Constraint factor calculation method for crack initiation in structure

Abstract

The invention discloses a method for calculating constraint factors of crack initiation in a structure, which is characterized in that on the basis of dispersion data of fracture toughness values KJQ of crack initiation of cracks with different sizes in the structure at different temperatures T and material ductile-brittle transition temperature RTNDT, the analysis process comprises the following steps: 1, analyzing the fracture toughness value KJQ of the cracks with different sizes in the structure along with the specific value a / W of the crack size a to the structure wall thickness W; performing linear analysis on the fracture toughness value KJQ data at different temperatures T to obtain a slope and an intercept; 2, analyzing the relationship between the intercept value and the difference (T-RTNDT) between the temperature T and the material ductile-brittle transition temperature RTNDT; thirdly, an ideal fracture toughness KJQ-index value is obtained through calculation; and fourthly, considering the ideal fracture toughness KJQ-index and the reference fracture toughness KJQ-base to obtain a constraint factor F value. The provided constraint factor calculation method can serve the fracture failure risk analysis of the primary loop pressure-bearing equipment of the nuclear energy system and better serve the analysis design of the nuclear energy equipment.

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 pipelines of the nuclear energy system are important barriers to prevent the leakage of radioactive coolant. Therefore, in the design analysis, nuclear energy engineers are very cautious in evaluating the integrity of the equipment. According to the requirements of nuclear energy specifications, the equipment integrity evaluation generally includes stress strength analysis, fatigue analysis, ratchet analysis and fracture failure risk analysis. One of the main reasons for conducting fracture failure risk analysis is that the pressure vessel of the pressurized water reactor is subjected to high doses of neutron irradiation throughout its service life, which will cause the ductility of the reactor pressure vessel material to decrease, resulting in a significant increase in the risk of uncontrollable fracture failure and the probability of radioactive coolant leakage. The design requires that the probability of uncontrollable fracture failure of the equipment needs to be kept at an extremely low probability level, so as to ensure that the probability of radioactive coolant leakage is kept at an extremely low probability and acceptable level. Therefore, in the design analysis, engineers need to combine the overall indicator characteristics of the reactor type to complete the reactor pressure vessel fracture failure risk analysis.

[0003] It is known that in the fracture failure risk analysis of equipment, the fracture toughness of the material is an extremely important parameter, which is closely related to the crack initiation. At the same time, the crack initiation is closely related to the local deformation of the crack, and the constraint factor can be used to describe the local deformation of the crack tip. The fracture toughness in the current nuclear energy specification is composed of the analysis area temperature T (unit ℃) and the ductile-brittle transition temperature RT of the material in the analysis area. NDT (Unit: °C) The difference between T-RT NDT (unit ℃) described in the calculation formula. However, some research work has shown that the ability of shallow cracks in structures to resist fracture failure risk is higher than that of deep cracks in structures. The internal reason is that the external applied energy required for the initiation of shallow cracks in structures and deep cracks in structures is different. The external applied energy required for the initiation of shallow cracks is higher than that required for the initiation of deep cracks. Further mechanism research points out that the initiation of shallow cracks in structures and the initiation of deep cracks in structures correspond to their own fracture toughness. It can be further known that the initiation of shallow cracks in structures and the initiation of deep cracks in structures correspond to different local deformation degrees of crack tips, that is, different constraint factors. Unfortunately, there is no crack initiation analysis calculation formula that considers the analysis area temperature, the ductile-brittle transition temperature of the material, and the local deformation of the crack tips of different sizes in the structure, that is, the fracture toughness calculation formula. The reason is that the initiation of cracks in structures will cause local deformation of the crack tip, and this local deformation needs to be expressed by constraint factors. At present, there is no established constraint factor calculation method for crack initiation in structures.

[0004] From the above description, it can be seen that the initiation of cracks in a structure will cause local deformation of the crack, and the constraint factor can be used to describe the local deformation of the crack. For a structure operating at service temperature, if a crack in the structure is initiated, the degree of local deformation of the crack caused by the operating environment is directly related to the constraint factor. At present, there is no calculation method for the local deformation index of the crack that describes the initiation of cracks in the structure, that is, the constraint factor calculation method. Therefore, it is necessary to establish a constraint factor calculation method for crack initiation in a structure to serve the fracture failure risk analysis of the primary circuit pressure equipment of the nuclear energy system and ensure the safety of nuclear energy equipment design. Summary of the invention

[0005] The purpose of the present invention is to establish a method for calculating the constraint factor of crack initiation in a structure by analyzing the crack initiation behavior and local deformation behavior of cracks of different sizes in the structure and using constraint factors to describe the local deformation behavior of the crack. Based on the established calculation method, it can serve the fracture failure risk analysis of the primary circuit pressure-bearing equipment of the nuclear energy system and better serve the analysis and design of nuclear energy equipment.

[0006] The technical solution of the present invention is as follows: A method for calculating a constraint factor of crack initiation in a structure comprises 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 cracks of different sizes in the material structure at different temperatures T is obtained through experiments. JQ Scattered data with the ratio a / W of crack size a to structure wall thickness W;

[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: Combine the parameter λ obtained in S40 to update the intercept c, and calculate the updated intercept c, i.e., c update ;

[0015]

[0016] 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;

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

[0018] S70: The benchmark 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);

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

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

[0021] 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.

[0022] 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 .

[0023] In the S10, -40°C ≤ RT NDT ≤0℃.

[0024] In S10, RT NDT Select -25℃.

[0025] In the step S20, the temperature T has a value range of -85°C ≤ T ≤ 35°C.

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

[0027] In the above S40, λ=96.53.

[0028] In the S50, c update The value ranges from 290.13 to 1220.00.

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

[0030] In the S60, K JQ-idealize The value ranges from 276.2 to 1117.1.

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

[0032] The significant effect of the present invention is that the fracture toughness value K of cracks of different sizes in the structure at different known temperatures T can be calculated by the provided calculation method. JQ The dispersion data and the ductile-brittle transition temperature RT of the material change with the ratio a / W of crack size a and structure wall thickness W. NDT Under such circumstances, a calculation method for the local deformation degree index of cracks that describes the initiation of cracks in the structure, namely, a constraint factor calculation method, is established, which can better serve the fracture failure risk analysis of the primary circuit pressure equipment of the nuclear energy system. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0034] Figure 2 is a parametric lambda analysis.

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

[0036] Many specific details are described in the following description to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without violating the connotation of the present application, so the present application is not limited by the specific implementation disclosed below.

[0037] The terms used in one or more embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to limit one or more embodiments of the present application. The singular forms of "a", "said" and "the" used in one or more embodiments of the present application and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used in one or more embodiments of the present application refers to and includes any or all possible combinations of one or more associated listed items.

[0038] It should be understood that, although the terms first, second, etc. may be used to describe various information in one or more embodiments of the present application, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of one or more embodiments of the present application, the first may also be referred to as the second, and similarly, the second may also be referred to as the first.

[0039] In order to achieve the above-mentioned invention object, a method for calculating the constraint factor of crack initiation in a structure is described, and the specific process is as follows:

[0040] S10: Obtain the ductile-brittle transition temperature RT of the material through experiments NDT , where RT NDT The unit is °C;

[0041] S20: The fracture toughness value K of cracks of different sizes in the material structure at different temperatures T is obtained through experiments. JQ Scattered data as the ratio of crack size a to structure wall thickness W, a / W, changes; temperature T is in °C and a / W is in mm / mm.

[0042] 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 ;

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

[0044] Where K JQ The unit is MPa·m 0.5 , the recommended a / W range 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 NDT , the following formula (2) is used to perform adaptive fitting analysis on the data to obtain the parameter λ;

[0046]

[0047] S50: Combine the parameter λ obtained in S40 to update the intercept c, and calculate the updated intercept c, i.e., c update ;

[0048]

[0049] 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;

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

[0051] Where K JQ-idealize The unit is MPa·m 0.5 , the recommended a / W range is 0.10≤a / W≤0.80.

[0052] S70: The benchmark fracture toughness K at the corresponding temperature T is obtained by formula (5): JQ-base , K JQ-base The maximum value a is the crack size a in S60 max K calculated when JQ-idealize The constraint factor F corresponding to the corresponding temperature T and the corresponding crack size a is obtained 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] 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.

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

[0057] Example 1 (compact tensile structure):

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

[0059] The detailed implementation process is as follows:

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

[0061] Table 1S30 analysis results

[0062] <![CDATA[T-RT NDT / ℃]]> Temperature / ℃ 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 <![CDATA[1220.0(c max )]]> 40 15 -686.2 1061.4 60 35 -686.2 1057.1

[0063] Enter S40 and obtain the parameter λ=96.53. The S40 analysis results are shown below. Figure 2 ;

[0064] Enter S50 and get C update , the results are shown in the table below;

[0065] Table 2 cupdat e-value

[0066]

[0067]

[0068] Enter S60 and obtain the idealized fracture toughness K JQ-idealize The results are shown in the table below;

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

[0070]

[0071]

[0072] Enter S70 and obtain the constraint factor F. The results are shown in the table below.

[0073] If T-RT NDT ≤-40℃, it is recommended that the constraint factor F be 1.00; if T-RT NDT ≥-20℃, then the constraint factor F is T-RT NDT = -20℃ corresponding constraint factor value; the constraint factors corresponding to other crack sizes and temperatures can be obtained by a / W and T-RT in the above tableNDT When using table extrapolation, the boundary values ​​in the table should be taken.

[0074] Table 4 Constraint factor F

[0075]

[0076] The above description is only a preferred embodiment of this patent and is not intended to limit this patent. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of this patent should be included in the scope of protection of this patent.

[0077] It should be noted that, for the above-mentioned method embodiments, for the sake of simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described action sequence, because according to the present application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0078] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0079] The preferred embodiments of the present application disclosed above are only used to help explain the present application. The optional embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of the present application. The present application selects and specifically 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 understand and use the present application well.

Claims

1. A method for calculating a constraint factor for crack initiation in a structure, characterized in that: 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 cracks of different sizes in the material structure at different temperatures T is obtained through experiments. JQ Scattered data with the ratio a / W of crack size a to structure wall thickness W; 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 benchmark 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, characterized in that: 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 step S20, the temperature T has a value range of -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 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 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 ranges from 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 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 S70, if T-RT NDT ≤-40℃, the constraint factor F is 1.00.

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