Method for predicting the degree of irradiation embrittlement of reactor pressure vessels

Abstract

An embodiment of the present invention provides a method for predicting the degree of radiation embrittlement of a reactor pressure vessel, wherein the degree of radiation embrittlement is related to the neutron fluence, and the method comprises: constructing a mathematical model related to the neutron fluence; predicting the degree of radiation embrittlement according to the mathematical model; wherein the mathematical model comprises a monotonically increasing composite function with an exponential function as a basic configuration and a monotonically increasing composite function with a power function as a basic configuration. By constructing a mathematical model and adding a monotonically increasing composite function with an exponential function as a basic configuration and a monotonically increasing composite function with a power function as a basic configuration to the mathematical model, the degree of radiation embrittlement of the reactor pressure vessel can be predicted more accurately even at a high neutron fluence.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of reactor pressure vessels, and in particular to a method for predicting the degree of radiation embrittlement of a reactor pressure vessel. Background Art

[0002] Reactor pressure vessels are generally made of low-temperature brittle materials. Under the working conditions of the reactor pressure vessel, the material will undergo radiation embrittlement. The low-temperature embrittlement will continue to increase. This will cause the reactor pressure vessel to rupture instantly after a period of service and when the radiation embrittlement reaches a certain degree, leading to a major accident. Therefore, it is necessary to understand the degree of radiation embrittlement of the reactor pressure vessel during the operation of a nuclear power plant.

[0003] In the prior art, there are methods for predicting the degree of irradiation embrittlement of reactor pressure vessels. The methods in the prior art are relatively accurate when the neutron fluence level is low, but the prediction results are low at high neutron fluence, resulting in inaccurate prediction results. Summary of the invention

[0004] In order to solve at least one aspect of the above-mentioned problem, an embodiment of the present invention provides a method for predicting the degree of radiation embrittlement of a reactor pressure vessel, wherein the degree of radiation embrittlement is related to the neutron fluence, and the method comprises: constructing a mathematical model related to the neutron fluence; predicting the degree of radiation embrittlement according to the mathematical model; wherein the mathematical model comprises a monotonically increasing composite function with an exponential function as a basic configuration and a monotonically increasing composite function with a power function as a basic configuration.

[0005] By constructing a mathematical model and adding a monotonically increasing composite function with an exponential function as the basic configuration and a monotonically increasing composite function with a power function as the basic configuration into the mathematical model, the degree of radiation embrittlement of the reactor pressure vessel can be predicted more accurately under high neutron injection. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1 A schematic diagram of the ductile-brittle transition temperature range provided by an embodiment of the present invention;

[0007] Figure 2 A schematic diagram of the radiation embrittlement mechanism provided by an embodiment of the present invention;

[0008] Figure 3 A schematic diagram of a first function image provided by an embodiment of the present invention;

[0009] Figure 4 A schematic diagram of a second function image provided by an embodiment of the present invention;

[0010] Figure 5A schematic diagram of an image showing how the degree of radiation embrittlement of a metal material varies with neutron fluence provided by an embodiment of the present invention;

[0011] Figure 6 ΔRT provided by the embodiment of the present invention NDT Schematic diagram of . DETAILED DESCRIPTION

[0012] The technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0013] An embodiment of the present invention provides a method for predicting the degree of radiation embrittlement of a reactor pressure vessel, comprising the following steps: constructing a mathematical model related to neutron injection; predicting the degree of radiation embrittlement according to the mathematical model; wherein the mathematical model includes a monotonically increasing composite function with an exponential function as a basic configuration and a monotonically increasing composite function with a power function as a basic configuration.

[0014] By constructing a mathematical model and adding a monotonically increasing composite function with an exponential function as the basic configuration and a monotonically increasing composite function with a power function as the basic configuration into the mathematical model, the degree of radiation embrittlement of the reactor pressure vessel can be predicted more accurately under high neutron injection.

[0015] The degree of irradiation embrittlement can be determined by the change in the reference non-plastic transition temperature (△RT NDT ) is used to measure the non-plastic transition temperature (RT NDT ) refers to the temperature at which a material can completely break without significant deformation under the action of impact. The degree of radiation embrittlement is related to the neutron flux. The greater the neutron flux, the greater the degree of radiation embrittlement. Neutron flux refers to the quotient obtained by dividing the number of neutrons entering a tiny sphere centered at a certain point in space by the maximum cross-sectional area of ​​the sphere. The size of the tiny sphere tends to 0. As the reactor pressure vessel ages, the accumulated neutron flux will continue to increase.

[0016] See also Figure 1, the energy absorbed by the metal material of the reactor pressure vessel when it is destroyed is related to the temperature. The energy absorbed by the metal material when it is destroyed can be used to measure the toughness and brittleness of the metal material. The higher the energy absorbed by the metal material when it is destroyed, the greater the toughness; the lower the energy absorbed by the metal material when it is destroyed, the greater the brittleness. The metal material of the reactor pressure vessel has a certain toughness. As the temperature decreases, the toughness will decrease accordingly, but there is an interval where the toughness decreases rapidly with temperature10. Within the interval10, the metal material will quickly change from toughness to brittleness. The temperature interval10 where the metal material quickly changes from toughness to brittleness is called the ductile-brittle transition temperature interval.

[0017] See also Figure 6 Curve 61 is a curve showing the change of absorbed energy with temperature when the material without radiation embrittlement is destroyed, and curve 62 is a curve showing the change of absorbed energy with temperature when the material with radiation embrittlement is destroyed. According to the common knowledge in the art, a representative specific energy value 63 is selected to determine the intersection of curve 61 and curve 62 with energy value 63. The intersection of curve 61 with energy value 63 is characteristic point 64, and the intersection of curve 62 with energy value 63 is characteristic point 65. The temperature difference 60 corresponding to characteristic point 64 and characteristic point 65 is △RT NDT Without testing, △RT NDT The method provided in the embodiment of the present invention may be used for prediction.

[0018] △RT NDT The metal material of the reactor pressure vessel is affected by radiation, and the reference non-plastic transition temperature increases. This phenomenon that the metal material of the reactor pressure vessel is prone to brittleness due to the increase in the reference non-plastic transition temperature is called radiation embrittlement. Under irradiation conditions, neutrons collide with atoms in the metal material, causing the collided atoms to become primary dislocated atoms. The primary dislocated atoms will trigger cascade collisions, forming a series of defects in the material; the defects will further evolve and at the same time accelerate the precipitation of solute atoms in the metal material to form clusters; irradiation conditions will also accelerate the segregation of phosphorus in the metal. These processes will change the microstructure of the metal material, affect the performance of the metal material, and lead to radiation embrittlement.

[0019] See also Figure 2The radiation embrittlement 20 is caused by the simultaneous action of multiple mechanisms. The mechanism of radiation embrittlement 20 can be roughly divided into the following four aspects: first, matrix damage 201, that is, the destruction of the microstructure caused by defects such as vacancies, interstitial atoms, and dislocation rings generated by radiation; second, copper-rich solute clusters 202, that is, due to the influence of radiation, copper atoms in the metal material precipitate and aggregate into clusters, and other atoms will further aggregate on the clusters with copper atoms as the core, making the cluster volume larger. The clusters exist between iron atoms, resulting in changes in the microstructure of the material; third, clusters formed by solute atoms other than copper atoms are called non-copper solute clusters 203. Solute atoms with lower content other than copper in the metal material precipitate and aggregate into clusters. The clusters exist between metal atoms, resulting in changes in the microstructure of the metal material; fourth, phosphorus segregation 204, that is, phosphorus precipitates at grain boundaries. Grain boundaries refer to the interfaces between grains with the same structure but different orientations. The precipitation of phosphorus at grain boundaries will lead to a decrease in the bonding strength of grain boundaries.

[0020] Each radiation embrittlement mechanism contributes to the degree of radiation embrittlement. The degree of radiation embrittlement can be expressed as a comprehensive reflection of the degree of radiation embrittlement contributed by each radiation embrittlement mechanism.

[0021] See also Figure 3 and Figure 4 In some embodiments, constructing a mathematical model related to neutron fluence includes: dividing these irradiation embrittlement mechanisms into two categories according to certain rules, representing the irradiation embrittlement degrees contributed by these two categories of mechanisms by a first function 30 with neutron fluence as an independent variable and a second function 40 with neutron fluence as an independent variable, respectively, and representing the irradiation embrittlement degree by the sum of the first function 30 and the second function 40, wherein the first function 30 is a monotonically increasing composite function with an exponential function as a basic configuration, and the second function 40 is a monotonically increasing composite function with a power function as a basic configuration, and the relationship between neutron fluence and irradiation embrittlement degree is represented in a quantitative manner. In some embodiments, the base of the exponential function is greater than 1; the exponent of the power function is greater than 0 and less than 1.

[0022] The first function 30 and the second function 40 include undetermined constants, which are determined by fitting multiple sets of data, wherein each set of data in the multiple sets of data at least includes an actual neutron fluence and an actually measured irradiation embrittlement degree corresponding to the actual neutron fluence.

[0023] It should be noted that Figure 3 and Figure 4The variation trend of the first function 30 and the second function 40 with the neutron fluence is only schematically shown, and the starting point of the function and the slope of the tangent line at each point on the function graph are not limited. By adjusting the undetermined constants in the first function 30 and the second function 40, the function graph may be translated in any direction, stretched in the horizontal and vertical directions, and compressed in the horizontal and vertical directions.

[0024] In the mathematical model constructed in the embodiment of the present invention, the effect of neutron fluence on the degree of irradiation embrittlement is reflected by the sum of the first function 30 and the second function 40, and each function represents the degree of irradiation embrittlement contributed by a certain type of mechanism.

[0025] In some embodiments, a first function 30 with neutron fluence as an independent variable is constructed; a second function 40 with neutron fluence as an independent variable is constructed; the degree of irradiation embrittlement is expressed as the sum of the first function 30 and the second function 40; wherein the first function 30 is a composite function with an exponential function as a basic configuration, and the base of the exponential function is greater than 1; and the second function 40 is a composite function with a power function as a basic configuration, and the exponent of the power function is greater than 0 and less than 1.

[0026] Each mechanism has different effects on the degree of irradiation embrittlement at different neutron fluences. The effect of each mechanism on the degree of irradiation embrittlement mentioned here refers to: when only this mechanism is considered, the degree of irradiation embrittlement contributed by the mechanism when the unit neutron fluence is changed, that is, the rate of change of the degree of irradiation embrittlement contributed by the mechanism with the neutron fluence.

[0027] The influence of the matrix damage 201 on the degree of radiation embrittlement is greater when the neutron injection is low, and the influence of the matrix damage 201 on the degree of radiation embrittlement gradually decreases with the increase of the neutron injection. However, if the copper content in the material is high (for example, more than 0.1wt%), the influence of the matrix damage 201 on the degree of radiation embrittlement will increase again as the neutron injection level reaches a high level.

[0028] When the neutron injection is low, the solute clusters formed by the copper-rich solute clusters 202 and the non-copper solute clusters 203 (such as manganese, silicon, nickel, etc.) have little effect on the degree of radiation embrittlement. As the neutron injection increases, the influence of the non-copper solute clusters 203 on the degree of radiation embrittlement becomes greater and greater.

[0029] When the neutron injection is low, the effect of phosphorus segregation 204 on the degree of radiation embrittlement is small, but with the increase of neutron injection, the effect of phosphorus segregation 204 on the degree of radiation embrittlement gradually increases.

[0030] In an embodiment of the present invention, the influence of these mechanisms on the degree of radiation embrittlement is divided into three categories according to the trend form: the first type of form includes the trend of change of the degree of radiation embrittlement caused by copper solute clusters 202, non-copper solute clusters 203 and phosphorus element segregation 204. In the first type of form, the influence of the mechanism on the degree of radiation embrittlement gradually increases with the increase of neutron injection, and the degree of radiation embrittlement contributed by the mechanism is represented by a first function 30; the second type of form includes the trend of change of the degree of radiation embrittlement caused by matrix damage 201. In the second type of form, the influence of the mechanism on the degree of radiation embrittlement gradually decreases with the increase of neutron injection, and the degree of radiation embrittlement contributed by the mechanism is represented by a second function 40; in addition, when the copper content is high, the trend of change of the degree of radiation embrittlement caused by the matrix damage 201 may also differentiate into a third type of form. In the third type of form, the degree of radiation embrittlement contributed by the mechanism is represented by the sum of the second function 40 and the first function 30.

[0031] See also Figure 5 Through the above explanation, we can understand that the overall radiation embrittlement degree of metal materials changes with the neutron injection rate, which first decreases and then increases. Figure 5 The variation trend 50 of the irradiation embrittlement degree with the neutron injection is schematically shown.

[0032] The above-mentioned contents related to the mechanism are only cognition in specific situations. In some cases, people may think that it is necessary to Figure 2 If more mechanisms are added to explain the radiation embrittlement phenomenon, it is also possible to believe that the trend of the four mechanisms will change to a certain extent. However, as long as the comprehensive trend of the radiation embrittlement degree with neutron injection conforms to Figure 5 As shown, it will not affect the scope of application of the present invention.

[0033] Specifically, the variation trend of the degree of irradiation embrittlement with neutron injection 50 is: the degree of irradiation embrittlement generally increases with the increase of neutron injection; at a lower neutron injection, the degree of irradiation embrittlement has a larger initial growth rate, and the rate of change of the degree of irradiation embrittlement is faster at this time; but with the increase of neutron injection, at a medium neutron injection, the growth rate of the degree of irradiation embrittlement gradually decreases, the rate of change of the degree of irradiation embrittlement gradually slows down, and the growth gradually tends to be gentle; at a higher neutron injection, the growth rate of the degree of irradiation embrittlement will gradually increase.

[0034] See also Figure 3 The first function 30 is a monotonically increasing composite function with an exponential function as a basic configuration, and the base of the exponential function is greater than 1. By reasonably setting the values ​​of each parameter in the first function 30, the first function 30 can reflect the first type of form.

[0035] See also Figure 4The second function 40 is a monotonically increasing composite function with a power function as a basic configuration, and the exponent of the power function is greater than 0 and less than 1. By reasonably setting the values ​​of each parameter in the second function 40, the second function 40 can reflect the second type of form.

[0036] By adding the first function 30 representing the first type of morphology into the mathematical model, the mathematical model can reflect the phenomenon that the rate of change of the degree of radiation embrittlement increases after the neutron injection reaches a certain level; by expressing the degree of radiation embrittlement as the sum of the first function 30 and the second function 40 in the mathematical model, the relationship between the actual degree of radiation embrittlement and the actual neutron injection can be more accurately reflected; and by inputting the neutron injection into the mathematical model, the degree of radiation embrittlement corresponding to the input neutron injection can be predicted.

[0037] In some embodiments, the neutron fluence is the fluence of neutrons with energy greater than or equal to 0.5 MeV. Since neutrons with energy less than 0.5 MeV do not have a significant effect on the structure of metal materials, in order to make the prediction result more accurate, the neutron energy can be screened, and when counting the neutron fluence, only the fluence of neutrons with energy greater than or equal to 0.5 MeV is counted.

[0038] In certain embodiments,

[0039] The first function 30 is:

[0040] The second function 40 is:

[0041] The degree of irradiation embrittlement is: ΔRT NDT =LBP+FBP;

[0042] Wherein, F is the neutron flux, the unit is the number of neutrons per square centimeter (n / cm 2 ), LBP is the value of the first function 30, FBP is the value of the second function 40, ΔRT NDT is the value of the irradiation embrittlement degree, and the values ​​of a, b, c, d, e, and f are determined by fitting multiple sets of data, wherein each set of data in the multiple sets of data at least includes an actual neutron fluence and an actually measured irradiation embrittlement degree corresponding to the actual neutron fluence. The above mathematical model is named CMVVER-2101 model.

[0043] Fitting is to connect a series of data with a smooth curve. This curve can be represented by a function. The fitting process is to find the function that best reflects the relationship between this series of data.

[0044] The multiple sets of data are usually derived from irradiation supervision data and accelerated irradiation test data. In the fitting process, the multiple sets of data are used to determine the undetermined constants in the first function 30 and the second function 40, wherein each set of data at least includes the actual neutron fluence and the actual irradiation embrittlement degree corresponding to the actual neutron fluence.

[0045] In some embodiments, when fitting, F0 can be set to 1×10 18 n / cm 2 , in order to reduce unnecessary fitting results.

[0046] In some embodiments, during the fitting process, after setting the value of F0, the value of f can be determined first, and then the values ​​of a, b, c, d, and e can be determined. f is more sensitive to the setting of the initial value during the fitting process and exhibits large fluctuations. In order to improve the effectiveness of the fitting results, during the fitting process, the value of f is first determined in the range of 0 to 1 according to the specific conditions of the multiple sets of data. Determining the value of f first can reduce the occurrence of unnecessary fitting results and make the fitting results more consistent with the radiation embrittlement data in the data. It should be noted that the present invention is not limited to first determining the value of f during the fitting process, and the value of f can also be determined together with a, b, c, d, and e.

[0047] In certain embodiments, when predicting the radiation embrittlement degree of the reactor pressure vessel, f=0.45.

[0048] In some embodiments, after determining the values ​​of F0 and f, the function configurations of the first function 30 and the second function 40 provided by the embodiments of the present invention are used in combination with the multiple sets of data to fit the values ​​of a, b, c, d, and e.

[0049] In some embodiments, when predicting the degree of irradiation embrittlement of the parent material of the reactor pressure vessel of the VVER-1000 nuclear power plant, by fitting multiple sets of data corresponding to the VVER-1000 nuclear power plant, it is obtained that a=0.6979, b=0.02251, c=5.324×10 -5 , d=6.886, e=0.6979.

[0050] In some embodiments, when predicting the degree of irradiation embrittlement of the weld of the reactor pressure vessel of a VVER-1000 nuclear power plant, by fitting multiple sets of data corresponding to the VVER-1000 nuclear power plant, it is obtained that a=0.6364, b=0.3190, c=-15.77, d=8.970, e=9.014×10 -8 .

[0051] After the values ​​of all the undetermined constants are determined, the neutron flux is substituted into the mathematical model to predict the degree of irradiation embrittlement corresponding to the neutron flux.

[0052] At the end of the 40-year lifespan, the peak fast neutron (E≥0.5MeV) injection into the reactor pressure vessel inner wall was 4.14×10 19 n / cm 2 The peak fast neutron injection of the weld is 3.87×10 19 n / cm 2 In order to confirm the degree of radiation embrittlement of metal materials at the end of their life, the above fast neutron injection is used as the input parameter F into the calculation formula to calculate the radiation embrittlement level ΔRT NDT The temperature is: base material 38°C, weld 47°C.

[0053] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for predicting the degree of radiation embrittlement of a reactor pressure vessel, wherein the degree of radiation embrittlement is related to the neutron fluence, characterized in that: Construct mathematical models related to neutron fluence; The degree of radiation embrittlement is predicted according to the mathematical model; wherein, The mathematical model includes a monotonically increasing composite function with an exponential function as a basic configuration and a monotonically increasing composite function with a power function as a basic configuration; Among them, the mathematical model related to neutron injection is constructed including: constructing a first function with the neutron fluence as an independent variable; constructing a second function with the neutron fluence as an independent variable; The radiation embrittlement degree is expressed as the sum of the first function and the second function; wherein, The first function is a monotonically increasing composite function with an exponential function as a basic configuration; The second function is a monotonically increasing composite function with a power function as a basic configuration.

2. The method according to claim 1, characterized in that: The base of the exponential function is greater than 1; The exponent of the power function is greater than 0 and less than 1.

3. The method according to claim 2, characterized in that: The first function and the second function contain undetermined constants, and the undetermined constants are determined by fitting multiple sets of data; wherein, Each set of data in the plurality of sets of data at least includes an actual neutron fluence and an actual radiation embrittlement degree corresponding to the actual neutron fluence.

4. The method according to claim 3, characterized in that: The first function is: ; The second function is: ; The degree of irradiation embrittlement is: ; Wherein, F is the neutron flux, LBP is the value of the first function, FBP is the value of the second function, ΔRT NDT is the value of the irradiation embrittlement degree, F0=1×10 18 n / cm 2 , a, b, c, d, e, f are unknown constants, f is greater than 0 and less than 1, and the values ​​of a, b, c, d, e, f are determined by fitting the multiple sets of data.

5. The method according to claim 4, characterized in that: The neutron fluence is a neutron fluence with energy greater than or equal to 0.5 MeV.

6. The method according to claim 4, characterized in that: In the fitting process, the value of f is determined first, and then the values ​​of a, b, c, d, and e are determined.

7. The method according to claim 6, characterized in that: When predicting the radiation embrittlement degree of the reactor pressure vessel, f=0.

45.

8. The method according to claim 7, characterized in that: When predicting the degree of radiation embrittlement of the parent material of the reactor pressure vessel, a=0.6979, b=0.02251, c=5.324×10 -5 , d=6.886, e=0.6979.

9. The method according to claim 7, characterized in that: When predicting the degree of radiation embrittlement of the weld of the reactor pressure vessel, a=0.6364, b=0.3190, c=-15.77, d=8.970, e=9.014×10 -8 .

10. The method according to claim 8 or 9, characterized in that: in, Predicting the degree of radiation embrittlement according to the mathematical model includes: After the values ​​of all the undetermined constants are determined, the neutron flux is substituted into the mathematical model to predict the degree of irradiation embrittlement corresponding to the neutron flux.

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