the yield stress increment of the material and the neutron injection based on the relationship between the irradiation defect structure function and the neutron injection and the second dispersion strengthening model. The embodiment of the present invention considers the influence of irradiation defects on the first parameter on the basis of the first dispersion strengthening model, corrects the first dispersion strengthening model to obtain the second dispersion strengthening model, determines the relationship between the yield stress increment of the material and the neutron injection according to the relationship between the irradiation defect structure function and the neutron injection and the second dispersion strengthening model, and can accurately determine the change trend of the yield stress increment with the neutron injection. The yield stress increment reflects the change of the hardening degree of the material, and the neutron injection reflects the irradiation time and increases with the increase of the irradiation time. Therefore, the embodiment of the present invention can accurately determine the hardening process of the material of the reactor vessel with irradiation, thereby improving the accuracy of determining the life of the reactor vessel. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a first embodiment of the present invention;

[0052] Figure 2 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a second embodiment of the present invention;

[0053] Figure 3 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a third embodiment of the present invention;

[0054] Figure 4 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a fourth embodiment of the present invention;

[0055] Figure 5 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a fifth embodiment of the present invention;

[0056] Figure 6 A schematic diagram of a defect structure function according to an embodiment of the present invention showing a variation trend of the defect structure function with neutron injection;

[0057] Figure 7 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to a sixth embodiment of the present invention;

[0058] Figure 8 A flowchart of the steps of a method for determining radiation hardening of a VVER type reactor pressure vessel according to an embodiment of the present invention;

[0059] Fig. 9 It is a schematic diagram of the variation trend of the yield strength increment of the VVER reactor pressure vessel according to the seventh embodiment of the present invention with the neutron injection. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0061] The various specific technical features described in the specific embodiments can be combined in any suitable manner without contradiction, for example, different embodiments and technical solutions can be formed by combining different specific technical features. In order to avoid unnecessary repetition, the various possible combinations of the specific technical features in the present invention will not be described separately.

[0062] It should be noted that the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element. "Multiple" means greater than or equal to two.

[0063] The embodiment of the present invention provides a method for determining the radiation hardening of a VVER type reactor pressure vessel, wherein the VVER type reactor pressure vessel adopts Cr-Mo-V heat-resistant low alloy steel material. The VVER type reactor refers to a water-water high energy reactor (VVER, Russian: Водо-водянойэнергетическийреактор, English transliteration: Vodo-VodyanoiEnergetichesky Reactor; English: Water-Water Energetic Reactor). Neutron irradiation of the reactor will cause radiation hardening and embrittlement of the pressure vessel material, cause changes in the material microstructure, reduce its mechanical properties, and affect the operating life of the pressure vessel and the safety of the reactor.

[0064] The following is an explanation of the principles of radiation hardening and embrittlement:

[0065] The changes in the mechanical properties of materials at a macroscopic level are related to the changes in the microstructure caused by irradiation. A large number of high-energy particles produced by nuclear reactions collide with the lattice atoms of the structural material. The lattice atoms absorb the kinetic energy of the high-energy particles and further collide with other lattice atoms in a cascade, producing a large number of supersaturated vacancies and interstitial atoms. Most of the vacancies and interstitial atoms produced by the cascade reaction quickly recombine, but some will still aggregate inside the crystal to form gaps, vacancy clusters or diffuse to the surface and grain boundaries, and then gradually evolve to form defects such as dislocation rings, stacking fault tetrahedrons and voids. High-energy particle bombardment of atoms will also produce transmutation elements. Smaller transmutation elements such as hydrogen and helium are easy to combine with vacancies, reducing the difficulty of nucleation of pores and accelerating the formation of pores. In addition, impurity atoms in the material rely on cascade reactions to accelerate diffusion and aggregation, leading to the formation of precipitated phases. Dislocations are the main carriers of plastic deformation of metal materials. Dislocations are microscopic defects inside the material. From a geometric point of view, dislocations are a kind of line defects and can be regarded as the boundary between the slipped part and the non-slipped part in the crystal. Their existence has a great influence on the physical properties of the material, especially the mechanical properties. The defects caused by irradiation hinder the movement of dislocations and are considered to be the main reason for the radiation hardening effect. The radiation embrittlement mechanism of reactor pressure vessel materials is divided into strengthening mechanism and non-strengthening mechanism. Under neutron irradiation, irradiation defects are formed inside the material. Elements such as copper, nickel, manganese, and silicon form radiation-induced clusters under irradiation, which leads to the strengthening and hardening of the material. Phosphorus and other impurity elements form segregation at dislocation lines, grain boundaries or phase boundaries, resulting in reduced strength of grain boundaries and phase boundaries.

[0066] like Figure 1 As shown, the present invention provides a method for determining the radiation hardening of a VVER type reactor pressure vessel, the method comprising:

[0067] S1. Modify the first dispersion strengthening model to the second dispersion strengthening model; wherein, the first dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the first parameter, the number of defects and the defect size, and the second dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the second parameter and the irradiation defect structure function; the first parameter is a function of the defect size, and the second parameter is independent of the defect size; the irradiation defect structure function is a function of the number of defects and the defect size; it should be noted that dispersion strengthening means that the metal matrix (metal or solid solution) contains highly dispersed second phase particles to achieve the purpose of improving strength. In dispersion strengthened materials, the dispersed phase is an obstacle to the movement of dislocation lines, and dislocation lines require greater stress to overcome the obstacle and move forward, so the strength of dispersion strengthened materials is high.

[0068] The first dispersion strengthening model in the embodiment of the present invention describes the yield stress increment Δσ of the material y The relationship between the number of defects N and the defect size d in the material, where the first dispersion strengthening model is an empirical formula of the dispersion strengthening theory, specifically:

[0069]

[0070] Among them, Δσ y represents the yield stress increment, α is the first parameter, which can be understood as the first pinning factor used to describe the dislocation barrier, M is the Taylor factor, G is the shear modulus, b represents the Burgers vector, N is the number of defects, and d is the defect size. In the process of increasing irradiation dose, the number and size of defects gradually increase, and the defects become more dense. In the first dispersion strengthening model, the first parameter α is only a function of the defect size.

[0071] S2, determining a second parameter of a second diffusion enhancement model;

[0072] S3, obtaining the relationship between the irradiation defect structure function and the neutron fluence;

[0073] S4. According to the relationship between the irradiation defect structure function and the neutron injection and the second diffusion strengthening model, the relationship between the yield stress increment and the neutron injection of the material is determined.

[0074] The embodiment of the present invention considers the influence of irradiation defects on the first parameter on the basis of the first dispersion strengthening model, corrects the first dispersion strengthening model to obtain the second dispersion strengthening model, determines the relationship between the yield stress increment and the neutron injection of the material according to the relationship between the irradiation defect structure function and the neutron injection and the second dispersion strengthening model, and can accurately determine the change trend of the yield stress increment with the neutron injection. The yield stress increment reflects the change of the hardening degree of the material, and the neutron injection reflects the irradiation time. The neutron injection increases with the increase of the irradiation time. Therefore, the embodiment of the present invention can accurately determine the hardening process of the material of the reactor vessel with irradiation, thereby improving the accuracy of determining the life of the reactor vessel.

[0075] In some embodiments, Figure 2 As shown, step S1 includes:

[0076] S11, the relationship between the modified yield stress increment and the critical shear stress increment;

[0077] S12. Determine a second diffusion strengthening model based on the relationship between the critical shear stress increment and the irradiation defect structure function.

[0078] The second dispersion strengthening model can be determined by correcting the relationship between the yield stress increment and the critical shear stress increment and according to the relationship between the critical shear stress increment and the irradiation defect structure function.

[0079] In some embodiments, Figure 3 As shown, step S11 includes:

[0080] S111. Based on the Schmid law of single crystal tensile test, the relationship between yield stress increment and critical shear stress increment is obtained:

[0081] Δσ y =MΔτ (1)

[0082] Among them, Δσ y is the yield stress increment, M is the Taylor factor, and Δτ is the critical shear stress increment;

[0083] It should be noted that materials will deform under the action of force. The area that satisfies Hooke's law is usually called the elastic deformation area, and the area that does not satisfy Hooke's law and the process is irreversible is called the plastic deformation area. Entering the plastic deformation area from the elastic deformation area is called yield. Its turning point is called the yield point. The stress at this point is called the yield stress or critical shear stress. Critical shear stress (Critical resolved shear stress), referred to as CRSS, refers to the minimum shear stress required to activate the slip system, which is called the critical shear stress. Its numerical value reflects the ability of the material to resist plastic deformation to a certain extent. Among them, the slip system represents a combination of a slip plane in the crystal and a slip direction on the plane. Schmid's law gives the relationship between external load, crystal orientation and critical shear stress. In the embodiment of the present invention, according to the Schmid's law of single crystal tensile experiment, the yield stress describes the macroscopic physical quantity of the material, and the critical shear stress describes the microscopic physical quantity of the material. The yield stress increment Δσ of the material is derived based on the correlation of the slip system. y The corresponding relationship with the critical shear stress increment Δτ.

[0084] S112. According to the principle of free random distribution of defects, the relationship between the yield stress increment and the critical shear stress increment is corrected to:

[0085] Δσ y =0.85α0×MΔτ (2)

[0086] Among them, 0.85 is the defect free random distribution coefficient, and α0 is the second parameter.

[0087] The second parameter α0 in the embodiment of the present invention is a second pinning factor that is independent of the defect size.

[0088] In some embodiments, Figure 4 As shown, step S12 includes:

[0089] S121. Obtain the relationship between the critical shear stress increment Δτ and the dislocation curvature θ and the defect spacing (L-2r):

[0090]

[0091] Where T(θ) is the depinning force of the dislocation fragment, which represents the critical force value at which the breakaway defect has a pinning effect on the vortex line; <f>is the value of mixed dislocation, (L-2r) is the defect spacing, G is the shear modulus, b is the Burgers vector, L is the distance between the two defect centroids, and r is the defect radius; the shear stress increment is related to the curvature of the dislocation and the defect spacing;

[0092] S122. Determine the yield stress increment Δσ based on the relationship between the defect spacing (L-2r) and the number of defects N and the defect size d. y The relationship between the second parameter α0 and the irradiation defect structure function f(N×d); wherein the relationship between the defect spacing (L-2r) and the defect number N and defect size d is:

[0093]

[0094] L is the distance between the two defect centroids, r is the defect radius, N is the number of defects, and d is the defect size;

[0095] According to formulas (1)-(4), the yield stress increment Δσ can be obtained y The relationship between the second parameter α0 and the irradiation defect structure function f(N×d):

[0096]

[0097] Where f(N×d) is the irradiation defect structure function, F represents the orientation factor of the dislocation, for screw dislocation F = 1, for edge dislocation F = 1.5, the formula <f>represents a mixed dislocation value between 1 and 1.5; <f>=1.25;

[0098]

[0099] In the embodiment of the present invention, based on the influence of irradiation defects on the yield strength increment, the influence of irradiation dose on the pinning factor is considered on the basis of the diffusion strengthening model, the first diffusion strengthening model is corrected and improved, and the second diffusion strengthening model is obtained.

[0100] In some embodiments, the hardening items for determining irradiation defects include dislocation rings and solute-rich clusters. It should be noted that under neutron irradiation, high-energy neutrons collide with lattice atoms, and the impacted lattice atoms undergo atomic displacement and cascade dislocation, resulting in lattice vacancies and interstitial atoms. With the development of the cascade, a space with high-density vacancies is formed, which is surrounded by a region of interstitial atoms with a higher density, and exists in the material in the form of point defects and point defect clusters. These point defects will cause an increase in the diffusion coefficients of solute atoms (silicon, manganese, nickel, etc.) and impurity atoms (copper, phosphorus, etc.) in the material, causing the migration of the above atoms, resulting in accelerated precipitation inside the material from a thermodynamic point of view; at the same time, the coupling between the generation and annihilation of point defects and the migration of solute atoms under irradiation causes the solute atoms and impurity atoms to form segregation and precipitation inside the material from a kinetic point of view. The defects formed in the material of the VVER reactor pressure vessel after neutron irradiation include:

[0101] 1) Irradiation defects: point defects, point defect clusters, dislocation rings, etc.

[0102] 2) Irradiation-induced precipitation: clusters or precipitation formed by solute elements such as copper, nickel, manganese, and silicon;

[0103] 3) Segregation of impurities at grain boundaries and phase boundaries: Radiation induces segregation of phosphorus, tin, etc. at phase boundaries and grain boundaries.

[0104] Since dislocation loops and solute clusters generated by irradiation coexist in the material, the embodiment of the present invention separates the radiation hardening of the two defects, dislocation loops and solute clusters, in the second diffusion strengthening model, distinguishes and quantitatively evaluates the two types of hardening contributions, and can accurately simulate and determine the radiation hardening development process of VVER-RPV steel from the mechanism triggering.

[0105] In the embodiment of the present invention, the second parameter α0 includes the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 , using the dislocation loop pinning factor α 01 Characterizing the radiation hardening contribution of dislocation loops using the solute-rich cluster pinning factor α 02 Characterizing the hardening contribution of solute-rich clusters.

[0106] like Figure 5 As shown, after step S122 in the embodiment of the present invention, the following steps are included:

[0107] S123, determine the yield stress increment Δσ y and the dislocation loop pinning factor α 01 , solute-rich cluster pinning factor α 02 and the relationship between the irradiation defect structure function f(N×d), the embodiment of the present invention clarifies the main hardening terms (dislocation loops and solute-rich clusters) on the basis of formula (5), and uses the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 To reflect the contribution of the two hardening terms, the yield stress increment Δσ is realized. y Effective separation of the contribution of radiation defect hardening in .

[0108] The second dispersion enhancement model in the embodiment of the present invention is:

[0109] Δσ y =0.517×Gb×[α 01 ×f(N1×d1)+α 02 ×f(N2×d2)] (7)

[0110] Among them, f(N1×d1) is the irradiation defect structure function of the dislocation loop, and f(N2×d2) is the irradiation defect structure function of the solute-rich cluster.

[0111] In some embodiments, step S2 includes: comparing the irradiation defect structure function f(N1×d1) of the dislocation ring under multiple neutron fluences, the irradiation defect structure function f(N2×d2) of the solute-rich cluster and the yield stress increment Δσ y Substituting into formula (7), we can obtain the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 .

[0112] The embodiment of the present invention establishes the relationship between defect hardening and defect structure function under multiple groups of specific neutron fluences through experimental data under high doses, and combines Figure 6 As shown in the figure, the values ​​of the defect structure functions of dislocation loops and solute-rich clusters measured under multiple neutron fluences are established. Figure 6 The curve is derived from the fitting of experimental data. The values ​​of the defect structure function of the dislocation loop, the values ​​of the defect structure function of the solute-rich cluster and the neutron fluence are fitted in the same graph to obtain Figure 6 The variation trend of the defect structure function with neutron injection, Figure 6 The horizontal axis in the figure represents the neutron flux Φ A , where the unit of neutron flux is n / m 2 , n represents neutrons, and m represents the unit meter. The amount of radiation per unit time is called the radiation rate, and the unit of radiation rate is n / m 2 ·s. The neutron fluence is the integral of the neutron fluence rate over time. Figure 6 The vertical axis represents the defect structure function f(N×d), and the unit of f(N×d) is m. Figure 6 The solid line in the figure shows the variation trend of the defect structure function of the dislocation ring fitted by the experimental data with the neutron injection, and the dotted line shows the variation trend of the defect structure function of the solute-rich cluster fitted by the experimental data with the neutron injection. Figure 6 It can be seen that when the neutron injection is less than 5.0×10 24 n / m 2 When the neutron injection is greater than 5.0×10 24 n / m 2 Afterwards, the values ​​of the defect structure functions of dislocation loops show an upward trend, while those of solute-rich clusters show a downward trend.

[0113] The embodiment of the present invention establishes multiple sets of experimental data of defect hardening and defect structure function under specific neutron fluence, solves the equation group of the second dispersion strengthening model, and obtains the main hardening defect dislocation ring pinning factor α 01 and solute-rich cluster pinning factor α 02 It should be noted that at least two sets of experimental data on defect hardening and defect structure function under specific neutron fluence in the embodiments of the present invention are required.

[0114] In some embodiments, Figure 7 As shown, step S3 includes:

[0115] S31, according to the cluster dynamics method, the first relationship N(Φ A ) and the second relation d(Φ A ), where the first relation represents the relationship between the number of defects N in the material and the neutron injection Φ A The second relationship characterizes the relationship between the defect size d in the material and the neutron injection Φ A relationship.

[0116] It should be noted that molecular dynamics simulations have found that the interaction between the initial dislocated atoms induced by neutrons or ions and the atoms of the lattice can lead to a series of cascade collision processes, which will not only produce a large number of point defects in the material, but also many defect clusters. The size distribution of the defects follows a power law change. The cascade collisions induced by high-energy initial dislocated atoms can also directly produce dislocation rings, stacking fault tetrahedrons, etc. A rate theory method in the cluster dynamics method uses total concentration and average size to replace defects of various sizes. Based on the molecular dynamics results, it simulates the evolution behavior of matrix damage defects under radiation hardening conditions. When using the cluster dynamics method, the spatial information of the defects is ignored. The principle of chemical reaction rate is borrowed to use the reaction rate to describe the interaction rate of various thermal defects or radiation defects in a uniform medium with infinite time and space constraints. Among them, in the cluster dynamics model, driven by temperature and radiation, the defects continue to diffuse and migrate. As the defects meet, a series of reactions occur between the defects, resulting in the change of the concentration of various defects over time. The evolution relationship of the defect concentration over time is related to the reaction rate between various defects.

[0117] The embodiment of the present invention uses the above cluster dynamics method to obtain the number of defects N and the neutron injection Φ in the material. A The first relationship between the defect size d in the material and the neutron injection Φ A The second relation of .

[0118] S32, the first relational expression N(Φ A ) and the second relation d(Φ A ) is substituted into the irradiation defect structure function to obtain the irradiation defect structure function f(N(Φ A ),d(Φ A )) and neutron fluence Φ A Among them, the first relationship N(Φ A ) and the second relation d(Φ A ) is substituted into formula (6):

[0119]

[0120] The irradiation defect structure function f(N(Φ A ),d(Φ A )) and neutron fluence Φ A Relationship:

[0121]

[0122] In some embodiments, Figure 8 As shown, step S4 includes:

[0123] S41, the irradiation defect structure function f(N(Φ A ),d(Φ A )) and neutron fluence Φ A Substitute the relationship into formula (7);

[0124] S42, get the yield stress increment and neutron fluence Φ A The relationship is:

[0125]

[0126] Among them, N1(Φ A ) is the number of defects in the dislocation loop, d1(Φ A ) is the defect size of the dislocation loop, N2(Φ A ) is the number of defects in the solute-rich cluster, d2(Φ A ) is the defect size of the solute-rich cluster.

[0127] The dislocation loop pinning factor α obtained by combining theoretical calculations in the present invention 01 , solute-rich cluster pinning factor α 02 and the irradiation defect structure function f(N(Φ A ),d(Φ A ), the yield stress increment is obtained and neutron fluence Φ A The relationship between the two defects, dislocation loops and solute-rich clusters, was used to distinguish and quantitatively evaluate the hardening contribution of the two types of defects, thereby accurately simulating and predicting the trend of the irradiation hardening behavior of the VVER reactor pressure vessel with neutron injection.

[0128] like Fig. 9 As shown in the figure, a VVER reactor pressure vessel steel shows a radiation hardening trend after long-term neutron irradiation under the accelerated test conditions of a high-flux reactor. Fig. 9 The horizontal axis represents the neutron flux Φ A The ordinate represents the yield stress increment Fig. 9 The solid line in the figure represents the yield stress increment fitted according to formula (8) With neutron injection Φ A The changing trend of reflects the fitting trend of the irradiation hardening of the VVER reactor pressure vessel with the change of neutron injection. Fig. 9 The data points distributed in the figure represent the yield stress increment data of the VVER pressure vessel steel after real reactor irradiation. The variation trend simulated in the embodiment of the present invention can match the real experimental value well, indicating that the yield stress increment data after real reactor irradiation is within the simulated yield stress increment, indicating that the radiation hardening method of the reactor pressure vessel of the present invention can accurately simulate the radiation hardening process of the reactor pressure vessel. Fig. 9 As shown, at the neutron flux Φ A About 1.5×10 24 n / m 2 The yield stress increment obtained by simulation is The actual yield stress increment obtained experimentally is about 150 MPa. It is about 140MPa. The yield stress increment obtained by simulation is slightly larger than the actual yield stress increment obtained by experiment. The difference is within the reasonable range of simulation prediction. The yield stress increment obtained by simulation can be used to determine whether the material can be used under the neutron injection, or the service life of the material can be predicted by simulation of the change trend. The embodiment of the present invention accurately simulates and predicts the change trend of the radiation hardening behavior of the VVER type reactor pressure vessel with the neutron injection in a quantitative manner.

[0129] In some embodiments, step S3 further includes:

[0130] Using multiple sets of first experimental data to calibrate the first relationship; wherein the first experimental data are neutron injection and the corresponding number of defects;

[0131] and / or,

[0132] A plurality of sets of second experimental data are used to calibrate the second relationship, wherein the second experimental data are neutron injection and corresponding defect size.

[0133] The embodiment of the present invention is based on the deviation and difference between the ideal material simulation calculation and the real material, and further corrects the microscopic parameters in the first relationship and the second relationship by comparing the experimental results to obtain the optimal defect evolution prediction cluster dynamics model, that is, to obtain a more accurate correspondence between the number of defects and the neutron injection, as well as the correspondence between the neutron injection and the defect size.

[0134] In some embodiments, after step S123, the method further includes:

[0135] Using multiple sets of third experimental data to calibrate the dislocation loop pinning factor α in the second dispersion strengthening model 01 and solute-rich cluster pinning factor α 02 , where the third experimental data are the corresponding data of the irradiation defect structure function of the dislocation loop, the irradiation defect structure function of the solute-rich cluster and the yield stress increment.

[0136] Based on the difference between the ideal second dispersion strengthening model and the real material, the embodiment of the present invention continuously corrects the dislocation loop pinning factor α within a reasonable range by comparing the fitted yield stress increment with the experimental results. 01 and solute-rich cluster pinning factor α 02 , and thus the variation of the radiation hardening value of VVER reactor pressure vessel steel with neutron injection can be effectively simulated and predicted.

[0137] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention.< / f> < / f> < / f> < / f>

Claims

1. A method for determining the radiation hardening of a VVER type reactor pressure vessel, characterized in that include: S1. Modifying the first dispersion strengthening model into a second dispersion strengthening model; wherein the first dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the first parameter, the number of defects and the defect size, and the second dispersion strengthening model characterizes the relationship between the yield stress increment of the material and the second parameter and the irradiation defect structure function; the first parameter is a function of the defect size, and the second parameter is independent of the defect size; the irradiation defect structure function is a function of the defect number and defect size; S2. determining the second parameter of the second dispersion enhancement model; S3, obtaining the relationship between the irradiation defect structure function and the neutron fluence; S4, determining the relationship between the yield stress increment and the neutron fluence of the material according to the relationship between the irradiation defect structure function and the neutron fluence and the second dispersion strengthening model; Wherein, step S1 comprises: S11, correcting the relationship between the yield stress increment and the critical shear stress increment; S12, determining the second dispersion strengthening model according to the relationship between the critical shear stress increment and the irradiation defect structure function; Step S11 includes: S111. Based on the Schmid law of single crystal tensile experiment, the relationship between the yield stress increment and the critical shear stress increment is obtained: Board y =MΔτ (1) Among them, Δσ y is the yield stress increment, M is the Taylor factor, and Δτ is the critical shear stress increment; S112. According to the principle of free random distribution of defects, the relationship between the yield stress increment and the critical shear stress increment is corrected to: Board y =0.85α0×MΔτ (2) Wherein, 0.85 is the defect free random distribution coefficient, and α0 is the second parameter; Step S12 includes: S121, obtaining the relationship between the critical shear stress increment, dislocation curvature, and defect spacing: where T(θ) is the depinning force of the dislocation fragment, <f> is the value of mixed dislocation, (L-2r) is the defect spacing, G is the shear modulus, and b is the Burgers vector;< / f> S122. Determine the relationship between the yield stress increment, the second parameter, and the irradiation defect structure function according to the relationship between the defect spacing, the defect number, and the defect size; wherein the relationship between the defect spacing, the defect number, and the defect size is: L is the distance between the two defect centroids, r is the defect radius, N is the number of defects, and d is the defect size; The relationship between the yield stress increment, the second parameter and the irradiation defect structure function is: Where f(N×d) is the irradiation defect structure function, The hardening terms that determine the irradiation defects include dislocation loops and solute-rich clusters, and the second parameter α0 includes the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 ; After step S122, including: S123, determining the yield stress increment Δσ y With the dislocation loop pinning factor α 01 , the solute-rich cluster pinning factor α 02 And the relationship between the irradiation defect structure function f(N×d), the second diffusion strengthening model is obtained: Board y =0.517×Gb×[α 01 ×f(N1×d1)+α 02 ×f(N2×d2)] (7) Among them, f(N1×d1) is the irradiation defect structure function of the dislocation loop, and f(N2×d2) is the irradiation defect structure function of the solute-rich cluster; Step S2 includes: The irradiation defect structure function f(N1×d1) of dislocation loops and the irradiation defect structure function f(N2×d2) of solute-rich clusters under multiple neutron fluences are compared with the yield stress increment Δσ. y Substituting into formula (7), we can obtain the dislocation loop pinning factor α 01 and solute-rich cluster pinning factor α 02 ; Step S3 includes: S31, according to the cluster dynamics method, the first relationship N(Φ A ) and the second relation d(Φ A ), where the first relation represents the relationship between the number of defects N in the material and the neutron injection Φ A The second relationship characterizes the relationship between the defect size d in the material and the neutron injection Φ A relationship; S32, the first relational expression N(Φ A ) and the second relation d(Φ A ) is substituted into the irradiation defect structure function to obtain the irradiation defect structure function f(N(Φ A ),d(Φ A )) and the neutron fluence Φ A relationship; Step S4 includes: S41, the irradiation defect structure function f(N(Φ A ),d(Φ A )) and the neutron fluence Φ A Substitute the relationship into formula (7); S42, the relationship between the yield stress increment and the neutron injection is obtained as follows: Board (ΦA) =0.517×Gb×[α 01 ×f(N1(Φ A ),d1(Φ A ))+a 02 ×f(N2(Φ A ),d2(Φ A ))] (8) Among them, N1(Φ A ) is the number of defects in the dislocation loop, d1(Φ A ) is the defect size of the dislocation loop, N2(Φ A ) is the number of defects in the solute-rich cluster, d2(Φ A ) is the defect size of the solute-rich cluster.

2. The method according to claim 1, characterized in that Step S3 also includes: Using multiple sets of first experimental data to calibrate the first relationship; wherein the first experimental data are neutron injection and corresponding defect quantity; and / or, The second relationship is corrected using multiple sets of second experimental data, wherein the second experimental data are neutron injection and corresponding defect size.

3. The method according to claim 1, characterized in that After step S123, the method further includes: Using multiple sets of third experimental data to calibrate the dislocation loop pinning factor α in the second dispersion strengthening model 01 and the solute-rich cluster pinning factor α 02 , wherein the third experimental data are the corresponding data of the irradiation defect structure function of the dislocation loop, the irradiation defect structure function of the solute-rich cluster and the yield stress increment.

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