Method for calculating constraint factor of crack initiation in structure

Abstract

The application discloses a method for calculating a constraint factor of crack initiation in a structure, and the crack initiation fracture toughness value K JQ of different sizes in the structure at different temperatures T NDT The dispersion data of the crack size a and the structure wall thickness W ratio a / W, the material ductile-brittle transition temperature RT JQ and the like are analyzed, and the analysis process is as follows: first, the fracture toughness value K NDT at different temperatures T is analyzed, and the slope and the intercept are obtained by performing linear analysis on the data; second, the relationship between the intercept value and the temperature T and the material ductile-brittle transition temperature RT NDT is analyzed; third, the ideal fracture toughness K JQ‑idealize is calculated; fourth, the constraint factor F value is obtained by considering the ideal fracture toughness K JQ‑idealize , the reference fracture toughness K JQ‑base and the like. The constraint factor calculation method can serve the fracture failure risk analysis of a primary loop pressure-bearing device of a nuclear energy system, and better serve the analysis and design of the nuclear energy device.

Description

Technical Field

[0001] This patent relates to the field of fracture mechanics technology, and specifically to a method for calculating the constraint factor of crack initiation in a structure. Background Art

[0002] The primary pressure-bearing equipment and piping in a nuclear power system are crucial barriers to preventing radioactive coolant leaks. Therefore, nuclear engineers are extremely cautious in evaluating equipment integrity during design analysis. According to nuclear energy regulations, equipment integrity evaluations generally include stress strength analysis, fatigue analysis, ratcheting analysis, and fracture failure risk analysis. A primary reason for conducting fracture failure risk analysis is that pressurized water reactor (PWR) pressure vessels are subjected to high neutron irradiation doses throughout their service life, which can reduce the ductility of the reactor pressure vessel material, significantly increasing the risk of uncontrolled fracture failure and the probability of radioactive coolant leakage. Design requirements require that the probability of uncontrolled fracture failure in equipment be kept to an extremely low level to ensure that the probability of radioactive coolant leakage remains extremely low and acceptable. Therefore, during design analysis, engineers need to consider the overall characteristics of the reactor model to complete the reactor pressure vessel fracture failure risk analysis.

[0003] It is known that in equipment fracture failure risk analysis, material fracture toughness is an extremely important parameter, closely related to crack initiation. At the same time, crack initiation is closely related to local deformation of the crack, and the constraint factor can be used to describe the local deformation at the crack tip. The fracture toughness in the current nuclear energy specification is a combination of the analysis area temperature T (unit: ° C) and the ductile-brittle transition temperature RT of the material in the analysis area. NDT (Unit: °C) The difference between T-RT NDT (unit: °C) is described by a calculation formula. However, some research has shown that shallow cracks in structures have a higher resistance to fracture failure than deep cracks. The underlying reason for this is that the external energy required for the initiation of shallow cracks in structures is different from that required for the initiation of deep cracks in structures. The external energy required for shallow crack initiation is higher than that required for the initiation of deep cracks. Further mechanistic research indicates that the initiation of shallow cracks in structures and deep cracks in structures correspond to different fracture toughnesses. Furthermore, it is known that the initiation of shallow cracks in structures and deep cracks in structures correspond to different degrees of local deformation at the crack tip, that is, different constraint factors. Unfortunately, a crack initiation analysis and calculation formula (i.e., a fracture toughness calculation formula) that considers the temperature of the analysis area, the ductile-brittle transition temperature of the material, and the local deformation at the crack tip of different sizes in the structure has not yet been established. This is because the initiation of cracks in structures causes local deformation at the crack tip, and this local deformation needs to be expressed through a constraint factor. Currently, there is no established method for calculating the constraint factor for crack initiation in structures.

[0004] As can be seen from the above explanation, crack initiation in a structure will cause localized deformation, and the constraint factor can be used to describe this localized deformation. If a crack initiates in a structure operating at service temperature, the degree of localized deformation caused by the operating environment is directly related to the constraint factor. Currently, there is no established method for calculating the localized deformation index that describes crack initiation in a structure, or the constraint factor. Therefore, a method for calculating the constraint factor for structural crack initiation is needed to analyze the fracture failure risk of primary-circuit pressure equipment in nuclear energy systems and ensure the safety of nuclear equipment design. Summary of the Invention

[0005] The purpose of this invention is to develop a method for calculating the constraint factor for crack initiation in structures by analyzing the crack initiation behavior and local deformation of cracks of varying sizes in structures and describing the local deformation behavior using constraint factors. This method can be used to analyze the fracture failure risk of primary-circuit pressure equipment in nuclear power systems, further enhancing the analysis and design of nuclear power equipment.

[0006] The technical solution of the present invention is as follows: A method for calculating the constraint factor of crack initiation in a structure, comprising the following steps:

[0007] S10: Obtain the ductile-brittle transition temperature RT of the material through experiments NDT ;

[0008] S20: The fracture toughness value K of the material structure at different temperatures T at which cracks of different sizes start to initiate is obtained through experiments. JQ Scattered data with the change of the ratio a / W of crack size a to the wall thickness W of the structure;

[0009] S30: Use linear fitting formula (1) to analyze the data at different temperatures T in S20, obtain the slope k and intercept c at different temperatures T, and record the corresponding different temperatures T and c max The largest value among the different intercept c values ​​is c max ;

[0010] K JQ =k*a / W+c (1)

[0011] where K JQ The unit is MPa·m 0.5 , the recommended a / W range is 0.10≤a / W≤0.80.

[0012] S40: Combine the intercept c in S30 and the corresponding different temperatures T, the ductile-brittle transition temperature RT of the material in S10 NDT , the following formula (2) is used to perform adaptive fitting analysis on the data to obtain the parameter λ;

[0013]

[0014] S50: update the intercept c by combining the parameter λ obtained in S40, and calculate the updated intercept c, i.e. c update ;

[0015]

[0016] S60: combine the slope k and the a / W ratio in S30, and c update in S50, and obtain the idealized fracture toughness K JQ-idealize value under different crack sizes by formula (4);

[0017] K JQ-idealize = k*a / W + c update (4)

[0018] S70: obtain the reference fracture toughness K JQ-base under the corresponding temperature T by formula (5), and then obtain the constraint factor F corresponding to the corresponding temperature T and the corresponding crack size a by formula (6);

[0019] K JQ-base = K JQ-idealize (a max / W) (5)

[0020] F = K JQ-idealize (a / W) / K JQ-base (6)

[0021] wherein the unit of F is MPa·m 0.5 / MPa·m 0.5 , K JQ-idealize (a / W) represents K JQ-idealize is a function of a / W, K JQ-idealize (a max / W) represents K JQ-idealize in the calculation, a / W takes a max / W.

[0022] The unit of RT NDT is ℃, the unit of temperature T is ℃, the unit of a / W is mm / mm, the unit of K JQ is MPa·m 0.5 , the unit of K JQ-idealize is MPa·m 0.5 , and the unit of F is MPa·m 0.5 / MPa·m 0.5 .

[0023] In S10, -40℃ ≤ RT NDT ≤ 0℃.

[0024] In the S10, the RT NDT -25℃ is selected.

[0025] In the S20, the value range of the different temperature T is -85℃≤T≤35℃.

[0026] In the S30, the a / W range is 0.10≤a / W≤0.80.

[0027] In the S40, λ=96.53.

[0028] In the S50, the value of c update is 290.13 to 1220.00.

[0029] In the S60, the a / W range is 0.10≤a / W≤0.80.

[0030] In the S60, the value of K JQ-idealize is 276.2 to 1117.1.

[0031] In the S70, if T-RT NDT ≤-40℃, the constraint factor F is 1.00.

[0032] The significant effect of the present application is that: through the provided calculation method, the fracture toughness value K JQ of the crack initiation of the structure under different temperature T and different crack size a can be known. NDT With the dispersion data of the crack size a and the structure wall thickness W ratio a / W, the material ductile-brittle transition temperature RT JQ , the calculation method of the crack local deformation degree index describing the crack initiation of the structure, i.e., the constraint factor calculation method, can better serve the fracture failure risk analysis of the nuclear energy system primary loop pressure-bearing equipment. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is the dispersion data of the fracture toughness value K JQ .

[0034] Figure 2 is the parameter λ analysis.

[0035] Figure 3 The analysis process of the present application is briefly described. DETAILED DESCRIPTION

[0036] In the following description, many specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be practiced in a variety of ways beyond the specific embodiments described herein without departing from the scope of the present application, and it is understood that similar changes in form and substitution of equivalent elements are intended to be included within the scope of the present application. It is therefore to be understood that the application can be practiced with modification and alteration, and that the application should not be limited to the described embodiments.

[0037] The terminology used in this disclosure of one or more embodiments is for the purpose of describing particular embodiments only and is not intended to be limiting of one or more embodiments. As used in this disclosure and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0038] It is to be understood that, although the terms first, second, etc. can be used herein to describe various information, these terms are not intended to denote a particular order or relationship between the information. For example, without departing from the scope of one or more embodiments, first can be termed second, and similarly, second can be termed first.

[0039] To achieve the above-mentioned object, the constraint factor calculation method of crack initiation in the structure is described, and the specific process is as follows:

[0040] S10: Obtain the ductile-brittle transition temperature RT of the material through experiment NDT , wherein RT NDT is the ductile-brittle transition temperature of the material, and the unit is ℃.

[0041] S20: Obtain the fracture toughness value K of crack initiation of different sizes in the structure of the material at different temperatures T through experiment JQ , wherein T is the temperature, the unit is ℃, and a / W is the ratio of crack size a to structure wall thickness W, the unit is mm / mm.

[0042] S30: Analyze the data at different temperatures T in S20 by using linear fitting formula (1) to obtain the slope k and intercept c at different temperatures T, and record the corresponding different temperatures T, c max , and the maximum value of different intercept c is c max .

[0043] K JQ = k*a / W + c (1)

[0044] , wherein K JQ is the fracture toughness value of crack initiation, the unit is MPa·m 0.5 , and the recommended range of a / W is 0.10≤a / W≤0.80.

[0045] S40: Combine the intercept c in S30 and the corresponding different temperatures T, the ductile-brittle transition temperature RT of the material in S10, and adaptively fit and analyze the data by using the following formula (2) to obtain the parameter λ NDT .

[0046]

[0047] S50: Update the intercept c by combining the parameter λ obtained in S40, and calculate the updated intercept c, i.e., c = c + λ update ;

[0048]

[0049] S60: Obtain the idealized fracture toughness K update value under different crack sizes by using formula (4) in combination with the slope k and a / W ratio in S30 and c JQ-idealize in S50.

[0050] K JQ-idealize = k * a / W + c update (4)

[0051] wherein K JQ-idealize is in MPa·m 0.5 , and the recommended a / W range is 0.10 ≤ a / W ≤ 0.80.

[0052] S70: Obtain the reference fracture toughness K JQ-base under the corresponding temperature T by formula (5), K JQ-base is the K max value calculated in S60 when the crack size a takes the maximum value a JQ-idealize , and then obtain the constraint factor F corresponding to the corresponding temperature T and the corresponding crack size a by formula (6).

[0053] K JQ-base = K JQ-idealize (a max / W) (5)

[0054] F = K JQ-idealize (a / W) / K JQ-base (6)

[0055] wherein F is in MPa·m 0.5 / MPa·m 0.5 , K JQ-idealize (a / W) indicates that K JQ-idealize is a function of a / W, and K JQ-idealize (a max / W) indicates that K JQ-idealize is calculated with a / W taking a max / W.

[0056] The parameters required in the analysis process include: the fracture toughness value K JQ of the crack initiation under different temperatures T and different sizes of the structure, the dispersion data of the crack size a and the structure wall thickness W ratio a / W, and the material ductile-brittle transition temperature RTNDT .

[0057] Example 1 (Compact Tension Specimen):

[0058] Brittle-ductile transition temperature RT of material 16MND5 NDT = -25℃, fracture toughness value K of different size cracks in structure at different temperature T JQ The dispersion data with the change of crack size a and structure wall thickness W ratio a / W is shown in Figure 1 .

[0059] The detailed implementation process is as follows:

[0060] Enter S30, obtain the slope k, intercept c and record the corresponding temperature T, S30 analysis results are shown in Table 1;

[0061] Table 1 S30 analysis results

[0062] T-RT NDT / ℃]] Temperature / °C Slope k c -60 -85 -92.9 383.6 -40 -65 -92.9 478.5 -20 -45 -686.2 1123.3 0 -25 -686.2 1090.3 20 -5 -686.2 1220.0(c max )]]> 40 15 -686.2 1061.4 60 35 -686.2 1057.1

[0063] Enter S40, obtain parameter λ = 96.53, S40 analysis results are shown below Figure 2 ;

[0064] Enter S50, obtain C update , results are shown in the following table;

[0065] Table 2 cupdat e value

[0066]

[0067]

[0068] Enter S60, obtain ideal fracture toughness K JQ-idealize value, results are shown in the following table;

[0069] Table 3 Ideal fracture toughness K JQ-idealize value

[0070]

[0071]

[0072] Enter S70, obtain constraint factor F, results are shown in the following table.

[0073] If T-RT NDT ≤ -40℃, the constraint factor F is recommended to be 1.00; if T-RT NDT ≥ -20℃, the constraint factor F is T-RT NDT = -20℃ corresponding constraint factor value; the constraint factor corresponding to other crack sizes and temperatures can be obtained through the a / W and T-RTNDT Interpolation yields that the border values in the table should be taken when using table extrapolation.

[0074] Table 4 Constraint factor F

[0075]

[0076] The above description is only preferred embodiments of the present patent, and is not used to limit the present patent. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present patent should be included in the protection scope of the present patent.

[0077] It should be noted that, for the foregoing method embodiments, in order to facilitate description, they are all expressed as a combination of a series of actions, but those skilled in the art should know that the present application is not limited by the action sequence described, because according to the present application, certain steps can be performed in other sequences or at the same time. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily essential to the present application.

[0078] In the above embodiments, the description of each embodiment has its own focus, and the parts not described in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0079] The preferred embodiments of the present application disclosed above are only used to help explain the present application. The alternative embodiments do not describe all the details and do not limit the present application to the specific embodiments described. Obviously, according to the content of the present application, many modifications and changes can be made. The present application selects and describes these embodiments in order to better explain the principles and practical applications of the present application, so that those skilled in the art can well understand and utilize the present application.

Claims

1. A method for calculating a constraint factor for crack initiation in a structure, characterized by: The following steps are involved: S10: Obtain the ductile-brittle transition temperature RT of the material through experiments NDT ; S20: The fracture toughness value K of the material structure at different temperatures T at which cracks of different sizes start to initiate is obtained through experiments. JQ Scattered data with the change of the ratio a / W of crack size a to the wall thickness W of the structure; S30: Use linear fitting formula (1) to analyze the data at different temperatures T in S20, obtain the slope k and intercept c at different temperatures T, and record the corresponding different temperatures T and c max The largest value among the different intercept c values ​​is c max ; K JQ =k*a / W+c (1) where K JQ The unit is MPa·m 0.5 , the recommended a / W range is 0.10≤a / W≤0.80; S40: Combine the intercept c in S30 and the corresponding different temperatures T, the ductile-brittle transition temperature RT of the material in S10 NDT , the following formula (2) is used to perform adaptive fitting analysis on the data to obtain the parameter λ; S50: Combine the parameter λ obtained in S40 to update the intercept c and calculate the updated intercept c, i.e. c update ; S60: Combine the slope k and a / W ratio in S30, c in S50 update , using formula (4) to obtain the idealized fracture toughness K under different crack sizes JQ-idealize value; K JQ-idealize =k*a / W+c update (4) S70: The baseline fracture toughness K at the corresponding temperature T is obtained by formula (5) JQ-base , and then the constraint factor F corresponding to the corresponding temperature T and the corresponding crack size a is obtained through formula (6); K JQ-base =K JQ-idealize (a max / W) (5) F=K JQ-idealize (a / W) / K JQ-base (6) The unit of F is MPa·m 0.5 / MPa·m 0.5 , K JQ-idealize (a / W) represents K JQ-idealize is a function of a / W, K JQ-idealize (a max / W) indicates K JQ-idealize In the calculation, a / W takes a max / W.

2. The method for calculating the constraint factor of crack initiation in a structure according to claim 1, characterized in that: The RT NDT The unit is ℃, temperature T is ℃, a / W is mm / mm, K JQ The unit is MPa·m 0.5 , K JQ-idealize The unit is MPa·m 0.5 、F unit is MPa·m 0.5 / MPa·m 0.5 .

3. The method for calculating the constraint factor of crack initiation in a structure according to claim 1, characterized in that: In the S10, -40°C ≤ RT NDT ≤0℃.

4. The method for calculating the constraint factor of crack initiation in a structure according to claim 3, wherein: RT NDT =-25℃。 5. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the above S20, the range of the different temperatures T is -85°C ≤ T ≤ 35°C.

6. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the above-mentioned S30, the range of a / W is 0.10≤a / W≤0.

80.

7. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the above-mentioned S40, λ=96.

53.

8. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the S50, c update The value range is 290.13 to 1220.

00.

9. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the above S60, the range of a / W is 0.10≤a / W≤0.

80.

10. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the S60, K JQ-idealize The value ranges from 276.2 to 1117.

1.

11. The method for calculating the constraint factor of crack initiation in a structure according to claim 4, characterized in that: In the above S70, if T-RT NDT ≤-40℃, the constraint factor F is 1.00.

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