A finite element modeling method for crystal plasticity based on image processing

Abstract

The present invention discloses a crystal plastic finite element modeling method based on image processing, which relates to the technical field of crystal modeling, and comprises the following steps: S1, obtaining a high-resolution image of a crystal, and removing the background area of ​​the high-resolution image to obtain a crystal morphology image; S2, dividing the crystal morphology image into a plurality of grids based on the grains of the crystal morphology image; S3, constructing a constraint coefficient for the crystal based on the plurality of grids of the crystal morphology image; S4, modeling the crystal using the constraint coefficient. The present invention predicts and analyzes the plastic deformation behavior of a crystal material by running a simulation in a finite element analysis software, which is conducive to a deep understanding of the plastic deformation mechanism of the crystal.

Description

Technical Field

[0001] The present invention relates to the technical field of crystal modeling, and in particular to a crystal plasticity finite element modeling method based on image processing. Background Art

[0002] In metal material processing engineering technology, accurate modeling and analysis of the material's microstructure is crucial to understanding the material's performance and behavior. Traditional modeling methods are often based on simplified assumptions and cannot accurately reflect the material's true microstructure. In addition, existing modeling methods do not adequately consider the material's true grain-scale microstructure information, which is quite different from the actual situation; therefore, a method that can perform crystal plasticity finite element modeling based on the true microstructure is needed. Summary of the invention

[0003] In order to solve the above problems, the present invention proposes a crystal plasticity finite element modeling method based on image processing.

[0004] The technical solution of the present invention is: a crystal plasticity finite element modeling method based on image processing comprises the following steps:

[0005] S1, obtaining a high-resolution image of the crystal, and removing the background area of ​​the high-resolution image to obtain a crystal morphology image;

[0006] S2, dividing the crystal morphology image into a plurality of grids based on the grains of the crystal morphology image;

[0007] S3, constructing constraint coefficients for the crystal based on several grids of the crystal morphology image;

[0008] S4. Use the constraint coefficient to model the crystal.

[0009] In the present invention, in S2, the grain structure is meshed according to the geometric shape and distribution of the grains. The meshing can be done by an adaptive meshing method to ensure that the mesh can accurately reflect the shape and distribution of the grains.

[0010] Furthermore, S3 includes the following sub-steps:

[0011] S31, obtaining deformation parameters of the crystal;

[0012] S32, calculating the stress transformation coefficient of each grain using the deformation parameters of the crystal;

[0013] S33, generating a constitutive plasticity equation for each grid according to the stress transformation coefficient of the grains contained in the grid;

[0014] S34, inputting all constitutive plastic equations into the generator to generate ideal plastic coefficients;

[0015] S35. Use the ideal plasticity coefficient to construct a constraint coefficient for the crystal.

[0016] The beneficial effect of the above further scheme is: in the present invention, the deformation parameters of the crystal describe the plastic deformation mechanism and deformation behavior of the single crystal, and thus can be used to characterize the plastic deformation elasticity of the grains; and then the mechanical properties between the grids, i.e., the constitutive plastic equation, are determined by using the grain conditions contained in each grid. All the values ​​of the constitutive plastic equation are input into the generator, and data analysis and processing are performed to obtain the ideal plastic coefficient, and the final constraint coefficient is obtained, which is used to constrain the crystal plastic deformation behavior.

[0017] Further, in S31, the deformation parameters of the crystal include the yield strength and tensile strength of the crystal.

[0018] Yield strength refers to the stress value when the material begins to undergo plastic deformation. Tensile strength refers to the maximum stress value that a material can withstand during the stretching process.

[0019] Furthermore, in S32, the stress transformation coefficient of the grain The calculation formula is:

[0020] ;

[0021] In the formula, represents the diameter of the grain, represents the perimeter of the grid where the grain is located, represents the yield strength of the crystal, represents the tensile strength of the crystal, represents a constant, Indicates the number of subgrains contained in a grain, Represents an exponent.

[0022] Furthermore, in S33, the constitutive plasticity equation of the grid is The expression is:

[0023] ;

[0024] In the formula, represents the symbolic function, represents the number of grains contained in the grid, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid with The number of adjacent grains, Indicates the grid with The mean value of the stress transformation coefficient of all grains adjacent to a grain is, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid with The number of adjacent grains, Indicates the grid with The mean value of the stress transformation coefficient of all grains adjacent to a grain is, represents the stress transformation coefficient of the first grain contained in the grid, represents the number of grains adjacent to the first grain in the grid, Represents the mean value of the stress transformation coefficient of all grains adjacent to the first grain in the grid.

[0025] Furthermore, in S34, the ideal plasticity coefficient The expression is:

[0026] ;

[0027] In the formula, represents the constitutive plasticity equation of the first grid, Indicates The constitutive plasticity equations for the grid are: Indicates The constitutive plasticity equations for the grid are: represents the activation function, represents the mean value of the constitutive plasticity equations of all grids, represents the standard deviation of the values ​​of the constitutive plasticity equations for all grids, represents the weights of the neurons that make up the generator, represents the bias of the neurons that make up the generator, Represents a random number between 0 and 1. represents the maximum value of the constitutive plasticity equation of all grids, represents the minimum value of the constitutive plasticity equation of all grids, Indicates the number of grids.

[0028] Furthermore, in S35, the constraint coefficient The calculation formula is:

[0029] ;

[0030] In the formula, represents the ideal plasticity coefficient, Represents the elongation of the crystal.

[0031] Further, S4 includes the following sub-steps:

[0032] S41, adjusting the elastic constant of the crystal using the constraint coefficient;

[0033] S42. Model the crystal using the adjusted elastic constants.

[0034] The beneficial effect of the above further scheme is that in the present invention, the elastic constant can describe the deformation behavior of the crystal when subjected to external force. In crystal software modeling, accurately obtaining and inputting the elastic constant can significantly improve the accuracy of the model. This is because the elastic constant directly reflects the interaction force between atoms or molecules inside the crystal, as well as the ability of the crystal to resist external stress. By accurately describing these mechanical properties, the actual behavior of the crystal can be simulated more accurately.

[0035] Further, in S32, the adjusted elastic constant The calculation formula is:

[0036] ;

[0037] In the formula, represents the elastic constant of the crystal, represents the constraint coefficient, Indicates rounding up.

[0038] The beneficial effects of the present invention are as follows: the present invention discloses a crystal plastic finite element modeling method based on image processing, analyzes the plastic deformation behavior and mechanical properties of the crystal by dividing a plurality of grids, obtains the constraint coefficient in combination with the structural parameters of the grain, and uses the constraint coefficient to assist modeling, thereby establishing a high-precision finite element model. The present invention predicts and analyzes the plastic deformation behavior of the crystal material by running a simulation in the finite element analysis software, which is conducive to a deep understanding of the plastic deformation mechanism of the crystal. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flowchart of the crystal plasticity finite element modeling method based on image processing. DETAILED DESCRIPTION

[0040] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0041] like Figure 1 As shown, the present invention provides a crystal plasticity finite element modeling method based on image processing, comprising the following steps:

[0042] S1, obtaining a high-resolution image of the crystal, and removing the background area of ​​the high-resolution image to obtain a crystal morphology image;

[0043] S2, dividing the crystal morphology image into a plurality of grids based on the grains of the crystal morphology image;

[0044] S3, constructing constraint coefficients for the crystal based on several grids of the crystal morphology image;

[0045] S4. Use the constraint coefficient to model the crystal.

[0046] In the present invention, in S2, the grain structure is meshed according to the geometric shape and distribution of the grains. The meshing can be done by an adaptive meshing method to ensure that the mesh can accurately reflect the shape and distribution of the grains.

[0047] In this embodiment of the present invention, S3 includes the following sub-steps:

[0048] S31, obtaining deformation parameters of the crystal;

[0049] S32, calculating the stress transformation coefficient of each grain using the deformation parameters of the crystal;

[0050] S33, generating a constitutive plasticity equation for each grid according to the stress transformation coefficient of the grains contained in the grid;

[0051] S34, inputting all constitutive plastic equations into the generator to generate ideal plastic coefficients;

[0052] S35. Use the ideal plasticity coefficient to construct a constraint coefficient for the crystal.

[0053] In the present invention, the deformation parameters of the crystal describe the plastic deformation mechanism and deformation behavior of the single crystal, and can therefore be used to characterize the plastic deformation elasticity of the grains; the mechanical properties between the grids, i.e., the constitutive plastic equation, are determined by using the grain conditions contained in each grid. All the values ​​of the constitutive plastic equation are input into the generator, and data analysis and processing are performed to obtain the ideal plastic coefficient, and the final constraint coefficient is obtained, which is used to constrain the crystal plastic deformation behavior.

[0054] In the embodiment of the present invention, in S31, the deformation parameters of the crystal include the yield strength and tensile strength of the crystal.

[0055] Yield strength refers to the stress value when the material begins to undergo plastic deformation. Tensile strength refers to the maximum stress value that a material can withstand during the stretching process.

[0056] In the embodiment of the present invention, in S32, the stress conversion coefficient of the grain The calculation formula is:

[0057] ;

[0058] In the formula, represents the diameter of the grain, represents the perimeter of the grid where the grain is located, represents the yield strength of the crystal, represents the tensile strength of the crystal, represents a constant, Indicates the number of subgrains contained in a grain, Represents an exponent.

[0059] In the embodiment of the present invention, in S33, the constitutive plasticity equation of the grid is The expression is:

[0060] ;

[0061] In the formula, represents the symbolic function, represents the number of grains contained in the grid, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid with The number of adjacent grains, Indicates the grid with The mean value of the stress transformation coefficient of all grains adjacent to a grain is, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid The number of adjacent grains, Indicates the grid The mean value of the stress transformation coefficient of all grains adjacent to a grain is, represents the stress transformation coefficient of the first grain contained in the grid, represents the number of grains adjacent to the first grain in the grid, Represents the mean value of the stress transformation coefficient of all grains adjacent to the first grain in the grid.

[0062] In the embodiment of the present invention, in S34, the ideal plasticity coefficient The expression is:

[0063] ;

[0064] In the formula, represents the constitutive plasticity equation of the first grid, Indicates The constitutive plasticity equations for the grid are: Indicates The constitutive plasticity equations for the grid are: represents the mean value of the constitutive plasticity equations of all grids, represents the standard deviation of the values ​​of the constitutive plasticity equations for all grids, represents the weights of the neurons that make up the generator, represents the bias of the neurons that make up the generator, Represents a random number between 0 and 1. represents the activation function, represents the maximum value of the constitutive plasticity equation of all grids, represents the minimum value of the constitutive plasticity equation of all grids, Indicates the number of grids.

[0065] In the embodiment of the present invention, in S35, the constraint coefficient The calculation formula is:

[0066] ;

[0067] In the formula, represents the ideal plasticity coefficient, Represents the elongation of the crystal.

[0068] In this embodiment of the present invention, S4 includes the following sub-steps:

[0069] S41, adjusting the elastic constant of the crystal using the constraint coefficient;

[0070] S42. Model the crystal using the adjusted elastic constants.

[0071] In the present invention, elastic constants can describe the deformation behavior of a crystal when subjected to external forces. In crystal software modeling, accurately obtaining and inputting elastic constants can significantly improve the accuracy of the model. This is because the elastic constants directly reflect the interaction forces between atoms or molecules inside the crystal, as well as the ability of the crystal to resist external stress. By accurately describing these mechanical properties, the actual behavior of the crystal can be simulated more accurately.

[0072] In the embodiment of the present invention, in S32, the adjusted elastic constant The calculation formula is:

[0073] ;

[0074] In the formula, represents the elastic constant of the crystal, represents the constraint coefficient, Indicates rounding up.

[0075] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A crystal plasticity finite element modeling method based on image processing, characterized in that: The following steps are involved: S1, obtaining a high-resolution image of the crystal, and removing the background area of ​​the high-resolution image to obtain a crystal morphology image; S2, dividing the crystal morphology image into a plurality of grids based on the grains of the crystal morphology image; S3, constructing constraint coefficients for the crystal based on several grids of the crystal morphology image; S4, using constraint coefficients to model the crystal; The S3 comprises the following sub-steps: S31, obtaining deformation parameters of the crystal; S32, calculating the stress transformation coefficient of each grain using the deformation parameters of the crystal; S33, generating a constitutive plasticity equation for each grid according to the stress transformation coefficient of the grains contained in the grid; S34, inputting all constitutive plastic equations into the generator to generate ideal plastic coefficients; S35, using the ideal plasticity coefficient, constructing a constraint coefficient for the crystal; In the above S32, the calculation formula of the stress conversion coefficient of the grain is: ； In the formula, represents the stress transformation coefficient of the grain, represents the diameter of the grain, represents the perimeter of the grid where the grain is located, represents the yield strength of the crystal, represents the tensile strength of the crystal, represents a constant, Indicates the number of subgrains contained in a grain, represents an index; In S33, the constitutive plasticity equation of the grid is expressed as: ； In the formula, represents the constitutive plasticity equation of the mesh, represents the symbolic function, Indicates the number of grains contained in the grid, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid with The number of adjacent grains, Indicates the grid The mean value of the stress transformation coefficient of all grains adjacent to a grain is, Indicates the grid contains The stress transformation coefficient of each grain is Indicates the grid with The number of adjacent grains, Indicates the grid The mean value of the stress transformation coefficient of all grains adjacent to a grain is, represents the stress transformation coefficient of the first grain contained in the grid, represents the number of grains adjacent to the first grain in the grid, represents the mean value of the stress transformation coefficients of all grains adjacent to the first grain in the grid; In S34, the expression of the ideal plasticity coefficient is: ； In the formula, represents the ideal plasticity coefficient, represents the constitutive plasticity equation of the first grid, Indicates The constitutive plasticity equations for the grid are: Indicates The constitutive plasticity equations for the grid are: represents the mean value of the constitutive plasticity equations of all grids, represents the standard deviation of the values ​​of the constitutive plasticity equations for all grids, represents the weights of the neurons that make up the generator, represents the bias of the neurons that make up the generator, Represents a random number between 0 and 1. represents the activation function, represents the maximum value of the constitutive plasticity equation of all grids, represents the minimum value of the constitutive plasticity equation of all grids, Indicates the number of grids; In the above S31, the deformation parameters of the crystal include the yield strength and tensile strength of the crystal.

2. The crystal plasticity finite element modeling method based on image processing according to claim 1, characterized in that: In S35, the calculation formula of the constraint coefficient is: ； In the formula, represents the constraint coefficient, represents the ideal plasticity coefficient, Represents the elongation of the crystal.

3. The crystal plasticity finite element modeling method based on image processing according to claim 1, characterized in that: The S4 comprises the following sub-steps: S41, adjusting the elastic constant of the crystal using the constraint coefficient; S42. Model the crystal using the adjusted elastic constants.

4. The crystal plasticity finite element modeling method based on image processing according to claim 3, characterized in that: In S42, the calculation formula of the adjusted elastic constant is: ； In the formula, represents the adjusted elastic constant, represents the elastic constant of the crystal, represents the constraint coefficient, Indicates rounding up.

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