Method for predicting cartridge case material properties from SEM images based on explicit FFT

Abstract

The present invention belongs to the field of cartridge case manufacturing, specifically to a method for predicting cartridge case material properties from SEM images based on explicit Fast Fourier Transform (FFT). The method comprises the following steps: S1, sampling the cartridge case material before stamping to produce an SEM sample; S2, taking a micrograph of the sample and performing electron backscatter diffraction analysis to obtain an SEM image and EBSD data; S3, creating a three-dimensional voxel map of a representative volume unit from the SEM image, and using the EBSD data to generate Euler angle information for each three-dimensional pixel; S4, calculating stress and strain data for the three-dimensional voxel map of the representative volume unit using an explicit Fast Fourier Transform (FFT) method; and S5, using a tensor sparse symbolic regression method to learn the stress and strain data generated in step S4 to generate a constitutive model for the cartridge case material. The present invention can accurately predict the large deformation plastic mechanical properties of the cartridge case material from the results of the microstructural analysis of the cartridge case material.

Description

Technical Field

[0001] The invention belongs to the field of cartridge case manufacturing, and in particular relates to a method for predicting cartridge case material properties from SEM based on explicit FFT. Background Art

[0002] Small-caliber ammunition cases are primarily produced through deep drawing of the shell material. Optimizing the stamping parameters and the non-structural parameters of the stamping die during the stamping process is crucial for efficient, high-quality manufacturing of small-caliber ammunition cases. However, due to the high costs of stamping experiments or small-batch production, experimental approaches that vary stamping parameters or design different non-structural parameters to test different parameter combinations are not feasible. Therefore, using simulation methods to analyze the deformation and force distribution of the shell material under different stamping process parameters, thereby identifying the optimal parameter combination, is a feasible solution for optimizing small-caliber ammunition processing.

[0003] During the deep drawing process of cartridge cases, the case material undergoes large plastic deformation. Constitutive models characterizing the mechanical behavior of the case material are key information for large deformation simulations. Different smelting, forging, and heat treatment schemes will affect the case material's microstructure and, consequently, its mechanical behavior. Constitutive models incorporating this material's microscopic information are crucial for accurately simulating this material's large deformation behavior. The polycrystal plasticity finite element method (FEM) is a common approach for establishing material constitutive models from microscopic information. However, the FEM requires meshing and the assembly of high-dimensional matrices, resulting in low computational efficiency. The polycrystal fast Fourier transform (FFT) method is an alternative to the FEM. It can directly utilize microscopic image information for calculations without meshing, requires less computation than the FEM, and is easily programmable for parallel computing. However, existing FFT methods are implicit solvers, which suffer from convergence and applicability issues when simulating highly nonlinear materials and high-speed deformation problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the performance of cartridge case materials from SEM based on explicit FFT, which realizes the direct acquisition of the material constitutive model by characterizing the microstructure of the cartridge case material without experiments.

[0005] The technical solution for achieving the object of the present invention is: a method for predicting the performance of cartridge case materials from electron scanning microscopy images based on explicit FFT, comprising the following steps:

[0006] Step S1: sampling the shell material before stamping to prepare a SEM sample;

[0007] Step S2: taking a micrograph of the sample and performing electron backscatter diffraction analysis to obtain SEM images and EBSD data;

[0008] Step S3: constructing a three-dimensional voxel map of a representative volume unit from the SEM image, and generating Euler angle information of the three-dimensional pixel points using EBSD data;

[0009] Step S4: using an explicit fast Fourier transform (FFT) method to calculate stress and strain data of a three-dimensional voxel map of a representative volume unit;

[0010] Step S5: Use the tensor sparse symbolic regression method to learn the stress and strain data generated in step S4 to generate a constitutive model of the shell material.

[0011] Furthermore, the three-dimensional voxel image in step S3 is a cube, and the number of voxels on a single side is an odd number between 62 and 100.

[0012] Furthermore, the specific method of step S3 is as follows:

[0013] Reduce the resolution of the SEM image to a 63N×63N pixel image, and divide the image with reduced resolution into N 2 Calculate the average number of grains n in a single image, from N 2 Take the closest An integer n′ of images are randomly arranged in the vertical image dimension, and a 63×63×63 representative volume unit 3D voxel image is generated based on the position of the center of each grain in each image; the Euler angle of each grain in the voxel image is given in combination with the EBSD data; different N values ​​are tried to ensure that N 2 Greater than n′.

[0014] Furthermore, step S4 specifically includes the following steps:

[0015] Step S41: setting single crystal plasticity model parameters;

[0016] Step S42: setting FFT calculation boundary conditions;

[0017] Step S43: performing explicit FFT calculation for each boundary condition;

[0018] Step S44: Generate average stress and average strain data sets on representative volume elements.

[0019] Furthermore, the single crystal plasticity model in step S41 is an explicit algorithm.

[0020] Furthermore, the boundary conditions in step S42 are deformation gradients corresponding to any of uniaxial tension or compression, biaxial tension or compression, triaxial tension or compression, and simple shear.

[0021] Furthermore, the explicit FFT method of step S43 is accelerated by a GPU graphics card having a CUDA core;

[0022] The calculation in step S43 is specifically as follows: for each loading, the stress of each voxel point is calculated using an explicit FFT procedure, and the average value is calculated;

[0023] The explicit FFT method discretizes the dynamic momentum balance partial differential equation into voxel points and uses FFT to calculate the spatial gradient to achieve explicit calculation. That is, only the physical quantities of the previous incremental step are used to calculate the physical quantities of the next incremental step, and this process is repeated recursively until the calculation of one load is completed.

[0024] Furthermore, each data group of the data set of step S44 contains 37 data, recording 9 deformation gradient components, 9 deformation gradient increment components, 9 first Piola Kirchhoff stress components, 9 first Piola Kirchhoff stress increment components, and 1 cumulative plastic strain of a representative volume unit at a certain moment in the deformation process.

[0025] Furthermore, the characteristic function set by the tensor sparse symbolic regression method in step S5 is set as:

[0026]

[0027] Where σ is the Cauchy stress, D is the strain rate, Γ is the cumulative plastic strain, I D is the invariant of D, I σ is the invariant of σ, I Dσ D is the combined invariant of σ, θ is a simple function of stress and strain, which can be one of σ, D, I, σσ, DD, 0.5(σD+Dσ)..., a, b, c, d is a number in the set discrete number series, which can be a number in (-2, -1, -0.5, 0, 0.5, 1, 2).

[0028] Compared with the prior art, the present invention has the following significant advantages:

[0029] (1) Compared with obtaining the mechanical properties of the cartridge case material through material mechanics experiments, the present invention predicts the mechanical properties of the cartridge case material through numerical calculation, which greatly reduces the experimental cost; the method proposed in the present invention can consider the influence of different smelting, forging, and heat treatment schemes on the cartridge case material before stamping; at the same time, this scheme can obtain stress-strain data under any loading path.

[0030] (2) Compared with the material mechanical property prediction scheme based on the polycrystalline plastic finite element method, the present invention uses the FFT homogenization method of pixel points or voxel points, which can directly utilize the microscopic characterization image data of the shell material without the need for grid division or assembly of the stiffness matrix. The mass matrix is ​​directly a diagonal matrix; the calculation process is faster and the calculation results are more accurate.

[0031] (3) Compared with the implicit FFT calculation method, the present invention uses an explicit dynamics method, which eliminates the need to solve large sparse linear equations and the computational stiffness of the Newton iteration. This eliminates the convergence issues inherent in the implicit FFT algorithm. Furthermore, the explicit FFT calculation method can directly use an explicit single-crystal plasticity model without computing the algorithmic stiffness of voxel points, facilitating GPU parallel computing. Consequently, the computational process is faster and more stable.

[0032] (4) Compared with the data-driven modeling based on neural networks, the tensor sparse symbolic regression method used in the present invention can establish an explicit algebraic constitutive model of the shell material, which has stronger generalization ability and thus more accurately predicts the mechanical properties of the material. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 The figure is a flow chart of the method for predicting shell material properties from SEM based on explicit FFT in the present invention.

[0034] Description of reference numerals:

[0035] 1-Casing material sample, 2-SEM image of the sample, 3-3D voxel map, 4-Stress component distribution after explicit FFT calculation, 5-Data set diagram, 6-Established constitutive model of the casing material. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0037] The present invention will be further described below with reference to specific examples, but they are not intended to limit the present invention.

[0038] like Figure 1 As shown, the present invention provides a method for directly predicting the performance of cartridge case materials from electron scanning microscopy images based on the dynamic fast Fourier transform method, comprising the following steps:

[0039] S1. Randomly sample the central area of ​​the shell material plate before stamping, grind and polish it to make a sample suitable for SEM observation.

[0040] S2. Take SEM photos of the sample and perform EBSD analysis to obtain a microstructure diagram and EBSD raw data that can represent the microscopic characteristics of the shell material.

[0041] S3. Use a small program written in Python to reduce the resolution of the micro-organizational structure chart, reduce the resolution to 63N×63N pixels, and divide the reduced resolution chart into N 2 Calculate the average number of grains n in a single image. 2 Take the closest An integer number of n' images is generated. Randomly arrange n' images in the vertical image dimension and generate a 63×63×63 representative volume unit 3D voxel image based on the position of each grain center in each image. Combined with EBSD data, the corresponding Euler angle is given to each grain in the voxel image. Try different N values ​​to ensure that N 2 Slightly larger than n′.

[0042] S4. The 3D voxel image and Euler angle information generated in the previous step are fed into the explicit FFT program for calculation. The single crystal plastic constitutive information for each voxel point is set based on the single crystal material information in the database. The single crystal plastic constitutive model is calculated using the forward Euler explicit method.

[0043] Set N C Boundary conditions include, but are not limited to, the average deformation gradient component value of the voxel point corresponding to uniaxial tension or compression in three directions, the average deformation gradient component value of the voxel point corresponding to biaxial tension and / or compression in multiple directions, the average deformation gradient component value of the voxel point corresponding to triaxial tension and / or compression in multiple directions, and the average deformation gradient component value of the voxel point corresponding to simple shear in six directions. For each loading, an explicit FFT procedure is used to calculate the stress at each voxel point and the average value is calculated.

[0044] The explicit FFT method discretizes the dynamic momentum balance partial differential equation into voxel points and uses FFT to calculate the spatial gradient, thereby achieving explicit calculation. That is, only the physical quantities of the previous incremental step are used to calculate the physical quantities of the next incremental step, and this process is repeated recursively until the calculation of one load is completed.

[0045] At the completion of each loading, 20 loading moments are evenly taken along the loading path, and the 9 deformation gradient components, 9 deformation gradient increment components, 9 first Piola Kirchhoff stress components, 9 first Piola Kirchhoff stress increment components, and 1 cumulative plastic strain of the representative volume element at each moment are recorded. Each loading generates 20 data groups, each containing 37 data points. All loadings are 20N in total. C data groups, forming a 20N C A dataset of double-precision floating-point matrices with 37 rows and 37 columns is saved in a file.

[0046] S5. Use the tensor sparse symbolic regression method to learn the dataset generated in S4. Set the characteristic function of tensor sparse symbolic regression to

[0047]

[0048] Set parameter values

[0049] a, b, c = (0, 0.5, 1, 1.5, 2, 3)

[0050] d=(-2,-1,-0.5,0,0.5,1,2)

[0051] θ=(I,D,σ,DD,σσ,0.5(σD+Dσ))

[0052] A total of 9072 characteristic functions are generated. Using the data of each data group in the data set, the values ​​of the 9072 characteristic functions corresponding to the data group are calculated and the centering and normalization processing of each characteristic function data is performed. C The data set with 37 rows and 20 columns is converted to 20N C A matrix with 9071 rows and 11 columns (one column with all zeros removed) was first used to perform sparse linear regression on this data matrix, and the HiLasso method was used to screen out 100 representative characteristic functions. Subsequently, a teaching simulation optimization swarm intelligence method was used to optimize and screen these 100 representative characteristic functions. The dual optimization objectives of minimizing error and minimizing the number of characteristic functions were set. The optimal combination of characteristic functions was selected and the coefficients were restored. This linear combination was used as the constitutive model of the cartridge case material, thereby achieving the goal of predicting the mechanical properties of the cartridge case.

[0053] The generated constitutive model of the cartridge case material is input into the cartridge case stamping simulation program to calculate the deformation and force distribution of the cartridge case material under different stamping processing parameters, so as to find the optimal parameter combination and realize the optimization of small-caliber ammunition processing.

Claims

1. A method for predicting cartridge case material properties from SEM images based on explicit FFT, characterized in that: The steps include: Step S1: Sampling the shell material before stamping to prepare a SEM sample; Step S2: taking a micrograph of the sample and performing electron backscatter diffraction analysis to obtain SEM images and EBSD data; Step S3: constructing a three-dimensional voxel map of a representative volume unit from the SEM image, and generating Euler angle information of the three-dimensional pixel points using EBSD data; Step S4: using an explicit fast Fourier transform (FFT) method to calculate stress and strain data of a three-dimensional voxel map of a representative volume unit; Step S5: Using the tensor sparse symbolic regression method to learn the stress and strain data generated in step S4, a constitutive model of the shell material is generated; The specific method of step S3 is as follows: Reduce the resolution of the SEM image to a 63N×63N pixel image, and divide the image with reduced resolution into N 2 Calculate the average number of grains n in a single image, from N 2 Take the closest An integer n′ of images are randomly arranged in the vertical image dimension, and a 63×63×63 representative volume unit 3D voxel image is generated based on the position of the center of each grain in each image; the Euler angle of each grain in the voxel image is given in combination with the EBSD data; different N values ​​are tried to ensure that N 2 greater than n′; Step S4 specifically includes the following steps: Step S41: setting single crystal plasticity model parameters; Step S42: setting FFT calculation boundary conditions; Step S43: performing explicit FFT calculation for each boundary condition; Step S44: generating a data set of average stress and average strain on a representative volume element; The characteristic function set by the tensor sparse symbolic regression method in step S5 is set as: Where σ is the Cauchy stress, D is the strain rate, Γ is the cumulative plastic strain, I D is the invariant of D, I σ is the invariant of σ, I Dσ D is the combined invariant of σ, θ is a simple function of stress and strain, which can be one of σ, D, I, σσ, DD, 0.5(σD+Dσ)..., a, b, c, d is a number in the set discrete number series, which is a number in (-2, -1, -0.5, 0, 0.5, 1, 2).

2. The method according to claim 1, characterized in that The three-dimensional voxel image in step S3 is a cube, and the number of voxels on a single side is an odd number between 62 and 100.

3. The method according to claim 2, characterized in that The single crystal plasticity model in step S41 is an explicit algorithm.

4. The method according to claim 3, characterized in that The boundary conditions in step S42 are: deformation gradients corresponding to any of uniaxial tension or compression, biaxial tension or compression, triaxial tension or compression, and simple shear.

5. The method according to claim 4, characterized in that The explicit FFT method in step S43 is accelerated by a GPU graphics card with a CUDA kernel; The calculation in step S43 is specifically as follows: for each loading, the stress of each voxel point is calculated using an explicit FFT procedure, and the average value is calculated; The explicit FFT method discretizes the dynamic momentum balance partial differential equation into voxel points and uses FFT to calculate the spatial gradient to achieve explicit calculation. That is, only the physical quantities of the previous incremental step are used to calculate the physical quantities of the next incremental step, and this process is repeated recursively until the calculation of one load is completed.

6. The method according to claim 1, characterized in that Each data group of the data set of step S44 contains 37 data, recording 9 deformation gradient components, 9 deformation gradient increment components, 9 first Piola Kirchhoff stress components, 9 first Piola Kirchhoff stress increment components, and 1 cumulative plastic strain of a representative volume unit at a certain moment in the deformation process.

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