A Material Microstructure Modeling Method Based on Controllable Partitioning of Polycrystalline Node Space

Abstract

This invention discloses a material microstructure modeling method based on controllable partitioning of polycrystalline node space, belonging to the field of metallic material simulation. The method first constructs the computational domain geometry based on element properties, determining boundary dimensions, total volume, and element centroids; it estimates the total number of grains based on the probability distribution of total volume and grain size, and samples and generates grain size and aspect ratio sample sequences; it establishes a three-dimensional mesh candidate point set with the maximum grain size as the step size, randomly selects grain center points, and generates a rotation matrix based on aspect ratio; it allocates unassigned elements within the grain ellipsoid space by calculating and sorting the equivalent sphere radius, using the nearest center method to fill unassigned elements; finally, it processes empty grains, statistically analyzes grain characteristics, and outputs the model. This invention can establish microstructure models of metallic materials with different degrees of plastic deformation, providing a theoretical basis for new material development and process optimization.

Description

Technical Field

[0001] This invention relates to the field of simulation calculation of metallic materials, and in particular to a method for modeling the microstructure of materials based on the controllable partitioning of polycrystalline node space. Background Technology

[0002] In materials science, the shape, orientation, and size distribution of grains in the microstructure of polycrystalline materials have a decisive influence on the macroscopic mechanical and physical properties of the materials. However, existing methods for modeling polycrystalline microstructures involving plastic deformation still suffer from several limitations: insufficient controllability of grain spatial distribution, lack of coupling mechanism between grain size and shape, susceptibility to empty grains and undistributed units during modeling, and difficulty in accurately reproducing the gradient structure and texture evolution formed during large strain processes. These shortcomings severely limit the effective reconstruction and simulation of typical phenomena such as grain refinement, morphological distortion, and non-uniform distribution under large plastic deformation processes such as rolling, forging, extrusion, and drawing, thus restricting the realization of high-precision process simulation and the reliability of new material design.

[0003] In existing technologies, some methods suffer from limited simulation accuracy due to weak control over grain size and shape, resulting in excessive randomness in the generated results and poor consistency with actual microstructures. This fails to meet the accuracy requirements of engineering applications. Another method uses the MTEX ​​tool to generate initial Euler angles, which are then converted and processed using third-party analysis software to obtain grain data for microstructure simulation. However, this approach is not only complex and reliant on commercial software, but also produces crystal orientations that deviate significantly from experimental results. It can only simulate equiaxed grain structures and cannot effectively reproduce the grain morphology evolution after plastic deformation, thus significantly limiting its application scope. Summary of the Invention

[0004] This application mentions a material microstructure modeling method based on controllable partitioning of polycrystalline node space, including:

[0005] S1. Determine the spatial location and number of nodes based on the given element attributes to form the geometric space of the computational domain. Determine the boundary dimensions and total volume of the computational domain based on the coordinates of all nodes, and calculate the centroid coordinates of each element.

[0006] S2. Based on the total volume and the preset probability distribution of grain size segments, calculate the average equivalent sphere diameter and average grain volume, and estimate the total number of grains that can be accommodated in the computational domain.

[0007] Based on the total number of grains and the probability distribution, a grain size sample sequence and an aspect ratio sample sequence are generated respectively. The aspect ratio is defined as the ratio of the lengths along the two coordinate axes within the selected observation plane.

[0008] S3. Using the maximum value of the average equivalent sphere in the grain size sample sequence along a certain coordinate axis in the selected observation plane as the grid step size, establish a three-dimensional grid candidate point set covering the computational domain, and randomly select the center point of each grain from the three-dimensional grid candidate point set.

[0009] Based on the sample values ​​in the aspect ratio sample sequence, a corresponding rotation matrix is ​​generated for each grain.

[0010] S4. Based on the unit centroid coordinates, grain center point, and rotation matrix, calculate the equivalent sphere radius according to the grain size sample and aspect ratio sample, and sort the grains in descending order of equivalent sphere radius; sequentially assign units whose centroids are located inside the ellipsoidal space of the current grain after the rotation matrix transformation and which have not yet been assigned to the grain; for the remaining unassigned units, the nearest center method is used to reassign them to the grain to which the nearest grain center point belongs in space.

[0011] S5. Inspect and process empty grains that have not been assigned units, statistically analyze the unit composition and geometric characteristics of all grains, and output the final microstructure model.

[0012] Furthermore, a corresponding rotation matrix is ​​generated based on the current range of the grain aspect ratio.

[0013] All grains are sorted in descending order based on the equivalent sphere radius to form a priority sequence for grain processing.

[0014] Each grain is processed sequentially according to the priority order. For each candidate unit, its centroid coordinates are transformed to the local coordinate system of the current grain.

[0015] In the local coordinate system, determine whether the transformed coordinates lie within the ellipsoidal space centered at the origin and with the length of the grain principal axis as the semi-axis;

[0016] If the spatial range condition is met, the cell is assigned to the currently processed grain and marked as assigned.

[0017] After processing all candidate units of the current grain, process the next grain according to the priority sequence;

[0018] For units that are still not assigned after all grains have been processed, the nearest center method is used for supplementary assignment.

[0019] Further, in step S4, the rotation ellipsoid space range of the current grain is determined based on the current grain center, the aspect ratio of the current grain, and the orientation rotation matrix of the current grain.

[0020] Further, in step S2, the average equivalent sphere diameter The calculation formula is:

[0021] ;

[0022] The formula for calculating the midpoint of the equivalent sphere diameter interval within the k-th grain size interval is as follows:

[0023] ;

[0024] in, The average equivalent sphere diameter, Let be the probability corresponding to the k-th grain size interval. This is represented by the total number of rows in the grain size distribution matrix. The minimum equivalent sphere diameter within the k-th grain size range. Let be the maximum equivalent sphere diameter within the k-th grain size range. It is the midpoint of the equivalent sphere diameter interval within the k-th grain size interval.

[0025] Further, in step S2, generating the grain size sample sequence by sampling means that for each interval in the grain size distribution matrix, if... The formula for calculating the average equivalent sphere diameter of a certain grain within the interval is:

[0026] ;

[0027] in, Let be the average equivalent sphere diameter of a certain grain within the interval. It refers to a uniform random variable that follows the interval (0,1).

[0028] Furthermore, in step S3, if the grain aspect ratio satisfies 0.8 ≤ grain aspect ratio ≤ 1.2, then a random rotation matrix is ​​generated using the quaternion sampling method.

[0029] If the grain aspect ratio is <0.8 or >1.2, then the 3rd order identity matrix is ​​used as the rotation matrix of the current grain.

[0030] Furthermore, in step S3, the specific method for establishing the set of candidate points for the three-dimensional mesh covering the computational domain is as follows:

[0031] Based on the grid step size, the number of grid points in the computational domain in the X, Y, and Z directions is calculated respectively. The value is the boundary size in the corresponding direction divided by the grid step size and then rounded up.

[0032] Generate uniformly distributed sets of node coordinates on the coordinate axes in three directions. The node coordinates in each direction start from the minimum boundary coordinate plus half the grid step size, and increase sequentially at intervals of the grid step size.

[0033] By performing a Cartesian product operation on the set of node coordinates in three directions, a set of candidate points for a three-dimensional mesh covering the entire computational domain is generated.

[0034] Further, in step S4, the semi-axis lengths of the three principal axes of the corresponding ellipsoidal space are determined based on the equivalent sphere radius and aspect ratio of the grain, the ellipsoidal volume is calculated, and the equivalent sphere radius is obtained by inverse calculation using the ellipsoidal volume. The formula for calculating the equivalent sphere radius is as follows:

[0035] ;

[0036] in, The equivalent sphere radius of the current grain. This is the sample vector of the current grain size. The aspect ratio of the current grain.

[0037] Furthermore, in step S4, the determination method for "the unit centroid is located inside the ellipsoidal space of the current grain after the rotation matrix transformation" includes: calculating the spatial vector of the unit centroid relative to the grain center, and multiplying the vector by the transpose of the rotation matrix to transform it to a local coordinate system with the grain principal axis as the coordinate axis;

[0038] Based on the semi-axis lengths of the three principal axes of the current grain, construct an elliptic equation discriminant to determine whether the cell is located within the ellipsoid of the current grain.

[0039] If it is located, then the cell is assigned to the current grain and the cell's allocation status is updated;

[0040] After all candidate units of the current grain have been screened, the next grain is processed according to the priority sequence.

[0041] Further, in step S4, the remaining units are reassigned using the nearest center method, specifically including: for each unassigned unit, calculating its Euclidean distance to all grain centers, and assigning it to the grain corresponding to the nearest grain center.

[0042] The beneficial effects of this application are as follows:

[0043] This invention discloses a material microstructure modeling method based on controllable partitioning of polycrystalline node space. First, the node distribution is determined according to element properties, constructing the computational domain geometry and calculating boundary dimensions, total volume, and element centroids. Based on the total volume and grain size probability distribution, the total number of grains is estimated, and sample sequences of grain size and aspect ratio are generated. A three-dimensional mesh candidate point set is established with the maximum grain size as the step size, grain center points are randomly selected, and a rotation matrix is ​​generated based on the aspect ratio. By calculating the equivalent sphere radius and sorting the grains in descending order, unassigned elements within the grain ellipsoidal space are sequentially assigned, with the nearest center method used to fill in the unassigned elements. Finally, empty grains are processed, grain geometric characteristics are statistically analyzed, and a microstructure model is output.

[0044] This invention proposes for the first time a material microstructure modeling method based on controllable spatial partitioning of polycrystalline nodes. Through innovations such as "controllable spatial partitioning of polycrystalline nodes," "closing algorithms for empty grains and unallocated units," and "parallel allocation using ellipsoid determination and nearest-center method," it effectively solves the problems of insufficient spatial controllability, incoordination of size and shape, and coexistence of empty grains and unallocated units in existing technologies for modeling the microstructure of polycrystalline materials under plastic deformation. It can accurately generate microcrystalline structures of varying degrees after plastic deformation such as rolling, forging, extrusion, and drawing, significantly improving modeling accuracy and speed. Furthermore, the operation process is simple, providing high-fidelity and scalable microstructure data support for predicting the properties of metallic materials, developing new materials, and optimizing processes. Attached Figure Description

[0045] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0046] Figure 1 This is a technical roadmap for a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application;

[0047] Figure 2 This is a schematic diagram of the nodes and elements of a three-dimensional cube model of a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application.

[0048] Figure 3 This is a grain size distribution diagram of a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application;

[0049] Figure 4 This is a grain aspect ratio distribution diagram of a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application;

[0050] Figure 5This is a grain center and orientation distribution diagram of a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application;

[0051] Figure 6 This is a cell assignment distribution diagram for a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application;

[0052] Figure 7 This is a microstructure model diagram of a material after rolling deformation, based on a material microstructure modeling method with controllable partitioning of polycrystalline node space mentioned in this application.

[0053] Figure 8 This is a process flow diagram of a material microstructure modeling method based on controllable partitioning of polycrystalline node space mentioned in this application. Detailed Implementation

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention, but the description is not intended to limit the present invention.

[0055] The purpose of this invention is to provide a material microstructure modeling method based on controllable partitioning of polycrystalline node space. Through innovations such as "controllable partitioning of polycrystalline node space", "closing algorithm for empty grains and unassigned units" and "parallel allocation of ellipsoid determination and nearest center method", it overcomes the difficulties of traditional microstructure modeling methods in terms of size and shape coupling, orientation space controllability, and handling of empty grains and unassigned units. It provides a scalable, repeatable, and verifiable modeling method for accurately reproducing the microstructure of large plastic deformation.

[0056] refer to Figure 8 This application mentions a material microstructure modeling method based on controllable partitioning of polycrystalline node space, including:

[0057] S1. Determine the spatial location and number of nodes based on the given element attributes to form the geometric space of the computational domain. Determine the boundary dimensions and total volume of the computational domain based on the coordinates of all nodes, and calculate the centroid coordinates of each element.

[0058] Construct a node matrix and a cell matrix, make initial cell divisions based on node coordinates, and calculate the centroid coordinates and computational domain of the corresponding cells based on the node coordinates in the node matrix.

[0059] First, a cube model is constructed within the computational domain and divided into nodes and cells. The node matrix is ​​then read. and unit matrix To satisfy the modeling of hexahedral solid element type, such as Figure 2 This is a schematic diagram of the nodes and elements of a 3D cube model.

[0060] ; (1)

[0061] in, Represented as a node matrix, Represented as node number. , This represents the total number of nodes, each with three-dimensional coordinates. These are the coordinates of the node along the X-axis. These are the coordinates of the node along the Y-axis. It is the coordinate value of the node along the Z-axis.

[0062] ; (2)

[0063] Here, B represents the cell matrix. The row and column formats of the node matrix A and the cell matrix B must be consistent with the cell type.

[0064] Represented as unit number, Represented as the coordinates of the nodes, for each element, , , This represents the number of nodes contained in the element. If it is a linear hexahedral element, then... If it is a tetrahedral element, then .

[0065] The formula for calculating the centroid of a unit cell is:

[0066] ; (3)

[0067] in, Represented as the first The coordinates of the geometric center point of each unit. .

[0068] In the modeling process, each element is a small volume of a cube or tetrahedron. To determine which grain an element belongs to, one cannot simply look at the nodes, but must consider the spatial position of the entire element. The centroid of an element is its representative location. During the grain allocation stage, the centroid, as a representative of the element's spatial position, is used to efficiently and stably determine whether it lies within the ellipsoidal space of a particular grain, avoiding the complexity of directly processing the coordinates of all the elements' nodes. Secondly, the centroid simplifies the element to a representative geometric point, significantly reducing the computational load for spatial relationship determination and improving modeling efficiency. Thirdly, using the centroid as the basis for allocation ensures that each element can only be uniquely assigned to one grain, fundamentally avoiding the problem of elements being cut or repeatedly assigned by multiple grains, thus guaranteeing the physical rationality of the model. Finally, in the subsequent statistical and analysis stages, the centroid coordinates provide crucial input for statistical analysis of geometric characteristics such as the spatial distribution and uniformity of the grains.

[0069] The formulas defining the minimum and maximum values ​​along the three-dimensional coordinate axes are as follows:

[0070] ; (4)

[0071] ; (5)

[0072] ; (6)

[0073] ; (7)

[0074] ; (8)

[0075] ; (9)

[0076] in, This is represented as the minimum coordinate value in the X-axis direction. Represented as the maximum coordinate value in the X-axis direction. This is represented as the minimum coordinate value in the Y-axis direction. This is represented as the minimum coordinate value along the Y-axis. This is represented as the minimum coordinate value in the Z-axis direction. It is represented as the minimum coordinate value in the Z-axis direction.

[0077] The formula for calculating the geometric boundary dimensions of the computational domain is:

[0078] ; (10)

[0079] The formula for calculating the length of the computational domain along the X-axis is:

[0080] ; (11)

[0081] The formula for calculating the length of the computational domain in the Y-axis direction is:

[0082] ;(12)

[0083] The formula for calculating the length of the computational domain along the Z-axis is:

[0084] ; (13)

[0085] in, It is expressed as the length of the computational domain in the X-axis direction. It is expressed as the length of the computational domain in the Y-axis direction. L represents the length of the computational domain along the Z-axis, and L represents the geometric boundary dimension of the computational domain.

[0086] The formula for calculating the total volume of the computational domain is:

[0087] ;(14)

[0088] in, It represents the total volume of the computational domain.

[0089] For example, the cube model has a side length of 0.3, uses linear hexahedral cells, has 60 cells per side, a total of 216,000 cells, and a total of 226,981 nodes.

[0090] refer to Figure 1 In step S1, a discrete geometric model of the material's microstructure is established by constructing and reading the node matrix and element matrix. This step calculates the centroid of each element and determines the geometric boundary and total volume of the computational domain, providing a precise geometric basis and spatial definition for subsequent grain generation and spatial partitioning. This ensures the accuracy of the model's geometric representation and the reliability of the computational domain's spatial measurement, providing the necessary input data for subsequent steps and laying the geometric foundation for the entire modeling process.

[0091] S2. Based on the total volume and the preset probability distribution of grain size segments, calculate the average equivalent sphere diameter and average grain volume, and estimate the total number of grains that can be accommodated in the computational domain.

[0092] In step S2, the grain size distribution matrix is ​​first given as follows: In the grain size distribution matrix, the first... The row is represented as Satisfies probability normalization: .

[0093] For the first Minimum equivalent sphere diameter within the segment grain size range Represented as the first The maximum equivalent sphere diameter within the segment grain size range. For the first The probability corresponding to the segment grain size range It is represented as the grain size distribution matrix, and R is represented as the real number field. This is expressed as the total number of rows in the grain size distribution matrix, such as... Figure 3 This is a grain size distribution diagram.

[0094] In step S2, the average equivalent sphere diameter The calculation formula is:

[0095] ; (15)

[0096] The formula for calculating the midpoint of the equivalent sphere diameter interval within the k-th grain size interval is as follows:

[0097] ; (16)

[0098] in, The average equivalent sphere diameter, This is represented by the total number of rows in the grain size distribution matrix. It is the midpoint of the equivalent sphere diameter interval within the k-th grain size interval.

[0099] The average grain volume is then calculated using the following formula:

[0100] ; (17)

[0101] in, The average grain volume is used to calculate the number of grains by combining the volume of the computational domain and the average grain volume. .

[0102] In this technical solution, the concept of equivalent sphere diameter is used to simplify irregular grain shapes into a sphere with an equivalent volume, and its diameter represents the average characteristic scale of the grain. By statistically segmenting the probability distribution, the obtained "average equivalent sphere diameter" avoids the imbalance of considering only a single size or major and minor axes, allowing the overall volume effect to be taken into account during the modeling process. Subsequently, the average grain volume is calculated using the average equivalent sphere diameter, and combined with the computational domain volume, the total number of grains can be estimated, thereby ensuring the rationality of the number and size distribution of grains in the model.

[0103] By employing equivalent spheroidization, the size of grains with different morphologies can be uniformly measured without losing the overall size distribution characteristics, avoiding statistical bias caused by directly using aspect ratios. Since the calculated number of grains matches the computational domain volume, problems such as insufficient grains leading to sparse space or excessive grains causing overlap and inadequate filling are avoided. Using the average equivalent sphere diameter as a unified scale allows for compatibility with grain distributions under different materials and deformation degrees, making the model easier to port and extend. This application's estimation method based on statistical distribution and equivalent sphere diameter can better reproduce the number density and volume distribution characteristics of grains in actual materials, thus making the microstructure modeling results closer to experimental observations.

[0104] In step S2, the formula for calculating the total number of grains is:

[0105] ; (18)

[0106] in, This represents the total number of grains. The fill factor is... Represented as the total volume of the computational domain. The average grain volume is denoted as .

[0107] It's important to note that the volume of the computational domain is filled by the volume of a number of grains. If the number of grains is not estimated, too few grains will result in voids within the domain, while too many will lead to severe overlap, both resulting in an undesirable microstructure. Estimating the total number of grains is crucial for selecting appropriate center points from the candidate sites. Incorrect grain count estimation will result in center points that are either too dense or too sparse, disrupting microstructure uniformity. Both the number and size of the grains determine the priority during allocation. If the number of grains is mismatched, the allocation process may result in empty grains or unallocated units.

[0108] Pre-estimating the total number of grains ensures the completeness of the model's filling. By matching the total grain volume with the computational domain volume, it ensures that the geometric space is fully and completely filled. Secondly, it improves the rationality of the grain spatial distribution. Strict volume constraints effectively prevent excessive or insufficient grain numbers, resulting in a more uniform microstructure in three-dimensional space and significantly reducing the amount of correction required later. Furthermore, this estimation significantly enhances the physical realism of the model. Since grain number density is a key physical parameter directly affecting the mechanical properties of materials, an accurate total grain count makes the final model closer to the microstructure of actual materials. Simultaneously, it improves overall computational efficiency. By precisely controlling the total number of grains in advance, it effectively avoids frequent repairs and repeated unit allocation operations caused by quantity mismatch in subsequent steps, thereby improving the speed and numerical stability of the modeling process.

[0109] Separate sampling to generate a grain size sample sequence means that for each interval in the grain size distribution matrix, if... The formula for calculating the average equivalent sphere diameter of a certain grain within the interval is:

[0110] ; (19)

[0111] in, Let be the average equivalent sphere diameter of a certain grain within the interval. It refers to a uniform random variable that follows the interval (0,1), such as Figure 4 This is a diagram showing the aspect ratio distribution of the grains.

[0112] For example, the number of samples to be generated for each interval in the grain size or aspect ratio distribution matrix is ​​determined as follows: First, the estimated total number of grains that can be accommodated in the computational domain is multiplied by the probability value set for that interval, and then the calculation result is rounded to obtain the specific number of grains to be sampled in that interval.

[0113] Generating aspect ratio sample sequences by sampling separately means: first, given the aspect ratio distribution matrix, denoted as... In the aspect ratio distribution matrix of the th Behavior ,satisfy , For the first The minimum value of the aspect ratio within the interval. Represented as the first The maximum value within the range of aspect ratio of the segment. Let k be the probability corresponding to the k-th segment's aspect ratio interval. Represented as an aspect ratio distribution matrix, This is expressed as the total number of rows in the aspect ratio distribution matrix.

[0114] It should be noted that the aspect ratio distribution matrix is ​​set because the grains of real materials are not ideal spheres or cubes. Especially after plastic deformation such as rolling and extrusion, their morphology will exhibit obvious elongation or flattening characteristics. The equivalent sphere diameter alone cannot describe the anisotropy of this morphology. The aspect ratio distribution matrix statistically quantifies the probability of grains with different major and minor axis ratios, enabling the model to accurately reproduce the mixed structure containing elongated, flattened, and near-equiaxed grains, thus more realistically reflecting the actual microstructure of the material.

[0115] The probability preset can directly control the proportion of different grain shapes in the model. If the probability is biased towards a larger aspect ratio, the model exhibits a typical rolled elongated structure; if it is biased towards a smaller aspect ratio, it reflects a compressed or flattened structure; a uniform or near-equiaxed distribution corresponds to an annealed structure. Secondly, the probability distribution affects the generation strategy of the grain orientation matrix. Grains with an aspect ratio deviating from 1 need to use an identity matrix to maintain the principal axis direction, while near-equiaxed grains use a random rotation matrix. An unreasonable probability setting will cause the grain orientation to lose its physical representativeness.

[0116] By introducing an aspect ratio distribution matrix and reasonably pre-setting its probabilities, the realism of the model is improved. By ensuring that the generated grain morphology distribution conforms to the statistical laws observed in experiments, the representativeness of the model to the microstructure of real materials is guaranteed. Secondly, this method enhances the controllability and applicability of the model. Researchers can flexibly adjust the probability distribution based on experimental data from specific deformation processes (such as rolling and forging) or different material systems (such as steel and aluminum alloys), thereby quickly and accurately constructing the corresponding microstructure model. The reasonable aspect ratio probability pre-setting provides a reliable initial geometric configuration for subsequent multi-scale simulation calculations, ensuring the physical basis for cross-scale simulations. This application effectively constrains the range of random sampling by pre-setting probabilities, avoiding oversampling or undersampling problems in certain size ranges that may be caused by completely random sampling, and significantly improving the stability and repeatability of the generated results.

[0117] The aspect ratio is defined as the ratio of lengths along two coordinate axes within a selected observation plane. For example, in a three-dimensional coordinate system, there are xy plane, yz plane, and xz plane. An observation plane is selected, taking the xy plane as an example. Within this observation plane, the aspect ratio is x / y or y / x.

[0118] For example, based on the grain size, an axis is selected among the x, y, and z axes, and the number of [items] obtained along this axis is approximately [number]. Grain size sample vector set The number is approximately Aspect Ratio Sample Vector Set .

[0119] It should be noted that for vector sets The direction of each vector must be within the selected observation plane.

[0120] The purpose of generating grain size sample vectors along selected coordinate axes is to transform the non-directional average equivalent sphere diameter into a length scale with a defined geometric direction, thereby providing a dimensional reference along the principal axis for the construction of ellipsoidal grains. This vector set ensures that each grain has a defined principal axis length parameter and guarantees that the number of samples strictly matches the total number of grains, providing complete dimensional data for subsequent spatial allocation. This operation is closely linked to subsequent steps: in the grain center generation stage, this sample vector assigns key dimensional attributes to each grain center point; in the rotation matrix determination stage, the principal axis length and aspect ratio together determine the spatial orientation strategy of the grains; finally, in the element allocation stage, this vector directly participates in defining the geometric space of the ellipsoidal grains, becoming the core basis for determining element assignment and ensuring the geometric consistency and physical realism of polycrystalline structure modeling.

[0121] By generating sample vectors of grain principal axis dimensions along selected coordinate axes, different grains are assigned different principal axis dimensions, effectively ensuring the diversity of grains in size and shape and avoiding excessive duplicate grains in the model. Secondly, by selecting a specific coordinate axis as the initial direction, the generated microstructure can exhibit clear directional characteristics, thereby accurately simulating typical orientation characteristics such as grain elongation along the processing direction during rolling. The number of sample vectors is strictly consistent with the estimated total number of grains, ensuring statistical consistency in the number of grains and spatial volume throughout the modeling process, significantly reducing the need for subsequent corrections. Finally, since the grain shape, size, and orientation directly determine the anisotropic mechanical response of the material (such as yield strength and stress distribution), this design greatly improves the physical realism of the simulation results, enabling the generated microstructure to more accurately reproduce the microstructural characteristics of real materials.

[0122] The aspect ratio and grain size samples together precisely determine the final geometric shape of each grain. By assigning a specific "morphological parameter" to each grain, the limitation that a single equivalent sphere diameter can only describe volume and cannot reflect shape anisotropy is overcome, allowing the model to simultaneously include grains of different shapes such as elongated, flattened, and near-equiaxed. Secondly, this sampling aims to reflect the statistical laws of actual deformed structures. Through the preset probability distribution, the generated model can statistically reproduce the typical grain morphology characteristics after a specific processing technology (such as rolling, extrusion, or annealing). Finally, the aspect ratio provides a key basis for the generation of the grain orientation matrix, and its value directly determines whether the grain should adopt a random isotropic orientation or a fixed anisotropic orientation in space.

[0123] In the generation of the grain center and rotation matrix, the combination of aspect ratio samples and size samples determines the specific lengths of the three axes of the ellipsoidal grain and directly determines whether to choose an identity matrix (fixed major axis direction) or a random rotation matrix (isotropic). In the element allocation, the lengths of the three axes of the ellipsoid defined by the aspect ratio are the core geometric parameters for determining whether the centroid of the element is located inside the grain, and directly affect the spatial assignment of the element.

[0124] S3. Using the maximum value of the average equivalent sphere in the selected observation plane along a certain coordinate axis in the grain size sample sequence as the grid step size, establish a three-dimensional grid candidate point set covering the computational domain, and randomly select the center point of each grain from the three-dimensional grid candidate point set.

[0125] In step S3, the specific method for establishing the three-dimensional mesh candidate point set covering the computational domain is as follows:

[0126] Based on the grid step size, the number of grid points in the computational domain in the X, Y, and Z directions is calculated respectively. The value is the boundary size in the corresponding direction divided by the grid step size and then rounded up.

[0127] Generate uniformly distributed sets of node coordinates on the coordinate axes in three directions. The node coordinates in each direction start from the minimum boundary coordinate plus half the grid step size, and increase sequentially at intervals of the grid step size.

[0128] By performing a Cartesian product operation on the set of node coordinates in three directions, a set of candidate points for a three-dimensional mesh covering the entire computational domain is generated.

[0129] For example, let the maximum value of the sample size vector be... Set the grid step size for the computational domain. .

[0130] The formula for calculating the number of grid points along the X-axis in the computational domain is:

[0131] ; (20)

[0132] The formula for calculating the number of grid points along the Y-axis in the computational domain is:

[0133] ; (twenty one)

[0134] The formula for calculating the number of grid points along the Z-axis in the computational domain is:

[0135] ; (twenty two)

[0136] in, This is expressed as the number of grid points along the X-axis. Represented as the number of grid points along the Y-axis. Represented as the number of grid points along the Z direction. The step size of the gridded candidate points, i.e., the distance between grid points, is used as a constraint. .

[0137] For example, a uniform set of nodes is generated in each dimension, and the coordinates of the grid points are generated: where the formula for calculating the coordinate values ​​along the X-axis is:

[0138] ; (twenty three)

[0139] The formula for calculating the grid step size is:

[0140] ; (twenty four)

[0141] in, This represents the index number of the current grid point along the X-axis, with a value range of... , The preset grid step size, This represents the actual calculated mesh step size. Similarly, the coordinate values ​​along the Y and Z axes are calculated. A three-dimensional Cartesian product is then formed to obtain the candidate point set. , , This represents the total number of grain centers to be selected. The candidate point is represented by the coordinates of the grain center. .

[0142] In step S3, each grain center point is randomly selected from the 3D mesh candidate point set. Based on the quantitative relationship between the total number of points in the 3D mesh candidate point set and the total number of grain centers to be selected, the selection method for the grain centers is determined: if the total number of points is greater than or equal to the total number of grain centers to be selected, then a number of different points in the 3D mesh candidate point set are randomly selected as grain centers, equal to the total number of grain centers to be selected; if the total number of points is less than the total number of grain centers to be selected, then all mesh points are first used as grain centers, and then a corresponding number of uniformly distributed random points are generated within the computational domain to supplement them, so that the total number of grain centers reaches the total number of grain centers to be selected. Figure 5 As shown, Figure 5 This is a diagram showing the distribution of grain centers and orientations.

[0143] In step S3, if the grain aspect ratio satisfies 0.8 ≤ grain aspect ratio ≤ 1.2, then a random rotation matrix is ​​generated using the quaternion sampling method.

[0144] If the grain aspect ratio is <0.8 or >1.2, then a 3rd-order identity matrix is ​​used as the rotation matrix for the current grain. Based on the sample values ​​in the aspect ratio sample sequence, a corresponding rotation matrix is ​​generated for each grain.

[0145] Based on aspect ratio samples Generate orientation rotation matrices; the set of generated rotation matrices is as follows. .like Shoemake's algorithm using quaternion sampling: Define a unit quaternion , The mapping from quaternions to rotation matrices yields... In this case, the grains are approximately equiaxed and their geometry is isotropic in three-dimensional space. Therefore, the rotation matrix can be obtained by random sampling of quaternions to ensure a uniform distribution on the rotation group.

[0146] in, The rotation matrix of the grain is represented as a 3x3 orthogonal matrix with a determinant of 1, and is used to represent the orientation of the grain in space. Represented as the aspect ratio of the grains, quaternion This is represented as a unit quaternion. A unit quaternion can uniquely represent a rotation in three-dimensional space. Represented as the imaginary part of the quaternion in the first direction. Represented as the imaginary part of the quaternion in the second direction. This is represented as the imaginary part of the quaternion in the third direction. They form a vector representing the direction of the rotation axis. It is represented as the real part of a quaternion and is used to determine the rotation angle.

[0147] Let be a random variable that ensures the quaternion is uniformly distributed on the four-dimensional hypersphere. Let be a random variable that ensures the rotation axis is uniformly distributed in the horizontal direction. Let be a random variable that ensures a uniform distribution of the rotation axis in the vertical direction.

[0148] like or The grain has a significant major or minor axis direction, and its geometry is anisotropic in space. In this case, the orientation is uniquely determined by the geometric axis. To avoid conflict with random rotation, a third-order identity matrix is ​​used as the rotation matrix of the current grain, that is, the major axis is aligned with the global coordinate axis.

[0149] S4. Based on the unit centroid coordinates, grain center point and rotation matrix, calculate the equivalent sphere radius according to the grain size sample and aspect ratio sample, and sort the grains from largest to smallest according to the equivalent sphere radius.

[0150] In step S4, the formula for calculating the equivalent sphere radius is:

[0151] ; (25)

[0152] in, The equivalent sphere radius of the current grain. This is the sample vector of the current grain size. The aspect ratio of the current grain.

[0153] The formula for calculating the major axis of an ellipsoid is:

[0154] ; (26)

[0155] The formula for calculating the central axis of an ellipsoid is:

[0156] ;(27)

[0157] in, Represented as the major axis of the ellipsoid, It is represented as the central axis of the ellipsoid. Represented as the minor axis of an ellipsoid, it is used to mathematically describe a three-dimensional ellipsoid with a specific size, shape, and spatial orientation, which represents the spatial region occupied by a grain.

[0158] In step S4, the rotation ellipsoid space range of the current grain is determined based on the current grain center, the aspect ratio of the current grain, and the orientation rotation matrix of the current grain.

[0159] The formula for calculating the volume of a rotating ellipsoid is:

[0160] ; (28)

[0161] in, If the volume is expressed as the volume of a rotating ellipsoid, then the equivalent sphere radius satisfies... .

[0162] Calculating the volume of the ellipsoid of revolution and inversely deducing the equivalent sphere radius requires careful consideration. The algorithm must allocate cells in descending order of grain size to prevent smaller grains from "cutting" the space occupied by larger grains, thus ensuring the geometric integrity of the microstructure. The purpose of calculating the volume of the ellipsoid of revolution is to obtain a true measure of the space occupied by the grains. Volume is the most objective physical quantity for measuring the "size" of an object, independent of shape. It's important to note that inversely calculating the equivalent sphere radius can standardize an irregularly shaped (ellipsoidal) grain into an ideal sphere with the same volume. All grains, regardless of their shape (elongated, flattened, or isometric), can be compared and ranked using the equivalent sphere radius. The algorithm can simply sort all grains in descending order and process them sequentially, implementing a strategy of prioritizing the allocation of larger grains.

[0163] The semi-axis lengths of the three principal axes of the corresponding ellipsoidal space are determined based on the equivalent sphere radius and aspect ratio of the grain. The ellipsoidal volume is then calculated, and the equivalent sphere radius is obtained by inverse calculation using the ellipsoidal volume.

[0164] It should be noted that the calculation of the equivalent sphere radius is necessary because directly comparing the individual axis lengths of ellipsoidal grains is unreasonable. A grain with a large dimension in one direction and small dimensions in other directions may have a smaller total volume than a grain with uniform dimensions in all directions. The formula for calculating the equivalent sphere radius is mathematically equivalent to using volume as the ranking criterion.

[0165] If the equivalent sphere diameter is used for sorting, for equiaxed grains (i.e., a≈b≈c), the equivalent sphere diameter is similar to the volume-based equivalent sphere radius calculation, and the two sorting methods are not significantly different. However, for strongly anisotropic grains, such as elongated or flattened grains, the equivalent sphere diameter completely ignores the volume differences caused by their shape, leading to serious misjudgments.

[0166] Units whose centroids are located inside the ellipsoidal space of the current grain after the rotation matrix transformation and which have not yet been assigned are assigned to the grain in turn; for the remaining unassigned units, the nearest center method is used to reassign them to the grain corresponding to the grain with the closest spatial distance to the grain center point.

[0167] The core reason for using equivalent sphere radii for sorting during grain allocation is that the spatial allocation principle of "large grains first" must be followed. If small grains are allocated first, they will occupy the limited unit space in advance, causing subsequent large grains to be unable to form completely due to insufficient space, thus disrupting the continuity of the microstructure.

[0168] All grains are sorted in descending order based on their equivalent sphere radius to form a priority sequence for grain processing.

[0169] The assignment function is defined based on the unit centroid coordinates, grain center, equivalent sphere diameter, aspect ratio, and rotation matrix. ,initial Indicates unassigned. Grain set. , This indicates the number of unassigned units. This indicates the number of units that have been allocated.

[0170] The allocation function determines whether a cell falls within a specific grain ellipsoid. Its input parameters include: the set of centroid coordinates for all cells, the set of center point coordinates for all grains, the equivalent sphere diameter, aspect ratio, and rotation matrix for each grain. Initially, the allocation function marks all cells as unallocated, establishing a spatial mapping between cells and grains. By determining whether the cell centroid lies within the ellipsoidal space defined by the grain center, size, shape, and orientation, the function dynamically assigns cells to their corresponding grains and updates the allocation status in real time. Based on a priority mechanism using equivalent sphere radii, this function ensures that larger grains receive priority allocation, effectively avoiding overlap conflicts between grains. This allocation function guarantees that all cells are appropriately allocated, achieving complete spatial filling of the computational domain and generating a microstructure model with both geometric accuracy and physical realism.

[0171] according to Descending order yields the priority sequence For a given grain in the priority sequence, let the grain center be... The major axis, middle axis, and minor axis are respectively , , If the grain ,but , , , denoted as a long ellipsoid. If ,but , , , represented as an oblate spheroid, in which .

[0172] The distinction between "elongated ellipsoids" and "flattened ellipsoids" based on aspect ratio can characterize the geometric morphology of grains under different deformation states. When the aspect ratio is greater than 1, the grain is defined as an elongated ellipsoid, corresponding to elongation deformation caused by processes such as rolling or drawing; when the aspect ratio is not greater than 1, the grain is defined as a flattened ellipsoid, corresponding to flattening deformation caused by extrusion or compression. This distinction provides an accurate geometric envelope region for element allocation, precisely determining the spatial assignment of elements through the ellipsoid equation, avoiding geometric distortion caused by the spherical assumption; on the other hand, while maintaining the overall volume conservation, it satisfies the requirements of statistical distribution of grain morphology and significantly improves the model's ability to characterize anisotropic microstructures, providing a reliable geometric basis for subsequent mechanical property simulation.

[0173] In the grain space allocation process based on ellipsoidal characterization, prioritizing the allocation of large-volume grains helps reduce coverage conflicts. It should be noted that the geometric space of multiple grains may simultaneously cover the same element. If a random allocation order is used, smaller grains will preferentially occupy elements within the space range of larger grains, leading to structural fragmentation of the large grains and severely compromising the geometric integrity of the microstructure. This application adopts an allocation strategy based on descending order of equivalent sphere radius, prioritizing the allocation of larger-volume grains. Since large grains have a wide spatial coverage, prioritizing their allocation prevents their space resources from being prematurely occupied by smaller grains, ensuring their structural integrity. Furthermore, after the large grains are prioritized, smaller grains can flexibly fill the remaining space, significantly reducing the probability of coverage conflicts between grains. Large grains often form the supporting framework of the microstructure in real materials; prioritizing their allocation helps maintain the geometric realism of the model. The implementation of this strategy effectively avoids the generation of empty grains, ensures that the grain volume distribution conforms to the preset statistical laws, and reduces the computational cost of subsequent corrections by reducing conflicts, thereby improving modeling efficiency. Since large grains have a dominant influence on the mechanical behavior of materials, this allocation order ensures that the final model can more realistically reflect the mechanical response characteristics of actual materials.

[0174] Prioritizing the allocation of small grains would result in the fragmentation of large grain space, leading to incomplete structures and requiring extensive repair of these fragmented grains. This would also significantly increase the empty grain rate and reduce allocation efficiency. Conversely, prioritizing the allocation of large grains ensures that they fully occupy their designated spatial framework, allowing smaller grains to flexibly fill the remaining space. This approach maintains the geometric accuracy of the grain structure while significantly reducing inter-grain coverage conflicts and subsequent repair operations. This sequential strategy effectively avoids the fragmentation effect of small grains by ensuring the integrity of large grain space, while optimizing spatial resource allocation. This results in a synergistic improvement in geometric accuracy, statistical rationality, and modeling efficiency.

[0175] Furthermore, each grain is processed sequentially according to a priority order. For each candidate unit, its centroid coordinates are transformed to the local coordinate system of the current grain.

[0176] In step S4, the method for determining that "the centroid of the unit cell is located inside the ellipsoidal space of the current grain after the rotation matrix transformation" includes: calculating the spatial vector of the unit centroid relative to the grain center; subtracting the grain center coordinates from the candidate unit centroid coordinates to represent the spatial position of the unit relative to the grain center; and multiplying this vector by the transpose of the rotation matrix to transform it to a local coordinate system with the grain principal axes as coordinate axes.

[0177] Based on the semi-axis lengths of the three principal axes of the current grain, construct an elliptic equation discriminant to determine whether the cell is located within the ellipsoid of the current grain.

[0178] If it is located, then the cell is assigned to the current grain and the cell's allocation status is updated;

[0179] After all candidate units for the current grain have been screened, the next grain is processed according to the priority sequence. The local coordinate system of the grain is an orthogonal reference system established with the major axis, median axis, and minor axis of the current grain as the reference. This coordinate system has a clear rotational correspondence with the global coordinate system representing the entire computational domain, and its coordinate axes coincide with the principal axes of the grain ellipsoid. When the grain exhibits arbitrary spatial orientation in the global coordinate system, the mathematical calculation of directly determining whether the centroid of the unit is located within its ellipsoidal space is extremely complex and prone to errors. By establishing a local coordinate system with the grain's own principal axis as the reference and transforming the unit coordinates to this coordinate system through a rotation matrix, the arbitrarily oriented ellipsoid can be transformed into a standard form, thereby simplifying the complex spatial geometry determination problem into a standardized ellipsoid equation calculation. This transformation significantly improves the computational efficiency and accuracy of unit attribution determination. At the same time, by explicitly representing the grain orientation, it ensures the geometric authenticity of the grain spatial morphology under different deformation states, making the generated microstructure more accurately reflect the anisotropic characteristics of the actual material and effectively reducing the probability of misclassification of boundary units.

[0180] For example, for the candidate unit set First, transform the unit coordinates to the local grain coordinate system and calculate the relative position vector. ,in, This represents the relative position vector of the centroid of the candidate unit cell in the principal axis coordinate system of the grain. Represented as the coordinates of the element center in the global coordinate system, i.e., the centroid coordinates. Represented as the current grain center coordinates. Based on the rotation matrix. Determine the orientation matrix of the grain ,in, Represented as the orientation matrix of the grains, , This represents the coordinates in the principal axis coordinate system of the grain. It determines whether a unit point falls within the principal axis centered at the origin, with a length of [missing information]. Within the ellipsoid, it is necessary to use To make a judgment, among which, Represented as the first The X-axis coordinates of the centroids of each unit cell in the principal axis coordinate system of the grain are given by: Represented as the first The Y-axis coordinates of the unit cell centroid in the principal axis coordinate system of the grain. Represented as the first The Z-axis coordinates of the centroid of each unit cell in the principal axis coordinate system of the grain.

[0181] For example, for any candidate cell, its relative position vector with respect to a specific grain center is defined as the vector difference between the coordinates of the cell's centroid in the global coordinate system and the coordinates of the grain center. This vector quantifies the spatial relative positional relationship between the cell and the grain center, and serves as the fundamental input for subsequent transformation to the local grain coordinate system for precise geometric determination. Figure 6 As shown, Figure 6 This is a distribution map of unit affiliations.

[0182] During grain element allocation, the relative position vector of candidate elements with respect to the grain center is calculated, transforming the global absolute coordinates into relative coordinates with the grain center as the origin. This eliminates the influence of the global coordinate system and lays the geometric foundation for subsequent coordinate transformations. This vector can be directly projected onto the local grain coordinate system through a rotation matrix, providing accurate input parameters for determining the allocation using the standard ellipsoid equation. By substituting the transformed relative positions into the standard ellipsoid equation in the local coordinate system, accurate determination of element spatial allocation can be achieved. This improves the accuracy of element allocation and avoids errors caused by absolute coordinate offsets. By uniformly adopting the standard ellipsoid equation for determination, computational efficiency is significantly improved. Simultaneously, it ensures that each element is allocated based on its actual spatial geometric relationship with the grain center, fundamentally guaranteeing the physical reality of grain partitioning and the reliability of the model.

[0183] In step S4, the remaining cells are reassigned using the nearest center method. Specifically, for each unassigned cell, its Euclidean distance to all grain centers is calculated, and it is assigned to the grain corresponding to the nearest grain center. Figure 6 This is a distribution map of unit affiliations.

[0184] For example, a set of unallocated units is defined. Calculate the Euclidean distances to the centers of all grains. ,in, It is represented as Euclidean distance.

[0185] The cell allocation process achieves its core function through the following mechanisms: First, it establishes a mapping relationship between cells and grains by matching the cell centroid with the grain ellipsoidal space through geometric determination, thus clarifying the spatial affiliation of each cell. Second, it ensures the integrity of the computational domain's spatial filling by using the nearest center method for subsequent allocation to ensure that all cells are eventually included in the grain set, fundamentally avoiding the generation of voids or abnormal overlaps. It supports volume-based priority sorting by allocating grains in descending order of equivalent sphere radius, ensuring that larger grains receive space resources first. This mechanism relies on the allocation function to dynamically track and update the cell allocation status, thereby effectively avoiding coverage conflicts and optimizing the allocation of space resources.

[0186] S5. Inspect and process empty grains that have not been assigned units, statistically analyze the unit composition and geometric characteristics of all grains, and output the final microstructure model.

[0187] In the final stage of modeling, the existence of empty grains without any assigned elements is first detected, and their indices are recorded in a set. Within this set of empty grains, for each empty grain, the Euclidean distance between its center coordinates and the centroids of all elements is calculated to determine the nearest element index. This nearest element is then reassigned to the current empty grain, and the corresponding element-grain affiliation is updated, ensuring that all grains contain at least one element and completely eliminating the empty grain phenomenon. After empty grain compensation, it is verified that the total number of assigned elements is completely consistent with the total number of elements in the computational domain, and the number of grains is confirmed to meet the preset value. Finally, complete statistical information containing the composition, size, and morphological characteristics of all grain elements is written into the model file, outputting a final microstructure model suitable for multi-scale simulation. The microstructure after rolling deformation is shown below. Figure 7 As shown.

[0188] In step S5, the statistical analysis of grain information mainly includes quantitative analysis of the characteristic parameters of each grain, such as equivalent sphere diameter, volume, or principal axis length. Specifically, the process involves: first, calculating a certain characteristic parameter for all grains, statistically setting the data, and then outputting the minimum, maximum, and arithmetic mean values ​​within that set to quantify the distribution range and central tendency of the grain population along that characteristic dimension.

[0189] This invention proposes for the first time a modeling method for simulating the microstructure of polycrystalline materials under plastic deformation using a controllable spatial partitioning technique. Through innovations such as "controllable spatial partitioning of polycrystalline nodes," "closing algorithms for empty grains and unallocated units," and "parallel allocation using ellipsoid determination and nearest-center method," it effectively solves the problems of insufficient spatial controllability, incoordination of size and shape, and the coexistence of empty grains and unallocated units in existing technologies for modeling the microstructure of polycrystalline materials under plastic deformation. It can accurately generate microcrystalline structures of varying degrees after plastic deformation such as rolling, forging, extrusion, and drawing, significantly improving modeling accuracy and speed. Furthermore, the operation process is simple, providing high-fidelity and scalable microstructure data support for predicting the properties of metallic materials, developing new materials, and optimizing processes.

[0190] Obviously, the above are merely examples for clear illustration and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

[0191] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0192] In this specification, the terms "a," "some," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that example or example that is included in at least one or more examples of the invention. The illustrative expressions of the above terms in this specification do not necessarily refer to the same example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more examples or examples. Moreover, those skilled in the art can combine and integrate the different examples and features described in this specification without contradiction.

[0193] It is understood that the above is exemplary and should not be construed as a limitation of the present invention. Those skilled in the art can make modifications, alterations, substitutions and variations to the above within the scope of the present invention.

Claims

1. A material microstructure modeling method based on polycrystalline node space controllable division, characterized in that, The method comprises the following steps: S1, determining the spatial position and number of nodes according to the given unit attribute, forming the geometric space of the calculation domain, determining the boundary size and total volume of the calculation domain based on the coordinates of all nodes, and calculating the centroid coordinates of each unit; S2, based on the total volume and the preset grain size segmentation probability distribution, calculating the average equivalent sphere diameter and the average grain volume, and estimating the total number of grains that can be accommodated in the calculation domain; According to the total number of grains and the probability distribution, respectively sample to generate grain size sample sequence and aspect ratio sample sequence, wherein the aspect ratio is defined as the length ratio in the selected observation plane along two coordinate axes. S3, taking the maximum value of the average equivalent sphere in the selected observation plane along a certain coordinate axis in the grain size sample sequence as the grid step, establishing a three-dimensional grid candidate point set covering the calculation domain, and randomly selecting each grain center point from the three-dimensional grid candidate point set; According to the sample values in the aspect ratio sample sequence, a corresponding rotation matrix is generated for each grain; S4, based on the unit centroid coordinates and the grain center points and the rotation matrix, the equivalent sphere radius is calculated according to the size sample and the aspect ratio sample of the grain, and the grains are sorted in descending order of the equivalent sphere radius; the unit centroid located in the ellipsoid space inside the current grain after the rotation matrix transformation and not yet allocated is allocated to the grain; For the remaining unallocated units, the nearest center method is used to reassign to the grain center point belonging to the grain with the nearest spatial distance; S5, checking and processing the empty grains of the unallocated units, counting the unit composition and geometric characteristics of all grains, and outputting the final microstructure model.

2. The material microstructure modeling method based on multi-grain node space controllable division according to claim 1, wherein: According to the numerical range of the current grain aspect ratio, a corresponding rotation matrix is generated; All grains are sorted in descending order based on the equivalent sphere radius to form a priority sequence for grain processing; According to the priority sequence, each grain is processed one by one, and for each candidate unit, its centroid coordinates are transformed to the local coordinate system of the current grain; In the local coordinate system, it is judged whether the transformed coordinates are located within the ellipsoid space range with the origin as the center and the grain major axis length as the semi-axis; If the space range condition is met, the unit is allocated to the current processing grain and marked as allocated; After completing the processing of all candidate units of the current grain, the next grain is processed according to the priority sequence; After processing all grains, the units that are still not allocated are supplemented by the nearest center method.

3. The material microstructure modeling method based on multi-grain node space controllable division according to claim 1, wherein: In step S4, the rotation ellipsoid space range of the current grain is determined according to the current grain center, the aspect ratio of the current grain, and the orientation rotation matrix of the current grain.

4. The material microstructure modeling method based on multi-grain node space controllable division according to claim 1, wherein: In step S2, the average equivalent spherical diameter D50 is calculated from the following formula: D50 = 1.56 x (V50 / π) ； The midpoint of the equivalent spherical diameter interval in the kth grain size interval is The calculation formula is: ； wherein, is the average equivalent spherical diameter, is the probability corresponding to the kth section of the grain size interval, denotes the total number of rows of the grain size distribution matrix, is the minimum equivalent spherical diameter within the kth section of the grain size interval, is the maximum equivalent spherical diameter within the kth section of the grain size interval, is the midpoint of the equivalent spherical diameter interval within the kth section of the grain size interval.

5. The material microstructure modeling method based on multi-grain node space controllable division according to claim 4, wherein: In step S2, sampling to generate a sequence of grain size samples respectively means that for each interval in the grain size distribution matrix, if the calculation formula of the average equivalent spherical diameter of a certain grain in the interval is: ； wherein is the average equivalent spherical diameter of a certain grain within the interval, is a uniform random variable subject to the interval (0, 1).

6. The material microstructure modeling method based on polycrystalline node space controllable division according to claim 1, characterized in that, in step S3, if the grain aspect ratio satisfies 0.8 ≤ grain aspect ratio ≤ 1.2, a random rotation matrix is generated based on quaternion sampling method; if the grain aspect ratio < 0.8 or the grain aspect ratio > 1.2, a 3-order unit matrix is used as the rotation matrix of the current grain.

7. The material microstructure modeling method based on polycrystalline node space controllable division according to claim 1, characterized in that, in step S3, the specific method for establishing the three-dimensional grid candidate point set covering the calculation domain is: based on the grid step, the grid point numbers in X, Y and Z directions of the calculation domain are calculated respectively, and the value is the upper integer of the boundary size of the corresponding direction divided by the grid step; uniformly distributed node coordinate sets are generated on the coordinate axes of the three directions, wherein the node coordinates of each direction take the minimum boundary coordinate plus half the grid step as the starting point, and increase by the grid step in turn; the three-dimensional grid candidate point set covering the entire calculation domain is generated by performing Cartesian product operation on the node coordinate sets in the three directions.

8. The material microstructure modeling method based on polycrystalline node space controllable division according to claim 1, characterized in that, in step S4, the half-axis lengths of the three principal axis directions of the ellipsoid space corresponding to the grain are determined according to the equivalent spherical radius and the aspect ratio of the grain, the ellipsoid volume is calculated, and the equivalent spherical radius is obtained by back calculation based on the ellipsoid volume, and the calculation formula of the equivalent spherical radius is: ； wherein, is the equivalent spherical radius of the current grain, is the grain size sample vector of the current grain, is the aspect ratio of the current grain.

9. The material microstructure modeling method based on polycrystalline node space controllable division according to claim 1, characterized in that, in step S4, the determination method of "the unit centroid is located inside the ellipsoid space of the current grain after the rotation matrix transformation" includes: calculating the space vector of the unit centroid relative to the grain center, and multiplying the vector by the transpose of the rotation matrix to transform to the local coordinate system with the grain principal axis as the coordinate axis; based on the half-axis lengths of the three principal axis directions of the current grain, an elliptic equation discriminant is constructed to determine whether the unit is located inside the ellipsoid of the current grain; if yes, the unit is divided to the current grain, and the allocation state of the unit is updated; after all the candidate units of the current grain are screened, the next grain is processed according to the priority sequence.

10. The material microstructure modeling method based on polycrystalline node space controllable division according to claim 1, characterized in that, in step S4, the nearest center method is used for supplementary allocation of the remaining units, which specifically includes: for each unallocated unit, the Euclidean distance to all grain centers is calculated, and the unit is allocated to the grain corresponding to the nearest grain center.

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