A cellular automaton-based prediction method for microstructure evolution during thermal shock loading

Abstract

The present invention discloses a cellular automaton-based method for predicting microstructural evolution during thermal shock loading. The method comprises high-temperature thermal shock experiments on materials, a CA model for grain growth after thermal shock loading, and a microstructural evolution prediction based on the experimental results and the CA model. The method relates to the field of computational materials science. By combining experimental data with a cellular automaton model, the method accurately predicts the microstructural evolution of materials under different high-temperature thermal shock conditions. By utilizing a probabilistic model and neighbor types, the method optimizes the calculation process and improves simulation efficiency. The method is suitable for high-temperature thermal shock analysis of various materials and conditions and has broad industrial application prospects. By combining a probabilistic nucleation model, a thermal activation mechanism, a curvature-driven mechanism, and a cellular automaton model, the method significantly improves prediction efficiency and reduces experimental costs, thus possessing significant application value.

Description

Technical Field

[0001] The present invention relates to the technical field of computational materials science, and in particular to a method for predicting microstructure evolution during thermal shock load action based on cellular automata. Background Art

[0002] Computational materials science is an emerging discipline that has developed with the rapid development of computer science and technology, integrating materials science, physics, chemistry, mechanics, metallurgy, and computer science. Its fundamental concept is based on the physical meaning of materials science, combined with the basic principles of related disciplines. Through modeling and calculation, it predicts the microstructure and performance of materials, providing a scientific basis for developing reasonable processing technologies during the development of new materials. When performing material calculations, it is necessary to select an appropriate solution method based on factors such as the object to be calculated, the conditions, and the requirements.

[0003] The simulation methods for the same spatial scale may be different, and the theoretical basis involved is also different. According to the size of the simulation space scale, the simulation methods can be divided into nanoscale, microscale, and macroscale. Among them, the representative simulation methods at the microscale (or mesoscale) include Monte Carlo (MC) and Cellular Automaton (CA). Compared with the MC method, the CA method is easier to introduce the evolution rules of physical problems and has gradually become the main means of simulating the evolution of material microstructures. However, most of the current CA simulation studies on nickel-based high-temperature alloys focus on studying the influence of heat treatment methods on the evolution of material microstructures, and there are few studies on the evolution of material microstructures during temperature loads. Summary of the Invention

[0004] To address the above issues, the present invention proposes a method for predicting the evolution of microstructures during thermal shock loading based on cellular automata. By simulating processes such as grain growth, recrystallization, and curvature drive, the microstructure changes of materials under thermal shock conditions can be predicted.

[0005] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A method for predicting microstructure evolution during thermal shock loading based on cellular automata, the method comprising the following steps:

[0007] S1: Conduct high temperature thermal shock tests on materials under different upper limit temperature conditions to obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and grain size under different conditions, as well as the change in δ phase content;

[0008] S2: Input basic parameters according to material properties and randomly assign orientation variables to each cell to establish the initial cell state, providing initial conditions for cell orientation changes and grain growth during the simulation process;

[0009] S3: According to the VonNeumann neighbor type, there is a certain probability that the grain boundary cells will not transform. The probability that the grain boundary cells will not transform is recorded as P1. Based on the probability P1, a preliminary judgment is made on the grain boundary cells. The grain boundary cells that do not transform in this system time step are identified. The grain growth rule is not judged, and the grain growth judgment is performed on the grain boundary cells that have transformed;

[0010] S4: For grain boundary cells that need to be judged for grain growth, based on the probabilistic nucleation model, it is assumed that the recrystallization nucleus is generated according to the probability P2. The probability P2 is used to determine whether a new recrystallization nucleus is generated, and the Moore neighbor type and the grain boundary energy change ΔE are used to determine whether a new recrystallization nucleus is generated. i→j Simulate the growth process of recrystallization nuclei;

[0011] S5: For the grain boundary cells that have not undergone recrystallization nucleus transformation in step S4, a determination is made based on the thermal activation mechanism. At each system time step, the difficulty of the grain boundary cells undergoing transformation is determined according to the probability P3.

[0012] S6: Assuming that the grain boundary cell that has not undergone recrystallization nucleus transformation in step S5 is C5, transformation determination is performed according to the Moore neighbor type and the curvature driven mechanism;

[0013] S7: For the grain boundary cells that still exist in step S6 and have not undergone recrystallization nucleus transformation, randomly select one cell from the 8 cells in the neighborhood of cell C5 and transform it according to probability P4;

[0014] S8: After all grain boundary cells are judged, the system time step is increased by one and the next cycle is continued;

[0015] S9: Based on the microscopic test results of the grains observed in the high-temperature thermal shock experiment in step S1, the system time step of the same grain size is linked to the corresponding number of thermal shock cycles and the upper limit temperature of the thermal shock load to obtain the following formula:

[0016]

[0017] Where CAS represents the system time step of the cellular automaton; C1 and C2 are unknown constants; N is the number of thermal shock cycles, T max is the upper limit temperature of thermal shock load;

[0018] S10: Use the formula obtained in step S9 to calculate the system time step CAS of the cellular automaton at the upper limit temperature of a given thermal shock load for a given number of thermal shock cycles, input the system time step CAS into the cellular automaton model for prediction, and obtain the corresponding grain size and material microstructure simulation diagram.

[0019] As a preferred solution of the present invention, the step S1 is implemented as follows:

[0020] Select multiple upper limit temperature conditions, and for each upper limit temperature T i , set different numbers of thermal shock cycles;

[0021] At different upper limit temperatures T i Multiple high-temperature thermal shock experiments were carried out under different conditions. After each experiment, the grain size, δ phase and carbide precipitation were observed, measured and recorded by instruments.

[0022] Analyze the data, draw a graph showing the change of grain size with the number of thermal shock cycles and a graph showing the change of δ phase content with the number of thermal shock cycles, and obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and grain size under different conditions, as well as the change in δ phase content.

[0023] As a preferred solution of the present invention, the VonNeumann neighborhood type means that the neighbors of each cell include the four cells above, below, left and right of it, and the Moore neighborhood type means that the neighbors of each cell include the eight cells around it.

[0024] As a preferred solution of the present invention, the method of performing preliminary judgment on the grain boundary cell according to the probability P1 specifically includes:

[0025] Traverse all cells and determine whether each cell is located at the grain boundary;

[0026] For each grain boundary cell, generate a random number α between 0 and 1 and compare the random number α with P1;

[0027] If α<P1, the grain boundary cell does not transform in the current system time step, and the grain growth rule is not determined;

[0028] If α ≥ P1, the grain boundary cell undergoes a transformation in the current system time step, and further grain growth discrimination is required.

[0029] As a preferred solution of the present invention, the probability P1 that the grain boundary cell does not undergo transformation is calculated as follows:

[0030] The change range of the δ-phase content obtained through microscopic observation is denoted as a% to b%. A random number c between 0 and 100 is generated using the random number generation function in MATLAB, and the size of c / 4 is compared with a and b:

[0031]

[0032] As a preferred embodiment of the present invention, step S4 specifically includes:

[0033] For each grain boundary cell that needs to be discriminated for grain growth, a random number β between 0 and 1 is generated. If β < P2, a new recrystallization nucleus is generated at the position of this grain boundary cell, and a new grain orientation number is assigned;

[0034] The calculation formula for the probability P2 is as follows:

[0035]

[0036] In the formula, C3 is a constant; ω is a parameter related to temperature;

[0037] The growth rule of the recrystallization nucleus is according to the Moore neighbor type. Randomly select one neighbor from the 8 neighbors of the new recrystallization nucleus for transformation, and judge the change in the grain boundary energy ΔE of this neighbor i→j ;

[0038] If ΔE i→j < 0, the cell state of the selected neighbor changes to the state of the recrystallization nucleus;

[0039] If ΔE i→j ≥ 0, the cell state of the selected neighbor does not change.

[0040] As a preferred embodiment of the present invention, the grain boundary energy E j of cell j is obtained by calculating the Hamiltonian function:

[0041]

[0042] In the formula, J is a positive grain boundary energy constant, δ is the Kronecker sum function, j is the jth neighbor of cell i, m represents the total number of neighbors of the cell, S i 、S j represent the orientation numbers of the corresponding cells;

[0043] Then the change in grain boundary energy ΔE i→j = E i - E j [[ID=; where, E i [[ID=; represents the grain boundary energy of cell i.

[0044] As a preferred solution of the present invention, the calculation formula of the probability P3 is:

[0045]

[0046] Where C0 is a constant; T0 is the short-term maximum operating temperature of the alloy; Q b represents the migration activation energy of the material; R is the gas constant.

[0047] As a preferred solution of the present invention, step S6 specifically includes: according to the Moore neighbor type, the 8 cells around cell C5 are marked from top to bottom and from left to right as: C1, C2, C3, C4, C6, C7, C8, C9; if there are 5 or more consecutive cells around cell C5 in the same state, then in the next system time step, the state of cell C5 is the same as the state of these 5 or more cells; if the states of any three cells among cells C2, C4, C6 and cell C8 are the same, then in the next system time step, the state of cell C5 is the same as the state of these three cells; if the states of any three cells among cells C1, C3, C7 and cell C9 are the same, then in the next system time step, the state of cell C5 is the same as the state of these three cells.

[0048] As a preferred solution of the present invention, the calculation formula of the probability P4 is:

[0049]

[0050] The beneficial effects of the present invention are as follows: by combining experimental data and a cellular automaton model, the microstructural evolution of materials under different high-temperature thermal shock conditions can be accurately predicted; by using a probabilistic model and neighbor types, the calculation process is optimized and the simulation efficiency is improved; it is suitable for high-temperature thermal shock analysis of different materials and conditions and has broad industrial application prospects; by combining a probabilistic nucleation model, a thermal activation mechanism, a curvature-driven mechanism and a cellular automaton model, the prediction efficiency can be significantly improved, the experimental cost can be reduced, and it has important application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0052] in:

[0053] Figure 1 is a flow chart of the method of the present invention;

[0054] Figure 2 Schematic diagram of Moore neighbor type case 1 in step S6 in an embodiment of the present invention;

[0055] Figure 3 2 is a schematic diagram of Moore neighbor type case 2 in step S6 in an embodiment of the present invention;

[0056] Figure 4 3 is a schematic diagram of Moore neighbor type case 3 in step S6 in an embodiment of the present invention;

[0057] Figure 5 Schematic diagram of the evolution of the microstructure of the GH4169 alloy with the number of thermal shock load cycles in an embodiment of the present invention;

[0058] Figure 6 It is a comparison diagram of the cellular automaton model prediction curve and the microscopic observation experimental data in the embodiment of the present invention. DETAILED DESCRIPTION

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field are within the scope of protection of the present invention.

[0060] like Figure 1 Figure 1 shows an embodiment of the present invention, which provides a cellular automaton-based method for predicting microstructural evolution during thermal shock loading. The method includes high-temperature thermal shock testing of materials, a CA model for grain growth after thermal shock loading, and a prediction of microstructural evolution based on the experimental results and the CA model. The experimental equipment used includes a multi-stage high-temperature heating furnace, a metallographic microscope, and a scanning electron microscope.

[0061] The method comprises the following steps:

[0062] S1: Conduct high temperature thermal shock tests on materials under different upper limit temperature conditions to obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and the grain size under different conditions, as well as the change in δ phase content;

[0063] The purpose of the high-temperature thermal shock experiment of materials is to obtain the relationship between the material grain size and the number of thermal shock cycles through experimental data, so as to later link the CA system time step with the corresponding number of thermal shock cycles and the upper limit temperature of thermal shock.

[0064] Specifically, step S1 is implemented as follows:

[0065] S11: Select multiple upper limit temperature conditions, and for each upper limit temperature T i , such as T1, T2, T3, set different numbers of thermal shock cycles, such as 100 times, 200 times, 300 times;

[0066] S12: At different upper limit temperatures T i Under the same conditions, multiple high-temperature thermal shock experiments were carried out. After each experiment, the grain size, δ phase and carbide precipitation were observed, measured and recorded using microscopes and other instruments.

[0067] S13: Analyze the data, draw a graph of the change of grain size with the number of thermal shock cycles and a graph of the change of δ phase content with the number of thermal shock cycles, and obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and grain size under different conditions, as well as the change in δ phase content, provide data support for subsequent simulation and prediction.

[0068] S2: Input basic parameters according to material properties, including grain size, temperature, etc., and randomly assign a certain orientation variable to each cell to establish the initial cell state, providing initial conditions for cell orientation changes and grain growth during the simulation process.

[0069] S3: The Von Neumann neighbor type means that the neighbors of each cell include the four cells above, below, left and right. According to the Von Neumann neighbor type, there is a certain probability that the grain boundary cells (those with one or more neighbor cells with different orientations) will not transform. The probability that the grain boundary cells will not transform is recorded as P1. Based on the probability P1, a preliminary judgment is made on the grain boundary cells. The grain boundary cells that do not transform in this system time step are identified. The grain growth rule judgment is not performed. The grain boundary cells that have transformed are subjected to the grain growth judgment of step S4.

[0070] Step S3 performs a preliminary judgment on the grain boundary cells to determine which grain boundary cells will not undergo transformation in the current period. The main purpose is to reduce the amount of calculation and concentrate computing resources on cells where grain growth may occur.

[0071] In one embodiment, the method for preliminarily judging the grain boundary cell according to the probability P1 includes:

[0072] Traverse all cells and determine whether each cell is located at the grain boundary;

[0073] For each grain boundary cell, generate a random number α between 0 and 1 and compare the random number α with P1;

[0074] If α<P1, the grain boundary cell does not transform in the current system time step, and the grain growth rule is not determined;

[0075] If α ≥ P1, then this grain boundary cell undergoes a transformation at the current system time step, and further grain growth discrimination is required.

[0076] Furthermore, the calculation method of the probability P1 that the grain boundary cell does not undergo a transformation is as follows:

[0077] The change range of the δ-phase content obtained through microscopic observation is denoted as a% - b%. A random number c between 0 and 100 is generated using the random number generation function in MATLAB, and the size of c / 4 is compared with a and b:

[0078]

[0079] S4: For the cells that require grain growth discrimination, based on the probability nucleation model proposed by Kugler et al., assume that recrystallization nuclei are generated according to the probability P2, determine whether new recrystallization nuclei are generated according to the probability P2, and simulate the growth of the nuclei according to the Moore neighbor type and the change in grain boundary energy ΔE i→j Simulate the growth of the nuclei;

[0080] The Moore neighbor type means that the neighbors of each cell include the eight cells around it;

[0081] The probability nucleation model is a model that describes the process of nucleation through probability methods. In materials science, nucleation is the initial stage of crystal growth, and the probability nucleation model is used to describe the probability of nucleation under given conditions. When the material is subjected to heat treatment or mechanical deformation, new nuclei will appear at the grain boundaries. The probability nucleation model determines whether new nuclei will be generated in a time step by introducing the probability parameter P2. This model assumes that the probability of nucleation is related to factors such as system energy change and temperature. For example, higher temperature and energy change are more likely to promote the formation of nuclei. During the simulation, each grain boundary cell judges whether to generate new nuclei based on the probability P2 in each time step. Once the nuclei are formed, the subsequent growth process will proceed according to certain growth rules.

[0082] In one embodiment, step S4 specifically includes:

[0083] For each grain boundary cell that requires grain growth discrimination, a random number β between 0 and 1 is generated. If β < P2, then a new recrystallization nucleus is generated at the position of this grain boundary cell, and a new grain orientation number is assigned;

[0084] The calculation formula of the probability P2 is as follows:

[0085]

[0086] In the formula, C3 is a constant, assume T max=1073.15K, C3 = 0.5, which can be used to verify that at different upper limit temperatures T max Under this condition, does C3 need to be adjusted or remain unchanged? ω is a temperature-related parameter, which is generally taken as a thermodynamic temperature value higher than the alloy dissolution temperature; T max is the upper temperature limit of thermal shock load;

[0087] The growth rule of the recrystallized nucleus is to randomly select a neighbor from the 8 neighbors of the new nucleus for transformation according to the Moore neighbor type, and determine the grain boundary energy change ΔE of the neighbor i→j ;

[0088] If ΔE i→j <0, the cell state of the selected neighbor is transformed into the state of recrystallization nucleus;

[0089] If ΔE i→j ≥0, the cell state of the selected neighbor does not change;

[0090] Grain boundary energy E of cell j j Calculated by the Hamiltonian function:

[0091]

[0092] Where J is the positive grain boundary energy constant, δ is the Kronecker summation function, j is the jth neighbor of cell i, m represents the total number of neighbors of the cell, and S i 、S j represents the orientation number of the corresponding cell;

[0093] Then the grain boundary energy change ΔE i→j =E i -E j ;E i represents the grain boundary energy of cell i.

[0094] S5: For the grain boundary cells that have not undergone recrystallization nucleus transformation in step S4, determination is made based on the thermal activation mechanism to determine the transformation probability of the grain boundary cells that have not generated recrystallization nuclei;

[0095] Thermal activation mechanisms describe the physical or chemical changes that occur in materials under thermal conditions. This mechanism is based on the excitation of atoms or molecules by thermal energy, causing them to overcome energy barriers and undergo a transformation. When a material is heated, the thermal energy allows atoms or molecules to gain sufficient energy to overcome the potential barriers surrounding them, leading to migration or reorganization. This process is called thermal activation. Under this thermal activation mechanism, whether a grain boundary cell undergoes a transformation is determined by a probability, P3. This probability typically depends on the temperature and the activation energy of the material. Higher temperatures increase the probability of a cell undergoing a transformation. Within each system time step, the probability of each grain boundary cell undergoing a transformation is determined based on the probability, P3. Through continuous thermal activation, the evolution of grain boundary cells under high temperature conditions is simulated.

[0096] For thermal shock loads, the higher the upper temperature limit of the thermal shock load, the easier it is for the cells at the grain boundary to overcome the energy barrier and transition to a new state. At each system time step, the difficulty of the grain boundary cell transition is determined by the probability P3. The calculation formula for probability P3 is:

[0097]

[0098] Where C0 is a constant, assuming that when T max =T0, P3=1; T max This is the upper limit temperature of the thermal shock load; T0 is the short-term maximum operating temperature of the alloy; Q b represents the migration activation energy of the material; R is the gas constant.

[0099] S6: Assuming that the grain boundary cell that has not undergone recrystallization nucleus transformation in step S5 is C5, according to the Moore neighbor type, the curvature driven mechanism is used to further determine the transformation of the untransformed grain boundary cell;

[0100] The curvature-driven mechanism describes grain growth and contraction, where the curvature of the grain boundary determines the direction and speed of grain boundary migration. Grain growth and contraction are influenced by the curvature of the grain boundary. Convex grain boundaries tend to contract, while concave grain boundaries tend to grow. This is because curvature leads to an uneven distribution of surface energy, driving atoms to migrate toward lower-energy regions. The change in grain boundary energy in the curvature-driven mechanism, ΔE, is i→j Used to simulate grain boundary migration. Regions of high curvature experience large energy changes, driving grain boundary movement. Based on the Moore neighborhood type and curvature-driven mechanism, untransformed grain boundary cells are identified, simulating the growth and contraction of grain boundaries under varying curvatures.

[0101] In one embodiment, step S6 specifically includes:

[0102] According to the Moore neighbor type, the eight cells around cell C5 are marked from top to bottom and from left to right as: C1, C2, C3, C4, C6, C7, C8, C9;

[0103] If there are 5 or more consecutive cells around cell C5 in the same state, then the state of cell C5 in the next system time step will be the same as their states;

[0104] If the states of any three cells among cells C2, C4, C6 and cell C8 are the same, then the state of C5 in the next system time step is the same as their states;

[0105] If the states of any three cells among cells C1, C3, C7 and cell C9 are the same, the state of C5 in the next system time step is the same as their states.

[0106] S7: For the grain boundary cells that still exist in step S6 and have not undergone recrystallization nucleus transformation, randomly select one cell from the 8 cells in the neighborhood of cell C5 and transform it with probability P4; by processing the untransformed grain boundary cells, the integrity of the model is ensured;

[0107] The calculation formula for probability P4 is:

[0108]

[0109] S8: After all grain boundary cells are judged, the system time step is increased by one and the next cycle is continued;

[0110] S9: Based on the microscopic test results of the grains observed in the high-temperature thermal shock experiment in step S1, the system time step of the same grain size is linked to the corresponding number of thermal shock cycles and the upper limit temperature of the thermal shock load to obtain the following prediction formula:

[0111]

[0112] Where CAS represents the system time step of the cellular automaton; C1 and C2 are unknown constants; N is the number of thermal shock cycles, T max is the upper limit temperature of thermal shock load;

[0113] Step S9 associates the experimental data with the simulation results to derive a prediction formula. Based on the experimental data, a relationship formula between the system time step CAS, the number of thermal shock cycles, and the upper limit temperature is derived.

[0114] S10: Use the formula obtained in step S9 to calculate the system time step CAS of the cellular automaton at the upper limit temperature of a given thermal shock load for a given number of thermal shock cycles, input the system time step CAS into the cellular automaton model for prediction, and obtain the corresponding grain size and material microstructure simulation diagram.

[0115] The cellular automaton (CA) model is a discrete mathematical model that simulates the evolution of complex systems by defining simple local rules. The CA model consists of a series of discrete cells, each of which has a certain state. Cells interact with their neighbors (such as Von Neumann neighbors or Moore neighbors) and update their states according to predetermined rules. In the cellular automaton model, the evolution of the system is based on local rules that define the state changes of cells under different conditions. For example, in this method, the orientation changes of cells, the transformation of grain boundaries, and the generation of crystal nuclei are all based on local rules of probability and neighbor type. Through the setting of initial conditions and multiple loop iterations, the CA model can simulate the behavior of complex systems. In this method, the CA model is used to simulate the microstructural evolution of materials under high-temperature thermal shock, and the grain size and microstructure are predicted through multiple time step iterations.

[0116] By combining the probabilistic nucleation model, thermal activation mechanism and curvature-driven mechanism, the CA model can accurately simulate the microstructural evolution of materials and provide reliable prediction results when combined with experimental data.

[0117] The method of the present invention will be further described below in conjunction with specific implementation examples, and the present invention can be better understood based on the implementation examples. It should be noted that the specific material ratios, process conditions, and results described in the following implementation examples are only intended to illustrate the method of the present invention and should not and will not limit the present invention described in detail in the claims.

[0118] In this embodiment, the prediction method of microstructure evolution during thermal shock loading based on cellular automata proposed in the present invention is applied to the prediction of microstructure evolution of GH4169 alloy under thermal shock, including the following steps:

[0119] S1: Conduct high temperature thermal shock tests on materials under different upper limit temperature conditions to obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and the grain size under different conditions, as well as the change in δ phase content;

[0120] S2: Input the basic parameters according to the material properties. Use a 1μm×1μm square unit cell, and the unit cell space consists of 400×400 two-dimensional square unit cells. The simulated area represents an actual sample of 400μm×400μm. Randomly assign a certain orientation variable to each unit cell. To balance the effect and the running speed of MATLAB, the number of orientations selected is 1000.

[0121] S3: According to the Von Neumann neighbor type, there is a certain probability that the grain boundary unit cells do not transform. Denote the probability that the grain boundary unit cells do not transform as P1. Make a preliminary judgment on the grain boundary unit cells according to the probability P1, identify the grain boundary unit cells that do not transform in the current system time step, then do not perform the determination of the grain growth rule, and perform the grain growth discrimination in step S4 for the grain boundary unit cells that transform;

[0122] The change range of the δ-phase content obtained through microscopic observation is denoted as 9% - 12%. Use the random number generation function in MATLAB to generate a random number c between 0 and 100, and compare c / 4 with the sizes of a and b:

[0123]

[0124] Traverse all the unit cells to judge whether each unit cell is located at the grain boundary;

[0125] For each grain boundary unit cell, generate a random number α between 0 and 1, and compare the random number α with P1;

[0126] If α < P1, then this grain boundary unit cell does not transform in the current system time step, and the determination of the grain growth rule is not performed;

[0127] If α ≥ P1, then this grain boundary unit cell transforms in the current system time step and further grain growth discrimination is required.

[0128] S4: For the unit cells that require grain growth discrimination, based on the probability nucleation model, assume that the recrystallization nuclei are generated according to the probability P2. For each grain boundary unit cell that requires grain growth discrimination, generate a random number β between 0 and 1. If β < P2, then a new recrystallization nucleus is generated at the position of this grain boundary unit cell, and a new grain orientation number is assigned;

[0129] The calculation formula of the probability P2 is as follows:

[0130]

[0131] In the formula, ω is a parameter related to temperature, generally taking the thermodynamic temperature value higher than the alloy dissolution temperature. In this simulation, the value of ω is selected as 2000K; T max is the upper limit temperature of the thermal shock load;

[0132] The growth rule of the recrystallized nucleus is to randomly select a neighbor from the 8 neighbors of the new nucleus for transformation according to the Moore neighbor type, and determine the grain boundary energy change ΔE of the neighbor i→j ;

[0133] If ΔE i→j <0, the cell state of the selected neighbor is transformed into the state of recrystallization nucleus;

[0134] If ΔE i→j ≥0, the cell state of the selected neighbor does not change;

[0135] Grain boundary energy E of cell j j Calculated by the Hamiltonian function:

[0136]

[0137] Where J is the positive grain boundary energy constant, δ is the Kronecker summation function, j is the jth neighbor of cell i, m represents the total number of neighbors of the cell, and S i 、S j represents the orientation number of the corresponding cell;

[0138] Then the grain boundary energy change ΔE i→j =E i -E j ;E i represents the grain boundary energy of cell i.

[0139] S5: For the grain boundary cells that have not undergone recrystallization nucleus transformation in step S4, determination is made based on the thermal activation mechanism to determine the transformation probability of the grain boundary cells that have not generated recrystallization nuclei;

[0140] For thermal shock loads, the higher the upper temperature limit of the thermal shock load, the easier it is for the cells at the grain boundary to overcome the energy barrier and transition to a new state. At each system time step, the difficulty of the grain boundary cell transition is determined by the probability P3. The calculation formula for probability P3 is:

[0141]

[0142] Where C0 is a constant, assuming that when T max =T0, P3=1; T max The upper limit temperature of the thermal shock load at this time; T0 is the short-term maximum operating temperature of GH4169 alloy, which is 1073.15K; Q b represents the migration activation energy of the material, which is 223.85 kJ / mol; R is the gas constant.

[0143] S6: Assuming that the grain boundary cell that has not undergone recrystallization nucleus transformation in step S5 is C5, according to the Moore neighbor type, the curvature driven mechanism is used to further determine the transformation of the untransformed grain boundary cell;

[0144] The idea that grain boundary curvature is the driving force of grain growth has been confirmed by numerous experiments and theoretical analyses. Straight grain boundaries and a 120° angle between them are necessary for a stable grain shape. Therefore, hexagonal grains are the most stable. Other shapes will cause the grain to continue growing until it reaches a stable shape.

[0145] According to the Moore neighbor type, if there are 5 or more consecutive cells around cell C5 in the same state, then the state of cell C5 in the next system time step is the same as their state, such as Figure 2 As shown ( is the state of cell C5 in the current system time step, is the state of cell C5 in the next system time step); if the states of any three cells among cells C2, C4, C6 and cell C8 are the same, then the state of C5 in the next system time step is the same as their states, such as Figure 3 As shown; if the states of any three cells among cells C1, C3, C7 and C9 are the same, then the state of C5 in the next system time step is the same as their states, as shown Figure 4 shown.

[0146] S7: For the grain boundary cells that still exist in step S6 and have not undergone recrystallization nucleus transformation, randomly select a cell from the 8 cells in the neighborhood of cell C5 and transform it according to probability P4. The selection of the cell is related to the grain boundary energy change ΔE i→j related;

[0147] The calculation formula for probability P4 is:

[0148]

[0149] S8: After all grain boundary cells are judged, the system time step is increased by one and the next cycle is continued;

[0150] S9: according to the microscopic test results of the grains observed in the high temperature thermal shock experiment in step S1, the system time step of the same grain size is associated with the corresponding number of thermal shock cycles and the upper limit temperature of the thermal shock load;

[0151] According to the microscopic observation test results, the time step of the CA system with the same grain size and the corresponding number of thermal shock cycles are shown in Table 1:

[0152] Table 1 Time step of CA simulation system and corresponding number of thermal shock load cycles for the same grain size

[0153]

[0154] Through analysis, it is found that the time step CAS and the number of thermal shock load cycles N have the following relationship:

[0155]

[0156] Through data fitting, it can be obtained that the upper limit temperature T of different thermal shock loads max The values ​​of the corresponding fitting parameters k are shown in Table 2:

[0157] Table 2 Upper limit temperature T of thermal shock load max The corresponding fitting parameter k

[0158] <![CDATA[Upper limit temperature T max / K]]> Fitting parameter k 873.15 859.41766 923.15 296.85856 973.15 85.04053

[0159] Drawing on the linear correspondence between MC simulation time and real time established by Radhakrishnan et al. in studying the evolution of 0.5Mo-Cr-V steel grains using the Monte Carlo method, the value of the fitting parameter k is related to temperature, and at the same time, the temperature and the time step are exponentially related, resulting in the following prediction formula:

[0160]

[0161] Where CAS represents the system time step of the cellular automaton; C1 and C2 are unknown constants; N is the number of thermal shock cycles, T max is the upper limit temperature of thermal shock load;

[0162] The data in Table 2 can be used to solve the values ​​of C1 and C2, and the constants C1 = 959930 and C2 = 17928 are obtained. Finally, the time step CAS, the number of thermal shock load cycles N, and the upper limit temperature of thermal shock load T are determined. max The relationship is shown in the formula:

[0163]

[0164] S10: Use the formula obtained in step S9 to calculate the system time step CAS of the cellular automaton at the upper temperature limit of the given thermal shock load for a given number of thermal shock cycles, input the system time step CAS into the CA model for prediction, and obtain the corresponding grain size and material microstructure simulation diagram, such as Figure 5 The experimental data of average equivalent diameter of grains were compared with the CA simulation data. Figure 6 shown.

[0165] Figure 6The solid line in the figure is the prediction result of the CA model. The analysis results show that the micro-experimental observation data all fall within the 95% confidence interval of the CA simulation curve. Therefore, it can be considered that the CA model can better predict the microstructure morphology of the specimens after different types of thermal shock loads.

[0166] In summary, the method of the present invention is based on the thermal activation mechanism, curvature drive mechanism, and grain boundary energy reduction mechanism, combined with the recrystallization nucleation and precipitation phase change phenomena in a partial area of ​​the sample after thermal shock load, to optimize the cellular state transition rules of grain growth of the alloy under thermal shock load, and establish a CA model of grain growth of the alloy after thermal shock load. This model is consistent with the physical mechanism and relevant theories of grain growth during thermal shock load, and can more comprehensively reflect the actual process of grain growth during thermal shock load.

[0167] By combining experimental data with a cellular automaton model, the present invention can accurately predict the microstructural evolution of materials under different high-temperature thermal shock conditions. By using a probabilistic model and neighbor types, the calculation process is optimized and the simulation efficiency is improved. The method is suitable for high-temperature thermal shock analysis of different materials and conditions and has broad industrial application prospects. By combining a probabilistic nucleation model, a thermal activation mechanism, a curvature-driven mechanism, and a cellular automaton model, the method can significantly improve prediction efficiency and reduce experimental costs, thus having important application value.

[0168] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any person skilled in the art can easily conceive of various modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should be included within the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for predicting microstructure evolution during thermal shock loading based on cellular automata, characterized in that: The method comprises the following steps: S1: Conduct high temperature thermal shock tests on materials under different upper limit temperature conditions to obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and grain size under different conditions, as well as the change in δ phase content; S2: Input basic parameters according to material properties and randomly assign orientation variables to each cell to establish the initial cell state, providing initial conditions for cell orientation changes and grain growth during the simulation process; S3: According to the VonNeumann neighbor type, there is a certain probability that the grain boundary cells will not transform. The probability that the grain boundary cells will not transform is recorded as P1. Based on the probability P1, a preliminary judgment is made on the grain boundary cells. The grain boundary cells that do not transform in this system time step are identified. The grain growth rule is not judged, and the grain growth judgment is performed on the grain boundary cells that have transformed; S4: For grain boundary cells that need to be judged for grain growth, based on the probabilistic nucleation model, it is assumed that the recrystallization nucleus is generated according to the probability P2. The probability P2 is used to determine whether a new recrystallization nucleus is generated, and the Moore neighbor type and the grain boundary energy change ΔE are used to determine whether a new recrystallization nucleus is generated. i→j Simulate the growth process of recrystallization nuclei; S5: For the grain boundary cells that have not undergone recrystallization nucleus transformation in step S4, a determination is made based on the thermal activation mechanism. At each system time step, the difficulty of the grain boundary cells undergoing transformation is determined according to the probability P3. S6: Assuming that the grain boundary cell that has not undergone recrystallization nucleus transformation in step S5 is C5, transformation determination is performed according to the Moore neighbor type and the curvature driven mechanism; S7: For the grain boundary cells that still exist in step S6 and have not undergone recrystallization nucleus transformation, randomly select one cell from the 8 cells in the neighborhood of cell C5 and transform it according to probability P4; S8: After all grain boundary cells are judged, the system time step is increased by one and the next cycle is continued; S9: Based on the microscopic test results of the grains observed in the high-temperature thermal shock experiment in step S1, the system time step of the same grain size is linked to the corresponding number of thermal shock cycles and the upper limit temperature of the thermal shock load to obtain the following formula: Where CAS represents the system time step of the cellular automaton; C1 and C2 are unknown constants; N is the number of thermal shock cycles, T max is the upper limit temperature of thermal shock load; S10: Use the formula obtained in step S9 to calculate the system time step CAS of the cellular automaton at the upper limit temperature of a given thermal shock load for a given number of thermal shock cycles, input the system time step CAS into the cellular automaton model for prediction, and obtain the corresponding grain size and material microstructure simulation diagram.

2. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: The steps of implementing step S1 are as follows: Select multiple upper limit temperature conditions, and for each upper limit temperature T i , set different numbers of thermal shock cycles; At different upper limit temperatures T i Multiple high-temperature thermal shock experiments were carried out under different conditions. After each experiment, the grain size, δ phase and carbide precipitation were observed, measured and recorded by instruments. Analyze the data, draw a graph of the change of grain size with the number of thermal shock cycles and a graph of the change of δ phase content with the number of thermal shock cycles, and obtain different upper limit temperatures T i The relationship between the number of thermal shock cycles and grain size under different conditions, as well as the change in δ phase content.

3. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: The Von Neumann neighborhood type means that the neighbors of each cell include the four cells above, below, left and right of it, and the Moore neighborhood type means that the neighbors of each cell include the eight cells around it.

4. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: The method for performing preliminary judgment on the grain boundary cell according to the probability P1 specifically includes: Traverse all cells and determine whether each cell is located at the grain boundary; For each grain boundary cell, generate a random number α between 0 and 1 and compare the random number α with P1; If α<P1, the grain boundary cell does not transform in the current system time step, and the grain growth rule is not determined; If α ≥ P1, the grain boundary cell undergoes a transformation in the current system time step, and further grain growth discrimination is required.

5. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 4, characterized in that: The probability P1 that the grain boundary cell does not undergo transformation is calculated as follows: The variation range of the δ phase content obtained through microscopic observation is recorded as a% to b%. A random number c between 0 and 100 is generated using the random number generation function in MATLAB. The value of c / 4 is compared with a and b:

6. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: The step S4 specifically includes: For each grain boundary cell that needs to be discriminated for grain growth, a random number β between 0 and 1 is generated. If β < P2, a new recrystallization nucleus is generated at the position of this grain boundary cell, and a new grain orientation number is assigned. The calculation formula of the probability P2 is as follows: In the formula, C3 is a constant; ω is a parameter related to temperature. The growth rule of the recrystallized nucleus is based on the Moore neighbor type. A neighbor is randomly selected from the 8 neighbors of the new recrystallized nucleus for transformation, and the grain boundary energy change ΔE of the neighbor is determined. i→j ; If ΔE i→j <0, the cell state of the selected neighbor is transformed into the state of recrystallization nucleus; If ΔE i→j ≥0, the cell state of the selected neighbor does not change.

7. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 6, characterized in that: Grain boundary energy E of cell j j Calculated by the Hamiltonian function: Where J is the positive grain boundary energy constant, δ is the Kronecker summation function, j is the jth neighbor of cell i, m represents the total number of neighbors of the cell, and S i 、S j represents the orientation number of the corresponding cell; Then the grain boundary energy change ΔE i→j =E i -E j Among them, E i represents the grain boundary energy of cell i.

8. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: The calculation formula of the probability P3 is: Where C0 is a constant; T0 is the short-term maximum operating temperature of the alloy; Q b represents the migration activation energy of the material; R is the gas constant.

9. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 1, characterized in that: Step S6 specifically includes: According to the Moore neighbor type, the 8 cells around the cell C5 are sequentially marked from top to bottom and from left to right as: C1, C2, C3, C4, C6, C7, C8, C9; if there are 5 or more consecutive cells around the cell C5 in the same state, then in the next system time step, the state of the cell C5 is the same as the state of these 5 or more cells; if the states of any three of the cells C2, C4, C6, and the cell C8 are the same, then in the next system time step, the state of the cell C5 is the same as the state of these three cells; if the states of any three of the cells C1, C3, C7, and the cell C9 are the same, then in the next system time step, the state of the cell C5 is the same as the state of these three cells.

10. The method for predicting microstructure evolution during thermal shock loading based on cellular automata according to claim 7, characterized in that: The calculation formula of the probability P4 is:

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