A high-resolution reconstruction method for modeling of lamellar microstructure

Abstract

The application provides a high-resolution reconstruction method for sheet microstructure modeling, and relates to the technical field of metal structure reconstruction. The application obtains sheet thickness and average grain size by performing morphology and EBSD characterization on a metal material, compiles a microstructure reconstruction program based on a space segmentation algorithm and a sheet division algorithm, and establishes a microstructure reconstruction model; the three-dimensional reconstruction model closest to the real microstructure is obtained by adjusting the control parameters in the reconstruction program, namely sheet orientation, grain distribution and iteration number; the application can quickly and accurately reconstruct the sheet microstructure, and the generated microstructure model has high compatibility and can be transplanted to various finite element software for simulation analysis.

Description

Technical Field

[0001] This invention relates to the field of metal structure reconstruction technology, and in particular to a high-resolution reconstruction method for modeling layered microstructures. Background Technology

[0002] Efficient microstructure design can further meet the requirements of lightweighting while maintaining high strength and excellent ductility. Among these, layered microstructures can effectively balance the strength and ductility of materials; however, their complex geometry makes 3D reconstruction and computer simulation difficult, which has become a major challenge in the rapid development of new lightweight, high-strength metallic materials. Developing a high-resolution reconstruction method for modeling layered microstructures is of great significance for the lightweight design of metallic materials.

[0003] Lamellar microstructures are particularly common in steel, mainly consisting of pearlite, martensite, and twins. Due to their varying thickness and random orientation within the material matrix, reconstructing their three-dimensional models is quite complex. Two-dimensional models are often used to reconstruct the microstructure of metallic materials, such as a scheme that utilizes EBSD data in conjunction with Dream.3D software to generate the microstructure. Patent CN113987695A, "A Crystal Plasticity Finite Element Modeling and Simulation Method," uses EBSD data of the material as a basis, obtains a two-dimensional reconstruction model of the material's microstructure through information filtering in Dream.3D software, and further uses it for crystal plasticity finite element simulation. Patent CN110222442A, "A Method for Establishing a Crystal Plasticity Constitutive Model for Fatigue Processes of Face-Centered Cubic Materials," utilizes image processing technology to output a polygonal grain model, combined with constitutive equations describing fatigue, for finite element simulation. Patent CN114496122A, "A Rapid Calibration Method for Plastic Constitutive Parameters of Polycrystalline Crystals," reconstructs a three-dimensional model of the microstructure based on voxel cubic and Voronoi space partitioning algorithms. Combined with an automated parameter calibration method, it improves the efficiency of finite element simulation of crystal plasticity.

[0004] Both patents CN113987695A, "A Finite Element Modeling and Simulation Method for Crystal Plasticity," and CN110222442A, "A Method for Establishing a Crystal Plastic Constitutive Model for Fatigue Process of Face-Centered Cubic Materials," employ two-dimensional reconstruction models for finite element simulation. However, two-dimensional models inherently introduce plane strain assumptions, which inevitably ignore the material's true mechanical response, leading to inaccurate simulation results. Patent CN114496122A, "A Rapid Calibration Method for Plastic Constitutive Parameters of Polycrystalline Crystals," uses voxel cubic and Voronoi space partitioning algorithms to reconstruct three-dimensional models, improving the accuracy of finite element simulation. However, voxel cubic reconstruction models cannot reproduce the fine structure of microstructures, and the polyhedra partitioned by the traditional Voronoi algorithm cannot perfectly follow grain growth laws, still failing to reconstruct microstructures with high resolution. Furthermore, the three patents mentioned above primarily focus on grain-scale microstructure reconstruction, with limited coverage of three-dimensional reconstruction of sub-grain-scale lamellar microstructures. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a high-resolution reconstruction method for modeling layered microstructures. This method can fully preserve the microscopic characteristics of layered structures while enabling rapid and accurate geometric model reconstruction, significantly improving the reliability of finite element simulations.

[0006] A high-resolution reconstruction method for modeling layered microstructures specifically includes the following steps:

[0007] Step 1: Characterize the morphology of the metallic material using EBSD to obtain its lamellar thickness and average grain size;

[0008] Step 2: Design a spatial segmentation algorithm with volume-weighted partitioning for grain-scale microstructure reconstruction;

[0009] The spatial partitioning algorithm is shown in Formula 1:

[0010]

[0011] Let space R 3 There are n spheres C on top n The resulting set is S = {C1(P1, r1), C2(P2, r2), C3(P3, r3), ..., C}. n (P n r n )}, center of the ball P i =(p ix p iy p iz ), p ix p iy p izLet r be the coordinates of the center of the i-th ball on the x, y, and z axes, respectively. i Let C be the radius of the i-th sphere. Therefore, the spatial region defined by the governing equations is C. i The weighted regions, and these n regions divide the space into a set of convex polyhedra; where Its geometric meaning is that point Q and sphere C i The square of the distance between the lines connecting the points of tangency;

[0012] Step 3: Design a lamellae partitioning algorithm to achieve lamellae partitioning of each convex polyhedron in space for subgrain-scale microstructure reconstruction. Specifically, after obtaining the minimum bounding box of the convex polyhedron through the lamellae partitioning algorithm, a face of the bounding box is randomly selected for two-dimensional lamellae partitioning. The lamellae partitioning of the convex polyhedron is achieved through three-dimensional stretching and Boolean operations.

[0013] The equations for solving the minimum bounding box are shown in formulas (2)-(6):

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Where the superscript k represents the k-th triangle and the subscript i represents the i-th component, assuming the convex polyhedron M is composed of n triangles, then Δp k q k r k The area is denoted as A. k , 0 < k < n; the total area of ​​the convex polyhedron M is denoted as A. M The centroid of triangle k is denoted as m. k The centroid-weighted average of a convex polyhedron M is denoted as m. M C i，j The covariance matrix is ​​derived from the population mean function. The eigenvectors of the covariance matrix are the direction vectors of the minimum bounding box, and the normalized direction vectors are denoted as v. i i, j = 0, 1, 2; C is the center of the bounding box; project the points on the convex polyhedron M onto the direction vector v. i Above, obtain the longest edge of the bounding box along its three axes. and the shortest side And record It is half the length of the bounding box.

[0020] The two-dimensional layer division is shown in formula (7):

[0021] V(p i )={p|d(p,p i )<d(p,p j ), i≠j, i, j=1, 2,…n} (7)

[0022] Where S = {p1, p2, p3, ..., p...} n Let} be a set of points on a two-dimensional plane, and d(p) i p j Let p be a point. i With p j Euclidean distance; V(p) i Then it means that the point p i A uniquely defined polygonal region. For each V(p) i A two-dimensional layer division is achieved by dividing a planar polygon into multiple parallel lines at equal intervals.

[0023] Step 4: Based on spatial segmentation algorithm and lamellae partitioning algorithm, write a microstructure reconstruction program and establish a microstructure reconstruction model;

[0024] The microstructure reconstruction model takes the lamellar thickness and average grain size obtained in step 1 as input parameters and outputs a three-dimensional geometric model of the microstructure.

[0025] Step 5: By adjusting the control parameters in the reconstruction program, namely the lamellar orientation, grain distribution and number of iterations, a three-dimensional reconstruction model that is closest to the real microstructure is obtained.

[0026] The definitions of the control parameters for lamellar orientation and grain distribution are shown in formulas (8)-(9):

[0027]

[0028]

[0029] in Let be the orientation angle of layer k in a defined spatial coordinate system, which is... and The mean; Let be the projection angle of layer k onto the i-axis; Let be the volume of the nth convex polyhedron as determined by formula (1); The numerical distribution is from The defined function description; σ and μ are sets respectively. The mean and standard deviation;

[0030] The iteration number control parameter is the number of iterations in the lamellar orientation and grain distribution control algorithm. Multiple iterations are performed to obtain the optimal spatial distribution morphology.

[0031] Step 6: Export the three-dimensional geometric model of the microstructure to complete the high-resolution reconstruction of the microstructure.

[0032] The beneficial effects of adopting the above technical solution are as follows:

[0033] This invention provides a high-resolution reconstruction method for modeling layered microstructures, which can quickly and accurately reconstruct layered microstructures. At the same time, the generated microstructure model has high compatibility and can be ported to various finite element software for simulation analysis. Attached Figure Description

[0034] Figure 1 This is a flowchart of the high-resolution reconstruction method in an embodiment of the present invention;

[0035] Figure 2 This is a geometric schematic diagram of the volume-weighted spatial partitioning in an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of the microstructure of the pearlitic wire in an embodiment of the present invention;

[0037] Figure (a) shows the microstructure morphology of the pearlite wire, and Figure (b) shows the grain distribution of the microstructure of the pearlite wire.

[0038] Figure 4 This is a grain model diagram from an embodiment of the present invention;

[0039] Figure (a) shows the grain model reconstructed by the traditional Voronoi partitioning algorithm, and Figure (b) shows the grain model reconstructed by the weighted volume partitioning algorithm.

[0040] Figure 5 These are diagrams illustrating the sheet microstructure reconstruction models for one and multiple iterations in embodiments of the present invention.

[0041] Figure 6 This is an image showing the impact of reconstructing the layered microstructure in an embodiment of the present invention.

[0042] Figure (a) shows the effect of different lamellar orientations on the reconstruction of lamellar microstructure, and Figure (b) shows the effect of different grain distributions on the reconstruction of lamellar microstructure.

[0043] Figure 7 The figure shows the experimental results in an embodiment of the present invention;

[0044] Figure (a) shows the pole figures and inverse pole figures of the experiment and simulation, and Figure (b) shows the Mises stress cloud diagram and stress-strain curve after the finite element simulation of crystal plasticity. Detailed Implementation

[0045] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0046] A high-resolution reconstruction method for modeling layered microstructures, such as Figure 1 As shown, the specific steps include:

[0047] Step 1: Characterize the morphology of the metallic material using EBSD. For extremely fine lamellar structures, the scan step size should be as small as possible to obtain the lamellar thickness and average grain size.

[0048] In this embodiment, for a pearlitic wire of a certain composition, a 4mm*2mm*2mm block sample was cut from the uniformly structured central area of ​​the wire rod. After sanding and argon ion polishing, the sample was characterized by morphology and EBSD using a scanning electron microscope to determine its microscopic characteristics such as lamellar thickness and average grain size. Figure 3 a and Figure 3 As shown in b.

[0049] Step 2: Design a spatial segmentation algorithm with volume-weighted partitioning for grain-scale microstructure reconstruction;

[0050] The spatial partitioning algorithm is shown in Formula 1:

[0051]

[0052] Let space R 3 There are n spheres C on top n The resulting set is S = {C1(P1, r1), C2(P2, r2), C3(P3, r3), ..., C}. n (P n r n )}, center of the ball P i =(p ix p iy p iz ), p ix p iy p iz Let r be the coordinates of the center of the i-th ball on the x, y, and z axes, respectively. i Let C be the radius of the i-th sphere. Therefore, the spatial region defined by the governing equations is C. i The weighted regions, and these n regions divide the space into a set of convex polyhedra; where Its geometric meaning is that point Q and sphere C i The square of the distance between the lines connecting the points of tangency; such as Figure 2As shown.

[0053] In this embodiment, the spatial segmentation algorithm reconstruction program is mounted on the Grasshopper platform. The average grain size obtained in step 1 is used as an input parameter and assigned to the spatial segmentation algorithm. By adjusting the grain distribution control parameters in the spatial segmentation algorithm, a microstructure model consistent with the actual grain distribution is obtained. Figure 4 a and 4b represent the grain reconstruction models obtained through traditional Voronoi partitioning and volume-weighted partitioning in this invention, respectively. Clearly, the grain reconstruction model obtained using the volume-weighted partitioning spatial segmentation algorithm better reflects the actual grain growth pattern.

[0054] Step 3: Design a lamellae partitioning algorithm to achieve lamellae partitioning of each convex polyhedron in space for subgrain-scale microstructure reconstruction. Specifically, after obtaining the minimum bounding box of the convex polyhedron through the lamellae partitioning algorithm, a face of the bounding box is randomly selected for two-dimensional lamellae partitioning. The lamellae partitioning of the convex polyhedron is achieved through three-dimensional stretching and Boolean operations.

[0055] The equations for solving the minimum bounding box are shown in formulas (2)-(6):

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Where the superscript k represents the k-th triangle and the subscript i represents the i-th component, assuming the convex polyhedron M is composed of n triangles, then Δp k q k r k The area is denoted as A. k , 0 < k < n; the total area of ​​the convex polyhedron M is denoted as A. M The centroid of triangle k is denoted as m. k The centroid-weighted average of a convex polyhedron M is denoted as m. M C i，j The covariance matrix is ​​derived from the population mean function. The eigenvectors of the covariance matrix are the direction vectors of the minimum bounding box, and the normalized direction vectors are denoted as v. i i, j = 0, 1, 2; C is the center of the bounding box; project the points on the convex polyhedron M onto the direction vector v. i Above, obtain the longest edge of the bounding box along its three axes. and the shortest side And record It is half the length of the bounding box.

[0062] The two-dimensional layer division is shown in formula (7):

[0063] V(p i )={p|d(p,p i )<d(p, pj), i≠j, i, j=1, 2,...n} (7)

[0064] Where S = {p1, p2, p3, ..., p...} n Let} be a set of points on a two-dimensional plane, and d(p) i p j Let p be a point. i With p j Euclidean distance; V(p) i Then it means that the point p i A uniquely defined polygonal region. For each V(p) i A two-dimensional layer division is achieved by dividing a planar polygon into multiple parallel lines at equal intervals.

[0065] In this embodiment, the sheet thickness obtained in step 1 is used as an input parameter in the sheet partitioning algorithm. The sheet partitioning algorithm is used to perform sheet segmentation on each convex polyhedron. The sheet microstructure reconstruction model after one iteration and multiple iterations is as follows: Figure 5 As shown, after multiple iterations, the spatial distribution of the layered microstructure becomes more uniform.

[0066] Step 4: Based on spatial segmentation and lamellae partitioning algorithms, write a microstructure reconstruction program, establish a microstructure reconstruction model, and use Python to write the microstructure reconstruction program. Then, mount the reconstruction program on the parametric modeling platform Grasshopper.

[0067] The microstructure reconstruction model takes the lamellar thickness and average grain size obtained in step 1 as input parameters, assigns them to the reconstruction program and performs iterative calculations; and outputs a three-dimensional geometric model of the microstructure.

[0068] Step 5: By adjusting the control parameters in the reconstruction program, namely the lamellar orientation, grain distribution and number of iterations, a three-dimensional reconstruction model that is closest to the real microstructure is obtained.

[0069] The definitions of the control parameters for lamellar orientation and grain distribution are shown in formulas (8)-(9):

[0070]

[0071]

[0072] in Let be the orientation angle of layer k in a defined spatial coordinate system, which is... and The mean; Let be the projection angle of layer k onto the i-axis; Let be the volume of the nth convex polyhedron as determined by formula (1); The numerical distribution is from The defined function description; σ and μ are sets respectively. The mean and standard deviation;

[0073] The iteration number control parameter is the number of iterations in the lamellar orientation and grain distribution control algorithm. Multiple iterations are performed to obtain the optimal spatial distribution morphology. Figure 6 Figures a and 6b illustrate the effects of different control parameters on the reconstruction of lamellar microstructures. By appropriately combining these three control parameters, an ideal microstructure reconstruction model can be quickly obtained.

[0074] Step 6: Export the three-dimensional geometric model of the microstructure to complete the high-resolution reconstruction of the microstructure for further finite element simulation.

[0075] In this embodiment, the 3D model of the microstructure is exported in STP or STEP format. This format is compatible with various finite element simulation software, significantly reducing the time cost of finite element simulation and shortening the project cycle. The reconstructed 3D model of the pearlite material's microstructure is imported into Abaqus simulation software for crystal plasticity finite element research. Figure 7 As shown. The pole figures obtained from experiments and simulations are consistent with the inverse pole figures. Figure 7 a), and the stress-strain curve ( Figure 7 b) The high degree of agreement indicates that the high-resolution reconstruction method for modeling layered microstructures in this invention has good effect and high reliability.

[0076] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A high-resolution reconstruction method for modeling layered microstructures, characterized in that, Includes the following steps: Step 1: Characterize the morphology of the metallic material using EBSD to obtain its lamellar thickness and average grain size; Step 2: Design a spatial segmentation algorithm with volume-weighted partitioning for grain-scale microstructure reconstruction; Step 3: Design a layer partitioning algorithm to achieve layer partitioning of each convex polyhedron in space for subgrain-scale microstructure reconstruction; Step 4: Based on spatial segmentation algorithm and lamellae partitioning algorithm, write a microstructure reconstruction program and establish a microstructure reconstruction model; Step 5: By adjusting the control parameters in the reconstruction program, namely the lamellar orientation, grain distribution and number of iterations, a three-dimensional reconstruction model that is closest to the real microstructure is obtained. Step 6: Export the three-dimensional geometric model of the microstructure to complete the high-resolution reconstruction of the microstructure.

2. The high-resolution reconstruction method for modeling layered microstructures according to claim 1, characterized in that, The spatial partitioning algorithm described in step 2 is shown in formula (1): (1)； Set space There are n spheres C on top n The set formed is center of the ball p ix p iy p iz Let x, y, and z be the coordinates of the center of the i-th ball on the x, y, and z axes, respectively. Let be the radius of the i-th sphere. Therefore, the spatial region determined by formula (1) is: The weighted regions, and these n regions divide the space into a set of convex polyhedra; where Its geometric meaning is that point Q and the sphere The square of the distance between the lines connecting the points of tangency.

3. The high-resolution reconstruction method for modeling layered microstructures according to claim 1, characterized in that, Step 3 specifically involves obtaining the minimum bounding box of the convex polyhedron through a slab partitioning algorithm, randomly selecting one face of the bounding box, performing two-dimensional slab partitioning, and then using three-dimensional stretching and Boolean operations to achieve slab partitioning of the convex polyhedron.

4. The high-resolution reconstruction method for modeling layered microstructures according to claim 3, characterized in that, The equations for solving the minimum bounding box are shown in formulas (2)-(6): (2)； (3)； (4)； (5)； (6)； where the superscript \(k\) represents the \(k\)-th triangle and the subscript \(i\) represents the \(i\)-th component. Assuming that the convex polyhedron \(M\) is composed of \(n\) triangles, then The area is denoted as , \(0 < k < n\); The total area of the convex polyhedron \(M\) is denoted as ; The centroid of triangle \(k\) is denoted as ; The weighted average of the centroids of the convex polyhedron \(M\) is denoted as ; is the covariance matrix, which is composed of the population mean function . The eigenvectors of the covariance matrix are the direction vectors of the minimum bounding box. After normalizing the direction vectors, they are denoted as , \(i,j = 0,1,2\); is the center of the bounding box; Project the points on the convex polyhedron \(M\) onto the direction vectors respectively, to obtain the longest sides and the shortest sides in the three axis directions of the bounding box, and denote as the half length of the bounding box.

5. The high-resolution reconstruction method for modeling layered microstructures according to claim 3, characterized in that, The two-dimensional layer division is shown in formula (7): (7)； in For a set of points on a two-dimensional plane, For point and Euclidean distance; This indicates that the point is... A uniquely determined polygonal region, for each Two-dimensional layering is achieved by dividing a planar polygon into multiple parallel lines at equal intervals.

6. The high-resolution reconstruction method for modeling layered microstructures according to claim 1, characterized in that, The microstructure reconstruction model described in step 4 uses the lamellar thickness and average grain size obtained in step 1 as input parameters to output a three-dimensional geometric model of the microstructure.

7. The high-resolution reconstruction method for modeling layered microstructures according to claim 1, characterized in that, The definitions of the lamellar orientation and grain distribution control parameters mentioned in step 5 are shown in formulas (8)-(9): (8)； (9)； in Let be the orientation angle of layer k in a defined spatial coordinate system, which is... , and The mean; i = x, y, z are the projection angles of layer k on the i-axis; Let n be the volume of the nth convex polyhedron; The numerical distribution is from The determined function description; and They are sets { The mean and standard deviation of |n=1,2,3,…}; The iteration number control parameter is the number of iterations in the lamellar orientation and grain distribution control algorithm. Multiple iterations are performed to obtain the optimal spatial distribution morphology.

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