A method for the simulation generation of a controlled metal virtual microstructure

Abstract

The application discloses a controlled metal virtual microstructure simulation generation method, a grain model taking a Voronoi tessellation model as a basis, different control parameters being given to a grain area of a metal material, different regularity degrees being given to the grain model to obtain an equiaxed grain model with different Poisson curve grain size distribution, a columnar grain model being obtained by giving a higher grain aspect ratio coefficient to the equiaxed grain model, a transition structure grain model being obtained by dividing the area and giving different grain aspect ratio coefficients to the grains in different areas based on the equiaxed grain model, and a bounded grain model being obtained by giving grain boundaries to the three kinds of grain models. The application gives control parameters such as grain size, grain regularity, grain boundary width and grain aspect ratio coefficient to the traditional Voronoi tessellation model, controls the generated metal virtual microstructure according to actual needs, and well matches the actual grain model.

Description

Technical Field

[0001] This invention belongs to the field of metal microstructure characterization technology, specifically relating to a controlled method for simulating and generating virtual metal microstructures. Background Technology

[0002] For metallic materials, microstructure is a key factor affecting material properties. By rationally controlling the microstructure, the desired material performance can be achieved. Most metallic materials in nature are polycrystalline, with grains being the basic units of their microstructure. Typically, in the manufacturing and use of metal products, the internal grain structure characteristics change due to processing techniques. Regardless of the type of metallic material, performance is a crucial factor determining product quality and lifespan; improving performance is an inevitable trend for the sustainable development of metallic materials.

[0003] In recent years, the residual compressive stress and gradient structure generated on the alloy surface have significantly improved the mechanical properties of the alloy, especially its fatigue strength. Existing technologies mainly employ a variety of typical modification treatment methods, such as high-energy shot peening, laser shot peening, ultrasonic surface rolling, and surface mechanical wear treatment (SMAT), to obtain the surface gradient structure.

[0004] Since the stress and strain of materials are related to grain size, shape, orientation, and distribution, finite element micromechanical simulations require modeling the grain structure within a finite element / computer-aided engineering (CAE) computational environment. Currently, the finite element method is increasingly used for micromechanical modeling of polycrystalline materials. Polycrystalline finite element modeling provides valuable insights into intergranular interaction behavior and local deformation mechanisms, serving as an effective tool for simulating the microforming process of small metal products and simulating localized damage processes in components during use. Constructing finite element models derived from real grain structures is crucial for accurate simulation.

[0005] Grain structures can be reconstructed by mapping metallographic observations to grain models and processing digital images or scanning electron microscopy (SEM) / electron backscatter diffraction (EBSD) data. However, these methods are often very time-consuming and labor-intensive in practical applications.

[0006] Voronoi mosaic models are currently used to represent virtual microstructures of metals because they provide a natural, time-saving, and labor-efficient solution for representing grain structures with non-uniform grain shapes. However, Voronoi mosaic models have fewer controlled parameters and represent grains rather randomly, failing to closely match real-world grain models. Summary of the Invention

[0007] To address the shortcomings and challenges of existing technologies, this invention aims to provide a controlled method for simulating and generating virtual metal microstructures. This invention relates to a novel method for characterizing metal microstructures. Based on the Voronoi mosaic model to represent virtual metal microstructures, it assigns control parameters such as grain size, grain regularity, grain boundary width, and grain aspect ratio to the traditional Voronoi mosaic model. According to actual needs, this allows for the controlled generation of virtual metal microstructures, which are then applied to finite element micromechanical model simulations.

[0008] This invention is achieved through the following technical solution:

[0009] A controlled method for simulating and generating virtual microstructures of metals is proposed. Based on the Voronoi mosaic model, three different grain models can be obtained by assigning different control parameters. Then, grain boundaries are assigned to the grain models to obtain bounded grain models.

[0010] The three different grain models are:

[0011] (1) By assigning different regularity to the grain model, equiaxed grain models with different Poisson curves for grain size distribution are obtained;

[0012] (2) By assigning a higher grain aspect ratio to the grains, a columnar crystal model can be obtained;

[0013] (3) By assigning different grain aspect ratios to grains in different regions, a transition structure grain model can be obtained;

[0014] The specific steps of the method of the present invention are as follows:

[0015] S1. Generate a rectangular region Ω, and divide the rectangular region Ω into N consecutive regular hexagons with the same side length.

[0016] S2. Extract the centers of all regular hexagons, and offset the centers of the regular hexagons to different degrees to obtain a discrete set of points.

[0017] S3. Based on the discrete point set as the centroid, perform Voronoi partitioning. Each convex hull polygon of the partition represents a grain, and at this time, the equiaxed grain model is obtained.

[0018] S4. Based on the equiaxed grain model, assign a grain aspect ratio coefficient k to the grain (k = 10, 15, 20...), and then obtain the columnar grain model.

[0019] S5. Based on the equiaxed grain model, different grain aspect ratios are assigned to grains in different regions to obtain a transitional structure grain model. The specific operation is as follows:

[0020] Divide the rectangular region Ω into three consecutive rectangular regions: region 1, region 2, and region 3, which are denoted by the symbols Ω1, Ω2, and Ω3, respectively.

[0021] Determine which region of Ω1, Ω2, Ω3 the endpoint P(X, Y) of all grains is in, and change the coordinates of point P according to the different regions where the grain endpoint P is located;

[0022] Find the grains that have lost their convex hull properties due to changes in the coordinates of the grain endpoints, and then modify the endpoints of the grains that have lost their convex hull properties to restore the convex hull properties of the grains.

[0023] S6. In the above three grain models, suppress the generation of edges smaller than 0.001 mm in the grain;

[0024] S7. Assign a width to each edge of the grain in the grain model to make it a grain boundary.

[0025] Compared with existing technologies, this invention, based on the Voronoi mosaic model to represent the virtual microstructure of metals, assigns control parameters such as grain size, grain regularity, grain boundary width, and grain aspect ratio to the traditional Voronoi mosaic model. According to actual needs, the generation of virtual microstructure of metals can be controlled, which closely matches the actual grain model. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the process of generating virtual metal microstructures according to the present invention.

[0027] Figure 2 This is a schematic diagram illustrating step one of the present invention, which involves dividing a rectangular region into continuously connected regular hexagons.

[0028] Figure 3 This is a schematic diagram of the offset of the center of the regular hexagon in step two of the present invention;

[0029] Figure 4 These are equiaxed crystal models with different degrees of regularity generated in step three of this invention;

[0030] Figure 5 The columnar crystal model with δ = 0.8 generated in step four of this invention;

[0031] Figure 6 This is a distribution diagram of dividing the rectangular area into region 1, region 2, and region 3 in step five of the present invention;

[0032] Figure 7 The grains that lose their convex hull characteristics in step five of this invention and their adjacent grains;

[0033] Figure 8 The grains that restore the convex hull characteristics in step five of this invention and their adjacent grains;

[0034] Figure 9 This is the transition structure grain model with δ = 0.8 generated in step five of this invention;

[0035] Figure 10 This is a schematic diagram illustrating how the presence of extremely short sides in the present invention leads to the generation of excess portions of grains during grain boundary formation.

[0036] Figure 11 This is a schematic diagram of grain boundary generation caused by grain endpoint displacement in step seven of the present invention;

[0037] Figure 12 This is a bounded virtual metal microstructure simulated in this invention. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings.

[0039] A method for controlled virtual microstructure generation of metals, process input Figure 1 As shown,

[0040] Step 1: Generate a rectangular region Ω, and divide the rectangular region Ω into N consecutive regular hexagons with the same side length;

[0041] Step 2: Extract the centers of all regular hexagons, offset the centers of the regular hexagons to different degrees, and define the value of δ to represent the degree of discreteness of the point set S offset, thus obtaining a discrete point set;

[0042] Step 3: Perform Voronoi partitioning based on the discrete point set as the centroid. Each convex hull polygon of the partition represents a grain, thus obtaining the equiaxed grain model. In step S2, δ represents the regularity of the grain. The larger δ is, the more uniform the grain becomes. δ = 1 indicates that all grains in the equiaxed grain model are regular hexagons; δ = 0 indicates that the equiaxed grain model is a pure Poisson Voronoi tessellation.

[0043] Step 4: Based on the equiaxed grain model, assign a grain aspect ratio coefficient k to the grains to obtain the columnar grain model.

[0044] Step 5: Divide the rectangular region into three sequentially connected rectangular regions: Region 1, Region 2, and Region 3. Based on the equiaxed grain model, assign different grain aspect ratios to the grains in different regions to obtain the transition structure grain model.

[0045] Step 6: In the above three grain models, suppress the generation of edges smaller than 0.001 mm in the grain;

[0046] Step 7: Assign a width to each edge of the grain in the grain model to make it a grain boundary.

[0047] This invention, through controlling the discreteness of seed point distribution, performs Voronoi partitioning using seed points; obtains equiaxed crystal grain models with different size distributions; stretches the equiaxed crystal model based on the equiaxed crystal grain model to obtain columnar crystal grain models; and, based on the equiaxed crystal grain model, obtains transitional structure grain models by dividing the grains in each region and stretching them differently. The specific steps are as follows:

[0048] Step 1:

[0049] In two-dimensional space, a rectangular region Ω∈{(x,y)|0<=x<=L,0<=y<=H} is generated;

[0050] Based on the defined average grain size D mm, the rectangular region is divided into N consecutive regular hexagons with the same side length, such as... Figure 2 As shown; the length of the sides of all regular hexagons is a mm;

[0051] ND 2 π = HL;

[0052] Step Two:

[0053] Extract the centers of all regular hexagons from step one to obtain the point set S = {P1, P2, ..., Pn};

[0054] like Figure 3 As shown, the coordinates of the offset point set S are: with the center P of the regular hexagon as the center point and R as the radius, draw a circle, so that P is randomly offset to the arc of the drawn circle.

[0055] The coordinates of the center point P before the offset are (x, y).

[0056] After the offset, the coordinates of P are (x+R sinθ, y+R cosθ).

[0057]

[0058] The value of δ is defined to represent the degree of discreteness of the offset of the point set S; δ∈[0,1];

[0059] δ = 1 indicates that the point set S does not shift, and δ = 0 indicates that the point set S has the greatest degree of shift.

[0060] Step 3: Generation of the equiaxed grain model

[0061] Based on the discrete point set S obtained in step two, Voronoi partitioning is performed, and each convex hull polygon of the partition represents a grain.

[0062] In step two, δ represents the regularity of the grains; the larger δ is, the more uniform the grains become.

[0063] δ = 1 indicates that all grains in the equiaxed crystal model are regular hexagons;

[0064] δ=0 indicates that the isometric crystal model is a pure Poisson Voronoi mosaic;

[0065] At this point, equiaxed grain models with different degrees of regularity are obtained; such as Figure 4 As shown.

[0066] Step 4: Generation of the columnar crystal model

[0067] Obtain the endpoints of the convex hull polygon derived from the discrete point P in step three. These endpoints form the point set J.

[0068] The points in point set J are sorted counterclockwise with reference point P.

[0069]

[0070] Stretching the x-coordinate of point set J by a factor of k changes the coordinate values.

[0071]

[0072] At this point, the original equiaxed grain model is changed to a columnar grain model; such as Figure 5 As shown.

[0073] The average aspect ratio of columnar crystal grains is approximately k.

[0074] Step 5: Generation of the transition structure grain model

[0075] The virtual grain structure of the transition structure divides the generation region of this structure into three consecutive regions, each with a different grain type:

[0076] (a) Includes grains within region 1 with an aspect ratio of approximately k1 = 10;

[0077] (b) Including region 2, the grains have an aspect ratio of approximately k2 = 5, and the grains in region 2 are interconnected with the grains in regions 1 and 3.

[0078] (c) Including region 3, the grains have an aspect ratio of approximately 1.

[0079] Step 5.1

[0080] like Figure 6 As shown, the rectangular region Ω generated in step one is divided into three consecutive rectangular regions: region 1, region 2, and region 3, denoted by the symbols Ω1, Ω2, and Ω3, respectively.

[0081] Ω = Ω1 + Ω2 + Ω3

[0082] Ω1∈{(x, y)|0<=x<=L1,0<=y<=H}, the average aspect ratio of the grains in this region is approximately k1, with k1 = 10 by default.

[0083] Ω2∈{(x, y)| L1<=x<=L2,0<=y<=H}, the average aspect ratio of the grains in this region is approximately k2, with a default k2=5.

[0084] Ω3∈{(x,y)| L2<=x<=L,0<=y<=H}, the average aspect ratio of the grains in this region is about 1;

[0085] Where 0 < L1 < L2 < L, L2 = L - 4 * R; L1 = L2 - 3 * R; the values ​​of L1 and L2 can be changed according to actual needs to control the number of grains in region 1, region 2 and region 3;

[0086] Where 1≤k3<k2<k1, the values ​​of k1, k2, and k3 can be freely set according to actual needs.

[0087] Step 5.2

[0088] Obtain the endpoints of the convex hull polygon divided based on the discrete point P in step three. The endpoints form a point set J. Divide the points in the point set J into J1, J2, and J3 according to their respective regions.

[0089] J = [J1 J2 J3]′

[0090]

[0091] In region 1, the grain J = J1 or J = [J1 J2]

[0092] In region 2, the grains J = [J1 J2] or J = [J2 J3]

[0093] In region 3, the grains J = J3 or J = [J2 J3]

[0094] Point set J1 is in region 1, point set J2 is in region 2, and point set J3 is in region 3.

[0095] Transform the x-coordinates of point set J1, J2, J3 to change the coordinate values.

[0096]

[0097]

[0098]

[0099] k1 > k2 > 1;

[0100] The size and position of regions 1, 2, and 3 have all changed, among which...

[0101] Ω=Ω1+Ω2+Ω3={(x,y)|0≤x≤k2(L2-L1)+k1L1+L-L2,0≤y≤H}

[0102] Ω1∈{(x,y)|0≤x≤10L1,0≤y≤H}

[0103] Ω2∈{(x,y)|10L1≤x≤k2(L2-L1)+k1L1,0≤y≤H}

[0104] Ω3∈{(x, y)|k2(L2-L1)+k1L1≤x≤k2(L2-L1)+k1L1+L-L2, 0≤y≤H}

[0105] Change the index of the endpoints in point set J, and sort the points in point set J counterclockwise with P as the reference point;

[0106] Within region 1, the average grain radius The average aspect ratio of the grains is approximately k1;

[0107] Within region 2, the average grain radius The average aspect ratio of the grains is approximately k2;

[0108] Within region 3, the average grain radius R3 = R0, and the average grain aspect ratio is 1;

[0109] Obtain the transitional structure grain model.

[0110] Step 5.3:

[0111] like Figure 7 As shown, some grains are located simultaneously in regions 1 and 2, or simultaneously in regions 2 and 3. Because each region has a different deformation coefficient for the grain aspect ratio, this leads to abnormal grain deformation, specifically, the grains lose their convexity hull characteristics. These grains need to be modified. The modified grains that restore their convexity hull characteristics are shown below. Figure 8 As shown, the specific steps are as follows:

[0112] Obtain the point set J of the grain endpoints that have lost the convex hull characteristic with P as the centroid in step 5.2;

[0113] Form a convex hull polygon from the point set J; the point set J will have two possible cases;

[0114] Scenario 1: Scenario 2:

[0115] Point (x) 1in y1in ), (x 2in y 2in ) Inside the convex hull polygon; Case 1: One endpoint is inside the convex hull polygon; Case 2: Two consecutive endpoints are inside the convex hull polygon;

[0116] Remove points inside the convex hull polygon to restore the convex hull properties of the grain.

[0117] Situation 1 at this time: Scenario 2:

[0118] Deleting points inside the convex hull polygon will change the shape of the grain, causing interference between the grain and adjacent grains; therefore, the corresponding endpoints of adjacent grains need to be changed.

[0119] In case 1, find the corresponding adjacent grains and obtain the point set J1 of the grain endpoints.

[0120] The corresponding point (x) in the grain 1in y 1in It needs to be changed;

[0121] Point (x) 1in y 1in The point becomes the line segment (x2, y2)(x n y n The projection point (x'1, y'1) on ).

[0122] In case 2, find the corresponding adjacent grains and obtain the point set J2 of the grain endpoints.

[0123] The corresponding point (x) in the grain 1in y 1in (x) 2in y 2in It needs to be changed;

[0124] Point (x) 1in y 1in (x) 2in y 2in The two points are transformed into the line segment (x3, y3)(x n y n The projection points (x'1, y'1) and (x'2, y'2) on the plane;

[0125] The shapes of adjacent grains change, but there is no interference between the grains;

[0126] The point set J1J2 at the endpoints of adjacent grains changes.

[0127]

[0128] The final obtained transition structure grain model is as follows Figure 9 As shown.

[0129] Step Six: Suppress the formation of grain edges smaller than 0.001 mm

[0130] When grain boundaries are formed, the presence of extreme edges causes the grain to differentiate into two parts: one is the main grain and the other is the excess part generated by extremely short edges. Therefore, it is necessary to suppress the formation of edges smaller than 0.001 mm. Figure 10 This is a schematic diagram illustrating how the presence of extremely short sides leads to the formation of excess portions of grains during grain boundary formation.

[0131] Delete edges smaller than 0.001 mm in the grain, extend the corresponding adjacent edges to make them intersect, regenerate a closed grain, and recalculate the endpoints of the grain.

[0132] Step 7: Assign width to each edge of the grain.

[0133] like Figure 10 As shown, each edge of the grain is offset inward by 0.005 mm along the normal direction of the edge, resulting in a grain boundary width of 0.001 mm. The specific steps are as follows:

[0134] Obtain the point set J of the regenerated grain endpoints with P as the centroid in step six;

[0135]

[0136] Calculate the unit vector of each edge of the grain and divide it into two vector sets according to the direction of the unit vector;

[0137]

[0138]

[0139] Calculate the unit vector of the grain angle bisector;

[0140]

[0141] α = [α1 α2 … α] n ]′

[0142] α is the set of half-angles corresponding to the grain endpoints;

[0143] The endpoints of the grains are shifted inward to re-obtain the point set J, as shown in the following formula:

[0144]

[0145] At this point, a schematic diagram of grain boundary formation due to grain tip displacement is shown below. Figure 11As shown, a bounded grain model is then obtained, such as... Figure 12 As shown.

[0146] The above description merely illustrates preferred embodiments of the present invention, and while the description is relatively specific and detailed, it should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications, improvements, and substitutions without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for controlled simulation generation of virtual microstructures in metals, characterized in that, The method uses the Voronoi mosaic model as the basic grain model. Different regularity is assigned to the grain model to obtain equiaxed grain models with different Poisson curves for grain size distribution. Based on the equiaxed grain model, a higher grain aspect ratio is assigned to the grains to obtain a columnar grain model. Based on the equiaxed grain model, the region is divided, and different grain aspect ratios are assigned to the grains in different regions to obtain a transitional structure grain model. Grain boundaries are then assigned to the above three grain models to obtain a bounded grain model. It represents the regularity of the grains. The larger the grain size, the more uniform the grains become. This indicates that all grains in the equiaxed crystal model are regular hexagons; , indicating that the isometric crystal model is a pure Poisson Voronoi mosaic.

2. The method for generating controlled virtual microstructures of metals according to claim 1, characterized in that, The method includes the following steps: S1. Generate a rectangular region Ω, and divide the rectangular region Ω into N regular hexagons with the same side length and in sequence. S2. Extract the centers of all regular hexagons, and offset the centers of the regular hexagons to different degrees, by defining... The value is used to represent the degree of discreteness of the offset of the point set S, thus obtaining a discrete point set; S3. Perform Voronoi division based on the discrete point set as the centroid. Each convex hull polygon obtained by the division represents a grain, and at this time, an equiaxed grain model is obtained. S4. On the basis of the equiaxed grain model, assign a grain aspect ratio coefficient k to the grains, and at this time, a columnar grain model is obtained. S5. Divide the rectangular region into three consecutive rectangular regions, namely region 1, region 2, and region 3. On the basis of the equiaxed grain model, assign different grain aspect ratio coefficients to the grains in different regions, so as to obtain a transitional structure grain model. The specific operations are as follows: 5-1. The three consecutive rectangular regions in the rectangular region Ω are respectively denoted by the symbols Ω1, Ω2, and Ω3. Assign different grain aspect ratio coefficients k1, k2, and k3 to the grains in the three regions of Ω1, Ω2, and Ω3, and 1≤k3<k2<k1. The grains in region Ω2 are connected to the grains in region Ω1 and region Ω3. 5-2. Determine in which of the regions Ω1, Ω2, and Ω3 the endpoint P(X,Y) of all grains is located, and change the coordinates of point P according to the different region positions of the grain endpoint P. 5-3. Find the grains that lose the convex hull property due to changing the grain endpoint coordinates, and then modify the endpoints of the grains that lose the convex hull property to restore the convex hull property of the grains. S6. In the above three grain models, suppress the generation of edges less than 0.001 mm in the grains. S7. Assign a width to each edge of the grains in the grain model to make it a grain boundary.

3. The method for generating controlled virtual microstructures of metals according to claim 2, characterized in that, The specific steps of S2 are as follows: 2-1. Extract the centers of all the regular hexagons in step S1 to obtain a point set S = {P1, P2,..., Pn}. 2-2. Offset the coordinates of the point set S: Taking the center P of the regular hexagon as the origin, draw a circle with a radius of R, so that P is randomly offset to the arc of the drawn circle. The coordinates of the center point P before offset are: The coordinates of P after offset are ,in ; 'a' is the length of the side of the regular hexagon; ; , This indicates the degree of dispersion of the point set S offset; The time indicates that the point set S does not shift; The time indicates that the offset of point set S is at its maximum.

4. The method for generating controlled virtual microstructures of metals according to claim 2, characterized in that, The specific steps of S4 are as follows: 4-1. Obtain the endpoints of the convex hull polygon divided based on the discrete point P in step S4. The endpoints form a point set J. The points in the point set J are sorted counterclockwise with P as the reference point. The formula is as follows: ； 4-2. Stretch the abscissa of the point set J by k times, and the coordinate value changes. The formula is as follows: ； At this time, the original equiaxed grain model is changed into a columnar grain model, and the average aspect ratio of the columnar grains is k.

5. The method for generating controlled virtual microstructures of metals according to claim 2, characterized in that, The specific steps of 5-2 are as follows: 5-2-1. Obtain the endpoints of the convex hull polygon divided based on the discrete point P in step S3. The endpoints form a point set J; divide the points in the point set J into J1, J2, and J3 according to the regions where they are located. The expression is as follows: ； ， ， ； For the grains in region 1, J = J1 or J = [J!J2]; for the grains in region 2, J = [J1J2] or J = [J2J3]; for the grains in region 3, J = J3 or J = [J2J3]; the point set J1 is in region 1, the point set J2 is in region 2, and the point set J3 is in region 3. 5-2-2. Transform the abscissa of the point sets J1, J2, and J3, and the coordinate value changes. The expression is as follows: ； ； ； The sizes and positions of the three regions Ω1, Ω2, and Ω3 all change, as shown in the following expressions: = ； ； ； ； 5-2-3. Change the index of the endpoints in point set J, and sort the points in point set J counterclockwise with P as the reference point; Within region 1, the average grain radius The average aspect ratio of the grains is k1; Within region 2, the average grain radius The average aspect ratio of the grains is k2; Within region 3, the average grain radius The average aspect ratio of the grains is 1; Obtain the transitional structure grain model.

6. The method for generating controlled virtual microstructures of metals according to claim 5, characterized in that, The grains that lose the convex hull characteristics in 5-3 are some grains that are simultaneously located in region 1 and region 2 or simultaneously located in region 2 and region 3. The steps for modifying the grains that have lost their convex hull properties include: (1) Obtain the point set J of the grains with discrete point P as the centroid and without convex hull characteristics in step 5-2; Form a convex hull polygon from the point set J; the point set J will have two possible cases; Case 1: Scenario 2: , Point (x) 1in ,y 1in ), (x 2in ,y 2in ) Inside the convex hull polygon; Case 1: One endpoint is inside the convex hull polygon; Case 2: Two consecutive endpoints are inside the convex hull polygon; (2) Delete the points inside the convex hull polygon to restore the convex hull properties of the grain. Situation 1 at this time: Scenario 2: , (3) Modify the corresponding endpoints of adjacent grains of the deleted points inside the convex hull polygon; First, in case 1, find the corresponding adjacent grains and obtain the point set J1 of the grain endpoints, whose expression is as follows: ； The corresponding point (x) in the grain 1in ,y 1in The point becomes a line segment (x2, y2) (x n ,y n The projection point (x'1, y'1) on ). Then, in case 2, find the corresponding adjacent grains and obtain the point set J2 of the grain endpoints, the expression of which is as follows: ； The corresponding point (x) in the grain 1in ,y 1in ) (x 2in ,y 2in The two points are transformed into the line segment (x3, y3). n ,y n The projection points (x'1, y'1) and (x'2, y'2) on the grain change the shape of adjacent grains without interference between them. The point set J1J2 of the endpoints of adjacent grains then changes, as expressed below: 。 7. The method for generating controlled virtual microstructures of metals according to claim 2, characterized in that, S6 specifically involves: deleting edges smaller than 0.001 mm in the grain, extending the corresponding adjacent edges to make them intersect, regenerating a closed grain, and recalculating the endpoints of the grain.

8. The method for generating controlled virtual microstructures of metals according to claim 2, characterized in that, Specifically, S7 is: Each edge of the grain is offset inward by 0.005 mm along the normal direction of the edge, resulting in a grain boundary width of 0.001 mm. The specific steps are as follows: 7-1. Obtain the point set J of the grain endpoints regenerated in step six with P as the centroid. Its expression is as follows: ； 7-2. Calculate the unit vector of each edge of the grain and divide it into two vector sets according to the different directions of the unit vector; ； ； 7-3. Calculate the unit vector of the grain angle bisector; ； ； α is the set of half-angles corresponding to the grain endpoints; 7-4. The endpoints of the grains are shifted inward to re-obtain the point set J, as shown in the following formula. = ； This yields a bounded grain model.

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