Screening method for fatigue-free analysis of nuclear-grade equipment
Through the screening method, it determines whether the nuclear-level equipment meets the infinite life design requirements, eliminates unnecessary fatigue analysis, solves the problem of high computing costs in nuclear power design, and achieves efficient fatigue analysis.
Patent Information
- Application Number
- CN202510322319.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-19
- Publication Date
- 2025-07-25
AI Technical Summary
The fatigue analysis and calculation cost of nuclear-grade equipment in existing nuclear power designs is high and complex, and it is difficult to improve analysis efficiency while ensuring accuracy.
Provide a screening method for fatigue-free analysis of nuclear-grade equipment. It determines whether the infinite life design requirements are met through the screening conditions. If it is met, detailed fatigue analysis will be exempted, otherwise detailed analysis will be carried out. Screening conditions include the number of pressure cycles, pressure fluctuation range, temperature difference and mechanical load.
Without reducing safety, the fatigue analysis process of nuclear-grade equipment is simplified, the analysis efficiency is improved, and theoretical support is provided for equipment structure design and optimization.
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Abstract
Description
Technical Field
[0001] This application belongs to the technical field of reactor structure fatigue analysis, and particularly relates to a screening method for exempting nuclear-grade equipment from fatigue analysis. Background Art
[0002] The nuclear-grade equipment contains high-temperature and high-pressure radioactive coolant, and its structural integrity is one of the important conditions to ensure the safe operation of nuclear reactors. During the service process of nuclear reactors, the nuclear-grade equipment is subjected to temperature and pressure fluctuations under various operating transients, resulting in fatigue damage in areas with relatively high stresses in the equipment. Once the fatigue damage in a certain area exceeds the limit, cracks are very likely to initiate, which may further lead to the rupture of the pressure-bearing boundary, thus directly threatening the safe operation of the nuclear reactor. Therefore, preventing fatigue failure needs to be considered in the design of nuclear-grade equipment to ensure the safe operation of nuclear reactors.
[0003] The current fatigue design in nuclear power design codes adopts the "safe life design" method, which is based on the design fatigue curve (S-N) obtained from theoretical analysis and verified by experiments, and is a fatigue analysis method based on the Miner linear cumulative damage theory and the cycle counting method. The Miner linear cumulative damage theory means that at a given stress level, each cycle generates an equal amount of damage, and the cyclic loads are independent of each other. Under cyclic loads, fatigue damage can be linearly accumulated. When the accumulated damage reaches a certain value, the specimen or component fails. For variable amplitude load histories, the fatigue analysis of nuclear power equipment generally uses large commercial software ANSYS to simulate the time history of stress and strain, selects the peak points as events, combines to obtain the alternating stress amplitude, and according to the design fatigue curve, the fatigue life corresponding to the stress amplitude can be determined, so as to obtain the cumulative fatigue usage factor, and finally judge whether it meets the fatigue design requirements according to the code.
[0004] According to the requirements of fatigue performance analysis in the nuclear power design codes RCC-M or ASME, first calculate the nodal stress values generated by the temperature field gradient and pressure at a time point, and select the stress peak time point as the event point in the fatigue analysis. The sum of the stresses at these event points and the stresses under mechanical external loads is used as the input value for storing the event stress. Then, combined with corresponding parameters such as the number of cycles and the material fatigue curve, the fatigue analysis module of the finite element software ANSYS is used to calculate the fatigue usage factor.
[0005] Due to the relatively complex operating conditions of nuclear power equipment and a large number of design transients, as the structure becomes more complex and the requirement for the precision of calculation results becomes higher and higher, the calculation cost increases sharply. Therefore, in order to accelerate the R & D process of nuclear power equipment, relevant methods for fatigue analysis need to be optimized to improve the R & D speed. Summary of the Invention
[0006] The purpose of this application is to overcome the defects of the prior art, so as to provide a screening method for exempting fatigue analysis of nuclear-grade equipment, which can improve the fatigue analysis efficiency of nuclear-grade equipment on the premise of effectively ensuring the calculation accuracy, and provide theoretical support for the structural design and optimization of nuclear-grade equipment.
[0007] To achieve the above purpose, this application provides the following technical solutions:
[0008] A screening method for exempting fatigue analysis of nuclear-grade equipment, which determines the design input for the fatigue analysis of nuclear-grade equipment. When the design transient meets all the screening conditions, the fatigue analysis is exempted; otherwise, the fatigue analysis is carried out. The screening conditions include:
[0009] Condition 1: During normal use, the number of cycles of the pressure rising from atmospheric pressure to the operating pressure and then returning to atmospheric pressure is less than the number of cycles corresponding to the stress amplitude S a of 3S m on the design fatigue curve;
[0010] Condition 2: During normal use, the pressure fluctuation range is less than the first threshold;
[0011] Condition 3: During startup and shutdown, the temperature difference between any two adjacent points on the equipment structure is less than the second threshold;
[0012] Condition 4: During normal use, the temperature difference between any two adjacent points is less than the third threshold;
[0013] Condition 5: For equipment made of materials with different elastic moduli or coefficients of thermal expansion, the algebraic value of the temperature change range during normal operation is less than the fourth threshold;
[0014] Condition 6: The stress range S r is less than the corresponding S a value on the design fatigue curve.
[0015] In some embodiments, the method sequentially judges Conditions 1 to 6. If all the conditions are met in sequence, the fatigue analysis is exempted; if one of the conditions is not met, the fatigue analysis is carried out.
[0016] In some embodiments, the calculation formula for the first threshold is as follows:
[0017]
[0018] In the formula, P D is the design pressure; S is the S 6 value obtained by looking up the design fatigue curve according to the number of cycles of 10 a ; S m is the design stress intensity at the operating temperature.
[0019] In some embodiments, the calculation formula for the second threshold is as follows:
[0020]
[0021] In the formula, S a is the value obtained by looking up the specified number of startup and shutdown cycles on the design fatigue curve; E is the elastic modulus at the average temperature of two adjacent points; α is the instantaneous expansion coefficient at the average temperature of two adjacent points.
[0022] In some embodiments, the calculation formula for the third threshold is as follows:
[0023]
[0024] In the formula, S is the value obtained by looking up on the design fatigue curve according to the number of cycles of 10 6 cycles.
[0025] In some embodiments, the calculation formula for the fourth threshold is as follows:
[0026]
[0027] In the formula, S is the value obtained by looking up on the fatigue curve according to the number of cycles of 10 6 cycles; E1 and E2 are the elastic moduli of two materials at the average temperature respectively; α1 and α2 are the instantaneous thermal expansion coefficients of two materials at the average temperature respectively.
[0028] In some embodiments, the stress range S r is the stress range caused by mechanical loads other than pressure.
[0029] In some embodiments, the design input includes material properties, design pressure, and design transients.
[0030] In some embodiments, the material properties include elastic modulus, thermal expansion coefficient, allowable stress intensity, and design fatigue curve data.
[0031] In some embodiments, the design transients include temperature, pressure transients, and occurrence times.
[0032] Compared with the prior art, the screening method for exempting fatigue analysis of nuclear-grade equipment provided by the present application has the following beneficial effects:
[0033] The screening method proposed by the present application is based on the fatigue analysis theory of "infinite life design". When the nuclear-grade equipment meets the requirements for exempting fatigue analysis proposed by the present application, it can avoid carrying out complex fatigue analysis processes for nuclear-grade equipment, improve the fatigue analysis efficiency of nuclear-grade equipment, and provide theoretical support for the structural design and optimization of nuclear-grade equipment. Brief Description of the Drawings
[0034] In order to more clearly illustrate the technical solution of the present application, the following is a brief introduction to the drawings required for the technical description.
[0035] Figure 1 A flowchart of a screening method for nuclear grade equipment exemption fatigue analysis provided for this application;
[0036] Figure 2 A schematic diagram of a specific process of a method for screening pressure vessels to exempt them from fatigue analysis provided in an embodiment of the present application. DETAILED DESCRIPTION
[0037] The following is further explained in detail through specific implementation methods.
[0038] like Figure 1 As shown, the present application provides a screening method for nuclear-grade equipment to be exempted from fatigue analysis, and determines the design input of nuclear-grade equipment fatigue analysis. The design input mainly includes the material properties of the analyzed equipment structure (elastic modulus E, thermal expansion coefficient α, allowable stress intensity S m , design fatigue curve data), design pressure P D and design transients (temperature, pressure transients and number of occurrences). When the design inputs meet all the screening conditions (1)-(6) below, fatigue analysis can be exempted; otherwise, detailed fatigue analysis of the equipment is required.
[0039] (1) Cycle from atmospheric pressure to operating pressure
[0040] During normal use, the pressure is increased from atmospheric pressure to the operating pressure and then returned to atmospheric pressure for a specified number of cycles not exceeding the stress amplitude S on the applicable design fatigue curve. a 3S m The number of cycles corresponding to the time.
[0041] (2) Fluctuation of normal operating pressure
[0042] During normal use, the entire specified pressure fluctuation range does not exceed the first threshold value.
[0043] The first threshold calculation formula is as follows:
[0044]
[0045] Where P D is the design pressure; S is the pressure calculated from the applicable design fatigue curve according to the number of cycles of 10 6 (If the total number of specified cycles exceeds 10 6 , then it is the S obtained by taking the maximum number of cycles limited by the applicable design fatigue curve) a Value; S m is the design stress intensity at the service temperature.
[0046] (3) Temperature difference caused by startup and shutdown
[0047] During startup and shutdown, the temperature difference between any two adjacent points on the equipment structure does not exceed the second threshold value.
[0048] The calculation formula for the second threshold value is as follows:
[0049]
[0050] In the formula, S a is the value obtained by looking up from the applicable design fatigue curve according to the specified number of startup and shutdown cycles; E is the elastic modulus at the average temperature of the two adjacent points; α is the instantaneous expansion coefficient at the average temperature of the two adjacent points.
[0051] (4) Temperature difference during normal operation
[0052] During normal operation, the temperature difference between any two adjacent points does not exceed the third threshold value.
[0053] The calculation formula for the third threshold value is as follows:
[0054]
[0055] In the formula, S is the value obtained by looking up from the applicable design fatigue curve according to the number of cycles of 10 6 (if the total specified number of cycles exceeds 10 6 , then it is the value obtained by taking the maximum number of cycles limited by the curve from the applicable design fatigue curve).
[0056] (5) Temperature difference between dissimilar materials
[0057] For equipment made of materials with different elastic moduli or thermal expansion coefficients, the algebraic value of the temperature change range during normal operation does not exceed the fourth threshold value.
[0058] The calculation formula for the fourth threshold value is as follows:
[0059]
[0060] In the formula, S is the value obtained by looking up from the applicable fatigue curve according to the number of cycles of 10 6 (if the total specified number of cycles exceeds 10 6 , then it is the value obtained by taking the maximum number of cycles limited by the curve from the applicable design fatigue curve); E1 and E2 are the elastic moduli of the two materials at the average temperature respectively; α1 and α2 are the instantaneous thermal expansion coefficients of the two materials at the average temperature respectively.
[0061] (6) Other mechanical loads
[0062] The stress intensity range S caused by all specified mechanical loads excluding pressure but including pipe reaction forces r shall not exceed the S corresponding to the number of cycles of 10 6 (if the total specified number of cycles exceeds 10 6 , then it is the maximum number of cycles defined by the curve on the applicable design fatigue curve) a value.
[0063] The screening method for exempting fatigue analysis of nuclear-grade equipment provided by this application is based on the infinite-life fatigue design theory. Without performing detailed stress analysis, it can give a simplified assessment of the fatigue life of nuclear-grade equipment within a reasonable safety range. It has a simple form and is easy to use, improving the fatigue analysis efficiency of nuclear-grade equipment and providing theoretical support for the structural design and optimization of nuclear-grade equipment.
[0064] Embodiment
[0065] In this embodiment, the technical solution of this application is implemented with a certain nuclear-grade pressure vessel as the object. As Figure 2 shown, the method specifically includes:
[0066] S1. Determine the design inputs for the fatigue analysis of nuclear-grade equipment. The design inputs include the material properties of the cylinder material and nozzle material of the pressure vessel, the design pressure P D and the design transient. The material properties include the elastic modulus E, the thermal expansion coefficient α, the allowable stress intensity S m , and the design fatigue curve data. The design transient includes temperature, pressure transient and the number of occurrences.
[0067] The cylinder material of the pressure vessel is 16MND5, and the nozzle material is 06Cr18Ni11Ti. Their material elastic modulus, thermal expansion coefficient and allowable stress intensity are shown in Table 1 and Table 2 respectively. The design fatigue curve data are shown in Table 3 and Table 4 respectively. The design pressure P D of the pressure vessel is 2.5 MPa, and the design transient temperature and pressure data and the number of times are shown in Table 5.
[0068] Table 1 Mechanical and physical properties of 16MND5
[0069]
[0070] Table 2 Mechanical and physical properties of 06Cr18Ni11Ti
[0071]
[0072] Table 3 Design fatigue curve applicable to 16MND5
[0073]
[0074] Table 4 Design fatigue curve applicable to 06Cr18Ni11Ti
[0075]
[0076] Table 5 Summary of design transient data
[0077]
[0078]
[0079] S2. Based on Table 1 involved in S1, count the number of cycles N when the pressure rises from atmospheric pressure to the operating pressure and then returns to atmospheric pressure, that is, the number of cycles N of the startup and shutdown transients is 576. It should be noted that N = 576 is an exemplary design input for illustrating the implementation scheme of this application.
[0080] S3. Interpolate and calculate S according to the design fatigue curve a = 3S m The corresponding number of cycles N0 is as follows
[0081] For the pressure vessel cylinder S a = 3S m = 3 × 184 MPa = 552 MPa, and interpolating gives N0 as 1099
[0082] For the nozzle S a = 3S m = 3 × 138 MPa = 414 MPa, and interpolating gives N0 as 6664
[0083] S4. Judge that the number of cycles N of startup and shutdown is 576, which is less than N0 calculated in S3 based on the cylinder material and nozzle material of the pressure vessel, and execute S5; otherwise, a detailed fatigue analysis should be carried out
[0084] S5. Based on Table 5 involved in S1, count that the maximum pressure fluctuation ΔP during normal operation (excluding seismic transients) is 1.29 MPa, and the total number of design transients N is 1.34×10 4 .
[0085] S6. N is less than 10 6 , for the cylinder, according to the design fatigue curve of the cylinder material (Table 3), the S value is obtained as 86 MPa according to the number of cycles of 10 6 , and calculate the effective pressure fluctuation according to the formula
[0086] ΔP e = P D × S / 3S m = 2.5 MPa × 86 MPa / 552 MPa = 0.39 MPa
[0087] For the nozzle, according to the designed fatigue curve of the nozzle material (Table 4), at a cycle number of 10 6 the S value is found to be 126 MPa, and the effective pressure fluctuation is calculated according to the formula:
[0088] ΔP e =P D ×S / 3Sm=2.5MPa×126MPa / 414MPa=0.76MPa。
[0089] S7. According to Table 5, the number of pressure fluctuations n greater than ΔP e is 680, which is greater than 0, so S8 is executed.
[0090] S8. For the cylinder, according to the designed fatigue curve (Table 3), interpolate the S a value corresponding to the cycle number n of 680 times, then:
[0091] ΔP0=P D ×S a / 3S m =2.5MPa×652MPa / 552MPa=2.95MPa;
[0092] For the nozzle, according to the designed fatigue curve (Table 4), interpolate the Sa value corresponding to the cycle number n of 680 times, which is 865 MPa, then:
[0093] ΔP0=P D ×S a / 3S m =2.5MPa×865MPa / 414MPa=5.22MPa。
[0094] S9. For the cylinder and the nozzle respectively, judge whether ΔP in S5 is less than ΔP0 in S8. If ΔP < ΔP0 is satisfied, then S10 is executed; otherwise, a detailed fatigue analysis should be carried out.
[0095] S10. Based on Table 5 involved in S1, the number of start-up and shut-down occurrences N is counted as 576. According to the temperature distribution of the start-up and shut-down transient structures, the maximum temperature difference ΔT during start-up and shut-down is obtained as 8.56 °C (the highest temperature during start-up and shut-down is 28.56 °C minus the room temperature of 20 °C).
[0096] S11. For the cylinder, according to the designed fatigue curve (Table 3), interpolate the corresponding S a value according to the cycle number N, and calculate according to the formula:
[0097] ΔT0=S a / 2Eα=690MPa / (2×204Gpa×11.22×10-6 / ℃) = 151℃;
[0098] For the nozzle, according to the design fatigue curve (Table 4), the corresponding S a value is 922 MPa, and it is calculated according to the formula:
[0099] T0 = S a / 2Eα = 922 MPa / (2×195 GPa×15.3×10 -6 / ℃) = 154℃.
[0100] For the shell and the nozzle respectively, judge whether the ΔT in S10 that meets the conditions is less than the ΔT0 in S11. If ΔT < ΔT0 is satisfied, then execute S13; otherwise, a detailed fatigue analysis should be carried out.
[0101] S13. Based on Table 5 involved in S1, the number of normal operation transient cycles N is counted as 1.34×10 4 , and according to the temperature distribution of the structure, the maximum temperature difference ΔT is obtained as 46.91℃ (the normal operation highest temperature 66.91℃ minus the room temperature 20℃).
[0102] S14. N is less than 10 6 . For the shell, according to the design fatigue curve (Table 3), the S value corresponding to the cycle number 10 6 is 86 MPa, and it is calculated according to the formula:
[0103] ΔT e = S / 2Eα = 126 MPa / (2×204 GPa×11.22×10 -6 / ℃) = 18.79℃;
[0104] For the nozzle, according to the design fatigue curve (Table 3), the S value corresponding to the cycle number 10 6 is 126 MPa, and it is calculated according to the formula:
[0105] ΔT e = S / 2Eα = 126 MPa / (2×195 GPa×15.3×10 -6 / ℃) = 21.12℃.
[0106] S15. Based on Table 5 in S10, according to the table, the number of transient times n with a temperature difference greater than ΔT e is 11600, which is greater than 0, so execute S16.
[0107] S16. For the shell, according to the design fatigue curve (Table 3), interpolate the S a value corresponding to the cycle number n of 111600 is 251 MPa, then:
[0108] ΔT0 = Sa / 2Eα = 251 MPa / (2 × 204 GPa × 11.22×10 -6 / ℃) = 54.81℃。
[0109] For the nozzle, interpolate the cycle number n corresponding to 111600 according to the design fatigue curve (Table 4), and the S a value is 352 MPa, then:
[0110] ΔT0 = S a / 2Eα = 352 MPa / (2 × 195 GPa × 15.3×10 -6 / ℃) = 59.03℃。
[0111] S17. For the shell and the nozzle respectively, judge whether ΔT in S13 is less than ΔT0 in S16. If ΔT < ΔT0 is satisfied, then execute S18; otherwise, detailed fatigue analysis should be carried out.
[0112] S18. Based on Table 5 involved in S1, count the normal operation transient cycle number N as 1.34×10 4 , and obtain the maximum temperature difference ΔT of dissimilar metals as 46.91℃ (the normal operation highest temperature 66.91℃ minus the room temperature 20℃) according to the temperature distribution of the structure.
[0113] S19. N is less than 10 6 . For the shell, according to the design fatigue curve (Table 3), the S value corresponding to the cycle number 10 6 is 86 MPa. For the nozzle, according to the design fatigue curve (Table 4), the S value corresponding to the cycle number 10 6 is 126 MPa. Take the smaller value of the S values as 86 MPa, and calculate the effective temperature fluctuation according to the formula:
[0114] ΔT e = S / 2(E1α1 - E2α2)
[0115] = 86 MPa / [2 × (195 GPa × 15.3×10 -6 / ℃ - 204 GPa × 11.22×10 -6 / ℃)] = 61.90℃。
[0116] S20. Judge whether ΔT in S18 is less than ΔT in S19 e . If ΔT < ΔT e is satisfied, then execute S21; otherwise, detailed fatigue analysis should be carried out.
[0117] S21. Based on Table 5 involved in S1, the number of seismic transients is 400 times, and the maximum stress intensity range S caused by the mechanical load acting on the nozzle during the earthquaker is 195.1 MPa.
[0118] S22, N is less than 10 6 , for the nozzle, according to the design fatigue curve (Table 4), the number of cycles is 10 6 The corresponding S value is 126 MPa.
[0119] S23. The number of transient cycles n with a stress range greater than S in Statistical Table 5 is 400, which is greater than 0, and S24 is executed.
[0120] S24. For the nozzle, interpolate according to the design fatigue curve (Table 4) to obtain the S value corresponding to the number of cycles n of 400 a is 1071 MPa.
[0121] S25. Judge the S in S21 r whether it is less than the S in S24 a , if S r < S a is satisfied, then S26 is executed; otherwise, a detailed fatigue analysis should be carried out.
[0122] S26. Through the above analysis, it is judged that the pressure vessel can be exempted from fatigue analysis.
[0123] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered by the protection scope of the present application.
Claims
1. A screening method for exemption from fatigue analysis of nuclear-grade equipment, characterized in that, Determine the design input for the fatigue analysis of nuclear-grade equipment. When the design transient meets all the screening conditions, the fatigue analysis is exempted; otherwise, the fatigue analysis is carried out. The screening conditions include: Condition 1: During normal use, the number of cycles in which the pressure rises from atmospheric pressure to the operating pressure and then returns to atmospheric pressure is less than the number of cycles corresponding to a stress amplitude S on the design fatigue curve a which is 3S m ; Condition 2: During normal use, the pressure fluctuation range is less than the first threshold; Condition 3: During startup and shutdown, the temperature difference between any two adjacent points on the equipment structure is less than the second threshold; Condition 4: During normal use, the temperature difference between any two adjacent points is less than the third threshold; Condition 5: For equipment made of materials with different elastic moduli or coefficients of thermal expansion, the algebraic value of the temperature change range during normal operation is less than the fourth threshold; Condition 6, stress range S r Less than the corresponding S on the design fatigue curve a value.
2. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1, characterized in that This method sequentially judges Conditions 1 to 6. If the conditions are met in sequence, the fatigue analysis is exempted; if one of the conditions is not met, the fatigue analysis is carried out.
3. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that The calculation formula for the first threshold is as follows: Wherein, P D is the design pressure; S is the S 6 value obtained by looking up according to the number of cycles of 10 a on the design fatigue curve; S m is the design stress intensity at the service temperature.
4. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that The calculation formula for the second threshold is as follows: where S a is the value obtained by looking up the specified number of start-up and shut-down cycles on the design fatigue curve; E is the elastic modulus at the average temperature of two adjacent points; α is the instantaneous expansion coefficient at the average temperature of two adjacent points.
5. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that, The calculation formula for the third threshold is as follows: Wherein, S is the value obtained by looking up according to the cycle number of 10 6 in the design fatigue curve.
6. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that The calculation formula for the fourth threshold is as follows: where S is the value obtained by looking up on the fatigue curve according to the number of cycles being 10 6 ; E1 and E2 are the elastic moduli of the two materials at the average temperature respectively; α1 and α2 are the instantaneous thermal expansion coefficients of the two materials at the average temperature respectively.
7. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that Stress range S r The stress range caused by mechanical loads other than pressure.
8. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 1 or 2, characterized in that The design input includes material properties, design pressure, and design transient.
9. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 8, characterized in that, The material properties include elastic modulus, coefficient of thermal expansion, allowable stress intensity, and design fatigue curve data.
10. The screening method for exemption from fatigue analysis of nuclear-grade equipment according to claim 8, characterized in that, The design transient includes temperature, pressure transient, and occurrence times.