A method for generating three-dimensional representative grain structure models based on EBSD data

Abstract

The present invention provides a method for generating a three-dimensional representative grain structure model based on EBSD data, which can realize the modeling of the 3D grain structure of polycrystalline dual-phase titanium alloys based on EBSD statistical information, and achieve further refined control of the shape of the grains. The present invention uses an ellipsoid structure that can take into account the aspect ratio of the grains instead of a sphere, innovatively realizing the use of two-dimensional EBSD statistical data information for the establishment of a near-real three-dimensional grain structure model, and on this basis, realizes the control of grain shape, successfully providing a three-dimensional model of two-phase grains with both microstructural feature statistical laws and orientation information statistical law characteristics for the subsequent simulation of the evolution process of the mechanical behavior of titanium alloy mesoscopic dual-phase grain structure under complex loads, and providing technical support for the subsequent more accurate simulation of the mechanical response process of complex polycrystalline dual-phase titanium alloys.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation, and in particular to a method for generating a three-dimensional representative grain structure model based on EBSD data. Background Art

[0002] The Crystal Plasticity Finite Element Method (CPFEM) is a computational method for simulating the microscopic behavior of materials. It combines the finite element method with crystal plasticity theory. Using CPFEM, we can study the influence of a material's microstructure on its macroscopic mechanical properties, as well as microscopic phenomena such as plastic deformation and texture evolution. It has widespread applications in materials science and engineering, particularly in studying the mechanical properties and deformation behavior of crystalline materials such as metals and alloys.

[0003] Establishing a 3D mesostructure model that is consistent with the alloy material's mesostructure morphology, size, proportions, and other characteristics is the primary condition for conducting finite element simulation studies of crystal plasticity. For the grain-scale mesostructure model of α+β duplex titanium alloy, it can be divided into 2D, 2.5D, and 3D models based on the subsequent finite element simulation unit type and the number of units along the thickness direction. Among them, the 2D model is only applicable to plane stress, plane strain, or axisymmetric algorithms, and cannot reflect the true morphological characteristics of the alloy microstructure in three-dimensional space, which greatly affects the reliability of the calculation results. Therefore, it is particularly important to obtain 3D grain structure for finite element mechanical behavior simulation of crystal plasticity under different load conditions.

[0004] With the development of synchrotron radiation sources and X-ray imaging and diffraction technology, X-ray microscopic 3D tomography technology, which is non-destructive, efficient, and high-resolution, has been applied to 3D microstructure modeling. However, the resolution capability achievable by synchrotron radiation in the above methods is very limited, usually at the μm level, and synchrotron radiation equipment is not easy to obtain, making it difficult to be widely used. In addition, the automatic continuous section FIB-EBSD imaging technology that has been successfully applied to 3D microstructure modeling also has the problem of being difficult to achieve widespread application due to the extremely high human and material costs of conducting experiments. In addition, many scholars have constructed two-dimensional and three-dimensional virtual equiaxed VORONOI polycrystalline models based on the statistical laws of grain shape for crystal plasticity finite element simulation. The virtual polycrystalline model method has high modeling efficiency and low cost, and has become one of the main methods for obtaining mesostructure models of crystal structures. However, the current polycrystalline model based on virtual equiaxed VORONOI simplifies the grains into spheres, which makes it difficult to reflect the elongation / compression effects and spatial orientation of the grains in the actual preparation process of polycrystalline materials. In addition, the current research on virtual polycrystalline modeling mainly focuses on single-phase materials, and the generation of mesoscopic organizational models of multiphase alloys has not been effectively considered. In addition, the VORONOI multi-deformation approximate grain modeling method will cause severe mesh distortion and is not suitable for extremely complex load conditions (such as high-speed impact conditions). Summary of the Invention

[0005] In view of this, the present invention provides a method for generating a three-dimensional representative grain structure model based on EBSD data, which can realize modeling of the 3D grain structure of polycrystalline duplex titanium alloy based on EBSD statistical information and achieve further fine control of the shape of the grains.

[0006] To achieve the above purpose, the technical solution of the present invention is as follows:

[0007] A method for generating a three-dimensional representative grain structure model based on EBSD data comprises: determining and generating three-dimensional grain quantitative feature information based on EBSD image statistical grain feature information; spatially clustering the quantitative feature information based on a clustering concept to generate an α-phase grain model, wherein a three-dimensional grid model for distributing statistical grains is established, and statistical information of the α-phase grains is collected for mean clustering distribution with characteristic distance information; and spatially clustering the quantitative feature information based on a clustering concept to generate a β-phase grain model, wherein the longest axis of each grain is counted based on the α grains generated after clustering, and the longest axis is scaled by a coefficient less than 1, and then redistributed at the original cluster center to achieve the generation of the β phase at the edge position of the grain.

[0008] Wherein, the mean cluster allocation includes:

[0009] The Euclidean distance of the mean clustering algorithm is replaced by the ellipsoid distance formula with characteristic distance information, and the azimuth angle of the ellipsoid's deflection is controlled by the rotation matrix. The shape of the grain is approximately defined by the size factor, the three-axis ratio and the spatial Euler angle.

[0010] Among them, when the quantitative feature information is clustered in space based on the clustering idea to generate the β-phase grain model, the grain segmentation is realized in the β-phase space again through mean clustering with characteristic distance according to the statistical information of the β-phase grains.

[0011] Among them, the generation is controlled by the three-axis ratio and the spatial Euler angle, and the deformation of the grain along the characteristic direction is finally achieved.

[0012] The specific method of generating three-dimensional grain quantitative feature information based on EBSD image statistical grain feature information is as follows:

[0013] The CTF format file is obtained through EBSD testing to obtain the surface density Sd, equivalent circle radius distribution Rd, dual-phase ratio Bp and dual-phase Euler angle distribution Ad of different phase grains, thereby obtaining spatial three-dimensional feature information: volume density Spatial sphere radius distribution refers to Rd distribution, two-phase proportion The three-dimensional grain Euler angle orientation follows the Ad distribution.

[0014] Beneficial effects:

[0015] 1. The method of the present invention for generating a three-dimensional representative grain structure model based on EBSD data adopts an ellipsoid structure that can take into account the aspect ratio of the grains instead of a sphere, innovatively realizing the establishment of a near-real three-dimensional grain structure model through the use of two-dimensional EBSD statistical data information, and on this basis realizing the control of grain shape, successfully providing a three-dimensional model of two-phase grains with both the statistical laws of microstructural characteristics and the statistical laws of orientation information for the subsequent simulation of the evolution process of the mechanical behavior of the mesoscopic two-phase grain structure of titanium alloys under complex loads, and providing technical support for the subsequent more accurate simulation of the mechanical response process of complex polycrystalline two-phase titanium alloys.

[0016] 2. In the preferred embodiment of the present invention, the generation of β-phase grains at the edge of α-grains in the equiaxed structure of titanium alloy is achieved, which is more consistent with the actual equiaxed microstructure morphology and provides a model support for subsequent research on the mechanical evolution process of titanium alloy microstructure under different loads.

[0017] 3. In a preferred embodiment of the present invention, in order to achieve the effect of overall grain growth along a characteristic orientation, the three-axis ratio of α-phase grains and β-phase grains can be set to 3:1:1, and the grain orientation can be controlled by Euler angles to obtain the final model. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1This is a schematic diagram of the overall implementation process of the present invention;

[0019] Figure 2 This is a schematic diagram of the effect of the α-phase primary distribution grain model in an embodiment of the present invention;

[0020] Figure 3 Schematic diagram of a three-dimensional model considering the spatial distribution of the β phase in an embodiment of the present invention;

[0021] Figure 4 This is a schematic diagram of a three-dimensional representative grain model finally generated in an embodiment of the present invention;

[0022] Figure 5 Schematic diagram of a three-dimensional representative grain model with characteristic orientation in an embodiment of the present invention. DETAILED DESCRIPTION

[0023] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0024] In response to the existing problems, the present invention proposes a method for generating a three-dimensional representative grain structure model based on EBSD data, and establishes a new idea of establishing a real three-dimensional representative volume element, which overcomes the problem that the traditional Voronoi grain-based method cannot achieve more precise control of grain morphology and orientation. The method of the present invention includes three parts: statistical grain feature information based on EBSD images, and determining the generation of three-dimensional grain quantitative feature information; clustering the quantitative feature information in space based on the clustering idea to generate an α-phase grain model, and clustering the quantitative feature information in space based on the clustering idea to generate a β-phase grain model. The overall process of the present invention is as follows: Figure 1 The specific steps are as follows:

[0025] Step 1: Count the grain feature information based on a two-dimensional EBSD image and generate three-dimensional grain representative volume element feature information, i.e., quantitative feature information. The specific method is as follows:

[0026] EBSD testing was performed on the 3D reconstructed microstructure. A CTF (Channel text file) format file was obtained through EBSD testing. Quantitative analysis using Channel5 software yielded 2D quantitative information, including the surface density Sd of grains of different phases, the equivalent circle radius distribution Rd, the dual-phase ratio Bp, and the dual-phase Euler angle distribution Ad.

[0027] Based on the acquired two-dimensional quantitative information, the spatial three-dimensional feature information rules are determined as follows:

[0028] ① Determine the number of grains distributed in three-dimensional space (volume density):

[0029] ② Shape parameters of spatial grains. In the present invention, the grains are first approximated by spheres, and the radius distribution of the spatial spheres refers to the Rd distribution;

[0030] ③ According to the two-dimensional grain Euler angle orientation distribution Ad, it is assigned to the three-dimensional grains in space according to statistical probability;

[0031] ④The spatial dual-phase ratio is approximately

[0032] In this embodiment, the CTF file obtained by the test is imported into channel5 and denoised to output information such as the phase type, grain number, equivalent circle radius distribution, and crystal orientation distribution of the grains in the field of view. The number of two-phase grains obtained by EBSD statistics is as follows: 271 representative α grains (smaller α grains are eliminated), 549 representative β grains, and the two-dimensional field of view size is 200×200μm. The approximate α grain density in the three-dimensional space is 1000 / μm 3 , while the volume density of β grains is 0.00856778 / μm 3 The proportion of the two phases is: the α phase accounts for 94%, and the volume proportion of the α phase is 91.14%.

[0033] Step 2: Based on the clustering idea, the quantitative feature information is clustered in space to generate an α-phase grain model, which includes the following steps:

[0034] Establish a three-dimensional space for allocating statistical grains. Use the LS-PrePost software to set the grid size to obtain a regular pure hexahedral grid model. Divide the three-dimensional space of a specified size into hexahedral units, and obtain the unit centroid coordinates e(x, y, z) corresponding to each unit.

[0035] The centroids are clustered and assigned to establish three-dimensional grains. The number of clusters is confirmed by the volume density. The clustering algorithm adopted in the present invention is a variant of the mean clustering idea, that is, the Euclidean distance of the mean clustering algorithm is replaced by the ellipsoid distance formula with characteristic distance information, and the azimuth angle of the deflection of the ellipsoid can be controlled by the rotation matrix. The shape of the grain can be approximately defined by the size factor, the three-axis ratio and the spatial Euler angle. In the present invention, the grain is first approximated by a sphere, that is, the three-axis ratio is set to 1:1:1, the spatial Euler angle is (0,0,0), and the size factor gives an equivalent circle radius distribution;

[0036] The centroid positions e(x, y, z) of the hexahedral units in the grid space are spatially clustered with characteristic distance information. The number of clusters is the number of grains N, and the initial cluster center position is n(x, y, z). The distributed grain seeds are randomly perturbed cyclically through the clustering algorithm to finally achieve three-dimensional grain generation. That is, global optimization is achieved to classify all units with the smallest characteristic distance from the random grain seed clustering into the same grain, and a three-dimensional α-phase grain structure model is obtained.

[0037] In this implementation, considering the effect and generation efficiency of the final generated model, a size of 60×60×60μm is adopted, and the grid unit size is set to 1.5μm. Then the total number of grid units is 216,000. According to the density of the two-phase grain body, the number of α-phase grains is 42, and the number of β-phase grains is 340. First, a grid of 60×60×60 is established in lsprepost for the subsequent allocation of statistical grains; then the α phase is initially allocated, that is, 42 grains and their characteristic information are sampled probabilistically from 271 α grains in the two-dimensional statistical EBSD data, and the equivalent circle radius distribution of the 42 α grains is allocated to the size factor. In addition, considering that the actual grains are non-uniformly equiaxed, the three-axis ratio is set to fluctuate randomly within the range of 1:1:1 to simulate the local ellipsoidization effect. At the same time, since the deformation of the grains is not considered, the spatial Euler angle is temporarily set to (0,0,0). Then cluster allocation is performed, and the grain shape tends to be stable when the number of iteration steps is 20, as shown in the following example. Figure 2 shown.

[0038] Step 3: Based on the clustering idea, the quantitative feature information is clustered in space to generate a β-phase grain model, which includes the following steps:

[0039] In actual situations, the β phase of the equiaxed structure of titanium alloy is often distributed at the edge of the α grains in the microstructure. Based on the α grains generated after clustering, the longest axis of each grain is statistically distributed. After setting a coefficient less than 1 to scale the longest axis, and redistributing it at the original cluster center, the β phase at the edge of the grain can be generated. The determination of the scaling coefficient must match the experimental statistical β phase space ratio. The β phase space ratio generated after scaling must be close to the experiment, such as Figure 3 shown.

[0040] The grain information corresponding to β is input, and the grain segmentation is achieved in the β phase space again through mean clustering with characteristic distance.

[0041] Furthermore, it is necessary to assign crystal orientations to the generated dual-phase grains according to statistical orientation probabilities so as to ultimately generate a three-dimensional representative grain structure model.

[0042] To achieve grain deformation along the characteristic direction, the grain can be equivalent to an ellipsoid. That is, the three-axis ratio is set to other ratios while the Euler angle is set to a specified direction. Repeat steps 1 to 3 to achieve grain deformation.

[0043] In this embodiment, 347 grains and their characteristic information are sampled from 549 β-phase grains by probability, and the equivalent circle radius distribution of the 347 β-phase grains is assigned to the size factor. At the same time, the three-axis ratio is set to 1:1:1 and the spatial Euler angle is (0,0,0). The three-dimensional representative grains finally generated are as follows: Figure 4To achieve the effect of overall grain growth along a characteristic orientation, this embodiment simultaneously sets the triaxial ratio of α-phase grains and β-phase grains to 3:1:1, and the grain orientation can be controlled by Euler angles. The final model is as follows Figure 5 shown.

[0044] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for generating a three-dimensional representative grain structure model based on EBSD data, characterized in that: Step 1: Count the grain feature information based on the two-dimensional EBSD image and generate three-dimensional grain quantitative feature information. The specific method is as follows: EBSD testing was performed on the 3D reconstructed microstructure. CTF format files were obtained through EBSD testing. Quantitative analysis using Channel5 software was used to obtain 2D quantitative information, including the surface density Sd of different phase grains, the equivalent circle radius distribution Rd, the dual-phase ratio Bp, and the dual-phase Euler angle distribution Ad. Based on the acquired two-dimensional quantitative information, the spatial three-dimensional feature information rules are determined as follows: ① Determine the number of grains distributed in three-dimensional space, i.e., volume density: ② Shape parameters of spatial grains: the grains are first approximated by spheres, and the radius distribution of spatial spheres refers to the Rd distribution; ③ According to the Euler angle distribution Ad of the two-dimensional grain phase, it is assigned to the three-dimensional grains in space according to statistical probability; ④The proportion of spatial dual phase is Step 2: Based on the clustering idea, the quantitative feature information is clustered in space to generate an α-phase grain model, which includes the following steps: Establish a three-dimensional space for allocating statistical grains. Use the LS-PrePost software to set the grid size to obtain a regular pure hexahedral grid model. Divide the three-dimensional space of a specified size into hexahedral units, and obtain the unit centroid coordinates e(x, y, z) corresponding to each unit. The centroids are clustered and assigned to establish three-dimensional grains. The number of clusters is determined by the volume density. The ellipsoid distance formula with characteristic distance information is used, and the azimuth of the ellipsoid's deflection can be controlled by the rotation matrix. The shape of the grain can be approximately defined by the size factor, the three-axis ratio, and the spatial Euler angle. The grain is first approximated by a sphere, that is, the three-axis ratio is set to 1:1:1, the spatial Euler angle is (0,0,0), and the size factor is assigned to the equivalent circle radius distribution. The centroid coordinates e(x, y, z) of the cells in the grid space are spatially clustered with characteristic distance information. The number of clusters is the number of grains N, and the initial cluster center position is n(x, y, z). The distributed grain seeds are randomly perturbed through the clustering algorithm cycle to ultimately achieve three-dimensional grain generation. That is, global optimization is performed to achieve that all cells with the smallest characteristic distance from the random grain seed cluster are grouped into the same grain, thus obtaining a three-dimensional α-phase grain structure model. Step 3: Based on the clustering idea, the quantitative feature information is clustered in space to generate a β-phase grain model, which includes the following steps: Based on the α grains generated after clustering, the longest axis of each grain after statistical distribution is scaled by a coefficient less than 1, and then redistributed at the original cluster center to achieve the generation of β phase at the edge of the grain. The determination of the scaling coefficient must match the experimental statistical β phase space ratio. Input the grain information corresponding to β, and again implement grain segmentation in the β phase space through mean clustering with characteristic distance; The generated dual-phase grains are assigned crystal orientations according to statistical orientation probabilities, thereby ultimately generating a three-dimensional representative grain structure model.

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