A Modeling Method of Controllable Nano-Gradient Polycrystalline Materials Based on Voronoi Tessellation

Abstract

The present invention proposes a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method. First, according to parameters such as the gradient direction, grain size, and number of grain layers required by the user, a box model of a perfect cube is initialized and generated, and the central coordinates of each perfect cube grain are saved. Then, the one-dimensional coordinates in the gradient direction and the two-dimensional coordinates of each grain in the non-gradient direction are merged to obtain a node list of the perfect cube grains. Next, random perturbations are applied to the node coordinates, and it is ensured that the nodes are all within the model box. Finally, the node list after adding perturbations is passed into the ATOMSK software to establish a polycrystalline model, and all atoms within the simulation box are saved and output as a model file to end. The present invention can construct nano-crystalline models of different sizes and gradient ratios; simplify the process of constructing the gradient crystal model and the parameter screening process, and greatly improve the efficiency of obtaining the nano-polycrystalline material model.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational materials science, and particularly relates to a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method. Background Art

[0002] Materials with gradient structures can achieve a synergistic improvement in strength and toughness and have advantages such as better fatigue resistance and corrosion resistance. In nano-polycrystalline materials, the interface between different grains is called a grain boundary. There are various interactions between grain boundaries and dislocations. Grain boundaries can emit or absorb dislocations, promoting dislocation movement; they can also act as obstacles to dislocation movement. During the deformation process of nano-gradient polycrystalline materials, the gradient structure induces non-uniform plastic deformation in each layer, resulting in non-uniform stress gradients in nano-gradient materials. This non-uniform dislocation distribution makes the deformation mechanism of nano-gradient grains different from that of non-gradient polycrystalline materials.

[0003] Nano-gradient polycrystalline materials are applicable to many fields such as aerospace and microelectronics industries. At present, researchers at home and abroad use techniques such as surface mechanical grinding to obtain materials with gradient structures and study the strengthening mechanism of gradient materials by relying on traditional experimental characterization methods. Under potential extreme working conditions, the research on the microstructural changes of nano-gradient materials has high implementation costs and great difficulties. Molecular dynamics simulation can provide guidance for revealing their micro-deformation principles.

[0004] Nano-polycrystalline materials rolled in the laboratory can meet the requirements of uniform and controllable gradients. However, the conventional modeling method for nano-polycrystalline materials randomly generates grain nodes based on random numbers and then randomly generates a nano-polycrystalline model with inconsistent sizes and random distributions. This method can only randomly generate a model according to the number of grains and cannot control the grain size gradient, making it unsuitable for the simulation research of nano-gradient polycrystalline materials. Summary of the Invention

[0005] In view of the above problems, the present invention proposes a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method. With the help of the ATOMSK software, an automatic generation algorithm for node seeds of single-element, multi-element crystal material systems, and system models including element substitution is formed to realize the generation of node seeds and modeling commands for gradient polycrystalline models. A good user interaction method is provided, and by inputting relevant parameters such as gradient mode, grain size, and element information, a target gradient polycrystalline material model can be quickly obtained.

[0006] In order to achieve the above invention purpose, the specific technical solution adopted by the present invention is as follows:

[0007] Provide a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method, the method comprising the following steps:

[0008] S1: Construct a box model for initializing the generation of perfect cubes, and obtain the central coordinates of each perfect cube grain.

[0009] S2: Extract the central coordinates of the perfect cube grains, and divide them into one-dimensional coordinates in the gradient direction and two-dimensional coordinates of grains of various sizes in the non-gradient direction. Merge them according to the set number of grain layers and the number of grains to obtain a node list of the perfect cube grains.

[0010] S3: Extract the node list of the perfect cube grains and apply random perturbations to obtain new node coordinates. Compare the new node coordinates with the boundaries of the model box one by one to ensure that the nodes are all within the model box.

[0011] S4: Extract the model box size information and element information obtained in step S1, extract the new node list obtained in step S3, and input them into the ATOMSK software to establish a polycrystalline model. After correcting the atomic periodicity, retain all atoms within the size of the simulation box to obtain a model file.

[0012] Further, in step S1, the construction of the box model for initializing the generation of perfect cubes specifically includes the following steps:

[0013] S11: Set the material parameters of the nano-gradient crystal material, including gradient mode a:b:c, gradient direction x or y or z, small grain size D1, number of grain layers L1, L2, L3, number of small grains N1, N2 in the non-gradient direction, element information and other parameters.

[0014] S12: Calculate the size of the model box according to the gradient mode, the small grain size, and the number of grain layers. The calculation method is as follows:

[0015] Boundary in the gradient direction:

[0016]

[0017] Boundary in the non-gradient direction:

[0018]

[0019] S13: Perform mesh division on the model box according to the gradient mode.

[0020] S14: Obtain the boundary coordinates of each perfect cube grain based on the mesh-divided model box.

[0021] Further, in step S2, obtaining the node list of the perfect cube grains specifically includes the following steps:

[0022] S21: Calculate the boundary coordinate list of each perfect cubic grain based on the gradient direction, grain size, and number of grain layers. The calculation method is as follows:

[0023] In the gradient direction:

[0024]

[0025] In the non-gradient direction:

[0026] Small grains:

[0027]

[0028] Medium grains:

[0029]

[0030] Large grains:

[0031]

[0032] Where In the list, the small grain size is D1, the medium grain size is D2, and the large grain size is D3; the numbers of small grains in the other two non-gradient directions are N1 and N2 respectively;

[0033] S22: To ensure that the periodic boundary is not damaged, set inverse gradient nodes with the opposite gradient to the current model outside the perfect grains generated within the simulation box size. The calculation method is as follows:

[0034] In the gradient direction, add on the basis of list (3):

[0035]

[0036] In the non-gradient direction, the boundary coordinates of each perfect cubic grain remain unchanged;

[0037] S23: Calculate the central node coordinates of each perfect cubic grain according to the boundary coordinates of each perfect cubic grain. Combine list (3) and (7), and perform the following transformation on all elements in lists (3) to (6) and the combined list:

[0038] In the gradient direction:

[0039]

[0040] In the non-gradient direction:

[0041] Small grains:

[0042]

[0043] Medium grains:

[0044]

[0045] Large grains:

[0046]

[0047] Among them

[0048] S24: Classify the one-dimensional coordinates of the central nodes of the perfect cubic grains in the gradient direction according to the grain size, and the classified list is as follows:

[0049] The central nodes of the perfect cubic small grains in the gradient direction are the first L1 items and the last L1 items of list (8), which are respectively:

[0050]

[0051] The central nodes of the perfect cubic large grains in the gradient direction are the (L1 + L2 + 1)-th item to the (L1 + L2 + 2L3)-th item of list (8), which are:

[0052]

[0053] The remaining items of list (8) are the central nodes of the perfect cubic medium grains in the gradient direction;

[0054] S25: Obtain the two-dimensional coordinates (n1, n2) of various sized grains in the non-gradient direction, and the generation method is:

[0055] For list groups (9) to (11), make all elements of list Direction 1 and all elements of list Direction 2 match once to generate a series of two-dimensional coordinates.

[0056] Among them, list group (9) should generate N1N2 two-dimensional coordinates, list group (10) should generate two-dimensional coordinates, and list group (11) should generate two-dimensional coordinates;

[0057] S26: Combine the one-dimensional coordinate (g) in the gradient direction and the two-dimensional coordinates (n1, n2) of various sized grains in the non-gradient direction to obtain the three-dimensional coordinates (x, y, z) of the central nodes of the perfect cubic grains, and the occupancy rules are as follows:

[0058] If the gradient direction is the X direction:

[0059] The one-dimensional coordinate (g) occupies the x position, and the two-dimensional coordinates (n1, n2) occupy the (y, z) positions;

[0060] If the gradient direction is the Y direction:

[0061] The one-dimensional coordinate (g) occupies y bits, and the two-dimensional coordinates (n1, n2) occupy (x, z) bits;

[0062] If the gradient direction is the Z direction:

[0063] The one-dimensional coordinate (g) occupies z bits, and the two-dimensional coordinates (n1, n2) occupy (x, y) bits.

[0064] Furthermore, in step S3, constructing a list of gradient crystal grain center nodes specifically includes the following steps:

[0065] S31: Generate a list of random numbers rand in the range of (-1, 1), and the number of its elements is equal to the number of three-dimensional coordinates (x, y, z) of the center nodes of the perfect cubic grains obtained in step S25;

[0066] S32: Calculate the new node (x′, y′, z′), and the calculation method is:

[0067] (x′, y′, z′) = (x + D × rand(i), y + D × rand(i), z + D × rand(i)) (12)

[0068] where D is the grain size, for small grains D = D1, for medium grains large grains

[0069] S33: Check whether all new nodes are within the current virtual simulation box, and the detection criteria are as follows:

[0070] If the gradient direction is the X direction:

[0071]

[0072] If the gradient direction is the Y direction:

[0073]

[0074] If the gradient direction is the Z direction:

[0075]

[0076] S34: If the detection in step S33 fails, then repeat steps S31 - S33 until the detection in step S33 passes.

[0077] Furthermore, in step S4, constructing a model of the gradient crystal material specifically includes the following steps:

[0078] S41: Set the element information of the nano-gradient crystal material, and input the element information, the new node coordinates obtained in S3, and the size of the simulation box into the external software ATOMSK for modeling;

[0079] S42: Pass the wrapping instruction to the external software ATOMSK to remove the atoms outside the model, then pass the cutting model instruction, and only retain the length of l in the gradient direction. Then output the model as a file. gradient

[0080] Compared with the prior art, the present invention has the following beneficial technical effects:

[0081] The present invention proposes a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method. With the help of the ATOMSK software, an automatic node seed generation algorithm for single-element, multi-element crystal material systems and system models including element substitution is formed to realize the generation of node seeds and modeling commands for the gradient polycrystalline model. Provide a good user interaction method, and quickly obtain the target gradient polycrystalline material model by inputting relevant parameters such as gradient mode, grain size, and element information. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flowchart of a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method provided by the present invention

[0083] Figure 2 is an interface diagram of an interactive operation software provided by the present invention.

[0084] Figure 3 is a nano-gradient crystal constructed by a user inputting parameters in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0085] In order to more clearly understand the above objects, features, and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0086] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention in this specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0087] The present invention provides a modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method. As Figure 1 shown, the specific steps of this method are as follows:

[0088] ​S11: Construct a box model for initializing the generation of perfect cubes. According to the material parameters of the nano-gradient crystal material set by the user, including gradient mode (a:b:c), gradient direction (x or y or z), small grain size (D1), number of grain layers (L1, L2, L3), number of small grains in the non-gradient direction (N1, N2), element information and other parameters, obtain the center coordinates of each perfect cube grain;

[0089] S12: Calculate the size of the model box according to the gradient mode, grain size, and number of grain layers. The calculation method is as follows:

[0090] Boundary in the gradient direction:

[0091]

[0092] Boundary in the non-gradient direction:

[0093]

[0094] S13: Perform mesh division on the model box according to the gradient mode;

[0095] S14: Obtain the boundary coordinates of each perfect cube grain according to the model box after mesh division.

[0096] Furthermore, in step S2, obtain the node list of the perfect cube grains, which specifically includes the following steps:

[0097] S21: Calculate the boundary coordinate list of each perfect cube grain according to the gradient direction, grain size, and number of grain layers. The calculation method is as follows:

[0098] In the gradient direction:

[0099] [0, D1, 2D1, …, L1D1, L1D1 + D2, L1D1 + 2D2, …, L1D1 + L2D2, L1D1 + L2D2 + D3, L1D1 + L2D2 + 2D3, …, L1D1 + L2D2 + L3D3]#(3)

[0100] In the non-gradient direction:

[0101] Small grains:

[0102]

[0103] Medium grains:

[0104]

[0105] Large grains:

[0106]

[0107] Among them

[0108] S22: To ensure that the periodic boundary is not destroyed, outside the perfect grains generated within the size of the simulation box, inverse gradient nodes with the opposite gradient to the current model are set, and the calculation method is as follows:

[0109] In the gradient direction, based on the list (3), add:

[0110] [L1D1 + L2D2 + (L3 + 1)D3,..., L1D1 + L2D2 + 2L3D3, L1D1 + (L2 + 1)D2 + 2L3D3,..., L1D1 + 2L2D2 + 2L3D3, (L1 + 1)D1 + 2L2D2 + 2L3D3,..., 2L1D1 + 2L2D2 + 2L3D3] #(7)

[0111] In the non - gradient direction, the boundary coordinates of each perfect cubic grain remain unchanged;

[0112] S23: According to the boundary coordinates of each perfect cubic grain, calculate the central node coordinates of each perfect cubic grain. Combine the list (3) and (7), and perform the following transformation on all elements in the lists (3) - (6) and the combined list:

[0113] For a list A[a0, a1,..., a n , generate a new list B[b1, b2,..., b n , where

[0114] In the gradient direction:

[0115]

[0116] In the non - gradient direction:

[0117] Small grains:

[0118]

[0119] Medium grains:

[0120]

[0121] Large grains:

[0122]

[0123] Among them

[0124] S24: Classify the one-dimensional coordinates of the central nodes of the perfect cubic grains in the gradient direction according to the grain size. The first L1 items of list (8) and the last L1 items are the central nodes of the perfect cubic small grains in the gradient direction. The items from the (L1 + L2 + 1)-th to the (L1 + L2 + 2L3)-th are the central nodes of the perfect cubic large grains in the gradient direction. The remaining items of list (8) are the central nodes of the perfect cubic medium-sized grains in the gradient direction;

[0125] S25: Obtain the two-dimensional coordinates (n1, n2) of grains of various sizes in the non-gradient direction. The generation method is as follows:

[0126] For list groups (9) to (11), make all elements of list Direction1 and all elements of list Direction2 match once to generate a series of two-dimensional coordinates.

[0127] Among them, list group (9) should generate N1N2 two-dimensional coordinates, list group (10) should generate two-dimensional coordinates, and list group (11) should generate two-dimensional coordinates;

[0128] S26: Combine the one-dimensional coordinate (g) in the gradient direction and the two-dimensional coordinates (n1, n2) of grains of various sizes in the non-gradient direction to obtain the three-dimensional coordinates (x, y, z) of the central nodes of the perfect cubic grains. The occupancy rules are as follows:

[0129] If the gradient direction is the X direction:

[0130] The one-dimensional coordinate (g) occupies the x position, and the two-dimensional coordinates (n1, n2) occupy the (y, z) positions;

[0131] If the gradient direction is the Y direction:

[0132] The one-dimensional coordinate (g) occupies the y position, and the two-dimensional coordinates (n1, n2) occupy the (x, z) positions;

[0133] If the gradient direction is the Z direction:

[0134] The one-dimensional coordinate (g) occupies the z position, and the two-dimensional coordinates (n1, n2) occupy the (x, y) positions.

[0135] Furthermore, in step S3, construct a list of central nodes of gradient crystal grains, which specifically includes the following steps:

[0136] S31: Generate a list of random numbers rand in the range of (-1, 1), and the number of its elements should be equal to the number of the three-dimensional coordinates (x, y, z) of the central nodes of the perfect cubic grains obtained in S25;

[0137] S32: Calculate the new node (x′, y′, z′), and the calculation method is as follows:

[0138] (x′, y′, z′) = (x + D × rand(i), y + D × rand(i), z + D × rand(i)) #(12)

[0139] where D is the grain size, for small grains D = D1, for medium grains for large grains

[0140] S33: Check whether all new nodes are within the current virtual simulation box, and the detection criteria are as follows:

[0141] If the gradient direction is the X direction:

[0142]

[0143] If the gradient direction is the Y direction:

[0144]

[0145] If the gradient direction is the Z direction:

[0146]

[0147] S34: If the detection in S33 fails, then repeat steps S31 - S33 until the detection in S33 passes.

[0148] Furthermore, in step S4, to construct the model of the gradient crystal material, the specific steps are as follows:

[0149] S41: Set the element information of the nano - gradient crystal material, and input the element information, the new node coordinates obtained in S3, and the size of the simulation box into the external software ATOMSK for modeling;

[0150] S42: Input the packaging instruction into the external software ATOMSK to remove the atoms outside the model, then input the cutting model instruction to keep only the length of l gradient in the gradient direction, and then output the model as a file.

[0151] Example 1:

[0152] Initialize the model: Enter the interface as shown in Figure 2 Set the gradient mode to 1∶2∶4, the gradient direction to the Y direction, the small grain size to the number of small - grain layers to 4, the number of medium - grain layers to 2, the number of large - grain layers to 1, the number of small grains in the X direction to 4, and the number of small grains in the Z direction to 4.

[0153] The dimensions of the model box are calculated as (160, 480, 160) using formulas (1) and (2).

[0154] Next, a list of boundary coordinates for each perfect cubic grain is calculated according to formulas (3)-(6). In the Y direction of the gradient, the boundary coordinates are [0, 40, 80, 120, 160, 240, 320, 480]; in the X direction of the non-gradient, the boundary coordinates are [0, 40, 80, 120, 160]; in the Z direction of the non-gradient, the boundary coordinates are [0, 40, 80, 120, 160].

[0155] After adding inverse gradient nodes, the size of the simulation box is updated to (160, 960, 160); the boundary coordinates in the Y direction are updated to [0, 40, 80, 120, 160, 240, 320, 640, 720, 800, 840, 880, 920, 960].

[0156] A list of central node coordinates for each perfect cubic grain is calculated according to formulas (8)-(11). In the Y direction of the gradient, the central node coordinates are [20, 60, 100, 140, 180, 280, 400, 560, 680, 760, 820, 860, 900, 940]; in the X direction of the non-gradient, the boundary coordinates are [20, 60, 100, 140]; in the Z direction of the non-gradient, the boundary coordinates are [20, 60, 100, 140].

[0157] A total of 114 perfect grain nodes are generated according to the method in step S25. The perturbation index is set to 0.45, and new node coordinates are obtained according to formula (12).

[0158] The simulation box size information, element information, and new node coordinates are passed into the ATOMSK software for modeling, and a cutting command is passed in to save the required atoms and output files.

[0159] The output model file is read using an external software OVITO, and the output results are as Figure 3 shown. Different grains are marked with different colors. It can be clearly seen that the grain size of the crystal gradually increases from left to right and meets the requirements of the periodic atomic boundary. This proves that the method can achieve the expected effect.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A modeling method for controllable nano-gradient polycrystalline materials based on the Voronoi tessellation method, characterized in that, The method includes the following steps: S1: Construct a box model for initializing the generation of perfect cubes, and obtain the central coordinates of each perfect cube grain; S2: Extract the central coordinates of the perfect cube grains, and divide them into one-dimensional coordinates in the gradient direction and two-dimensional coordinates of grains of various sizes in the non-gradient direction. Combine them according to the set number of grain layers and the number of grains to obtain a node list of perfect cube grains; S3: Extract the node list of the perfect cube grains and apply random perturbations to obtain new node coordinates, and compare the new node coordinates with the model box boundaries one by one to ensure that the nodes are all within the model box; S4: Extract the model box size information and element information obtained in step S1, extract the new node list obtained in step S3, and input them into the ATOMSK software for polycrystal model establishment. After correcting the atomic periodicity, retain all atoms within the size of the simulation box to obtain a model file.

2. The modeling method of a controllable nano-gradient polycrystalline material based on the Voronoi tessellation method according to claim 1, characterized in that, In step S1, the construction of the box model for initializing the generation of perfect cubes specifically includes the following steps: S11: Set the material parameters of the nano-gradient crystal material, including the gradient mode a:b:c, the gradient direction x or y or z, the small grain size D1, the number of grain layers L1, L2, L3, the number of small grains N1, N2 in the non-gradient direction, and the element information; S12: Calculate the size of the model box according to the gradient mode, the small grain size, and the number of grain layers. The calculation method is as follows: Boundary in the gradient direction: Boundary in the non-gradient direction: S13: Perform mesh division on the model box according to the gradient mode; S14: Obtain the boundary coordinates of each perfect cube grain according to the model box after mesh division.

3. The modeling method of the controllable nano-gradient polycrystalline material according to claim 2, wherein In step S2, obtaining the node list of perfect cube grains specifically includes the following steps: S21: Calculate the boundary coordinate list of each perfect cube grain according to the gradient direction, grain size, and number of grain layers. The calculation method is as follows: In the gradient direction: [0, D1, 2D1, …, L1D1, L1D1+D2, L1D1+2D2, …, L1D1+L2D2, L1D1+L2D2+D3, L1D1+L2D2+2D3, …, L1D1+L2D2+L3D3] (3) In the non-gradient direction: Small grains: Medium grains: Large grains: Among them in the list, there are small grain size D1, medium grain size D2, and large grain size D3; the numbers of small grains in the other two non-gradient directions are N1 and N2 respectively; S22: To ensure that the periodic boundary is not damaged, set inverse gradient nodes with the opposite gradient to the current model outside the perfect grains generated within the size of the simulation box. The calculation method is as follows: In the gradient direction, based on the list (3), add: [L1D1+L2D2+(L3+1)D3, …, L1D1+L2D2+2L3D3, L1D1+(L2+1)D2+2L3D3, …, L1D1+2L2D2+2L3D3, (L1+1)D1+2L2D2+2L3D3, …, 2L1D1+2L2D2+2L3D3] (7) In the non-gradient direction, the boundary coordinates of each perfect cube grain remain unchanged; S23: Calculate the central node coordinates of each perfect cubic grain according to the boundary coordinates of each perfect cubic grain; Combine list (3) and (7), and perform the following transformation on all elements in lists (3) to (6) and the combined list: In the gradient direction: In the non-gradient direction: Small grain: Medium grain: Large grain: Among them S24: Classify the one-dimensional coordinates of the central nodes of the perfect cubic grains in the gradient direction according to the grain size. The classified list is as follows: The central nodes of the perfect cubic small grains in the gradient direction are the first L1 items and the last L1 items of list (8), respectively: The central nodes of the perfect cubic large grains in the gradient direction are the (L1 + L2 + 1)-th item to the (L1 + L2 + 2L3)-th item of list (8), which are: The remaining items in list (8) are the central nodes of the perfect cubic medium grains in the gradient direction; S25: Obtain the two-dimensional coordinates (n1, n2) of grains of various sizes in the non-gradient direction. The generation method is: For list groups (9) to (11), make all elements in list Direction 1 and all elements in list Direction 2 match once to generate a series of two-dimensional coordinates; Among them, the list group (9) should generate N1N2 two-dimensional coordinates, and the list group (10) should generate two-dimensional coordinates, and the list group (11) should generate two-dimensional coordinates; S26: Combine the one-dimensional coordinates (g) in the gradient direction and the two-dimensional coordinates (n1, n2) of grains of various sizes in the non-gradient direction to obtain the three-dimensional coordinates (x, y, z) of the central nodes of the perfect cubic grains. The occupancy rules are as follows: If the gradient direction is the X direction: The one-dimensional coordinate (g) occupies the x position, and the two-dimensional coordinate (n1, n2) occupies the (y, z) positions; If the gradient direction is the Y direction: The one-dimensional coordinate (g) occupies the y position, and the two-dimensional coordinate (n1, n2) occupies the (x, z) positions; If the gradient direction is the Z direction: The one-dimensional coordinate (g) occupies the z position, and the two-dimensional coordinate (n1, n2) occupies the (x, y) positions.

4. The modeling method of the controllable nano-gradient polycrystalline material according to claim 3, characterized in that In step S3, construct a list of central nodes of gradient crystal grains, which specifically includes the following steps: S31: Generate a list of random numbers rand of (-1, 1), and the number of its elements is equal to the number of three-dimensional coordinates (x, y, z) of the central nodes of the perfect cubic grains obtained in step S25; S32: Calculate the new node (x′, y′, z′), and the calculation method is: (x′, y′, z′) = (x + D × rand(i), y + D × rand(i), z + D × rand(i)) (12) where D is the grain size, with small grains D = D1, medium grains large grains S33: Check whether all new nodes are within the current virtual simulation box. The detection criteria are as follows: If the gradient direction is the X direction: If the gradient direction is the Y direction: If the gradient direction is the Z direction: S34: If the detection in step S33 fails, repeat steps S31 - S33 until the detection in step S33 passes.

5. The modeling method of the controllable nano-gradient polycrystalline material according to claim 1, wherein In step S4, construct a model of the gradient crystal material, which specifically includes the following steps: S41: Set the element information of the nano-gradient crystal material, and input the element information, the new node coordinates obtained in S3, and the size of the simulation box into the external software ATOMSK for modeling; S42: Pass the packaging instruction to the external software ATOMSK to remove the atoms outside the model, then pass the cutting model instruction, and only retain the length of l in the gradient direction. Then output the model as a file. gradient Next, output the model as a file.

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