Polycrystalline metal material microstructure modeling method with grain dominant orientation

Abstract

A modeling method for a microstructure of a polycrystalline metal material with crystal grain dominant orientation comprises the following steps that firstly, orientation information of all rolled crystal grains is obtained through EBSD, the orientation information is embodied in an Euler angle mode, and the format is # imgabs0 #; secondly, parameter fitting is conducted on all Euler angles # imgabs1 # through a multivariate normal distribution function, and the Euler angles # imgabs1 # are obtained; and obtaining a mean vector mu and a covariance matrix C of the fitting function. 3, according to the multivariate normal distribution function obtained through fitting, the value # imgabs2 # of the Euler angle consistent with the original grain orientation distribution condition is randomly generated, and meanwhile # imgabs3 # is guaranteed; 4, the generated Euler angle serves as the material attribute to be input into a polycrystalline metal material model, and a polycrystalline metal model with the grain orientation distribution condition the same as that of a real material can be constructed.

Description

(1) Technical field:

[0001] The invention relates to a method for modeling the microstructure of a polycrystalline metal material with a preferred grain orientation, and belongs to the technical field of modeling the microstructure of a polycrystalline metal material. (2) Background technology:

[0002] Polycrystalline metal materials are crystal structures composed of many grains with different structures and orientations. In a polycrystalline structure, the arrangement of atoms or ions within the grains is orderly and conforms to a specific crystal structure, typically face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close-packed (HCP). The orientations of different grains are generally different, connected and transitioned by grain boundaries, both of which have a significant impact on the mechanical properties of polycrystalline materials. In some engineering applications, specific grain orientations can improve material performance. For example, in aircraft manufacturing, lightweight alloys often require specific grain orientations to improve their mechanical properties in a specific direction. Therefore, when designing and manufacturing polycrystalline metal materials, specific processes are used to control the dominant orientation of the polycrystalline metal material in a certain crystal direction.

[0003] Preferred grain orientation in polycrystalline metal materials typically occurs after the material has undergone certain processing steps, such as rolling, stretching, and extrusion. This causes the grains within the material to elongate in the rolling direction, resulting in the polycrystalline material having a strong orientation in that direction. Certain grain directions gradually become dominant relative to other directions, resulting in a normal distribution of grain orientations in the rolled polycrystalline metal material. The grain orientation of polycrystalline metal materials is closely related to their mechanical properties. Establishing a microstructure modeling method for polycrystalline metal materials that is consistent with the orientation distribution of real polycrystalline metal materials is of great significance for studying their mechanical properties.

[0004] From the grain orientation difference distribution diagram of the rolled polycrystalline metal material ( Figure 1 ) can be seen in the figure that the grain orientation distribution of the polycrystalline metal material after rolling presents a certain degree of normal distribution, and the orientation difference of 0° is the dominant orientation. The present invention combines the grain orientation distribution characteristics of the polycrystalline metal material after rolling to propose a microstructure modeling method for polycrystalline metal materials with a dominant grain orientation. The method uses a multivariate normal distribution function to perform parameter fitting on the Euler angles of the polycrystalline metal material after rolling, and generates a mean vector and covariance matrix of the fitting function. According to the mean vector and covariance matrix obtained by fitting, many new groups of Euler angle values that conform to the same multivariate normal distribution function are generated. These Euler angles are input into the model of the polycrystalline metal material as material properties to generate a polycrystalline metal model with the same grain orientation distribution as the real material. (3) Summary of the invention:

[0005] 1. Purpose: The purpose of the present invention is to propose a microstructure modeling method for polycrystalline metal materials with a preferred grain orientation, which can not only fit the Euler angles of the polycrystalline metal materials obtained after rolling, but also generate Euler angles with the same orientation distribution based on the fitting results, thereby providing material parameters for constructing a polycrystalline metal material model with the same orientation distribution.

[0006] 2. Technical Solution: Based on the Euler angles of rolled polycrystalline metal materials, an algorithm for fitting and generating Euler angles of materials is established. By fitting the Euler angles of the materials using a multivariate normal distribution function, a multivariate normal distribution function that can describe the distribution of the Euler angles of the materials is obtained. Based on this function, a polycrystalline metal material model with the same orientation distribution as the rolled polycrystalline metal material can be obtained. It includes the following steps:

[0007] Step 1: Use EBSD to obtain the grain orientation IPF map of the rolled polycrystalline metal material ( Figure 2 ), EBSD can obtain the lattice direction of each pixel by measuring the position and shape of the diffraction spot, thereby obtaining the orientation information of the grain. With the help of the tools provided by EBSD, the orientation information of n groups of grains can be presented in the form of Euler angles in the format of Export and save these Euler angles representing grain orientation information.

[0008] Step 2: Use the multivariate normal distribution function to calculate n sets of Euler angles Perform parameter fitting to obtain the mean vector μ and covariance matrix C of the fitting function.

[0009] ①The mean vector μ is expressed as:

[0010]

[0011] in, For variables The mean of .

[0012] ②The covariance matrix C is expressed as:

[0013]

[0014] in, Representing variables and The covariance between .

[0015] The formula for calculating covariance is:

[0016] Step 3: Based on the fitted multivariate normal distribution function, randomly generate the value of the Euler angle that is consistent with the original grain orientation distribution At the same time ensure

[0017] ①The fitted multivariate normal distribution function is expressed as:

[0018]

[0019] in, is the observed value vector of Euler angles, is the mean vector of Euler angles, C is the covariance matrix of Euler angles, and det(C) represents the determinant of the covariance matrix.

[0020] ②The generated The value is clipped to the specified range

[0021]

[0022] Step 4: Input the generated Euler angles as material properties into the model of the polycrystalline metal material to construct a polycrystalline metal model with the same grain orientation distribution as the real material.

[0023] This paper proposes a method for modeling the microstructure of polycrystalline metal materials with a preferred grain orientation. The method has the following advantages: fitting the Euler angles of the rolled polycrystalline metal material and generating Euler angles with the same orientation distribution based on the fitting results. Therefore, a large number of Euler angles with the same orientation distribution can be generated based on a small number of representative Euler angle values, providing material parameters for constructing a model of the polycrystalline metal material with the same orientation distribution. (4) Description of the accompanying drawings:

[0024] Figure 1 The present invention is based on the background art of the present invention, which is a distribution diagram of grain orientation differences of a rolled polycrystalline metal material.

[0025] Figure 2 This is the grain orientation IPF diagram of the polycrystalline metal material after rolling in step 1 of the present invention.

[0026] Figure 3 The figure shows a comparison between the real Euler angle pole figure of the material of the present invention and the Euler angle pole figure generated after fitting.

[0027] Figure 4 This is a flow chart of the microstructure modeling method of polycrystalline metal materials with preferred grain orientation according to the present invention. (V) Specific implementation methods:

[0028] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0029] According to the grain orientation distribution of the polycrystalline metal material after rolling, a model with the same orientation distribution is generated. Figure 4 The specific steps of this method are as follows:

[0030] Step 1: Use EBSD to analyze the rolled polycrystalline metal material and obtain the Euler angles of 1000 grains in the format of Export and save these Euler angles representing grain orientation information.

[0031] Step 2: Use Python's NumPy library to perform parameter fitting, use the np.mean function to calculate the three-dimensional mean vector of the Euler angle, and use the np.cov function to calculate the third-order covariance matrix of the Euler angle. The mean vector of the fitting function is (89.90, 179.89, 209.94), and the covariance matrix is

[0032] Step 3: Based on the fitted multivariate normal distribution function, use the np.random.multivariate_normal function to randomly generate 1000 sets of Euler angle values If the generated If the value of is outside the range of [0,360], it is clipped using max(min(x,360).

[0033] Step 4: Compare the polar graph of the real Euler angle of the material with the polar graph of the Euler angle generated after fitting ( Figure 3 ), we can see that the grain orientation distribution is basically the same. The generated Euler angles can be input as material properties into the polycrystalline metal model to construct a polycrystalline metal model with the same grain orientation distribution as the real material.

Claims

1. A method for microstructure modeling of polycrystalline metal materials with preferred grain orientation, characterized by: The multivariate normal distribution function is used to perform parameter fitting on the Euler angles of the rolled polycrystalline metal material. Based on the fitted function, many new sets of Euler angles are generated. These Euler angles are input into the polycrystalline metal material model as material properties to generate a polycrystalline metal model with the same grain orientation distribution as the real material. It includes the following steps: Step 1: Use EBSD to obtain the orientation information of n groups of grains in the format of Step 2: Use the multivariate normal distribution function to calculate n sets of Euler angles Perform parameter fitting to obtain the mean vector μ and covariance matrix C of the fitting function. Step 3: Randomly generate m sets of Euler angle values based on the fitted function At the same time ensure Step 4: Input the generated Euler angles as material properties into the model of the polycrystalline metal material to construct a polycrystalline metal model with the same grain orientation distribution as the real material.

2. The method of obtaining orientation information of n groups of grains using EBSD according to claim 1, characterized in that: In step 1, EBSD is used to measure the position and shape of the diffraction spot, obtain the lattice direction of each pixel, and obtain the orientation information of the grains in the form of Euler angles.

3. The method of claim 1 wherein the multivariate normal distribution function is used to perform parameter fitting, and wherein the mean vector μ and the covariance matrix C of the fitting function are obtained, wherein: In step 2, based on the values of the Euler angles, the mean vector and covariance matrix are calculated using the following formulas. ①The mean vector μ is expressed as: in, For variables The mean of . ②The covariance matrix C is expressed as: in, Representing variables and The covariance between . The formula for calculating covariance is:

4. The method of claim 1 , wherein the Euler angles are generated according to the function obtained by fitting, wherein: In step 3, the values of the Euler angles are generated and clipped according to the fitted multivariate normal function. ①The fitted multivariate normal distribution function is expressed as: in, is the observed value vector of Euler angles, is the mean vector of Euler angles, C is the covariance matrix of Euler angles, and det(C) represents the determinant of the covariance matrix. ③The generated The value is clipped to the specified range 5. The method of claim 1 , wherein the polycrystalline metal model has the same grain orientation distribution as the real material, wherein: In step 4, the pole figures of the actual Euler angles of the material can be compared with the pole figures of the Euler angles generated after fitting. After confirming that the error between the two is not large, the Euler angles can be input into the polycrystalline metal model as a material property.

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