Prediction method based on one-dimensional stress corrosion crack inversion crack initiation duration

Abstract

The invention belongs to the technical field of stress corrosion cracking prediction simulation, and provides a stress corrosion cracking whole-process efficient prediction method of a stress distribution model based on an evolved substance transmission model and an Irwin small-range yield theory, which comprises the following steps of: completing theoretical derivation of the first two parts and designing an MATLAB program based on a mathematical model after modeling; and parameters are checked by referring to data points obtained by an experiment through a dimensionless method, and finally, the target of predicting the whole process of stress corrosion cracking is achieved. Through the method provided by the invention, the high efficiency of the numerical method can be brought into full play, the problem of inaccurate prediction caused by too large calculation resource consumption of fine finite element modeling analysis and neglect of a real physical process by pure data fitting is effectively solved, and an important method is provided for estimating the crack initiation duration in actual engineering. The method is high in universality and easy to master and implement.

Description

Technical Field

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

[0002] Stress corrosion cracking is a widespread phenomenon in the primary circuit of nuclear power plants, and it often occurs at dissimilar metal butt welds. This is because such components are exposed to a complex water chemical environment and are subjected to external loads. At this time, it usually only takes a force far less than the limit load in a conventional environment to cause damage, which makes it difficult to predict and extremely harmful. What is even more tricky is that the time for stress corrosion initiation in nuclear pipelines is extremely long, reaching the order of several years or more. At present, there is no experimental test method that can effectively predict the crack initiation time of key materials in nuclear material pipelines in a high-temperature water environment. Therefore, it is urgent to develop a mixed test and simulation method to effectively estimate the initiation time of stress corrosion cracks in key components of nuclear material pipelines in a high-temperature water environment.

[0003] Most of the prediction studies on stress corrosion cracking at home and abroad are based on qualitative analysis, lacking the real mechanism research of mechanical and chemical coupling, and most of the literature adopts simplified models, such as fitting the experimental data points to achieve the prediction effect. The analysis results have certain deviations and applicable conditions, and it is difficult to accurately reflect the mechanical behavior and physical properties. In view of the fact that it takes a long time (one thousand hours or even longer) and a lot of cost to obtain an accurate data point in the experiment; on the other hand, although the fine finite element analysis based on commercial software can obtain more accurate results, it will consume more computing resources and take a long time to solve. In summary, it is very necessary to develop a set of prediction methods based on real physical and mechanical properties and at the same time efficient. Summary of the invention

[0004] The purpose of the present invention is to provide a stress corrosion cracking prediction program for the whole process of 690 alloy in nuclear power cooling water loops based on the stress distribution model of the evolutionary material transport model and Irwin's small-scale yield theory. This method can take into account both high efficiency and accuracy in line with the real physical process, and can effectively solve the problem that the phenomenological method based solely on experimental data ignores the real physical process, resulting in inaccurate prediction and the need to consume large computing resources to establish an accurate finite element model. It can even be extended to the stress corrosion problem of different types of metal 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 in the thickness direction of the 690 alloy specimen, and its thickness is represented by L. Take the crack initiation end as the origin of the coordinate, and the other end of the specimen is located at x = L. Assume that the crack tip is at x = a c The position of a c The derivative with respect to time is the instantaneous rate of crack evolution; the spatial coordinate of the starting point of the passivation layer formed on the surface of the 690 alloy specimen in a corrosive environment is x = a c The thickness of the passivation layer is the material constant and is set to l p ;

[0007] S2: Establish an evolving material transport model;

[0008] Introduce a field variable c∈[0,1], c(x,t) represents the situation where material atoms near the spatial position x at time t are missing due to corrosion, that is,

[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 of 690 alloy atoms after corrosion loss;

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

[0016] T is the system ambient temperature;

[0017] Substituting (2) into (1) we can get the control equation of c:

[0018]

[0019] The hydrostatic pressure p is calculated by the following formula:

[0020]

[0021] where σ a Indicates the tensile stress load borne by the specimen;

[0022] represents the equivalent stress intensity factor considering the corrosion effect, which is obtained by substituting equation (5) into equation (6):

[0023]

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

[0025]

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

[0027] S3: numerical simulation of the model;

[0028] S3.1: parameter input and grid division;

[0029] S3.2: Establish the numerical discretization format of the model;

[0030] S4: Get the crack tip position a c An image that changes over time t.

[0031] In S1, L=25mm.

[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 205Mpa.

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

[0038] In S2, c| t＝0 =1, a c =1.25mm.

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

[0040] In S3.1, the thickness L = 25 mm, 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, specimen external load σ a=205Mpa; divide the spatial domain x∈(0,L) into uniform grids, Δx is recorded as the spatial grid size, Δt is recorded as the time grid, Δt=0.1Δx 2 .

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

[0042] In S3.2, the two-dimensional function c(x,t) is expressed by the function value at the node. To represent the value of function c at the jth spatial grid point in the i-th time step; substitute the initial value; then gradually update along the time direction; make the following updates at each time step: use the difference to approximate the equation (3) to the value, and use the conservation law format at the end of equation (3), that is, use

[0043]

[0044] Then, we can discretize equation (3) by combining the above equation to obtain:

[0045]

[0046] After updating the function c, substitute into (5) and (6) to solve K I Then compare the value of K I With intensity factor threshold like Then enter the next time step update; if Then increase a c The value until Until then, the next time step update is started. c When increasing It also stops when it increases, indicating that the material enters the mechanical fracture stage.

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

[0048] In S3.2, in a c When increasing It also stopped when it increased, indicating that the 690 alloy specimen entered the mechanical fracture stage.

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

[0050] The significant effect of the present invention is that, for the stress corrosion phenomenon of 690 alloy in nuclear power water circuit, compared with the existing phenomenological fitting prediction method, the method provided by the present invention can quickly and accurately obtain a rough prediction of the entire stress corrosion process, or reversely estimate the time required for crack initiation. This method can provide a certain degree of guidance for predicting potential cracks that are initiating. Moreover, the method is highly versatile and can be extended to the stress corrosion process of other types of materials and media. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of geometric parameters

[0052] Figure 2 Example diagram of prediction result analysis DETAILED DESCRIPTION

[0053] 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.

[0054] 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.

[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 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.

[0056] The specific implementation scheme of the present invention is described below in conjunction with the technical scheme and the accompanying drawings.

[0057] The first step is to use the scene and define the geometry parameters.

[0058] Assume a 690 alloy specimen, whose thickness is represented by L. In this example, L = 25 mm. The application scenarios considered are as follows Figure 1 As shown, the spatial coordinate x can be established in the thickness direction, and the crack initiation end is taken as the coordinate origin. The other end of the specimen is located at x = L. Assuming that the crack tip is at x = ac The position of a c The value of will increase with time evolution. c The derivative with respect to time is the instantaneous rate of crack evolution. A dense passivation layer will form on the surface of the 690 alloy specimen in a corrosive environment. The starting point of the passivation layer is the crack tip, and its spatial coordinate is x = a c The thickness of the passivation layer is the material constant and is set to l p For 690 alloy, take l p =0.5mm. Passivation layer terminal (x = a c +l p ) to the end of the specimen (x=L) is the 690 alloy material area.

[0059] The second step is to evolve the material transfer model.

[0060] Establish a one-dimensional material transport model, such as Figure 1 As shown. Introduce a field variable c∈[0,1], c(x,t) represents the situation where the material atoms near the spatial position x at time t are missing due to corrosion. 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. The mass conservation equation should be satisfied, that is,

[0061]

[0062] Where j is the percentage mass transfer flux, the expression can be obtained by

[0063]

[0064] Given, where D is the equivalent diffusion coefficient of the material, which has been calibrated by experiment; p is the hydrostatic pressure, whose expression will be given later; Δv = 10 -30 nm 3 k is the volume release rate of 690 alloy atoms after corrosion loss; B =1.38×10 -21 J / K is the Boltzmann constant; T is the system ambient temperature, which can take any positive value as needed. The first term on the right side of equation (2) represents diffusion, and the second term describes the migration process of alloy atoms to the corrosive environment caused by the hydrostatic pressure gradient at the crack tip. Substituting equation (2) into (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] Here 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) can calculate 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 represents the tensile stress load borne by the specimen, which is 205 MPa in one embodiment; represents the equivalent stress intensity factor considering the corrosion effect, which is the only unknown quantity in equation (5) and 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, so that at a certain point it exceeds the critical stress intensity factor K of the passivation layer. IC For 690 alloy we take The following crack growth criterion is used here: a c The value of keeps increasing until Down to K IC Until the following.

[0075] The above model also needs to add the boundary conditions of the field variable c at the crack tip and the other end of the specimen. At the crack tip, the presence of the passivation layer inhibits the diffusion effect, which is the first term on the right side of equation (2). Substituting equation (5) into equation (2) and removing the diffusion term, the boundary condition at the crack tip can be obtained:

[0076]

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

[0078] At the same time, the initial conditions need to be given, that is, the initial distribution of corrosion conditions in 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 needs to be simulated numerically to achieve the purpose of stress corrosion life prediction. Here we take the MATLAB simulation platform as an example to introduce the steps of model numerical simulation.

[0081] (1) Parameter input and mesh division. Input the following parameters according to the actual situation. Here we select thickness L = 25 mm 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, specimen external load σ a =205MPa. Then the spatial domain x∈(0,L) is divided into uniform grids, here 100 grids are divided. Here Δx is used to denote the spatial grid size, and Δt is used to denote the time grid (here Δt=0.1Δx is selected). 2 ).

[0082] (2) Establish the numerical discrete format of the model. Replace the two-dimensional function c(x, t) with the function value at the node. For example, To represent the value of function c at the jth spatial grid point in the i-th time step. Substitute the initial value (in this example, ). Then gradually update along the time direction. At each time step, the following update is performed: Equation (3) is approximated to a numerical value using the difference. Here, the last term of Equation (3) needs to use the conservation law format, that is,

[0083]

[0084] Then, we can discretize equation (3) by combining the above equation to obtain:

[0085]

[0086] After updating the function c, substitute into (5) and (6) to solve K I The integral equation can be solved by using the rectangular formula. Then compare K I With intensity factor threshold like Then enter the next time step update; if Then increase a c The value until Until then, the next time step update is started. c When increasing It also stops when it increases, indicating that the material enters the mechanical fracture stage.

[0087] Step 4: Stress corrosion life prediction.

[0088] After the above calculations are completed, the crack tip position a can be drawn c The image changes with time t, such as Figure 2As shown in Figure 2, the image is stepped. The width of the first step indicates the crack initiation time t. inc , expressed as, this example calculates t inc = 43 years. The total time the program runs represents the stress corrosion life of the material, expressed as t span In this example, we calculate t span = 57 years. This allows a quick prediction of stress corrosion life, which cannot be measured using current test methods, to be made on a desktop computer in just a few seconds.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] 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 predicting crack initiation time based on one-dimensional stress corrosion crack inversion, characterized in that: The following steps are involved: S1: Establish a spatial coordinate x in the thickness direction of the 690 alloy specimen, and its thickness is represented by L. Take the crack initiation end as the origin of the coordinate, and the other end of the specimen is located at x = L. Assume that the crack tip is at x = a c The position of a c The derivative with respect to time is the instantaneous rate of crack evolution; the spatial coordinate of the starting point of the passivation layer formed on the surface of the 690 alloy specimen in a corrosive environment is x = a c The thickness of the passivation layer is the material constant and is set to l p ; S2: Establish an evolving material transport model; Introduce a field variable c∈[0,1], c(x,t) represents the situation where material atoms near the spatial position x at time t are missing due to corrosion, that is, 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 of 690 alloy atoms after corrosion loss; k B =1.38×10 -21 J / K is the Boltzmann constant; T is the system ambient temperature; Substituting (2) into (1) we can get the control equation of c: The hydrostatic pressure p is calculated by the following formula: where σ a Indicates the tensile stress load borne by the specimen; represents the equivalent stress intensity factor considering the corrosion effect, which is obtained by substituting equation (5) into equation (6): Substituting (5) into (2) and removing the diffusion term, we obtain the boundary condition at the crack tip: At the other end of the specimen, j| x＝L =0 S3: numerical simulation of the model; S3.1: parameter input and grid division; S3.2: Establish the numerical discretization format of the model; S4: Get the crack tip position a c An image that changes over time t.

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

3. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 2 is 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 is 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 is 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 is 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 is characterized in that: In S2, σ a Take 205Mpa.

8. The method for predicting crack initiation time based on one-dimensional stress corrosion crack inversion according to claim 1 is characterized in that: In S2, 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 is 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 is characterized in that: In S3, 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 is characterized in that: In S3.1, the thickness L = 25 mm, 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, specimen external load σ a =205Mpa; divide the spatial domain x∈(0,L) into uniform grids, Δx is recorded as the spatial grid size, Δt is recorded as the time grid, 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 are 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, t) is expressed by the function value at the node. To represent the value of function c at the jth spatial grid point in the i-th time step; substitute the initial value; then gradually update along the time direction; make the following updates at each time step: use the difference to approximate the equation (3) to the value, and use the conservation law format at the end of equation (3), that is, use Then, we can discretize equation (3) by combining the above equation to obtain: After updating the function c, substitute into (5) and (6) to solve K I Then compare the value of K I With intensity factor threshold like Then enter the next time step update; if Then increase a c The value until Until then, enter the next time step update. c When increasing It also stops when it increases, indicating that the material enters the mechanical fracture stage.

14. A 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. A 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 increasing It also stopped when it increased, indicating that the 690 alloy specimen entered the mechanical fracture stage.

16. A 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 of 690 alloy specimen t span =57 years.

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