A method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion

Abstract

This invention belongs to the field of stress corrosion cracking prediction and simulation technology. It provides an efficient method for predicting the entire stress corrosion cracking process based on an evolutionary mass transport model and a stress distribution model derived from Irwin's small-scale yield theory. The method includes the following steps: after completing the theoretical derivation and modeling in the first two parts, a MATLAB program based on the mathematical model is designed. The parameters are then verified using a dimensionless method while referencing experimentally obtained data points. Finally, the goal of predicting the entire stress corrosion cracking process is achieved. The method provided by this invention fully leverages the efficiency of numerical methods, effectively solving the problems of excessive computational resources consumed by detailed finite element modeling and analysis, and inaccurate predictions caused by pure data fitting neglecting the actual physical process. It provides an important method for estimating crack initiation time in practical engineering. This method is highly versatile, easy to master, and easy to implement.

Description

Technical Field

[0001] This patent relates to the field of stress corrosion cracking prediction and simulation technology, specifically to a prediction method based on one-dimensional stress corrosion crack inversion to determine crack initiation time. Background Technology

[0002] Stress corrosion cracking is a widespread phenomenon in the primary loop of nuclear power plants, often occurring at dissimilar metal butt welds. This is because these components are exposed to a complex aqueous chemical environment while being subjected to external loads. Typically, only forces far less than the ultimate load under normal conditions are required to cause damage, making it difficult to predict and extremely dangerous. Even more challenging is the extremely long initiation time of stress corrosion cracking in nuclear piping, reaching several years or more. Currently, there is no experimental testing method to effectively predict the crack initiation time of critical materials in nuclear material piping under high-temperature water conditions. Therefore, there is an urgent need to develop a hybrid testing and simulation method to effectively estimate the stress corrosion crack initiation time of critical components in nuclear material piping under high-temperature water conditions.

[0003] Most domestic and international research on the prediction of stress corrosion cracking is based on qualitative analysis, lacking research on the true mechanism of mechanochemical coupling. Furthermore, most literature uses simplified models, such as fitting experimentally measured data points to achieve predictive effects. These analytical results have certain biases and limitations in applicability, making it difficult to accurately reflect mechanical behavior and physical properties. Obtaining accurate data points experimentally requires a considerable amount of time (a thousand hours or even longer) and significant costs. On the other hand, while refined finite element analysis based on commercial software can yield more accurate results, it consumes substantial computational resources and takes a long time to solve. Therefore, it is essential to develop a prediction method that is based on real physical and mechanical properties and is also highly efficient. Summary of the Invention

[0004] The purpose of this invention is to provide a program for predicting the entire stress corrosion cracking process of alloy 690 in nuclear power plant cooling water circuits, based on an evolutionary mass transport model and a stress distribution model derived from Irwin's small-scale yield theory. This method balances high efficiency with accuracy in reflecting real physical processes. It effectively addresses the problems of phenomenological methods relying solely on experimental data, which neglect real physical processes and thus lead to inaccurate predictions, and the high computational costs required to establish accurate finite element models. Furthermore, it can be extended to stress corrosion problems of different types of metallic materials in different media.

[0005] The technical solution of the present invention is as follows: A method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion, comprising the following steps:

[0006] S1: Establish a spatial coordinate x along the thickness direction of the 690 alloy specimen, with the thickness represented by L. Taking the crack initiation point as the origin, the other end of the specimen is located at x = L. Assume the crack tip is at x = a c Position, a c The derivative with respect to time represents the instantaneous rate of crack evolution; the spatial coordinates of the initiation point of the passivation layer that forms on the surface of the 690 alloy specimen in a corrosive environment are x = a. c The thickness of the passivation layer is set to l, which is a material constant. p ;

[0007] S2: Establish an evolutionary mass transport model;

[0008] Introducing a field variable c∈[0,1], c(x,t) represents the state of material atoms near spatial position x at time t that are lost due to corrosion, i.e.

[0009]

[0010] Where j is the percentage mass transfer flux, expressed as:

[0011]

[0012] Where D is the equivalent diffusion coefficient of the material;

[0013] p is the hydrostatic pressure;

[0014] Δv is the volume release rate after atomic corrosion loss in alloy 690;

[0015] k B =1.38×10 -21 J / K is the Boltzmann constant;

[0016] T represents the system ambient temperature;

[0017] Substituting equation (2) into equation (1) yields the governing equation for c.

[0018]

[0019] The hydrostatic pressure p is calculated using the following formula;

[0020]

[0021] Where σ a This indicates the tensile stress load borne by the specimen;

[0022] The equivalent stress intensity factor, which takes corrosion effects into account, is obtained by substituting equation (5) into equation (6) and solving:

[0023]

[0024] Substituting equation (5) into equation (2) and removing the diffusion term, we obtain the boundary conditions at the crack tip:

[0025]

[0026] At the other end of the sample, j| x＝L =0

[0027] S3: Numerical simulation of the model;

[0028] S3.1: Parameter input and mesh generation;

[0029] S3.2: Establish the numerical discretization scheme for the model;

[0030] S4: Determine the location of the crack tip a c A graph showing how the time t changes.

[0031] In S1, L = 25 mm.

[0032] l p =0.5mm.

[0033] In S2, when c is 1, it means that the material is not corroded, and when c is 0, it means that the material is completely corroded.

[0034] In S2, Δv = 10 -30 nm 3 .

[0035] In S2, Where CW represents the amount of cold deformation of the specimen.

[0036] In S2, σ a Take 205 MPa.

[0037] In S2, the equivalent stress The corresponding critical stress intensity factor

[0038] In S2, c| t＝0 =1, a c =1.25mm.

[0039] In S3, the MATLAB simulation platform is used.

[0040] In S3.1, the thickness L = 25 mm, and the passivation layer thickness l p =0.5mm, temperature T=697K, stress intensity factor threshold Volume release rate Δv = 10 -30 nm 3 Cold deformation CW = 0.2, external load on specimen σ a=205 MPa; Divide the spatial domain x∈(0,L) into a uniform grid, Δx is denoted as the spatial grid size, Δt is denoted as the time grid size, and Δt = 0.1Δx 2 .

[0041] In S3.1, 100 grids were divided.

[0042] In S3.2, the two-dimensional function c(x,t) is represented by the function values ​​at the nodes. Let c represent the value of function c at the j-th spatial grid point at the i-th time step; substitute the initial value; then update it step by step along the time direction; at each time step, make the following update: approximate the numerical value of equation (3) using the difference method, and finally use the conservation law scheme in equation (3), that is, use

[0043]

[0044] Then, by discretizing equation (3) using the above equation, we can obtain:

[0045]

[0046] After updating function c, substitute equations (5) and (6) to solve for K. I The value of K is then compared. I With intensity factor threshold like Then proceed to the next time step update; if Then increase a c The value until Up to this point, we proceed to the next time step update. In a c When it increases If the temperature stops increasing, it indicates that the material has entered the mechanical fracture stage.

[0047] In S3.2, a c =1.25mm.

[0048] In S3.2, in a c When it increases The fact that the fracture stopped when the fracture rate increased indicates that the 690 alloy specimen entered the mechanical fracture stage.

[0049] S4, crack initiation time t inc =43 years; Stress corrosion life (t) of alloy 690 specimen span =57 years.

[0050] The significant advantage of this invention lies in its ability to rapidly and accurately predict the entire stress corrosion process of 690 alloy in nuclear power plant water circuits, compared to existing phenomenological fitting prediction methods, or to estimate the time required for crack initiation. This method can provide guidance for predicting potential cracks that are initiating. Furthermore, this method is highly versatile and can be extended to stress corrosion processes in other types of materials and media. Attached Figure Description

[0051] Figure 1 Geometric parameter diagram

[0052] Figure 2 Example diagram of prediction result analysis Detailed Implementation

[0053] Many specific details are set forth in the following description to provide a full understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of this application; therefore, this application is not limited to the specific embodiments disclosed below.

[0054] The terminology used in one or more embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the scope of one or more embodiments of this application. The singular forms “a,” “the,” and “the” used in one or more embodiments of this application and in the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” used in one or more embodiments of this application refers to and includes any or all possible combinations of one or more associated listed items.

[0055] It should be understood that although the terms first, second, etc., may be used to describe various information in one or more embodiments of this application, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, first may also be referred to as second without departing from the scope of one or more embodiments of this application, and similarly, second may also be referred to as first.

[0056] The specific implementation scheme of the present invention will be described below with reference to the technical solution and accompanying drawings.

[0057] The first step is to define the usage scenario and geometric parameters.

[0058] Assume a 690 alloy specimen with a thickness denoted by L, where L = 25 mm in this example. The considered application scenarios are as follows: Figure 1 As shown, a spatial coordinate x can be established along the thickness direction. Taking the crack initiation point as the origin, the other end of the specimen is located at x = L. Assume the crack tip is at x = a.c Position, a c The value of a will continue to increase over time. c The derivative with respect to time is the instantaneous rate of crack evolution. In a corrosive environment, a dense passivation layer forms on the surface of the 690 alloy specimen. The initiation point of this passivation layer is the crack tip, with spatial coordinates x = a. c The thickness of the passivation layer is set to l, which is a material constant. p For alloy 690, take l p =0.5mm. Passivation layer terminal (x=a) c +l p The area from the end of the specimen (x=L) is the 690 alloy material region.

[0059] The second step is to develop an evolutionary model of mass transport.

[0060] Establish a one-dimensional mass transport model, such as Figure 1 As shown. A field variable c∈[0,1] is introduced, where c(x,t) represents the loss of material atoms near spatial position x at time t due to corrosion. When c is 1, it indicates no corrosion; when c is 0, it indicates complete corrosion. The mass conservation equation should be satisfied, i.e.

[0061]

[0062] Where j is the percentage mass transfer flux, the expression can be derived from...

[0063]

[0064] Given, where D is the equivalent diffusion coefficient of the material, which has been experimentally calibrated; p is the hydrostatic pressure, the expression of which will be given later; Δv = 10 -30 nm 3 The volume release rate after atomic corrosion loss in alloy 690; k B =1.38×10 -21 J / K is the Boltzmann constant; T is the ambient temperature of the system, which can be any positive value as needed. The first term on the right-hand side of equation (2) represents diffusion, and the second term describes the migration process of alloy atoms to the corrosive environment induced by the hydrostatic pressure gradient at the crack tip. Substituting equation (2) into equation (1) yields the governing equation for c.

[0065]

[0066] Note that the left end of the domain of the spatial coordinate x in the above formula is the position of the crack tip.

[0067] The equivalent diffusion coefficient is determined by the following formula:

[0068]

[0069] Where CW represents the amount of cold deformation of the specimen. Substituting CW and temperature T into formula (3) yields the equivalent diffusion coefficient.

[0070] (2) The hydrostatic pressure p in the formula can be calculated by the following formula;

[0071]

[0072] Where σ a This indicates the tensile stress load borne by the specimen, which is taken as 205 MPa in one embodiment; The equivalent stress intensity factor, which takes into account corrosion effects, is the only unknown in equation (5). It can be obtained by substituting equation (5) into the following stress equilibrium integral equation:

[0073]

[0074] Under corrosion, the equivalent stress intensity factor in equation (5) will increase, to the point that it exceeds the critical stress intensity factor K of the passivation layer at a certain moment. IC For alloy 690, we take The following crack propagation criterion is used here: a c The value keeps increasing until... Down to K IC That's all for now.

[0075] The above model also needs to include boundary conditions for the field variable c at the crack tip and the other end of the sample. At the crack tip, the presence of the passivation layer inhibits diffusion, i.e., the first term on the right-hand side of equation (2). Substituting equation (5) into equation (2) and removing the diffusion term yields the boundary conditions at the crack tip:

[0076]

[0077] At the other end of the sample, we have j| x＝L =0.

[0078] Initial conditions also need to be provided, namely the initial distribution of corrosion within the material, c|. t＝0 and the initial crack length a c Here we take c| t＝0 =1, a c =1.25mm.

[0079] The third step is numerical simulation of the model.

[0080] The above model requires numerical simulation to predict stress corrosion life. Here, we use the MATLAB simulation platform as an example to introduce the steps for implementing numerical simulation of the model.

[0081] (1) Parameter input and mesh generation. Input the following parameters according to the actual situation. Here we select thickness L = 25mm and passivation layer thickness l. p =0.5mm, temperature T=697K, stress intensity factor threshold Volume release rate Δv = 10 -30 nm 3 Cold deformation CW = 0.2, external load on specimen σ a =205 MPa. Subsequently, the spatial domain x∈(0,L) is divided into a uniform grid, here with 100 grids. Here, Δx is used to denote the spatial grid size, and Δt is used to denote the time grid (here, Δt = 0.1Δx is chosen). 2 ).

[0082] (2) Establish the numerical discretization scheme for the model. The two-dimensional function c(x,t) is represented by the function values ​​at the nodes. For example, using... Let c represent the value of function c at the j-th spatial grid point at the i-th time step. Substitute the initial value (in this example, c) into the value. Then, it is updated step by step along the time direction. At each time step, the following update is made: Equation (3) is approximated to a numerical value using the difference method. Here, the last term of Equation (3) needs to use the conservation law scheme, that is, using...

[0083]

[0084] Then, by discretizing equation (3) using the above equation, we can obtain:

[0085]

[0086] After updating function c, substitute equations (5) and (6) to solve for K. I The value of can be found using the rectangle formula for solving the integral equation. Then compare K. I With intensity factor threshold like Then proceed to the next time step update; if Then increase a c The value until Up to this point, the program proceeds to the next time step for updating. The program is in a... c When it increases If the temperature stops increasing, it indicates that the material has entered the mechanical fracture stage.

[0087] Step 4: Stress corrosion life prediction.

[0088] After the above calculations are completed, the location 'a' of the crack tip can be drawn. c The graph of how it changes with time t, such as Figure 2As shown, the image presents a stepped pattern. The width of the first step represents the crack initiation time t. inc Let be the denoting factor, and in this example, we calculate t. inc = 43 years. The total program execution time represents the stress corrosion life of the material, expressed in t. span This means that the calculation in this example has t. span =57 years. This allows for rapid prediction of stress corrosion life, a parameter currently unmeasurable by existing testing methods, within seconds on a desktop computer.

[0089] The above description is merely 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 shall be included within the scope of protection of this patent.

[0090] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0091] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0092] The preferred embodiments disclosed above are merely illustrative of this application. The optional embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this application. These embodiments are selected and specifically described in this application to better explain the principles and practical applications of this application, thereby enabling those skilled in the art to better understand and utilize this application.

Claims

1. A method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion, characterized in that: Includes the following steps: S1: Establish a spatial coordinate x along the thickness direction of the 690 alloy specimen, with the thickness represented by L. Take the crack initiation point as the origin of the coordinate system. Then, the other end of the specimen is located at x = L. Assume the crack tip is at x = a c Position, a c The derivative with respect to time represents the instantaneous rate of crack evolution; the spatial coordinates of the initiation point of the passivation layer that forms on the surface of the 690 alloy specimen in a corrosive environment are x = a. c The thickness of the passivation layer is set to l, which is a material constant. p ; S2: Establish an evolutionary mass transport model; Introducing a field variable c∈[0,1], c(x,t) represents the state of material atoms near spatial position x at time t that are lost due to corrosion, i.e. Where j is the percentage mass transfer flux, expressed as: Where D is the equivalent diffusion coefficient of the material; p is the hydrostatic pressure; Δv is the volume release rate after atomic corrosion loss in alloy 690; k B =1.38×10 -21 J / K is the Boltzmann constant; T represents the system ambient temperature; Substituting equation (2) into equation (1) yields the governing equation for c. The hydrostatic pressure p is calculated using the following formula; Where σ a This indicates the tensile stress load borne by the specimen; The equivalent stress intensity factor, which takes corrosion effects into account, is obtained by substituting equation (5) into equation (6) and solving: Substituting equation (5) into equation (2) and removing the diffusion term, we obtain the boundary conditions at the crack tip: At the other end of the sample, j| x＝L =0 S3: Numerical simulation of the model; S3.1: Parameter input and mesh generation; S3.2: Establish the numerical discretization scheme for the model; S4: Determine the location of the crack tip a c A graph showing how the time t changes.

2. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S1, L = 25 mm.

3. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 2, characterized in that: L p <0.5mm.

4. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, when c is 1, it means that the material is not corroded, and when c is 0, it means that the material is completely corroded.

5. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, Δv = 10 -30 nm 3 .

6. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, Where CW represents the amount of cold deformation of the specimen.

7. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, σ a Take 205 MPa.

8. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, the equivalent stress The corresponding critical stress intensity factor 9. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S2, c| t＝0 =1, a c =1.25mm.

10. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S3, the MATLAB simulation platform is used.

11. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S3.1, the thickness L = 25 mm, and the passivation layer thickness l p =0.5mm, temperature T=697K, stress intensity factor threshold Volume release rate Δv = 10 -30 nm 3 Cold deformation CW = 0.2, external load on specimen σ a =205 MPa; Divide the spatial domain x∈(0,L) into a uniform grid, Δx is denoted as the spatial grid size, Δt is denoted as the time grid size, and Δt = 0.1Δx 2 .

12. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 11, characterized in that: In S3.1, 100 grids were divided.

13. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 11, characterized in that: In S3.2, the two-dimensional function c(x, f) is represented by the function values ​​at the nodes. Let c represent the value of function c at the j-th spatial grid point at the i-th time step; substitute the initial value; then update it step by step along the time direction; at each time step, make the following update: approximate the numerical value of equation (3) using the difference method, and finally use the conservation law scheme in equation (3), that is, use Then, by discretizing equation (3) using the above equation, we can obtain: After updating function c, substitute equations (5) and (6) to solve for K. I The value of K is then compared. I With intensity factor threshold like Then proceed to the next time step update; if Then increase a c The value until Up to this point, we proceed to the next time step update; in a c When it increases If the temperature stops increasing, it indicates that the material has entered the mechanical fracture stage.

14. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 13, characterized in that: In S3.2, a c =1.25mm.

15. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 13, characterized in that: In S3.2, in a c When it increases The fact that the fracture stopped when the fracture rate increased indicates that the 690 alloy specimen entered the mechanical fracture stage.

16. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1, characterized in that: In S4, the crack initiation time t inc =43 years; Stress corrosion life (t) of alloy 690 specimen span =57 years.

Images