A method for modeling pitting corrosion simulation cellular automaton with fast stress influence

Abstract

The application discloses a kind of pitting simulation cellular automaton modeling methods of fast adding stress influence, the method is: the whole pitting model is converted into two-dimensional cell space containing all reaction elements by computer language method, while the stress-strain distribution of each metal cell in each pitting pit in each step is calculated by using finite element method in the process of pitting growth, then the influence factor of stress-strain on each metal cell is calculated by stress calculation model, return cellular automaton model for iterative calculation, the width and depth of pitting development and pitting current are obtained.In the existing cellular automaton simulation for pitting, most of them are for the simulation under the steady-state growth of pitting, and it is difficult to create components when loading, and the cellular automaton and finite element cells are difficult to correspond one by one.The model has the randomness characteristics of pitting, and is fast and simple in the connection between cellular automaton and finite element, and can be easily iterated, which provides strong help for the study of pitting damage of metal materials.

Description

Technical Field

[0001] This invention belongs to the field of computational materials simulation, and specifically relates to a method for modeling pitting corrosion cellular automata by rapidly applying stress. Background Technology

[0002] Because the characteristics of cellular automata closely match the pitting corrosion process of metals, the cellular automata method is simpler and faster than experimental methods due to their complexity and time-consuming nature. Furthermore, the stochastic nature of the cellular automata method is remarkably similar to the development of pitting corrosion, making it more advantageous than other computational methods for studying pitting corrosion. Therefore, many researchers utilize cellular automata to simulate the pitting corrosion process. Previous studies have mostly focused on the steady-state of pitting corrosion, and since metal service conditions inevitably involve loading, studies incorporating stress conditions have not specifically demonstrated the connection between cellular automata and finite element modeling. This method, based on the establishment of a pitting corrosion cellular automata, rapidly builds a finite element component model corresponding one-to-one with each cell in the cellular automata, accurately reflecting the stress and strain calculated by the finite element method for each cell, thus reflecting the influence of stress on pitting corrosion. Summary of the Invention

[0003] The purpose of this invention is to investigate the effect of adding stress to each iteration of the cellular automaton using the finite element method, based on the establishment of a cellular automaton model that can prove the randomness of pitting.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for rapidly applying stress to simulate cellular automata modeling of pitting corrosion, comprising the following steps:

[0006] Step (1): Simulate the pitting corrosion process of metal materials in a corrosive environment. The molecules or atoms represented by the actual chemical reactions are represented by cells. A total of six types of cells are set: M represents the metal matrix cell; H represents the corrosive reaction cell in the pitting pit; R represents the active metal ion cell generated by the corrosion of the metal matrix; F represents the corrosion products generated by the hydrolysis of active metal ions; D represents the blockage cell generated by the reaction; and W represents the solution in the corrosive environment.

[0007] Step (2): Based on the cell type set in Step 1, the electrochemical corrosion model of carbon steel is established. Taking iron as an example, based on the basic electrochemical theory, when iron is in a corrosive environment, the iron dissolution occurs as shown in Equation (1):

[0008] Fe→Fe 2+ +2e - (1)

[0009] The hydrolysis reaction of metal ion Fe2+ is shown in equation (2):

[0010] Fe 2+ +H₂O→FeOH + +H + (2)

[0011] The corrosion products generated by the hydrolysis of metal ions will react on the surface of the metal matrix to form FeOHsolid, a blocker that hinders the diffusion of substances. The reaction formulas are (3) and (4).

[0012]

[0013]

[0014] The cell evolution rules in this corrosion model were determined. Neutral solution and the Fe metal substrate were represented by W and M cells, respectively. The Fe²⁺ metal ions formed after Fe corrosion were represented by R cells. F cells represented the formation of FeOH⁺ corrosion products through hydrolysis of metal ions with a certain probability. Additionally, D cells represented the FeOHsolid, a solid blockage layer formed on the surface metal layer, hindering outward diffusion from other cells. H cells represented corrosive substances in the environment. When at least one corrosive cell H existed around the metal substrate, M cells were converted into active metal ion R cells with a probability of P_corr. Simultaneously, the metal substrate M in contact with the solution in the pit had a certain probability of being corroded in the corrosive environment and also converted into metal ions. In this model, all cells except the metal cells could move randomly.

[0015] The parameters involved in the rules for each cellular reaction and diffusion reaction are as follows:

[0016] When at least one H cell exists near cell M, a certain corrosion probability is satisfied. Metal cell M is corroded into active metal ion cell R, and the position of M is replaced by the newly generated R. The corrosion probability is P-corr; stress multiplied by stress influence factor.

[0017] When at least one neutral cell W is present near the active metal ion cell R, hydrolysis generates corrosion product F and corrosive cell H. The position of R is replaced by cell F, and W is replaced by cell H. The hydrolysis probability is P-HY.

[0018] After the active metal ion cells R and corrosion product cells F diffuse beyond the pitting pit, they form a blockage D covering the pit opening. Inside the pit, W is replaced by cells D, and outside the pit, W is replaced by cells D. The probability of blockage formation is Pdd.

[0019] Corrosion-causing plugs will rupture under certain conditions, and their rupture strength is represented by Nd.

[0020] Cells H, R, and F will diffuse, and their diffusion probabilities are denoted as Pdiff-H, Pdiff-R, and Pdiff-F.

[0021] Step (3): Establish the initial pitting corrosion model of the cellular automaton. The corrosion model is set as a two-dimensional lattice space composed of 1100×1000 square units. The upper 100 layers of cells are non-corrosive neutral cells W, and the lower 1000 layers are metal matrix cells M. A 4×5 basic pit is set at the middle position of the uppermost metal cell as the basic point for pitting corrosion. At the same time, the neighbor problem of the cellular automaton model is considered. The von Neumann neighborhood is selected for CA modeling, and the mutual influence between the observed principal cell and the four adjacent cells above, below, left and right is considered.

[0022] Step (4): Establish the connection between the cellular automata and the finite element model;

[0023] 1. In the cellular automaton model before stress is applied, the positions of all cells are recorded using continuous numbers (1 to 1100×1000). The numbers 0-6 represent cells M, F, H, R, D and W respectively. All cells in the model have numbers representing their positions. The positions of all non-M cells except the neutral cell W are recorded and stored in an array.

[0024] 2. Since the finite element method calculates the stress and strain of metal cells, a 1000×1000 finite element model is established, and materials are created. After assigning elastic and plastic properties to the parts, the assembly is defined.

[0025] 3. Create the component mesh in advance. The mesh is a 1000×1000 square mesh, which corresponds exactly to each cell.

[0026] 4. Create two analysis steps. First, define the mesh that does not participate in the finite element analysis. Second, define the finite element analysis step and perform stress and strain calculations using the finite element method.

[0027] 5. Define the interaction. In the initial analysis step one, create the "model change" interaction, commonly known as the "birth and death element". This means that the non-M cell array is input into the finite element to become the element of the model change interaction. Its function is that it is not available in the finite element analysis step. The initial 1000×1000 part will become a pit shape, and each metal cell will be preserved. Calculate the stress and strain of each cell separately, and the finite element pit is created.

[0028] 6. Create a load by applying the same tensile stress to both boundary lines of the model;

[0029] 7. Submit the analysis job. After the analysis is completed, the equivalent strain and hydrostatic pressure of each metal cell involved in the finite element calculation will be obtained in the file path, which will be used to calculate the stress influence factor. The local anodic current density and pitting corrosion influence factor under stress conditions will be calculated using the kinetic equations established by Gutman. The equation takes the following form:

[0030]

[0031]

[0032]

[0033] In equations (5) to (7), I represents the anodic current generated by deformation, In represents the anodic current generated without deformation, ΔP represents the hydrostatic pressure, Vm represents the molar volume of the metal, Δε represents the equivalent plastic strain, ε0 represents the strain at the beginning of strain hardening, σm represents the hydrostatic pressure, R is the gas constant, and T represents the temperature. Equation (6) represents elastic deformation, and equation (7) represents plastic deformation.

[0034] The above 1-7 are stored in the cellular automaton program as a function, which facilitates iterative loops.

[0035] Step (5): Start and end of cellular automaton pitting simulation: During a cellular automaton simulation, the environmental factors of the metal cells are determined. Based on the reaction rules in step (2) above, the corrosion probability, diffusion probability, hydrolysis probability, blockage formation probability and blockage fracture intensity are set. The number of iterations and the pitting program end rules are also set, and a large number of simulations are repeated.

[0036] Step (6): Graphically process the pitting environment within the time step to be observed, record the width and depth of the pitting, and use the current change during the pitting process to describe the impact of pitting. The formula for calculating the pitting current is shown in equation (8):

[0037]

[0038] Where N(t) represents the total number of metal matrix cells dissolved at time t, F is the Faraday constant, M is the average molecular weight, ρ is the density, and z represents the average number of electrons lost per atom in the metal matrix during corrosion and dissolution.

[0039] This invention offers significant advantages over existing technologies: Most current cellular automata simulations of pitting corrosion focus on steady-state growth, and creating components during loading is difficult, making it hard to establish a one-to-one correspondence between cellular automata and finite element cells. The model in this invention addresses the stochastic nature of pitting corrosion and provides a quick and easy connection between cellular automata and finite element methods, facilitating iteration and providing powerful assistance in studying pitting corrosion damage in metallic materials. Attached Figure Description

[0040] Figure 1 The diagram shows the process of adding stress to the cellular automata of the present invention. a) Directly creating square components; b) Directly dividing square meshes and forming elements; c) Determining non-metallic cellular elements in pitting pits and removing them in the analysis step; d) Result analysis and pitting pit morphology.

[0041] Figure 2 The survival probability of pitting corrosion pits is given by different blockage strengths and formation probabilities.

[0042] Figure 3 The evolution of pitting depth over time under 150 MPa tensile stress and no stress conditions.

[0043] Figure 4 The corrosion current curves are for a tensile stress of 150 MPa and an unstressed condition. Detailed Implementation

[0044] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0045] A method for stress modeling using a pitting corrosion cellular automata, specifically implemented with the following steps:

[0046] Step (1): Establish a two-dimensional cellular space to simulate the corrosion environment. Transform the various elements involved in the reaction during the pitting corrosion process into each cell in the cellular space. M represents the metal matrix cell, H represents the corrosive reaction cell in the pitting pit, R represents the active metal ion cell generated by the corrosion of the metal matrix, F represents the corrosion products generated by the hydrolysis of active metal ions, D represents the occlusion cell generated by the reaction, and W represents the neutral solution in the reaction process.

[0047] Step (2): Define the initial cell settings and distribution: The corrosion model is set as a two-dimensional lattice space composed of 1100×1000 square units. The top 100 layers of cells are non-corrosive neutral cells W, and the bottom 1000 layers are metal matrix cells M. A 4×5 basic pit is set at the top center of the metal cells as the basic pitting point. At the same time, the cellular automaton model neighbor problem is considered. The von Neumann neighborhood is selected for CA modeling. The mutual influence between the observed principal cell and the four adjacent cells above, below, left and right is considered. The positions of all cells are recorded with continuous numbers (1 to 1100×1000). The numbers 0-6 represent cells M, F, H, R, D and W respectively. All cells in the model have numbers representing their positions.

[0048] Step (3): Set the cellular reaction and diffusion parameters, where the parameters involved in each cellular reaction rule are as follows:

[0049] When at least one H cell exists near cell M, a certain corrosion probability is satisfied: the metal cell M is corroded into an active metal ion cell R, and the position of M is replaced by the newly generated R. The corrosion probability is P-corr=0.3; the corrosion probability under stress is multiplied by the stress influence factor.

[0050] When at least one neutral cell W is present near the active metal ion cell R, hydrolysis generates corrosion product F and corrosive cell H. The position of R is replaced by cell F, and W is replaced by cell H. The hydrolysis probability is P-HY = 0.1.

[0051] After the active metal ion cells R and corrosion product cells F diffuse beyond the pitting pit, they form a blockage D covering the pit opening. Inside the pit, W is replaced by cells, and outside the pit, W is replaced by cells D. The probability of blockage formation is Pdd = 0.5.

[0052] Corrosion blockages will rupture under certain conditions, and their rupture strength is represented by Nd, with a value of 11.

[0053] Cells H, R, and F will diffuse, with diffusion probabilities Pdiff-H = 0.1, Pdiff-R = 0.1, and Pdiff-F = 0.1.

[0054] Step (4): Establish the connection between the cellular automata and the finite element model, such as... Figure 1 The process is as follows:

[0055] 1. In the cellular automaton model before stress is applied, record the positions of all non-M cells except for the neutral cell W, and store them in an array;

[0056] 2. Since the finite element method calculates the stress and strain of metal cells, a 1000×1000 finite element model is established, and materials are created. After assigning elastic and plastic properties to the component, the assembly is defined within it.

[0057] 3. Create the component mesh in advance. The mesh is a 1000×1000 square mesh, which corresponds exactly to each cell.

[0058] 4. Create two analysis steps. First, define the mesh that does not participate in the finite element analysis. Second, define the finite element analysis step and perform stress and strain calculations using the finite element method.

[0059] 5. Define the interaction. In the initial analysis step one, create the "model change" interaction, commonly known as the "birth and death element". That is, input the non-M cell array in step 1 above into the finite element to become the element of the model change action. Its function is that it is unusable in analysis step 2, that is, it disappears. In this way, the initial 1000×1000 part becomes the shape of pitting, and each metal cell is preserved. Calculate the stress and strain of each cell separately, and the finite element pitting is created.

[0060] 6. Create a load by applying a tensile stress of 75 MPa to both boundary lines of the model;

[0061] 7. Submit the analysis assignment. After the analysis is completed, the equivalent strain and hydrostatic pressure of each metal cell involved in the finite element calculation will be obtained in the file path. The stress influence factor will be calculated using the dynamic equation established by Gutman. According to formula (7), T = 298K, R = 8.314J·mol -1 ·K -1 V m =7.0923×10 -6 m 3 mol -1 (Fe), with a yield strain of 0.2%.

[0062] The above 1-7 are stored in the cellular automaton program as a function, which facilitates iterative loops.

[0063] Step (5): Start and end of cellular automaton pitting simulation: In one cellular automaton simulation, the cell size is 25nm, the time step of each iteration is 0.025s, the environmental factors of the metal cell are determined, and the corrosion probability, diffusion probability, hydrolysis probability, blockage formation probability and blockage fracture intensity are set according to the reaction rules in step (2) above. The number of iterations and the pitting program end rules are also set, and a large number of simulations are repeated.

[0064] Step (6): The pitting environment within the time step to be observed is graphically processed, the width and depth of the pitting are recorded, and the influence of the pitting is described by the change of current during the pitting process. In formula (8), F is the Faraday constant, which is 96485 C / mol, the average molecular weight is M = 55.4 g / mol, the density is ρ = 7.93 g / cm3, and the average number of electrons lost by each atom during the corrosion and dissolution of stainless steel is represented by z, which is z = 2.19.

[0065] To further understand the relationship between pitting corrosion lifetime and simulation parameters, seven corrosion probability parameters (Pcorr values ​​of 0.001, 0.005, 0.01, 0.03, 0.05, 0.07, and 0.1), four occlusion formation probability parameters, and seven occlusion intensities (Nd values ​​of 5, 7, 11, 15, 18, and 21) were set, resulting in a total of 168 parameter combinations. Simulations were repeated 30 times under each parameter combination, for a total of 5040 simulations. Each simulation was set to run for 5000 steps. Figure 2 The lifespan of pitting corrosion within 5000 simulated steps under different conditions was statistically analyzed. When the corrosion probability is 0.01, the probability of pitting corrosion survival generally tends to increase as Nd increases, but there is also a local decrease, which is consistent with the randomness of pitting corrosion.

[0066] use Figure 1 The method establishes the effect of stress introduced during pitting corrosion. Figure 3 and Figure 4 The figures show the evolution of corrosion current and pitting depth over time under stress and without stress conditions in the pitting corrosion simulation process. It is evident that the influence of stress is minimal in the first 20 seconds of the simulation, but increases significantly after 20 seconds. Stress and strain are mainly concentrated at the bottom of the pit, increasing the stress corrosion sensitivity at the bottom and generating corrosion tips that deepen continuously as the corrosion process progresses. By 60 seconds of simulation, the pit depth under stress conditions is approximately four times that under stress-free conditions.

Claims

1. A method for rapidly incorporating stress effects into the modeling of pitting corrosion cellular automata, characterized in that: The method is as follows: the entire pitting corrosion model is transformed into a two-dimensional cellular space containing all reactive elements using computer language. At the same time, during the pit growth process, the stress and strain distribution of each metal cell in the pit is calculated using the finite element method. Then, the influence factor of stress and strain on each metal cell is calculated through the stress calculation model. The calculation is then returned to the cellular automata model for iterative calculation to obtain the width and depth of pitting corrosion development and the pitting current. Step (1): Establish a two-dimensional cellular space simulating the corrosion environment, and transform the various elements participating in the reaction during the pitting corrosion process into each cell in the cellular space. Here, M represents the metal matrix cell, H represents the corrosive reaction cell in the pitting pit, R represents the active metal ion cell generated by the corrosion of the metal matrix, F represents the corrosion products generated by the hydrolysis of active metal ions, D represents the blockage cell generated by the reaction, and W represents the neutral solution in the reaction process. These cells undergo reaction changes under a specific condition. Step (2): Define the initial cell settings and distribution: The corrosion model is set as a two-dimensional lattice space composed of 1100×1000 square units. The upper 100 layers of cells are non-corrosive neutral cells W, and the lower 1000 layers are metal matrix cells M. A 4×5 basic pit is set at the middle position of the uppermost metal cell as the basic point for pitting corrosion. At the same time, the cellular automaton model neighbor problem is considered. The von Neumann neighborhood is selected for CA modeling. The mutual influence between the observed principal cell and the four adjacent cells above, below, left and right is considered. Step (3): Establish a basic cellular automaton program to address the reactions and diffusion that occur during pitting corrosion, and incorporate the influence of stress factors using the finite element method. The steps are as follows: 3.1 The initial pitting model, i.e. all cells before pitting occurs, is represented by a matrix, and each initial position is represented by a number, with different types of cells represented by different numbers; the positions (numbers) of all non-metallic cells except for the upper half of neutral cells and metal matrix cells are recorded. 3.2 Create a complete basic metal pitting model (1000×1000) and create material properties; 3.3 Define component instances and create a 1000×1000 mesh; 3.4 Set up two analysis steps: the initial analysis step is to define a mesh that does not participate in the finite element method, and the finite element analysis step is to define the loading and perform finite element stress and strain calculations. 3.5 Define loads and interactions; 3.6 Submit the analysis, obtain the equivalent hydrostatic pressure strain at all metal cell points through the finite element method, and use it for the subsequent calculation of pitting stress factor. Step (4): Cellular automaton pitting simulation start and end: During a cellular automaton simulation, the environmental factors of the metal cell are determined. Based on the reaction rules in step (1) above, the corrosion probability, diffusion probability, hydrolysis probability, blockage formation probability and blockage fracture strength are set. The number of iterations and the pitting program end rules are set, and a large number of simulations are repeated. Step (5): Graphically process the pitting environment within the time step to be observed, record the width and depth of the pitting, and use the current change during the pitting process to describe the impact of pitting.

2. The method for rapidly incorporating stress effects into pitting corrosion simulation cellular automata modeling according to claim 1, characterized in that: In step (3), 3.5, the loads and interactions are defined as follows: The interaction is defined as follows: In the initial analysis step one, a "model change" interaction is created, commonly known as a "life and death element". That is, a non-M cell array is input into the finite element to become a model change element. Its function is that it is not available in the finite element analysis step. The initial 1000×1000 part becomes a pitted pit shape, and each metal cell is preserved. The stress and strain of each cell are calculated separately, and the finite element pitting pit is created. The load is defined as applying the same tensile stress to both boundary lines of the model.

3. The method for rapidly incorporating stress effects into pitting corrosion simulation cellular automata modeling according to claim 1, characterized in that: In step (3), 3.6, it is necessary to calculate the stress influence factor of the metal cell and use the kinetic equation established by Gutman to calculate the local anodic current density under stress conditions. The pitting corrosion influence factor is expressed in the following form: ；（1） ；（2） ；（3） In equations (1) to (3), I represents the anodic current generated by deformation, In represents the anodic current generated without deformation, ΔP represents the hydrostatic pressure, Vm represents the molar volume of the metal, Δε represents the equivalent plastic strain, ε0 represents the strain at the beginning of strain hardening, σm represents the hydrostatic pressure, R is the gas constant, and T represents the temperature; where equation (2) represents elastic deformation and equation (3) represents plastic deformation.

4. The method for rapidly incorporating stress effects into pitting corrosion simulation cellular automata modeling according to claim 1, characterized in that: In step (1), the cell is used to represent various reactive substances during pitting corrosion. The reactions correspond to cell transformation rules, cell movement and replacement, and the parameters involved in each cell reaction and diffusion reaction rule are as follows: When there is at least one H cell near the M cell, the metal cell M is corroded into an active metal ion cell R with a certain corrosion probability, and the corrosion probability is P-corr. The active metal ion cell R hydrolyzes to generate corrosion product F and corrosive cell H, with a hydrolysis probability of P-HY; After the active metal ion cells R and corrosion product cells F diffuse beyond the pitting pit, they form a blockage D covering the pit opening. The probability of blockage formation is Pdd. Corrosion-induced blockages can rupture under certain conditions, and their rupture strength is represented by Ndd. Cells H, R, and F will diffuse, and their diffusion probabilities are denoted as Pdiff-H, Pdiff-R, and Pdiff-F.

5. The method for rapidly incorporating stress effects into pitting corrosion simulation cellular automata modeling according to claim 1, characterized in that: In step (1) and step (5), the formula for calculating the pitting current is as follows: ； Where N(t) represents the total number of metal matrix cells dissolved at time t, F is the Faraday constant, M is the average molecular weight, ρ is the density, and z represents the average number of electrons lost by each atom in the metal matrix during the corrosion and dissolution process.

6. The method for rapidly incorporating stress effects into pitting corrosion simulation cellular automata modeling according to claim 1, characterized in that: The specific steps also include: (1) Determine the cell size in the cellular automaton and the specific time represented by the number of iteration steps in the cellular automaton; (2) Set the cellular automata start rules and the pitting simulation stop rules; (3) Establish the connection between cellular automata and finite element software, and provide feedback on the influence of stress and strain by calculating the stress influence factor; (4) Ensure the process is complete and perform a large number of iterative calculations to obtain the width and depth of pitting development and the pitting current.

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