Modeling method for closed grain microstructure of sintered nano-silver material in specified boundary range

Abstract

A modeling method for a closed grain microstructure of a sintered nano-silver material in a specified boundary range comprises the following steps: step 1, determining a generation range of a grain microstructure two-dimensional model, and randomly generating N initial seed points in the range; 2, a Delaunay triangular net is automatically constructed based on the initial random seed points, and a closed polygon, namely an initial sintered nano-silver grain microstructure, is formed; 3, traversing each initial random seed point and the grain area where the initial random seed point is located, and calculating coordinates of additional seed points needing to be added into the initial random seed points according to a seed point adding algorithm of the constraint sintering nano-silver grain microstructure; 4, a Delaunay triangular net is reconstructed based on the new seed points, and a closed and bounded sintered nano-silver grain microstructure is formed; and 5, obtaining grain microstructure geometric information in a specified boundary range, and establishing a sintered nano-silver grain microstructure finite element model in finite element software. According to the method, the extension range of the sintered nano-silver grain boundary is restrained by adding an additional seed point at a specific position, so that the intersection point of the grain boundary and a specified boundary line does not need to be calculated, the operation steps of drawing the sintered nano-silver grain microstructure in a Voronoi diagram are optimized, and the working efficiency is improved. And accurate microstructure geometric information input is provided for subsequent finite element modeling analysis.

Description

(1) Technical Field:

[0001] The present invention relates to a method for modeling the closed-grain mesoscopic structure of sintered nano-silver materials within a specified boundary range, and belongs to the technical field of mesoscopic structure modeling of sintered nano-silver materials. (2) Background Art:

[0002] Sintered nano-silver materials are solid materials composed of a large number of grains ranging from micrometers to nanometers in size, randomly arranged or combined in a specific orientation. Although the physical properties of individual sintered nano-silver grains exhibit anisotropic characteristics, due to the random distribution of grains with different orientations, sintered nano-silver materials still show isotropy macroscopically, which enables sintered nano-silver materials to be widely used in many fields such as mechanical manufacturing, aerospace, electronics, and semiconductors.

[0003] In two-dimensional space, the grains of sintered nano-silver materials usually appear as irregular polygons, and due to the influence of factors such as initial nucleation, grain boundary migration, and local stress, uniformly growing grains tend to follow the Voronoi structure distribution. When constructing the mesoscopic structure of sintered nano-silver grains based on the traditional Voronoi diagram drawing method, after obtaining the mesoscopic structure of the grains according to the random seed points, it is also necessary to cut the structure outside this range according to the desired model size, and at the same time, it is necessary to calculate the intersection points of the boundaries of the sintered nano-silver grains and the model boundary line to obtain the vertex coordinates of all grains, which is convenient for modeling in finite element software.

[0004] In order to optimize the operation steps when drawing the mesoscopic structure of sintered nano-silver grains by the Voronoi diagram and skip the step of calculating the intersection points of the grain boundaries and the model boundary line, the present invention proposes a seed point addition algorithm based on the generation principle of the Voronoi diagram. By adding additional seed points outside the specified boundary range, the generation range of the mesoscopic structure of sintered nano-silver grains within the boundary is restricted, ensuring that the generated mesoscopic structure of the grains fully fills the specified boundary region, and at the same time, each sintered nano-silver grain within the region is closed and bounded. Thus, it is not necessary to calculate the intersection coordinates of the grain boundaries and the model boundary line, simplifying the operation steps when drawing the mesoscopic structure of sintered nano-silver grains by the Voronoi diagram, and providing accurate input of mesoscopic structure geometric information for subsequent finite element modeling analysis. (3) Summary of the Invention:

[0005] 1. Objective: The objective of the present invention is to propose a method for modeling the closed-grain mesoscopic structure of sintered nano-silver materials within a specified boundary range. This method constrains the mesoscopic structure of the grains by adding additional seed points outside the specified boundary range, ensuring that the mesoscopic structure of the sintered nano-silver grains generated within the specified boundary range is closed and bounded.

[0006] 2. Technical Solution: Based on the generation principle of Voronoi diagrams, a seed point addition algorithm for constraining the mesoscopic structure of grains is established. By adding additional seed points, the generation range of the mesoscopic structure of sintered silver nanoparticles within a specified boundary is restricted. This method can ensure that the generated mesoscopic structure of grains completely fills the specified boundary region, and at the same time, each mesoscopic structure of sintered silver nanoparticles within the region is closed and bounded. It includes the following steps:

[0007] Step 1: Generate initial random seed points within a specified range. Determine the generation range of the two-dimensional model of the mesoscopic structure of grains, and restrict the generation range of the mesoscopic structure of sintered silver nanoparticles to a closed rectangular region whose boundary range satisfies the following conditions: Ω = {(x, y) ∈ R 2 | x ∈ [X0, X1], y ∈ [Y0, Y1]}. Randomly generate N initial seed points within this range. The number of seed points is consistent with the number of grains inside the mesoscopic structure model of sintered silver nanoparticles. The set P0 of initial random seed points satisfies the following conditions: P0 = {p1, p2, … p n}, p i ∈ Ω, where p i = (x i , y i ) is the coordinate of the i-th initial seed point.

[0008] Step 2: Establish the initial mesoscopic structure of sintered silver nanoparticles. Automatically construct a Delaunay triangulation network based on the set P0 of initial random seed points, calculate the circumcenter of each triangle, and connect the circumcenters of each triangle with those of adjacent triangles to form a closed polygon, which is the initial mesoscopic structure of sintered silver nanoparticles. If a triangle is located on the outermost side and there is no adjacent triangle for a certain side, then take the perpendicular bisector ray of this side as the initial grain boundary. Due to the existence of some closed grain boundaries extending outside the specified range Ω and non-closed grain boundaries, at this time, the mesoscopic structure of sintered silver nanoparticles with closed inner boundaries within the specified range Ω cannot completely fill the specified range Ω, and additional constraints on the boundary range of its grains are required.

[0009] Step 3: Add additional seed points to constrain the mesoscopic structure of sintered silver nanoparticles. Traverse each initial random seed point and its corresponding grain region, and calculate the coordinates of the additional seed points that need to be added to the set P0 of initial random seed points according to the seed point addition algorithm for constraining the mesoscopic structure of sintered silver nanoparticles. Take the i-th initial random seed point (x i , y i ) and its corresponding grain region as an example:

[0010] ① If the corresponding grain region does not intersect any of the specified boundary lines, then this region is closed and bounded within the specified range Ω, and no additional seed points need to be added.

[0011] ② If the grain region where it is located intersects with the specified boundary line x = X0, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point added are (2X0 - x i , y i ).

[0012] ③ If the grain region where it is located intersects with the specified boundary line x = X1, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point added are (2X1 - x i , y i ).

[0013] ④ If the grain region where it is located intersects with the specified boundary line y = Y0, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point added are (x i , 2Y0 - y i ).

[0014] ⑤ If the grain region where it is located intersects with the specified boundary line y = Y1, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point added are (x i , 2Y1 - y i ).

[0015] Step 4: Re-establish the mesoscopic structure of sintered silver nanoparticles with closed and bounded grains within the specified range Ω. Based on the new seed point set P1, reconstruct the Delaunay triangle mesh, calculate the circumcenter of each triangle, and connect it with the circumcenters of adjacent triangles to form a closed and bounded two-dimensional mesoscopic structure of sintered silver nanoparticles. Due to the existence of additional seed points, the extension of the grain boundaries within the specified range Ω is restricted and limited, and all sintered silver nanoparticles within this range are closed and bounded.

[0016] Step 5: Establish a finite element model of the mesoscopic structure of sintered silver nanoparticles. Obtain the geometric information of the mesoscopic structure of grains within the specified boundary range, and establish a finite element model of the mesoscopic structure of sintered silver nanoparticles in finite element software.

[0017] The present invention provides a method for modeling the mesoscopic structure of closed grains of sintered silver nanomaterials within a specified boundary range. Its main advantages are as follows: Based on the generation principle of the Voronoi diagram, by adding additional seed points at specific positions, the extension range of the grain boundaries of sintered silver nanoparticles is restricted, ensuring that all grains generated within the specified boundary range are closed and bounded, and the vertices of the sintered silver nanoparticles do not exceed the specified range Ω. Thus, it is not necessary to calculate the intersection points of the grain boundaries and the specified boundary lines, optimizing the operation steps when drawing the mesoscopic structure of sintered silver nanoparticles using the Voronoi diagram, and providing accurate input of geometric information of the mesoscopic structure for subsequent finite element modeling analysis. (IV) Description of the Drawings:

[0018] Figure 1 It is the modeling flowchart for generating the closed-grain mesoscopic structure of sintered nano-silver material within the specified boundary range in the present invention

[0019] Figure 2 They are the initial random seed points generated within the specified range in Step 1 of the present invention

[0020] Figure 3 It is the initial mesoscopic structure of sintered nano-silver grains established in Step 2 of the present invention

[0021] Figure 4 They are the additional seed points added in Step 3 of the present invention

[0022] Figure 5 It is the closed and bounded mesoscopic structure of sintered nano-silver grains within the specified boundary range re-established in Step 4 of the present invention

[0023] Figure 6 It is the two-dimensional finite element model of the mesoscopic structure of sintered nano-silver grains established in Step 5 of the present invention (V) Specific implementation manners:

[0024] Next, the technical solutions in the embodiments of the present invention will be clearly and detailedly described in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention

[0025] For the modeling of 20 closed mesoscopic structures of sintered nano-silver grains within the specified boundary range x∈[0,50], y∈[0,50], according to Figure 1 the following process, the specific steps of this method are as follows:

[0026] Step 1: Generate initial random seed points within the specified range. Determine the generation range of the two-dimensional model of the mesoscopic structure of sintered nano-silver grains and limit it to the closed rectangular area: Ω={(x,y)∈R 2 |x∈[0,50], y∈[0,50]}. Randomly generate 20 initial seed points within this range, and their positions are represented by blue dots in Figure 2 . The number of seed points is consistent with the number of grains inside the mesoscopic structure model. The set of initial random seed points satisfies the following conditions: P0={p1, p2, … p n}, p i ∈Ω, where p i =(x i , y i ) is the coordinate of the i-th initial seed point

[0027] Step 2: Establish the initial mesoscopic structure of sintered silver nanoparticles. Based on the initial set of random seed points P0, a Delaunay triangular mesh is automatically constructed. The circumcenter of each triangle is calculated, and the circumcenters of each triangle are connected to those of adjacent triangles by solid lines. The closed polygon formed is the initial mesoscopic structure of the sintered silver nanoparticles. If a triangle is on the outermost side and there is no adjacent triangle for a certain side, the perpendicular bisector ray of this side is taken as the initial grain boundary and is distinguished by a dashed line, as Figure 3 shown. For the mesoscopic structure of sintered silver nanoparticles with closed boundaries within a specified range, Figure 3 different colors are used for filling in Figure 3 . The unfilled area is the infinitely extending area with non-closed boundaries. Due to the existence of some closed grain boundaries extending outside the specified range Ω and non-closed grain boundaries, the mesoscopic structure of sintered silver nanoparticles with closed boundaries within the specified range Ω at this time cannot completely fill the specified range Ω, and additional constraints on the boundary range of its grains are required.

[0028] Step 3: Add additional seed points to constrain the mesoscopic structure of sintered silver nanoparticles. Traverse each initial random seed point and its corresponding grain region. According to the seed point addition algorithm for constraining the mesoscopic structure of sintered silver nanoparticles, calculate the coordinates of the additional seed points that need to be added to the initial set of random seed points P0. For the initial random seed points whose corresponding grain regions intersect the specified boundary line, Figure 4 the serial numbers corresponding to these seed points are shown in black numbers in Figure 4 . Taking the 2nd seed point as an example, the sintered silver nanoparticle grain region it belongs to intersects the boundary lines x = X0 and y = Y0 and extends infinitely outward. According to the seed point addition algorithm, additional seed points with coordinates (2X0 - x2, y2) and (x2, 2Y0 - y2) need to be added. The coordinates of all additional seed points that need to be added after calculation are distinguished by red dots in Figure 4 shown.

[0029] Step 4: Re-establish the closed and bounded mesoscopic structure of sintered silver nanoparticles within the specified range Ω. Based on the new set of seed points P1, a Delaunay triangular mesh is re-constructed. The circumcenter of each triangle is calculated and connected to the circumcenters of adjacent triangles to form a closed and bounded two-dimensional mesoscopic structure of grains. Due to the existence of additional seed points, the extension of the sintered silver nanoparticle grain boundaries within the specified range Ω is constrained and limited, and all the sintered silver nanoparticles within this range are closed and bounded, as Figure 5 shown.

[0030] Step 5: Establish a finite element model of the mesoscopic structure of sintered silver nanoparticles. Obtain the geometric information of the grain mesoscopic structure within the specified boundary range Ω, and establish a finite element model of the closed and bounded mesoscopic structure of sintered silver nanoparticles with 20 grains within the boundary range x ∈ [0, 50], y ∈ [0, 50] in the finite element software, asFigure 6 as shown

Claims

1. A method for modeling the closed-grain microstructure of sintered nano-silver material within a specified boundary range, characterized by: Based on the generation principle of the Voronoi diagram, a seed point addition algorithm for constraining the mesoscopic structure of grains is established. By adding additional seed points, the generation range of the mesoscopic structure of sintered silver nanoparticles within a specified boundary is restricted. This method can ensure that the generated mesoscopic structure of grains completely fills the specified boundary region, and at the same time, each mesoscopic structure of sintered silver nanoparticles within the region is closed and bounded. It includes the following steps: Step 1: Determine the generation range of the two-dimensional model of the mesoscopic structure of grains, and randomly generate N initial seed points within this range; Step 2: Automatically construct a Delaunay triangular mesh based on the initial random seed points. The closed polygon formed is the initial mesoscopic structure of sintered silver nanoparticles; Step 3: Traverse each initial random seed point and its corresponding grain region. According to the seed point addition algorithm for constraining the mesoscopic structure of sintered silver nanoparticles, calculate the coordinates of the additional seed points that need to be added to the initial random seed points; Step 4: Reconstruct the Delaunay triangular mesh based on the new seed points to form a closed and bounded mesoscopic structure of sintered silver nanoparticles; Step 5: Obtain the geometric information of the mesoscopic structure of grains within the specified boundary range, and establish a finite element model of the mesoscopic structure of sintered silver nanoparticles in finite element software.

2. The generation range of the two-dimensional model for determining the grain mesostructure according to claim 1, wherein: In step 1, the generation range of the mesoscopic structure of sintered silver nanoparticles is limited to a closed rectangular area whose boundary range satisfies the following conditions: Ω = {(x, y) ∈ R 2 |x ∈ [X0, X1], y ∈ [Y0, Y1]}.

3. The establishment of the initial mesoscopic structure of sintered silver nanoparticles according to claim 1, characterized in that: In Step 2, a Delaunay triangular mesh is constructed based on the set of initial random seed points. Calculate the circumcenter of each triangle, and connect the circumcenters of each triangle with those of adjacent triangles. The closed polygon formed is the initial mesoscopic structure of sintered silver nanoparticles. If a triangle is located on the outermost side and there is no adjacent triangle for a certain side, then take the perpendicular bisector ray of this side as the initial grain boundary.

4. The mesoscopic structure of sintered nano - silver grains with additional seed - point constraints according to claim 1, characterized in that: In step 3, each initial random seed point and its corresponding grain region are traversed. According to the seed point addition algorithm that constrains the mesoscopic structure of sintered nano-silver grains, the coordinates of the additional seed points to be added to the initial random seed points are calculated. Taking the i-th initial random seed point (x i , y i ) and its corresponding grain region as an example: ① If the grain region where it is located does not intersect any of the specified boundary lines, then this region is closed and bounded within the specified range Ω, and no additional seed points need to be added. ② If the grain region where it is located intersects with the specified boundary line x = X0, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point are (2X0 - x i , y i ). ③ If the grain region where it is located intersects with the specified boundary line x = X1, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point are (2X1 - x i , y i ). ④ If the grain region where it is located intersects with the specified boundary line y = Y0, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point are (x i , 2Y0 - y i ). ⑤ If the grain region where it is located intersects with the specified boundary line y = Y1, then this region is non-closed within the specified range Ω, and the coordinates of the additional seed point are (x i , 2Y1 - y i ).

5. The mesoscopic structure of sintered silver nanoparticles with a closed bounded within a specified range re-established according to claim 1, characterized in that: In Step 4, reconstruct the Delaunay triangular mesh based on the new set of seed points. Calculate the circumcenter of each triangle, and connect it with the circumcenters of adjacent triangles to form a closed and bounded two-dimensional mesoscopic structure of sintered silver nanoparticles. Due to the existence of additional seed points, the extension of the grain boundaries within the specified range is constrained and restricted, and all the sintered silver nanoparticles within this range are closed and bounded.

6. The finite element model for establishing the mesoscopic structure of sintered silver nanoparticles according to claim 1, wherein: In Step 5, obtain the geometric information of the mesoscopic structure of grains within the specified boundary range, and establish a finite element model of the mesoscopic structure of sintered silver nanoparticles in finite element software.

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