Interconversion method of shear section rate and impact absorption energy conversion curve

Abstract

The invention discloses a mutual conversion method of a shear section rate and an impact absorption energy conversion curve, and relates to the technical field of material aging analysis, the method comprises the following steps: S1, carrying out an impact test at a plurality of temperatures to obtain a plurality of groups of test data; s2, performing nonlinear fitting on the test data to obtain a shear section rate transformation curve and / or an impact absorption energy transformation curve of the material; s3, mutual conversion between the shear section rate conversion curve and the impact absorption energy conversion curve is achieved through the relation between the C value and the D value in the shear section rate conversion curve function and the C value and the D value in the impact absorption energy conversion curve function. By adopting the method provided by the invention, the test results can be mutually evaluated and verified; and meanwhile, when individual test data is abnormal and only one transformation curve is obtained, an estimated value of another transformation curve can be obtained under the condition of not supplementing the test data.

Description

Technical Field

[0001] This invention belongs to the field of material aging analysis technology, specifically relating to a method for the mutual conversion of shear cross-sectional area and impact absorption energy transformation curves. Background Technology

[0002] The reactor pressure vessel (RPV) of a commercial nuclear power plant is typically a massive pressure-bearing structure made of ferritic steel, operating in extremely harsh environments. Due to the effects of high-energy neutrons and high temperatures, the performance of RPV materials deteriorates significantly. This degradation is primarily manifested in the shift of the transition curve towards the high-temperature region, leading to a marked increase in the material's low-temperature brittleness. Monitoring this degradation is essential to protect the safety of the RPV. Charpy impact testing is commonly used to determine the material's transition curve.

[0003] Monitoring tests of in-service RPV materials are a collective term for a series of tests, with the determination of transition curves being a key component. The high radioactivity of the test samples significantly increases the complexity of the tests, making the determination of transition curves more difficult and costly compared to non-radioactive tests.

[0004] Generally, experiments require a series of tests at multiple temperatures, with 1 to 3 tests at each temperature, and a total of 15 to 18 test samples; the number of samples cannot be increased indefinitely. Typically, the shear ratio transition curve and the impact absorbed energy transition curve can be obtained simultaneously from the test data. However, if individual test data are abnormal, only one transition curve can be obtained. When test data is limited, the validity of the data becomes crucial. Based on this, this invention proposes a method to obtain another transition curve without adding additional test data. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a method for the mutual conversion of shear cross-sectional area and impact absorbed energy transformation curves. Using this method, test results can be compared to verify the validity of the data. Furthermore, when an anomaly occurs in the test and only one transformation curve is obtained, this method can be used to obtain an estimated value of the other transformation curve.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves includes the following steps:

[0008] S1. Conduct impact tests at multiple temperatures to obtain multiple sets of test data;

[0009] S2. By performing nonlinear fitting on the experimental data, the shear section ratio transformation curve and / or impact absorption energy transformation curve of the material are obtained. The functional expression of the transformation curve is:

[0010] (1)

[0011] In formula (1):

[0012] T represents temperature;

[0013] V(T) is the impact test measurement value corresponding to the temperature, including shear ratio and impact absorbed energy;

[0014] V upper This refers to the upper plateau value, which is the impact test measurement value corresponding to the upper plateau interval.

[0015] V lower The lower plateau value refers to the impact test measurement value corresponding to the lower plateau range.

[0016] C and D are the fitting parameters;

[0017] tanh() is a hyperbolic tangent function, with an S-shaped curve that is initially low and then rises.

[0018] S3. By using the relationship between the C and D values ​​in the shear section ratio transformation curve function and the C and D values ​​in the impact absorption energy transformation curve function, the mutual conversion between the shear section ratio transformation curve and the impact absorption energy transformation curve is realized.

[0019] Furthermore, in the method for converting the shear ratio and impact absorption energy conversion curves as described above, the test data in step S1 includes the test temperature and the impact test measurement values ​​corresponding to each test temperature, and the impact test measurement values ​​include the shear ratio and impact absorption energy of the material.

[0020] Furthermore, regarding the method for mutual conversion between shear ratio and impact absorbed energy transformation curves as described above, when fitting the material's shear ratio transformation curve in step S2, the upper plateau value V... upper =100, corresponding to the mean value of the measured values ​​obtained in the impact test with a shear cross-sectional area of ​​100%; lower plateau value V lowe= 0; The values ​​of parameters C and D are determined by nonlinear fitting of the test temperature and the measured shear cross-sectional area corresponding to the test temperature using formula (1).

[0021] Furthermore, regarding the method for mutual conversion between shear ratio and impact absorption energy transformation curve as described above, when fitting the impact absorption energy transformation curve of the material in step S2, the lower plateau value V... lower A constant less than or equal to 3J; upper plateau value V upper The calculation formula is:

[0022] (2)

[0023] In formula (2):

[0024] USE0 is the upper plateau absorbed energy in the impact absorption energy transformation curve of the material in its original state, in J. The USE0 value is obtained through experiments.

[0025] ΔT F The ductile-brittle transition temperature increment caused by irradiation, in °C, ΔT F The value is calculated based on the formula in US NUREG / CR6551 or other relevant literature;

[0026] The values ​​of parameters C and D are determined by nonlinear fitting of the test temperature and the corresponding impact absorption energy measurement value using formula (1).

[0027] Furthermore, the experimental steps for determining the USE0 value using the method for mutual conversion between shear cross-sectional area and impact absorption energy transformation curve as described above are as follows: conduct impact tests on the material at different temperatures in its original state to obtain the measured values ​​of impact absorption energy at different temperatures; perform data fitting between the test temperature and the corresponding measured values ​​of impact absorption energy to obtain the impact absorption energy transformation curve of the material in its original state; the upper plateau value of the impact absorption energy transformation curve in its original state is USE0.

[0028] Furthermore, in the method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves as described above, in step S3:

[0029] Through statistical analysis and fitting of historical irradiation embrittlement test data, the parameter C in the shear section ratio transformation curve function and the impact absorbed energy transformation curve function has the following relationship:

[0030] (3)

[0031] In formula (3):

[0032] C SFA The parameter C in the shear section ratio transformation curve function;

[0033] C en The parameter C represents the function that represents the transformation curve of the impact absorbed energy.

[0034] Furthermore, in the method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves as described above, in step S3:

[0035] Through statistical analysis and fitting of historical irradiation embrittlement test data, the parameter D in the shear section ratio transformation curve function and the impact absorbed energy transformation curve function has the following relationship:

[0036] (4)

[0037] In equation (4):

[0038] D SFA The parameter D in the shear section ratio transformation curve function;

[0039] D en The parameter D represents the function that represents the transformation curve of the impact absorbed energy.

[0040] Furthermore, in the method for converting between shear ratio and impact absorption energy conversion curve as described above, in step S3: when only the shear ratio conversion curve function is obtained through data fitting, the Cen and Den values ​​in the impact absorption energy conversion curve function are obtained using formulas (3) and (4); then the Cen and Den values ​​are substituted into formula (1) to obtain the impact absorption energy conversion curve function.

[0041] Furthermore, in the method for mutual conversion between shear ratio and impact absorption energy transformation curve as described above, in step S3: when only the impact absorption energy transformation curve function is obtained through data fitting, C in the shear ratio transformation curve function is obtained using formulas (3) and (4). SFA Value, D SFA Value; then C SFA Value, D SFA Substituting the value into formula (1) yields the shear cross-sectional area ratio transformation curve function.

[0042] Compared with the prior art, the method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves provided by the present invention has the following beneficial effects:

[0043] This method establishes the relationship between the C and D values ​​in the shear section ratio transformation curve function (which characterize the transformation curve shape) and the C and D values ​​in the impact absorbed energy transformation curve function, thereby enabling the mutual conversion between the shear section ratio transformation curve and the impact absorbed energy transformation curve. Experimental results can be cross-evaluated and verified to validate the data's validity. Furthermore, when individual experimental data show anomalies and only one transformation curve is obtained, this method can provide an estimate of another transformation curve without supplementing experimental data, thus saving costs. Attached Figure Description

[0044] To further illustrate the above and other advantages and features of this application, the specific embodiments of this application will be described in more detail below with reference to the accompanying drawings. The accompanying drawings, together with the following detailed description, are included in and form a part of this specification. It should be understood that these drawings only depict typical examples of this application and should not be considered as limiting the scope of this application.

[0045] Figure 1This is a flowchart illustrating a method for converting shear cross-sectional area and impact absorbed energy conversion curves provided in the implementation embodiment.

[0046] Figure 2 This is the shear section ratio transformation curve of the material;

[0047] Figure 3 The above is a comparison chart of the shear cross-sectional area transformation curve obtained by fitting experimental data in the example and the shear cross-sectional area transformation curve obtained by converting the impact absorbed energy transformation curve function. Detailed Implementation

[0048] Exemplary embodiments of this application will be described below with reference to the accompanying drawings. For clarity and brevity, not all features of actual implementations are described in the specification. However, it should be understood that many implementation-specific decisions must be made in the development of any such actual embodiment to achieve the developer's specific goals, such as complying with constraints related to the system and business, and these constraints may vary depending on the implementation. Furthermore, it should be understood that while development work can be very complex and time-consuming, such development work is merely a routine task for those skilled in the art who benefit from the content of this application.

[0049] It should also be noted that, in order to avoid obscuring this application with unnecessary details, only the equipment structure and / or processing steps closely related to the solution according to this application are shown in the accompanying drawings, while other details that are not closely related to this application are omitted.

[0050] The embodiments or examples disclosed below are used to implement this application. To simplify the disclosure of this application, the components and methods of specific examples are described below. Of course, they are merely examples and are not intended to limit this application.

[0051] Due to the effects of high-energy neutrons and high temperatures, the performance of RPV materials in commercial nuclear power plants undergoes significant degradation. This degradation is primarily manifested in the shift of the transition curve towards the high-temperature region, leading to a marked increase in the material's low-temperature brittleness. Testing personnel typically conduct impact tests to determine the material's transition curve, enabling the monitoring and assessment of the reactor pressure vessel's embrittlement level. The test subjects are a predetermined number of samples placed inside the reactor pressure vessel beforehand. Because of the high radioactivity inherent in nuclear facilities, the complexity and difficulty of the tests are greatly increased, and the number of samples available for impact testing is limited. Therefore, the operation of impact tests must be carefully controlled to avoid sample waste due to errors.

[0052] Normally, both shear area ratio transition curves and impact absorbed energy transition curves can be obtained simultaneously from experimental data. However, if individual experimental data exhibit anomalies, only one transition curve may be obtained. To address this issue, this invention provides a method for the mutual conversion of shear area ratio and impact absorbed energy transition curves. Using this method, experimental results can be compared to verify the validity of the data; furthermore, when anomalies occur in the experiment and only one transition curve is obtained, this method can provide an estimate of the other transition curve without requiring additional experimental data. See also... Figure 1 The flowchart shown illustrates the method, which includes the following steps:

[0053] S1. Impact tests are conducted at multiple temperatures to obtain multiple sets of test data. The test data includes the test temperature and the corresponding impact test measurements at each test temperature. The impact test measurements include the shear area ratio and impact absorbed energy of the material.

[0054] S2. By performing nonlinear fitting on the experimental data, the transformation curve function of the material is obtained.

[0055] like Figure 2 As shown, in the coordinate axis containing the material's transformation curve, the horizontal axis represents the test temperature, and the vertical axis represents the impact test measurement value. The transformation curve has a hyperbolic tangent function form and exhibits an S-shape, initially low and then high, divided into an upper plateau region, a lower plateau region, and a transformation region. The upper plateau region corresponds to the high-temperature area where the impact test measurement value of the S-shaped transformation curve tends to stabilize. The impact test measurement value corresponding to the upper plateau region is the upper plateau value, denoted as V. upper The lower plateau region is the low-temperature area where the impact test measurement value of the S-shaped transition curve tends to stabilize. The impact test measurement value corresponding to the lower plateau region is the lower plateau value, denoted as V. lower The transition zone is the mid-temperature region corresponding to the middle section of the S-shaped transition curve.

[0056] Test temperature, impact test measurement, maximum value V upper and minimum value V lower Satisfy the following expression:

[0057] (1)

[0058] In formula (1):

[0059] T represents temperature;

[0060] V(T) is the impact test measurement value corresponding to the temperature, including shear ratio and impact absorbed energy;

[0061] C and D are the fitting parameters;

[0062] tanh() is a hyperbolic tangent function, which has an S-shaped form that is low at first and then high.

[0063] In some embodiments, for the shear section ratio transition curve, the upper plateau value V upper The value is 100, corresponding to the average value of the measured values ​​obtained in the impact test with a shear cross-sectional area of ​​100%; the lower plateau value V lower The value is 0. Formula (1) is used to perform nonlinear fitting on the test temperature and the measured shear cross-sectional area corresponding to the test temperature to determine the values ​​of parameters C and D, thereby obtaining the shear cross-sectional area-temperature transition curve and its functional expression.

[0064] In some embodiments, for the impact absorption energy transition curve, the lower plateau value V lower It is a constant, usually set to a value less than or equal to 3J; the upper platform value V upper The calculation formula is:

[0065] (2)

[0066] In formula (2):

[0067] USE0 is the upper plateau absorbed energy in the impact absorption energy transition curve of the material in its original state, in J. The USE0 value is obtained experimentally, specifically by conducting impact tests on the material at different temperatures in its original state and obtaining the measured impact absorption energy values ​​at different temperatures; by fitting the test temperatures and the corresponding measured impact absorption energy values, the impact absorption energy transition curve of the material in its original state can be obtained; the upper plateau value of the impact absorption energy transition curve in its original state is USE0.

[0068] ΔT F ΔT represents the temperature increment of the ductile-brittle transition of a material induced by irradiation, in °C. F The value is calculated based on the formula in American NUREG / CR6551 or other relevant literature.

[0069] Formula (1) is used to perform nonlinear fitting on the test temperature and the measured value of the impact absorption energy corresponding to the test temperature, and the values ​​of parameters C and D are determined, thereby obtaining the impact absorption energy-temperature transition curve and its functional expression.

[0070] S3. By using the relationship between the C and D values ​​in the shear section ratio transformation curve function and the C and D values ​​in the impact absorption energy transformation curve function, the mutual conversion between the shear section ratio transformation curve and the impact absorption energy transformation curve can be achieved.

[0071] The parameter C in the shear ratio transformation curve function is denoted as Ci. SFA The parameter C in the impact absorption energy transformation curve is denoted as C0. enThis application, through statistical analysis and fitting of historical irradiation embrittlement test data, obtains the following relationship between the two:

[0072] (3)

[0073] In one specific embodiment, C is obtained through statistical analysis and fitting of historical irradiation embrittlement data from VVER-1000 nuclear power plants. SFA With C en The relationship between the two is as follows:

[0074]

[0075] The parameter D in the shear ratio transformation curve function is denoted as Di. SFA The parameter D in the impact absorption energy transformation curve is denoted as D. en This application, through statistical analysis and fitting of historical irradiation embrittlement test data, has established the following relationship between the two:

[0076] (4)

[0077] In one specific embodiment, D is obtained through statistical analysis and fitting of historical irradiation embrittlement data from the VVER-1000 nuclear power plant. SFA With D en The relationship between the two is as follows:

[0078]

[0079] In other embodiments, the coefficients of the function expressions of formulas (3) and (4) may differ depending on the historical data.

[0080] In some embodiments, when individual impact absorption energy test measurements are abnormal, and only the shear ratio transformation curve function is obtained through data fitting, but the impact absorption energy transformation curve function cannot be obtained, C in the impact absorption energy transformation curve function is obtained using formulas (3) and (4). en Value, D en Value, then C en Value, D en Substituting the value into formula (1) yields the impact absorption energy transformation curve function.

[0081] In other embodiments, when individual shear ratio test measurements are abnormal, and only the impact absorption energy transformation curve function is obtained through data fitting, but not the shear ratio transformation curve function, C in the shear ratio transformation curve function is obtained using formulas (3) and (4). SFA Value, D SFA Value, then CSFA Value, D SFA Substituting the value into formula (1) yields the shear cross-sectional area ratio transformation curve function.

[0082] Example

[0083] A VVER-1000 nuclear power plant needs to complete a monitoring test. In its 17th year of operation, the monitoring module was extracted. Neutron measurements and transport calculations have been completed, and the fast neutron fluence is 1.78E19n / cm². 2 Impact tests on the base metal are now required to guide reactor operation and monitor the implementation of tests.

[0084] The data from this impact test are shown in Table 1.

[0085] Table 1 Impact Test Data

[0086] Serial Number Test temperature, °C Impact absorption energy, J Shear cross-sectional area ratio, % 1 28 255 100 2 -72 34 7 3 -22 93 29 4 -22 190 62 5 78 258 100 6 3 260 100 7 -47 23 9 8 -72 22 5 9 -47 106 25 10 -22 174 48 11 -72 18 4 12 -97 14 2 13 -47 150 35

[0087] Step 1: Fit the shear section ratio transformation curve function based on the experimental data.

[0088] Formula (1) is used as the functional form of the transformation curve:

[0089] (1)

[0090] In this embodiment, the upper plateau value V of the shear cross-sectional area ratio upper =100, lower platform value V lower When the value equals 0, the shear cross-sectional area test data are fitted using formula (1) to obtain C. SFA =-23.4383, D SFA =31.5521, therefore the function expression for the shear ratio transition curve is:

[0091] (5)

[0092] Step 2: Fit the impact absorption energy transformation curve function based on the experimental data.

[0093] In this embodiment, the upper plateau value V of the impact absorption energy is calculated according to formula (2). upper =257.6667, lower plateau value V lower Equal to 2.7, the impact absorption energy test data were fitted using formula (1) to obtain C. en =-32.6099, D en =36.7787, therefore the functional expression for the impact absorption energy transformation curve is:

[0094] (6)

[0095] Step 3: Obtain the shear ratio transformation curve function from the impact absorbed energy transformation curve function.

[0096] After reviewing the historical data of the nuclear power plant database, the parameter C, which characterizes the shape of the shear ratio transition curve, was obtained through fitting. SFA D SFA The parameter C characterizing the shape of the impact absorbed energy transition curve en D en The following relationship exists:

[0097] (7)

[0098] (8)

[0099] In step 2, C is obtained through fitting. en =-32.6099, D en =36.7787. Using conversion formulas (7) and (8), C can be obtained. SFA =-25.0647, D SFA =30.67636. Therefore, the transformed shear ratio transition curve function is:

[0100] (9)

[0101] Figure 3 A comparison chart is shown between the shear ratio transformation curve obtained by fitting experimental data and the shear ratio transformation curve obtained by converting the impact absorbed energy transformation curve function. From Figure 3 As can be seen, the two curves have a good fit, which verifies that the method provided in this application has reliable accuracy.

[0102] The present invention provides a method for mutual conversion between shear cross-sectional area ratio and impact absorbed energy transformation curves. By establishing the relationship between the C and D values ​​in the shear cross-sectional area ratio transformation curve function, which characterize the shape of the transformation curve, and the C and D values ​​in the impact absorbed energy transformation curve function, the method achieves mutual conversion between the shear cross-sectional area ratio transformation curve and the impact absorbed energy transformation curve. The experimental results can be cross-evaluated and verified to confirm the validity of the data. At the same time, when individual experimental data show anomalies and only one transformation curve is obtained, this method can obtain an estimated value of another transformation curve without supplementing experimental data, thus saving costs.

[0103] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention is also intended to include these modifications and variations.

Claims

1. A method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves, comprising the following steps: S1. Conduct impact tests at multiple temperatures to obtain multiple sets of test data; S2. By performing nonlinear fitting on the experimental data, the shear section ratio transformation curve and / or impact absorption energy transformation curve of the material are obtained. The functional expression of the transformation curve is: （1） In formula (1): T represents temperature; V(T) is the impact test measurement value corresponding to the temperature, including shear ratio and impact absorbed energy; V upper This refers to the upper plateau value, which is the impact test measurement value corresponding to the upper plateau interval. V lower The lower plateau value refers to the impact test measurement value corresponding to the lower plateau range. C and D are the fitting parameters; tanh() is a hyperbolic tangent function, with an S-shaped curve that is initially low and then rises. S3. By using the relationship between the C and D values ​​in the shear section ratio transformation curve function and the C and D values ​​in the impact absorption energy transformation curve function, the mutual conversion between the shear section ratio transformation curve and the impact absorption energy transformation curve is realized.

2. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 1, characterized in that, The test data in step S1 includes the test temperature and the impact test measurement values ​​corresponding to each test temperature. The impact test measurement values ​​include the shear cross-sectional area and impact absorbed energy of the material.

3. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 2, characterized in that, When fitting the shear ratio transformation curve of the material in step S2, the upper plateau value V upper =100, corresponding to the mean value of the measured values ​​obtained in the impact test with a shear cross-sectional area of ​​100%; lower plateau value V lowe= 0; The values ​​of parameters C and D are determined by nonlinear fitting of the test temperature and the measured shear cross-sectional area corresponding to the test temperature using formula (1).

4. The method for mutual conversion between shear cross-sectional area ratio and impact absorbed energy conversion curve according to claim 2, characterized in that, When fitting the impact absorption energy transformation curve of the material in step S2, the lower plateau value V lower A constant less than or equal to 3J; upper plateau value V upper The calculation formula is: （2） In formula (2): USE0 is the upper plateau absorbed energy in the impact absorption energy transformation curve of the material in its original state, in J. The USE0 value is obtained through experiments. ΔT F The ductile-brittle transition temperature increment caused by irradiation, in °C, ΔT F The value is calculated based on the formula in US NUREG / CR6551 or other relevant literature; The values ​​of parameters C and D are determined by nonlinear fitting of the test temperature and the corresponding impact absorption energy measurement value using formula (1).

5. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 4, characterized in that, The specific experimental steps for determining the USE0 value are as follows: conduct impact tests on the material at different temperatures in its original state to obtain the measured values ​​of impact absorbed energy at different temperatures; perform data fitting between the test temperature and the corresponding measured values ​​of impact absorbed energy to obtain the impact absorbed energy transformation curve of the material in its original state; the upper plateau value of the impact absorbed energy transformation curve in its original state is the USE0 value.

6. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to any one of claims 1-5, characterized in that, In step S3: Through statistical analysis and fitting of historical irradiation embrittlement test data, the parameter C in the shear section ratio transformation curve function and the impact absorbed energy transformation curve function has the following relationship: （3） In formula (3): C SFA The parameter C in the shear section ratio transformation curve function; C en The parameter C represents the function that represents the transformation curve of the impact absorbed energy.

7. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 6, characterized in that, In step S3: Through statistical analysis and fitting of historical irradiation embrittlement test data, the parameter D in the shear section ratio transformation curve function and the impact absorbed energy transformation curve function has the following relationship: （4） In equation (4): D SFA The parameter D in the shear section ratio transformation curve function; D en The parameter D represents the function that represents the transformation curve of the impact absorbed energy.

8. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 7, characterized in that, In step S3: When only the shear cross-sectional area ratio transformation curve function is obtained through data fitting, the Cen and Den values ​​in the impact absorption energy transformation curve function are obtained by using formula (3) and formula (4); then the Cen and Den values ​​are substituted into formula (1) to obtain the impact absorption energy transformation curve function.

9. The method for mutual conversion between shear cross-sectional area and impact absorbed energy transformation curves according to claim 7, characterized in that, In step S3: When only the impact absorption energy transformation curve function is obtained through data fitting, C in the shear section ratio transformation curve function is obtained using formulas (3) and (4). SFA Value, D SFA Value; then C SFA Value, D SFA Substituting the value into formula (1) yields the shear cross-sectional area ratio transformation curve function.

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