A method and system for generating a three-dimensional initial organization of cellular automata

Abstract

This disclosure relates to the field of integrated computational materials technology, and particularly to a method and system for generating three-dimensional initial structures using cellular automata. The disclosure comprises two stages: two-dimensional cross-sectional reconstruction and three-dimensional internal reconstruction. First, three two-dimensional structures are reconstructed based on experimental cross-sectional data, and these are spatially spliced ​​together using a boundary coupling mechanism to serve as fixed surface boundary conditions for the three-dimensional structures. Subsequently, nucleation and growth occur within the three-dimensional space, with the number of internal nucleation points dynamically adjusted through an iterative feedback mechanism until the generated three-dimensional structure meets preset statistical error requirements. This disclosure solves the problem of distorted surface morphology of three-dimensional initial structures in existing technologies, achieving high-fidelity simulation of both microstructural statistical characteristics and surface morphology, providing reliable initial conditions for high-precision simulation of subsequent processes such as thermal deformation.

Description

Technical Field

[0001] This disclosure relates to the field of integrated computational materials technology, and in particular to a method and system for generating three-dimensional initial tissues using cellular automata. Background Technology

[0002] Cellular automata (CA) models are powerful tools for simulating the microstructure evolution of materials during thermal processing (such as recrystallization and grain growth). The accuracy of their simulation predictions heavily depends on the initial microstructure settings. An ideal initial microstructure should simultaneously meet two conditions: first, its macroscopic statistical characteristics (such as average grain size and size distribution) should be consistent with experimental characterization results; second, its microscopic morphology characteristics (especially the grain morphology on the simulated domain surface) should exhibit physical realism consistent with the microstructure of the actual material.

[0003] However, current 3D CA models rely on a random generation method based on 2D experimental statistical information for their initial microstructure. This method extracts statistical information such as average grain size and grain size distribution from one or two cross-sectional microstructures, and then uses Voronoi segmentation or Monte Carlo methods to randomly generate grain structures in 3D space according to the extracted statistical distribution. This method ensures that the generated 3D microstructure matches the experimental cross-sectional results in an overall statistical sense, but the grain morphology of the outer surface (and any internal virtual cross-section) of the generated 3D microstructure is a completely random, idealized polygon. When using this initial microstructure to simulate recrystallization and other processes, and attempting to compare and verify it with the experimental microstructure morphology in different directions after deformation, the physical distortion of the initial surface morphology leads to the loss of the basis for comparison. This defect is particularly fatal for morphology-sensitive microstructures such as mixed grains.

[0004] The core problem with existing technology is that it mistakenly equates "statistical realism" with "morphological realism." This method merely transplants the statistical results of two-dimensional cross-sections, completely discarding the crucial physical information about the surface morphology contained in the two-dimensional image.

[0005] In summary, there is currently a lack of an effective method to generate a three-dimensional CA initial tissue that not only matches statistical features but also has a surface morphology consistent with experimental observations, starting from limited two-dimensional experimental data. This deficiency is a key bottleneck preventing CA simulation from playing a greater role in engineering applications that require rigorous morphological comparison and verification. Summary of the Invention

[0006] To address the aforementioned issues, this disclosure provides a method and system for generating three-dimensional initial tissues using cellular automata, which solves the problem that the surface morphology of existing three-dimensional CA initial tissues cannot achieve consistency with experimental cross-sectional results.

[0007] In a first aspect, a method for generating three-dimensional initial tissues using cellular automata includes: Two-dimensional cross-section reconstruction: three cross-sectional data of the experimental material are obtained, and the corresponding two-dimensional cellular automata structures are reconstructed respectively. During the reconstruction process, nucleation points are set according to the grain size distribution statistically obtained from the experiment, and the two-dimensional structures are continuously spliced ​​in space through boundary coupling to form the surface boundary conditions of the three-dimensional structure. Three-dimensional space construction: Create a three-dimensional CA space, and map the three two-dimensional tissues reconstructed from the two-dimensional cross-section to three orthogonal surfaces in the three-dimensional space, fixing the cell orientation in the boundary conditions of the orthogonal surfaces; The three-dimensional internal reconstruction involves nucleation and growth within the internal region of the three-dimensional CA space. An iterative feedback mechanism is used to adjust the number of internal three-dimensional nucleation points until the generated three-dimensional tissue meets the preset statistical error requirements, at which point the final three-dimensional initial tissue is output.

[0008] Furthermore, the corresponding two-dimensional cellular automata organization is reconstructed, including: The grains are divided into n intervals according to size. For the i-th interval, the corresponding number of two-dimensional nucleation points are placed and the grains are grown until the average size of the grains in that interval meets the first preset error range. After all intervals have been grown in sequence, if the two-dimensional space is not filled, grain growth continues until the entire two-dimensional space is filled. If the difference between the percentage distribution of grains after filling and the experimental data exceeds the second preset error range, then clear the current structure and re-execute nucleation growth.

[0009] Furthermore, the number of two-dimensional nucleation points is calculated by the sum of grain volumes within the size range, the sum of all grain volumes on the experimental section, the size of the CA space, and the average grain size.

[0010] Furthermore, boundary coupling enables the continuous spatial splicing of various two-dimensional tissues, including: Let the three sections be P1, P2 and P3; When reconstructing P1, its boundary cells are not initialized; When reconstructing P2, the cell orientation value of one side boundary is forcibly set to the orientation value of the corresponding side boundary of P1; When reconstructing P3, the cell orientation values ​​of its two side boundaries are forcibly set to the orientation values ​​of the corresponding side boundaries of P1 and P2, respectively, to ensure that the three two-dimensional tissues can be seamlessly spliced ​​into a three-dimensional continuous surface.

[0011] Furthermore, the number of internal 3D nucleus points is adjusted through an iterative feedback mechanism, including: Three-dimensional nucleation points are randomly placed within a three-dimensional space to grow grains until the space is filled. Calculate the average grain size of the three-dimensional structure and compare it with the average grain size obtained from experimental statistics; If the error requirement is not met, determine whether the current iteration number k is less than the maximum number of attempts m; If k < m, keep the number of three-dimensional nucleation points unchanged and re-perform random nucleation and growth; If k ≥ m, adjust the number of three-dimensional nucleation points according to the deviation direction between the average grain size of the three-dimensional structure and the average grain size obtained from experimental statistics, reset the iteration number k, and re-perform nucleation and growth.

[0012] Further, adjusting the number of three-dimensional nucleation points according to the deviation direction between the average grain size of the three-dimensional structure and the average grain size obtained from experimental statistics specifically includes: If the average grain size of the three-dimensional structure < the average grain size obtained from experimental statistics, indicating that the simulated grains are too fine, reduce the number of three-dimensional nucleation points; If the average grain size of the three-dimensional structure > the average grain size obtained from experimental statistics, indicating that the simulated grains are too coarse, increase the number of three-dimensional nucleation points.

[0013] Further, the number of three-dimensional nucleation points is calculated from the total volume represented by the three-dimensional cells, the two-dimensional average grain size, and the total number of grains on the three surfaces in the three-dimensional CA.

[0014] Further, in the grain growth process, the Moore neighbor model is used to calculate the conversion probability of the cell orientation. The conversion probability is inversely proportional to the distance between the neighbor cell and the central cell, and the sum of the conversion probabilities of all neighbors is 1; The neighbor cells are divided into several types, and different types of neighbors correspond to different conversion probability weights; Calculate the sum of the conversion probabilities of the cells with the same orientation value among all neighbors and use it as the conversion probability to a certain orientation of the two-dimensional and three-dimensional neighbor cells.

[0015] Further, it also includes: To increase the randomness of grain growth, a randomness determination is introduced during the grain growth process, specifically including: Generate a random number Nr and compare it with the preset growth probability Pr; only when Nr is greater than Pr, is the central cell allowed to undergo an orientation change.

[0016] In a second aspect, a cellular automaton three-dimensional initial structure generation system includes: A two-dimensional cross-section reconstruction unit, a three-dimensional space construction unit, and a three-dimensional internal reconstruction unit; Two-dimensional section reconstruction unit is used to acquire three section data of experimental material and reconstruct the corresponding two-dimensional cellular automata structure respectively. During the reconstruction process, nucleation points are set according to the grain size distribution statistically obtained from the experiment, and the two-dimensional structures are continuously spliced ​​in space through boundary coupling to form the surface boundary conditions of the three-dimensional structure. The three-dimensional space building unit is used to create a three-dimensional CA space, which maps the three two-dimensional tissues reconstructed from the two-dimensional section to three orthogonal surfaces in the three-dimensional space, and fixes the cell orientation in the boundary conditions of the orthogonal surfaces. The three-dimensional internal reconstruction unit is used to perform nucleation and growth in the internal region of the three-dimensional CA space, and adjusts the number of internal three-dimensional nucleation points through an iterative feedback mechanism until the generated three-dimensional tissue meets the preset statistical error requirements, and outputs the final three-dimensional initial tissue.

[0017] This disclosure includes at least the following beneficial effects: This disclosure solves the problem of distorted surface morphology in the prior art for three-dimensional initial microstructures, achieving high-fidelity simulation of both microstructure statistical characteristics and surface morphology, providing reliable initial conditions for high-precision simulation of subsequent processes such as thermal deformation. It not only ensures the authenticity of the generated three-dimensional CA initial microstructure grain size statistics but also guarantees the accuracy of its surface microstructure morphology.

[0018] Other features and advantages of this disclosure will be set forth in the following description and will be apparent in part from the description or may be learned by practicing the disclosure. The objects and other advantages of this disclosure may be realized and obtained by means of the structures pointed out in the description and the accompanying drawings. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the method flow for generating embodiments of this disclosure; Figure 2 A system architecture diagram is generated for the embodiments of this disclosure; Figure 3 Schematic diagram of the microstructure and grain size distribution of a certain steel at different cross sections; Figure 4 This is a schematic diagram of a cellular automata method for generating three-dimensional initial tissues based on multi-section experimental data. Figure 5 A schematic diagram illustrating the boundary cells of tissue in a two-dimensional cross-section simulation; Figure 6 This is a schematic diagram of the growth process of nucleation point grains in a two-dimensional cellular space. Figure 7 This is a schematic diagram of the neighbor distribution of a two-dimensional central cell; Figure 8 This is a schematic diagram of two-dimensional grain growth; Figure 9 This is a schematic diagram illustrating the process of grain growth in two-dimensional space. Figure 10 Schematic diagrams showing the microstructure and grain size distribution of different cross sections in the simulation; Figure 11 This is a schematic diagram of the neighbor distribution of the three-dimensional central cell; Figure 12 This is a schematic diagram of the grain growth process in three-dimensional cellular space. Figure 13 A schematic diagram of the reconstructed three-dimensional cellular automata organization; Figure 14 A schematic diagram of a three-dimensional cellular automaton structure generated from an unreconstructed surface structure; Figure 15 A schematic diagram illustrating the average grain size variation in a thermocompressed cross-section simulated for two different initial microstructures.

[0021] In the diagram: 1—2D neighbor type I, 2—2D neighbor type II, 3—2D neighbor type III, 4—2D neighbor type IV, 5—3D neighbor type I, 6—3D neighbor type II, 7—3D neighbor type III. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0023] like Figure 1 As shown, a method for generating three-dimensional initial tissues using cellular automata includes: S101, Two-dimensional cross-section reconstruction: three cross-sectional data of the experimental material are obtained, and the corresponding two-dimensional cellular automata structures are reconstructed respectively. During the reconstruction process, nucleation points are set according to the grain size distribution statistically obtained from the experiment, and the two-dimensional structures are continuously spliced ​​in space through boundary coupling to form the surface boundary conditions of the three-dimensional structure. S102, 3D space construction, creating a 3D CA space, mapping the three 2D tissues reconstructed from the 2D section to three orthogonal surfaces in the 3D space, and fixing the cell orientation in the boundary conditions of the orthogonal surfaces; S103, 3D internal reconstruction, performs nucleation and growth in the internal region of the 3D CA space, and adjusts the number of internal 3D nucleation points through an iterative feedback mechanism until the generated 3D tissue meets the preset statistical error requirements, and outputs the final 3D initial tissue.

[0024] In practice: This disclosure includes two stages: two-dimensional cross-sectional microstructure reconstruction and three-dimensional microstructure reconstruction. First, three different initial two-dimensional microstructures of cellular automata are reconstructed based on different experimental cross-sectional data, and these are used as three surface microstructures of the three-dimensional microstructure. Then, three-dimensional reconstruction is performed based on these surface microstructures. By adjusting the number of nucleation points in the cellular automata space, the three-dimensional microstructure corresponding to the experimental cross-section can be accurately simulated, thus providing reliable initial conditions for subsequent simulation of higher-precision thermal deformation microstructure.

[0025] A cellular automata-based method for generating three-dimensional initial microstructures based on multi-section experimental data uses a digital space composed of tiny square (or cubic) meshes to represent the material region. Each mesh is a computational unit, called a cell, containing two state variables (grain orientation value and nucleation marker value), where the grain orientation value is an integer between 1 and 180. In this CA space, adjacent meshes with the same orientation aggregate into a "grain," and the actual physical size of the mesh is determined based on experimental results. This three-dimensional initial microstructure generation method includes two stages: two-dimensional cross-sectional microstructure reconstruction and three-dimensional microstructure reconstruction. Before the two-dimensional cross-sectional microstructure reconstruction, experimental results for the side and top sections of the microstructure are obtained from the experimental results. The sections are numbered sequentially, with the side sections numbered 1 and 2, and the top section numbered 3. The average grain size and grain size volume distribution of each section are statistically analyzed.

[0026] Two-dimensional average grain size and three-dimensional average grain size Calculate using formula (1).

[0027] (1) In the formula For the r-th grain, Let be the area of ​​the r-th grain. Let be the volume of the r-th grain.

[0028] The steps for reconstructing the two-dimensional cross-section structure are as follows: (1) Let P =1.

[0029] (2) According to the section numberP The experimental results were used to create a two-dimensional CA space of the same size, specify the cell values ​​at the boundaries, and create the number of nucleation points. N i (P), Quantity percentage f i e (P) and average grain size d i e The set (P) is as follows: N 1(P), N 2(P), ... N n (P)), ( f 1 e (P), f 2 e (P), ... f n e (P)) and ( d 1 e (P), d 2 e (P), ... d n e (P)), f i e (P) represents the proportion of the number of grains in the i-th grain size range on the experimental section numbered P to the total number of grains. d i e (P) represents the number. P The values ​​of all grains within the i-th grain size range on the simulated cross section are calculated according to the two-dimensional average grain size using formula (1). N i (P) represents the number of nucleation points required in CA to achieve the experimental grain size ratio and the experimental average grain size, and n is the total number of grain size ranges.

[0030] (3) Let i =1.

[0031] (4) Input the number of nucleation points N i (P), average grain size d i e (P) and quantity percentage f i e (P), and set j =1.

[0032] (5) Randomly nucleate in the generated two-dimensional cell space: select from cells that have never had an orientation value. N i (P) cells are selected, and each cell is assigned a random orientation value and a nucleation label, where the nucleation label is represented as... i The value of .

[0033] (6) Nucleation markers are i The nucleation point of the value grows in the two-dimensional CA space until it satisfies formula (2).

[0034] (2) In the formula, Representative number is P The values ​​of all grains within the i-th grain size range on the simulated cross section are calculated according to the two-dimensional average grain size using formula (1). This is the grain size error coefficient, with a value ranging from 0 to 0.2.

[0035] (7) Determine whether the condition is met. i ≥n, if not satisfied i After adding 1, repeat steps 4 to 7.

[0036] (8) If satisfied i If the value is greater than or equal to n, then we continue to determine whether all cells have orientation values. If not, it means that the two-dimensional cell space is not filled by the grain, and the grain continues to grow in the two-dimensional space.

[0037] (9) If all cells have orientation values, then according to formula (3), it is determined whether the simulated grain number ratio is close to the experimental results.

[0038] (3) In the formula, Representative number is P The proportion of the number of grains in the i-th grain size range on the simulated cross section to the total number of grains. This is the quantity percentage error coefficient, with a value range of 0 to 0.3.

[0039] (10) If formula (3) is not satisfied, clear the nucleated and grown grains in the two-dimensional space and continue with steps 5 to 10.

[0040] (11) If formula (3) is satisfied, then determine whether the section numbering is satisfied. P ≥3, if not satisfied, then P Add 1 and update P The value is generated based on all previously reconstructed two-dimensional organizations. P Set the boundary conditions for each section, and then repeat steps 2 to 11.

[0041] (12) If the section numbering is satisfied P If the value is ≥3, then the three-dimensional tissue reconstruction stage begins.

[0042] The steps in the three-dimensional tissue reconstruction stage are as follows: (1) Create the corresponding three-dimensional cell space and use the three reconstructed sections as the surface organization of the three-dimensional cell.

[0043] (2) Create the number of core points N 3D .

[0044] (3) Let k =1.

[0045] (4) Randomly nucleate in the generated three-dimensional cellular space: select from cells that have never had an orientation value. N 3D Each cell is assigned a random orientation value.

[0046] (5) The grains grow in three-dimensional space until all cells in the three-dimensional space have orientation values.

[0047] (6) Determine whether the average grain size satisfies formula (4).

[0048] (4) In the formula, The simulated result value is calculated based on the three-dimensional average grain size according to formula (1). In order to combine the statistical results of all experimental sections, the value of the two-dimensional average grain size was calculated according to formula (1).

[0049] (7) If formula (4) is not satisfied, determine whether it is satisfied. k ≤ m This is to avoid the number of nucleation points in three-dimensional space. N 3D An improper setting can cause an infinite loop where the corresponding conditions cannot be met. The value of m must be greater than 4. k ≤ m ,but k Add 1 and update k Then, clear the nucleated and grown grains in three-dimensional space, leaving only three surface structures, and continue with steps 4-7; if the conditions are not met... k ≤ m Then determine whether it satisfies d 3D s < d 2D e If this condition is met, it indicates that the simulated average grain size is smaller than the experimental size, and therefore the number of nucleation sites is lower. N3D The value needs to be reduced by 1. If this condition is not met, it indicates that the simulated average grain size is larger than the experimental size, and therefore the number of nucleation sites is lower. N 3D We need to add 1, then clear the nucleated and grown grains in the three-dimensional space, leaving only the three surface structures, and continue with steps 2 to 7.

[0050] (8) If formula (4) is satisfied, the three-dimensional structure is output and the process ends.

[0051] In one embodiment, the number of nucleation points N i (P) is calculated according to formula (5).

[0052] (5) In the formula, the ceil function rounds up. The sum of grain volumes within the i-th grain size range on the experimental cross section P represents the total volume of the grains. The sum of the volumes of all grains on the experimental section designated P represents the total volume of the grains. This represents the size of the CA space.

[0053] In one embodiment, in the second step of the two-dimensional cross-sectional structure reconstruction process, the cell values ​​at the boundary are determined by the previously reconstructed cross-sectional structure, for the cross-section number... P For a reconstructed 2D organization with a value of 1, the boundary cells are not initialized, but for the section numbering... P =2 reconstructed two-dimensional organization, in order to match the section numbering P The two-dimensional structure with a value of 1 remains continuous, and the orientation value and section number of its left boundary cell are also considered. P =1, the right boundary cell orientation values ​​are the same, while for section numbering P =3 reconstructed two-dimensional organization, in order to match the numbering P =1 and P The two-dimensional structure with a density of 2 remains continuous, thus forming the three surfaces of the three-dimensional structure, with the boundary cells on the left side oriented and numbered. P The reconstructed organization with =1 has the same top structure, and its bottom boundary cell orientation and numbering are the same. P =2 The top of the restructured organization is the same.

[0054] In one embodiment, step 6 of the two-dimensional cross-sectional tissue reconstruction process is marked as nucleation. i The growth steps of the nucleation point of the value in the two-dimensional CA space are as follows: (1) Let q =1.

[0055] (2) Determine if the cell at this location has an orientation value and if its neighbors have a nucleation marker of i. If not, q Add 1 and update q.

[0056] (3) If the cell at this location has an orientation value and its neighbors include a neighbor with a nucleation marker of i, determine whether the following conditions are met. N r > P r , N r A random number less than 1. P r The probability of grain growth is denoted by a value ranging from 0.3 to 0.7. This criterion is designed to increase the randomness of grain growth, thereby satisfying the distribution law. If this condition is not met... N r > P r , q Add 1 and update q .

[0057] (4) If satisfied N r > P r Calculate the conversion probability to the orientation of a two-dimensional neighbor cell labeled i with a tangible core.

[0058] (5) Find the orientation with the highest conversion probability. If the conversion probabilities of several orientations are the same, randomly select an orientation and record the orientation change of the central cell.

[0059] (6) q Add 1 and update q .

[0060] (7) Determine whether the condition is met. q > N 2D , N 2D The total number of cells in the two-dimensional cellular space. If this condition is not met, repeat steps 2 to 7.

[0061] (8) If satisfied q > N 2D Then, based on the changes in the orientation of the cells, the two-dimensional cell space is updated, and the process ends.

[0062] In one embodiment, step 8 of the two-dimensional cross-sectional structure reconstruction process, the step of grains continuing to grow in two-dimensional space, is as follows: (1) Let q =1.

[0063] (2) Determine whether the condition is met. N r > P rFurthermore, the cell at this location has no orientation value while its neighboring cells do. If this condition is not met, q Add 1 and update q .

[0064] (3) If satisfied N r > P r Given that the cell at this location has no orientation value while its neighboring cells have orientation values, calculate the probability of conversion to a certain orientation of a two-dimensional neighboring cell.

[0065] (4) Find the orientation with the highest conversion probability. If the conversion probabilities of several orientations are the same, randomly select an orientation and record the orientation change of the central cell.

[0066] (5) q Add 1 and update q .

[0067] (6) Determine whether the condition is met. q > N 2D If the condition is not met, repeat steps 2 to 6.

[0068] (7) If satisfied q > N 2D Then, based on the changes in the orientation of the cells, the two-dimensional cell space is updated, and the process ends.

[0069] In one embodiment, the nucleation marker is... i The steps for calculating the conversion probability to a certain orientation of a two-dimensional neighboring cell are as follows: Step 4 of the growth process of the nucleation point in the two-dimensional CA space and Step 3 of the continued growth process of the grain in the two-dimensional space. (1) An improved two-dimensional Moore neighbor is used to calculate the conversion probability. There are 20 neighbors and 4 types. It is stipulated that the conversion probability of the central cell to the neighbor orientation is inversely proportional to its distance from the neighbor. The total conversion probability to the 20 neighbor cells is 1. Therefore, the conversion probabilities to two-dimensional neighbor types I, II, III and IV are 0.0806, 0.057, 0.0403 and 0.0360, respectively.

[0070] (2) Calculate the sum of the cell conversion probabilities of the same orientation values ​​among the 20 neighbors, and use it as the conversion probability to a certain orientation of the two-dimensional neighbor cell.

[0071] In one embodiment, the number of nucleation points N 3D Calculate according to formula (6).

[0072] (6) In the formula, The total volume represented by a three-dimensional cell. The two-dimensional average grain size was calculated for all experimental cross sections. This represents the total number of grains on the three surfaces of a three-dimensional CA.

[0073] Furthermore, in step 5 of the three-dimensional tissue reconstruction stage, the grain growth process in three-dimensional space is as follows: (1) Let q =1.

[0074] (2) Determine whether the condition is met. N r > P r Furthermore, the cell at this location has no orientation value while its neighboring cells do. If this condition is not met, q Add 1 and update q .

[0075] (3) If satisfied N r > P r Given that the cell at this location has no orientation value while its neighboring cells have orientation values, calculate the probability of conversion to a certain orientation of a three-dimensional neighboring cell.

[0076] (4) Find the orientation with the highest conversion probability. If the conversion probabilities of several orientations are the same, randomly select an orientation and record the orientation change of the central cell.

[0077] (5) q Add 1 and update q .

[0078] (6) Determine whether the condition is met. q > N 3D If the condition is not met, repeat steps 2 to 6.

[0079] (7) If satisfied q > N 3D Then, based on the changes in the orientation of the cells, the three-dimensional cell space is updated, and the process ends.

[0080] In one embodiment, the third step of isometric grain growth in three-dimensional space, the calculation steps for the conversion probability to a certain orientation of a three-dimensional neighboring cell, are as follows: (1) The conversion probability is calculated using three-dimensional Moore neighbors. There are 26 neighbors and 3 types. It is stipulated that the conversion probability of the central cell to the neighbor orientation is inversely proportional to its distance from the neighbor. The total conversion probability to the 26 neighbor cells is 1. Therefore, the conversion probabilities to three-dimensional neighbor types I, II, and III are 0.0302, 0.0370, and 0.0523, respectively. The number of neighbor type I is 8, the number of neighbor type II is 12, and the number of neighbor type III is 6.

[0081] (2) Calculate the sum of the cell conversion probabilities of the same orientation values ​​among the 26 neighbors, and use it as the conversion probability to a certain orientation of the three-dimensional neighbor cell.

[0082] like Figure 2 As shown, a cellular automata three-dimensional initial tissue generation system includes: Two-dimensional cross-section reconstruction unit 201, three-dimensional space construction unit 202 and three-dimensional interior reconstruction unit 203; Two-dimensional section reconstruction unit 201 is used to acquire three section data of the experimental material and reconstruct the corresponding two-dimensional cellular automata structure respectively. During the reconstruction process, nucleation points are set according to the grain size distribution statistically obtained from the experiment, and the two-dimensional structures are continuously spliced ​​in space through boundary coupling to form the surface boundary conditions of the three-dimensional structure. The three-dimensional space construction unit 202 is used to create a three-dimensional CA space, which maps the three two-dimensional tissues reconstructed from the two-dimensional section to three orthogonal surfaces in the three-dimensional space, and fixes the cell orientation in the boundary conditions of the orthogonal surfaces. The three-dimensional internal reconstruction unit 203 is used to perform nucleation and growth in the internal region of the three-dimensional CA space, and adjusts the number of internal three-dimensional nucleation points through an iterative feedback mechanism until the generated three-dimensional tissue meets the preset statistical error requirements, and outputs the final three-dimensional initial tissue.

[0083] In practice: This disclosure comprises two stages: two-dimensional cross-sectional reconstruction and three-dimensional internal reconstruction. First, three two-dimensional structures are reconstructed based on experimental cross-sectional data and spatially spliced ​​together using a boundary coupling mechanism, serving as fixed surface boundary conditions for the three-dimensional structures. Subsequently, nucleation and growth occur within the three-dimensional space, with the number of internal nucleation points dynamically adjusted through an iterative feedback mechanism until the generated three-dimensional structure meets preset statistical error requirements. This disclosure solves the problem of distorted surface morphology of initial three-dimensional structures in existing technologies, achieving high-fidelity simulation of both microstructural statistical characteristics and surface morphology, providing reliable initial conditions for high-precision simulation of subsequent processes such as thermal deformation.

[0084] Existing technologies can only guarantee that the three-dimensional microstructure is consistent with the experiment in terms of statistical characteristics (such as average grain size). However, this disclosure, through a "from the surface to the core" reconstruction strategy, forces the surface morphology of the three-dimensional microstructure to be completely consistent with the experimental cross-section. This solves the long-standing problem of idealized and distorted surface microstructure in three-dimensional CA simulation, making the simulation model not only aligned in terms of data, but also close to the real material in terms of physical morphology.

[0085] Because the initial microstructure generated by this disclosure has a realistic surface morphology, systematic errors caused by differences in initial surface morphology are eliminated. In subsequent thermal deformation (such as hot compression) simulations, the nucleation and growth behavior of grains will be based on the evolution of the real initial geometric boundaries, thus making the simulated predicted cross-sectional microstructure and grain size change curves fit the experimental results better, verifying the reliability of the simulation.

[0086] This disclosure employs a "batch nucleation and growth" strategy based on grain size ranges. Addressing the complexity of competitive growth among grains of different sizes in mixed-grain structures (a mixture of large and small grains), this method precisely preserves the specific size distribution characteristics observed in experiments by sequentially controlling nucleation and growth termination conditions according to ranges, thus avoiding the problem of small grains being excessively consumed by large grains in traditional one-time nucleation methods.

[0087] This disclosure introduces an intelligent "iterative feedback mechanism" and "infinite loop protection logic" in the 3D reconstruction stage. By first utilizing randomness to attempt the problem (keeping the number of nucleus points constant), and then adaptively adjusting the number of nucleus points (increasing or decreasing according to dimensional deviations) after failure, it leverages the randomness advantage of the CA method while ensuring convergence through closed-loop control. This mechanism effectively avoids invalid calculations and infinite loops, improving computational efficiency while maintaining accuracy.

[0088] By introducing an improved Moore neighbor model and a stochastic determination mechanism, this disclosure simulates the anisotropy and thermal fluctuation effects during grain growth. Compared with the traditional equal-probability growth model, the grain boundaries generated by this method are more natural, and the microstructure is closer to the physical growth state of real materials.

[0089] To enable those skilled in the art to better understand this disclosure, the principles of this disclosure are explained below in conjunction with the accompanying drawings: Microstructure and grain size distribution of a certain steel at different cross sections during initial hot compression are as follows: Figure 3 As shown, P =1 and P =2 represents two side sections. P =3 is the top surface. The average grain sizes of these three surfaces are calculated according to formula (1), which are 139.10 μm, 130.94 μm and 160.56 μm, respectively, indicating a clear mixed-crystal structure. First, the two-dimensional cross-sectional structure is reconstructed, as follows: Figure 4As shown. Based on the experimental results, 220×220 cells were created, each cell representing a size of 2.5 μm × 2.5 μm. Therefore, the simulated cross-section represents an actual tissue size of 550 μm × 550 μm. (Due to the cross-section numbering...) P =1, at this point the boundary cell is not initialized. But the section numbering P The reconstructed organization with a value of 2, and the orientation value and section number of its left boundary cell. P The right boundary cell orientation values ​​of =1 are the same, such as Figure 5 As shown; for section number P The reconstructed two-dimensional tissue with a value of 3, and the orientation and numbering of its left-side boundary cells. P The reconstructed organization with =1 has the same top structure, and its bottom boundary cell orientation and numbering are the same. P =2 The top of the restructured organization is the same, such as Figure 5 As shown.

[0090] according to Figure 3 Mid-section number P The experimental results with a value of 1 show that the total number of grain size ranges n is 7, and their proportion is [missing information]. f i e The (P) set is (0.0909, 0.1818, 0.3864, 0.2500, 0.0909, 0, 0), with an average grain size of d i e The (P) set is (27.64 µm, 55.53 µm, 102.03 µm, 141.91 µm, 182.89 µm, 0, 0), with the number of nucleation points... N i (P) According to formula (5), its set is (3, 6, 12, 8, 3, 0, 0), and the quantity ratio error coefficient is... The grain size error coefficient is 0.11. It is 0.2. First, based on the number of nucleation points... N i (P) The set assigns random orientation values ​​and nucleation labels to the selected cells, and then lets the nucleation labels be... i The nucleation point of the value grows in two-dimensional space, and the growth process is as follows: Figure 6 As shown, the probability of growing up P r Take 0.4, N 2D For a 220×220, two-dimensional neighbor cells are as follows: Figure 7As shown, there are 20 neighbors, divided into 4 types. The conversion probabilities of the central cell orientation value to two-dimensional neighbor types I, II, III, and IV are 0.0806, 0.057, 0.0403, and 0.0360, respectively. Figure 8 For an example of two-dimensional grain growth, the grid... Let represent a cell with no orientation value, whose neighboring orientation values ​​are 1, 2, and 3. The probability of merging to a neighbor with orientation value 1 is 0.0806 + 0.057 + 0.0403 + 2. 0.0360 = 0.2499, the probability of converting to the neighbor orientation value 2 is 0.0806 + 0.057 + 0.0403 + 2. 0.0360 = 0.2499, the probability of converting to the neighbor orientation value 3 is 2. 0.0806+2 0.057+4 0.0403+2 0.0360 = 0.5084. Since the probability of conversion to orientation value 3 is high, the orientation of the central cell changes from 1 to 3.

[0091] After all nucleation points in the batch have grown to full size, it is necessary to determine whether all cells in the two-dimensional space have an orientation value, such as... Figure 4 As shown, if some cells lack orientation values, the grain continues to grow in two-dimensional space, and the growth steps are as follows: Figure 9 As shown, this process is repeated until all cells in the two-dimensional cellular space have orientation values. Then, according to formula (3), it is determined whether the simulated grain number ratio is close to the experimental results. If not, the above steps are repeated, and finally, the numbering is completed. P The organization with =1 has been restructured, such as Figure 10 As shown, the set of its quantity proportions is (0.0938, 0.1875, 0.3750, 0.2812, 0.0625, 0, 0), and the sum of the differences between it and the experimental proportion set is 0.0796, satisfying formula (3). When numbering P The organization with =1 has been restructured, numbered. P The tissue with a value of 2 was reconstructed using the steps described above, with the experimental tissue representing the percentage of the total number of tissues. f i e The (P) set is (0.0667, 0.2667, 0.4667, 0.1000, 0.0667, 0.0333, 0), with an average grain size of d i eThe (P) set is (32.2756 µm, 67.5838 µm, 99.6075 µm, 137.6688 µm, 176.9784 µm, 207.8423 µm, 0), with the number of nucleation points... N i (P) According to formula (5), its set is (3, 9, 16, 4, 3, 2, 0), and the set of the proportion of simulation results is (0.0588, 0.2647, 0.4706, 0.0882, 0.0882, 0.0294, 0). The sum of the differences between the simulation results and the experimental results is 0.0509, which satisfies formula (3). Finally P The tissue with a value of 3 was reconstructed using the steps described above, with the experimental tissue representing the percentage of the total number of tissues. f i e The (P) set is (0.0400, 0.2800, 0.3600, 0.1600, 0.1200, 0, 0.0400), with an average grain size of d i e The (P) set is (30.3562 µm, 66.8951 µm, 103.6927 µm, 142.43 µm, 181.4985 µm, 0, 265.1968 µm), with the following number of nucleation points. N i (P) According to formula (5), its set is (2, 7, 9, 5, 4, 0, 2), the set of the number proportions of the simulation results is (0.0385, 0.2692, 0.3462, 0.1538, 0.1538, 0, 0.0015), and the sum of the differences between the simulation results and the experimental results is 0.1046, which satisfies formula (3).

[0092] After reconstructing the tissue in three sections, 220×220×220 cells were created, each representing a size of 2.5 μm×2.5 μm×2.5 μm. Therefore, the simulated actual tissue size is 550 μm×550 μm×550 μm. (Number of nucleation points) N 3D The result is 42 according to formula (6). Figure 4 The process involves random nucleation, followed by isometric growth in three-dimensional space, where the neighbors are not identical to those in two-dimensional space. Figure 11 As shown. There are three types of neighbors, totaling 26 neighbors. Type I neighbors number 8, with a conversion probability of 0.0302; Type II neighbors number 12, with a conversion probability of 0.0370; and Type III neighbors number 6, with a conversion probability of 0.0523. Figure 8Similar to calculating the sum of transformation probabilities in two dimensions, determining which orientation a cell should transform to in its neighboring cells, the process of equiaxial growth in three-dimensional space is as follows: Figure 12 As shown, the probability of growth is... P r Just like in two dimensions, take 0.4. N 3D Given a value of 220×220×220, after all cells in the three-dimensional space have orientation values, determine whether formula (4) is satisfied, where... The value is 141.57 µm, while the simulation results are... The calculated result is 104.76 µm. Since it does not satisfy formula (4), we need to determine whether it satisfies the requirement. k ≤ m , m Take 6, because k =1, satisfying k ≤ m ,therefore k Change to 2, clear the nucleated and grown grains in three-dimensional space, retaining only three surface tissue cells, and then continue to repeat the random nucleation steps, as follows. Figure 4 As shown. Due to the simulation results of 5 calculations. None of them satisfy formula (4). To avoid entering an infinite loop, we then check whether they satisfy the formula. d 3D s < d 2D e Since this condition is met, the number of nucleation points is... N 3D To reduce the value by 1 to 41, and to clear the nucleated and grown grains in three-dimensional space, leaving only three surface tissue cells, the nucleation and growth process is repeated. This process is then repeated until the final simulation result is output. It is 140.12 µm, and the three-dimensional tissue is as follows Figure 13 As shown, by slicing the original tissue along a certain direction, it can be found that the three-dimensional tissue is basically continuous.

[0093] To further verify the error in thermal deformation microstructure results caused by different initial surface microstructures in the simulation, the step of reconstructing the cross-sectional microstructure as the three-dimensional surface microstructure was omitted in the three-dimensional microstructure reconstruction step. Instead, random nucleation and grain growth in three-dimensional space were directly performed to generate a three-dimensional initial microstructure with similar average grain size, such as... Figure 14 As shown. The average grain size of this three-dimensional structure. It is 140.13 µm, however, regardless of the section number P =1 or section number P =2 surface structure, all with Figure 3 The experimental tissues showed significant differences, at which point the cross-section numbering was adjusted. PThe sum of the proportion of grains with a size of 1 and the difference in experimental results is calculated using formula (3) as 0.9403, and the section number is... P The sum of the proportion of grain size with a value of 2 and the difference between the experimental results is calculated using formula (3) to be 0.7777. This huge difference makes the average grain size of the cross section significantly different from the experimental results. The simulated cross section numbering P =1 and P The average grain sizes of 101.9473 µm and 109.5227 µm for 2 are significantly different from the experimental results of 135.2679 µm and 130.94 µm. The grains reconstructed using the method presented in this paper... Figure 13 The three-dimensional structure in the text, its section numbering P =1 and P The average grain size of the surface microstructure with a =2 is 126.4489 µm and 133.8225 µm, which is close to the experimental results. Figure 15 The average grain size change of the thermally compressed cross-section was simulated for two different initial microstructures. It can be found that the average grain size change of the reconstructed 3D initial microstructure considering the surface microstructure closely matches the experimental results during thermal compression, while the average grain size change of the reconstructed 3D initial microstructure without considering the surface microstructure differs significantly from the experimental results.

[0094] Although the present disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure.

Claims

1. A method for generating a three-dimensional initial tissue using a cellular automaton, the method comprising the steps of: Comprising: ​ Two-dimensional cross-section reconstruction to obtain three cross-section data of the experimental material, and respectively reconstruct the corresponding two-dimensional cellular automaton tissues; During the reconstruction process, set the nucleation points according to the grain size distribution statistically obtained from the experiment, and make each two-dimensional tissue continuously spliced in space through boundary coupling to form the surface boundary conditions of the three-dimensional tissue; Three-dimensional space construction, create a three-dimensional CA space, map the three two-dimensional tissues reconstructed from the two-dimensional cross-sections to three orthogonal surfaces in the three-dimensional space respectively, and fix the cell orientations in the orthogonal surface boundary conditions; Three-dimensional internal reconstruction, perform nucleation and growth in the internal region of the three-dimensional CA space, and adjust the number of internal three-dimensional nucleation points through an iterative feedback mechanism until the generated three-dimensional tissue meets the preset statistical error requirements, and output the final three-dimensional initial tissue.

2. A method for generating a three-dimensional initial tissue of a cellular automaton according to claim 1, wherein Reconstructing the corresponding two-dimensional cellular automaton tissue includes: Divide the grains into n intervals according to their sizes. For the i-th interval, put the corresponding number of two-dimensional nucleation points and let them grow until the average grain size in this interval meets the first preset error range; After the growth of all intervals is completed in sequence, if the two-dimensional space is not filled, continue the grain growth until the entire two-dimensional space is filled; If the difference between the proportion distribution of the filled grain numbers and the experimental data exceeds the second preset error range, clear the current tissue and re-perform nucleation growth.

3. A method for generating a three-dimensional initial tissue of a cellular automaton according to claim 2, wherein The number of two-dimensional nucleation points is calculated by the sum of the grain volumes in the size interval, the sum of the volumes of all grains on the experimental cross-section, the size of the CA space, and the average grain size.

4. A method for generating a three-dimensional initial tissue of a cellular automaton according to claim 1, wherein Making each two-dimensional tissue continuously spliced in space through boundary coupling includes: Let the three cross-sections be P1, P2, and P3 respectively; When reconstructing P1, no initial value is set for its boundary cells; When reconstructing P2, force the cell orientation value on one side of its boundary to be the orientation value of the corresponding side of P1; When reconstructing P3, force the cell orientation values on both sides of its boundary to be the orientation values of the corresponding sides of P1 and P2 respectively to ensure that the three two-dimensional tissues can be seamlessly spliced into a three-dimensional continuous surface.

5. A method for generating a three-dimensional initial tissue of a cellular automaton according to claim 1, wherein Adjusting the number of internal three-dimensional nucleation points through an iterative feedback mechanism includes: Randomly put the number of three-dimensional nucleation points inside the three-dimensional space and perform grain growth until it is filled; Calculate the average grain size of the three-dimensional tissue and compare it with the average grain size statistically obtained from the experiment; If the error requirement is not met, judge whether the current iteration number k is less than the maximum attempt number m; If k < m, keep the number of three-dimensional nucleation points unchanged and re-perform random nucleation and growth; If k ≥ m, adjust the size of the number of three-dimensional nucleation points according to the deviation direction between the average grain size of the three-dimensional tissue and the average grain size statistically obtained from the experiment, reset the iteration number k, and re-perform nucleation and growth.

6. The method for generating three-dimensional initial tissue using cellular automata according to claim 5, characterized in that, The number of three-dimensional nucleation points is adjusted based on the deviation direction between the average grain size of the three-dimensional microstructure and the experimentally statistically average grain size. Specifically, this includes: If the average grain size of the three-dimensional structure is less than the average grain size statistically obtained from experiments, it indicates that the simulated grains are too fine, so the number of three-dimensional nucleation points should be reduced. If the average grain size of the three-dimensional structure is greater than the average grain size statistically obtained from experiments, it indicates that the simulated grains are too coarse, so the number of three-dimensional nucleation points should be increased.

7. The method for generating three-dimensional initial tissue using cellular automata according to claim 6, characterized in that, The number of three-dimensional nucleation points is calculated using the total volume represented by the three-dimensional cell, the average two-dimensional grain size, and the total number of grains on the three surfaces of the three-dimensional CA.

8. The method for generating three-dimensional initial tissue using cellular automata according to claim 1, characterized in that, The Moore neighbor model is used to calculate the conversion probability of cell orientation during the grain growth process. The conversion probability is inversely proportional to the distance of neighbor cells from the central cell, and the sum of the conversion probabilities of all neighbors is 1. Neighbor cells are divided into several types, and different types of neighbors correspond to different conversion probability weights; Calculate the sum of the conversion probabilities of cells with the same orientation values ​​among all neighbors, and use this as the conversion probability to a certain orientation of two-dimensional and three-dimensional neighbor cells.

9. The method for generating three-dimensional initial tissue using cellular automata according to claim 1, characterized in that, Also includes: To increase the randomness of grain growth, randomness determination is introduced during the grain growth process, specifically including: Generate a random number Nr and compare it with a preset growth probability Pr; the central cell is allowed to change orientation only if Nr is greater than Pr.

10. A cellular automata three-dimensional initial tissue generation system, characterized in that, include: Two-dimensional cross-section reconstruction unit, three-dimensional space construction unit, and three-dimensional internal reconstruction unit; Two-dimensional section reconstruction unit is used to acquire three section data of experimental material and reconstruct the corresponding two-dimensional cellular automata structure respectively. During the reconstruction process, nucleation points are set according to the grain size distribution statistically obtained from the experiment, and the two-dimensional structures are continuously spliced ​​in space through boundary coupling to form the surface boundary conditions of the three-dimensional structure. The three-dimensional space building unit is used to create a three-dimensional CA space, which maps the three two-dimensional tissues reconstructed from the two-dimensional section to three orthogonal surfaces in the three-dimensional space, and fixes the cell orientation in the boundary conditions of the orthogonal surfaces. The three-dimensional internal reconstruction unit is used to perform nucleation and growth in the internal region of the three-dimensional CA space, and adjusts the number of internal three-dimensional nucleation points through an iterative feedback mechanism until the generated three-dimensional tissue meets the preset statistical error requirements, and outputs the final three-dimensional initial tissue.

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