Molecular dynamics simulation method for predicting precipitation phase strengthening effect of material

Abstract

This invention discloses a molecular dynamics simulation method for predicting the strengthening effect of precipitates in materials, comprising: S1, establishing a unit cell model, expanding the cell, adding dislocations, replacing atoms to establish a matrix phase model containing one dislocation, optimizing the model structure, and deleting atoms within a cylindrical region of the same size as the target precipitate; S2, establishing a unit cell model, expanding the cell, replacing atoms to establish a precipitate model, optimizing the model structure, and deleting atoms outside the cylindrical region of the target precipitate; S3, merging the matrix phase model and the precipitate model obtained in steps S1 and S2 to obtain a dislocation / precipitate model, applying shear strain to the model, and statistically analyzing the relationship curve between the critical shear stress and the size of the cylindrical precipitate to guide the selection of actual alloy composition. This invention achieves continuous simulation of the process of dislocations passing through nanorod-shaped precipitates, accurately evaluates the age-strengthening effect, and supports the optimization of alloy composition and heat treatment processes.

Description

Technical Field

[0001] This invention belongs to the field of computer simulation analysis technology, and relates to a molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials. Background Technology

[0002] The rapid development of the aerospace industry has placed higher demands on the strength, hardness, and stability of materials such as Au-Ag-Cu ternary alloys used in key components like slip rings and brushes. Age hardening is the core strengthening mechanism of this type of alloy, where dislocations interact with precipitated phases by bypassing or cutting through them, significantly improving the material's mechanical properties.

[0003] However, due to the high cost of materials such as Au-Ag-Cu alloys, and the fact that the precipitates during aging are at the nanoscale, and that the dislocation-precipitate evolution is a continuous process, it is difficult to observe directly experimentally. Existing molecular dynamics simulations mostly target spherical / near-spherical precipitates, which deviate from actual rod-shaped precipitates. Traditional atomic substitution methods are only applicable to precipitates with the same structure as the matrix and cannot construct heterostructure precipitates such as L10. Furthermore, the uneven distribution and aggregation of multi-component atoms lead to insufficient accuracy in simulation results, making it difficult to meet the precise simulation requirements for Au-Ag-Cu alloys. In summary, using existing methods severely affects the accuracy of experimental results, and the research findings are insufficient. Therefore, developing a molecular dynamics simulation method that can construct heterostructured, regularly morphologically regular, and uniformly distributed nanorod-shaped precipitates, and accurately predict dislocation-precipitate interactions and strengthening effects, is of great significance for shortening alloy development cycles and reducing R&D costs.

[0004] Chinese patent CN117153272A, published on December 1, 2023, discloses a molecular dynamics modeling and verification method based on the ratio of dislocation to precipitate phase. The method includes: 1) establishing molecular dynamics models with different ratios of dislocation length to precipitate phase spacing ranging from 1 to 4; 2) setting molecular dynamics simulation parameters; 3) performing molecular dynamics simulation calculations based on the selected simulation parameters; 4) statistically analyzing the results of calculations using different ratio molecular dynamics models; and 5) comparing and verifying the simulation results with characterization calculations. This verifies the interaction law between dislocations and precipitates. However, the patent itself adds precipitates using an atom substitution method, directly replacing matrix phase atoms with corresponding atoms in the precipitate phase. The resulting precipitate phase structure is limited to being consistent with the matrix phase. For example, if the matrix phase is an FCC structure, the resulting precipitate phase structure cannot be an L10 structure. Furthermore, the atomic arrangement of the precipitated phase is random. When two or more atoms are replaced, a type of atom aggregation may occur, resulting in an uneven distribution of precipitated phase atoms. In addition, the shape is spherical. All these shortcomings make this technology unsuitable for alloys such as Au-Ag-Cu. Summary of the Invention

[0005] The purpose of this invention is to provide a molecular dynamics simulation method for predicting the strengthening effect of precipitates in materials, realizing the simulation of the continuous process of dislocations passing through nanorod-shaped precipitates, accurately evaluating the age-strengthening effect, and supporting the optimization of alloy composition and heat treatment process.

[0006] The technical solution adopted in this invention is:

[0007] A molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials is as follows: S1. Establish a single-cell model, then expand the cell, add dislocations, replace atoms, establish a matrix phase model containing one dislocation, optimize the model structure, and delete atoms in the cylindrical region of the same size as the target precipitation within the model. S2, establish a single-cell model, expand the cell and replace atoms to establish a precipitation phase model, optimize the model structure, and delete atoms outside the cylindrical region of the same size as the target precipitation phase in the model; S3. Combine the matrix phase model and precipitate phase model obtained in steps S1 and S2 to obtain the dislocation / precipitate phase model. Apply shear strain to the model and statistically analyze the relationship curve between the critical shear stress and the size of the cylindrical precipitate phase to guide the selection of actual alloy composition.

[0008] The invention is further characterized by: In steps S1 and S2, a single-cell model is established using Atomsk, and the model structure is optimized using energy minimization.

[0009] In step S1, the initial size of the matrix phase model is set based on the target precipitate size, wherein the initial model length is ≥3 × the tangent diameter of the target precipitate orientation, and the initial model height = initial model width = dislocation length ≥1.5 × the tangent diameter of the target precipitate orientation.

[0010] In step S2, the initial size of the precipitate model is set based on the target precipitate size. The initial model length is ≥ 2 × the directional tangent diameter of the target precipitate, and the initial model height is equal to the initial model width, which is greater than or equal to the directional tangent diameter of the target precipitate.

[0011] In step S3, in the dislocation / precipitate model, the height of the cylindrical precipitate is perpendicular to the Burgers vector of the dislocation.

[0012] The direction of the shear strain applied in step S3 is: the coordinate system is defined according to the crystal orientation and crystal axis, and the positive direction of the strain is along the positive x-axis.

[0013] The shear strain applied in step S3 is a uniform gradient, and the magnitude of the strain rate is related to the z-axis coordinate value z0 of the surface. The maximum value of the z-axis coordinate is denoted as z. max Strain rate = 0.05 + 0.1 × (z0 ÷ z) max-1 )Å / ps.

[0014] In step S3, the entire motion process is simulated and calculated using the EAM potential function. The critical shear stress of the dislocation motion process is statistically analyzed to characterize the strengthening effect of different precipitates. The law of the age strengthening effect of the alloy with the change of the cylindrical precipitate size is obtained, which guides the selection of actual alloy composition.

[0015] The beneficial effects of this invention are: (1) The method of the present invention can optimize the structure of the matrix phase and the precipitate phase separately by modeling separately, avoiding the segregation of some atoms, making the atomic arrangement of the model closer to the ideal crystal, and making it easier to change the type of precipitate phase; (2) The method of the present invention can establish heterostructure (such as L10 type) precipitates on matrix phases with face-centered cubic (FCC structure) and body-centered cubic structures by deleting atoms and merging models. The precipitates have more diverse shapes and can be compatible with more atomic structures. (3) The method of the present invention applies a gradient distribution of strain rate to the model to accurately simulate the interaction process of dislocations and precipitates when the material is under stress, and calculates the critical shear stress of the dislocation movement process to characterize the strengthening effect of precipitates of different sizes. (4) The method of the present invention can simultaneously perform simulation calculations of the strengthening effect of precipitates with different structures, sizes and atomic compositions. Compared with traditional simulation methods, it has a wider range of applications and higher efficiency, and can further assist in the optimization design of material composition and heat treatment process in the industry. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram showing the direction and magnitude of the shear strain applied to the model in the method of the present invention; Figure 3 These are low-magnification TEM dark-field images of the two Au-Ag-Cu alloys in Example 1 of this invention; Figure 4 This is a schematic diagram of the structure of a matrix phase model containing a dislocation obtained in Embodiment 1 of the present invention; Figure 5 The critical shear stress curves of rod-shaped precipitates of different sizes obtained in Example 1 of the present invention are shown. Detailed Implementation

[0017] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0018] This invention provides a molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials, such as... Figure 1 As shown, please follow these steps: S1. A single-cell model is established using Atomsk. The cell is then expanded, dislocations are added, and atoms are replaced to establish a matrix phase model containing one dislocation. The model structure is optimized using energy minimization. Then, atoms in a cylindrical region of the same size as the target precipitation are deleted from the optimized matrix phase model. The size of the target precipitate was obtained by observing and measuring the actual alloy sample using a transmission electron microscope. Furthermore, the initial size of the matrix model was set based on the size of the target precipitate observed by the transmission electron microscope, wherein the initial model length was ≥3 × the orientation tangent diameter of the target precipitate, and the initial model height = initial model width = dislocation length ≥1.5 × the orientation tangent diameter of the target precipitate.

[0019] S2, a single-cell model is established using Atomsk, then the cell is expanded and atoms are replaced to establish an initial precipitate model. The model structure is optimized using energy minimization, and then atoms outside the cylindrical region that is the same size as the target precipitate are deleted from the precipitate model after optimization. The initial size of the precipitate model is set based on the size of the target precipitate observed by transmission electron microscopy. The initial length of the model is ≥2 × the directional tangent diameter of the target precipitate, and the initial height of the model is equal to the initial width of the model, which is ≥ the directional tangent diameter of the target precipitate.

[0020] S3, combine the matrix phase model and precipitate phase model processed in steps S1 and S2 to obtain the dislocation / precipitate phase model, as follows: Figure 1 As shown, in this model, the height of the cylindrical precipitate is perpendicular to the Burgers vector (i.e., the direction of dislocation movement) b, in order to calculate the maximum strengthening effect.

[0021] Subsequently, a uniformly gradient shear strain was applied to the dislocation / precipitate model, and the model was subjected to a tangential force of magnitude τ. For example... Figure 2 As shown, the strain direction and magnitude are as follows: Based on the crystal orientation and crystal axis, a coordinate system is defined, with the positive strain direction along the positive x-axis; the strain rate magnitude is related to the z-axis coordinate value z0 of the plane, and the maximum z-axis coordinate value is denoted as z0. max Strain rate = 0.05 + 0.1 × (z0 ÷ z) max -1 )Å / ps.

[0022] Finally, the EAM potential function was selected to simulate the entire motion process, and the critical shear stress of the dislocation motion process was statistically analyzed to characterize the strengthening effect of different precipitates. The law of the age strengthening effect of the alloy with the change of precipitate size was obtained, which guides the selection of actual alloy composition.

[0023] Example 1: See Figure 3The images show low-magnification TEM dark-field images of two Au-Ag-Cu alloys. The left image is Au-20Ag-10Cu, and the right image is Au-35Ag-5Cu. The black areas represent the α-matrix phase of the FCC structure, and the white areas represent the nanorod-shaped precipitates. The diameter of the rod-shaped precipitates in both alloys is mainly distributed in the range of 10–20 Å, and the height is mainly distributed in the range of 20–200 Å. In this embodiment, four precipitates with a diameter of 10 Å and heights of 20 Å, 40 Å, 60 Å, and 80 Å were selected as the initial research objects. The invention will be further described in detail below with reference to other accompanying figures, using Au-based electrical contact materials as an example.

[0024] This embodiment uses a molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials, and is implemented according to the following steps: S1. A single-cell model is established using Atomsk. This model is then expanded, dislocations are added, and atoms are replaced to create a matrix phase model containing one dislocation. Energy minimization is used to optimize the model structure. Finally, atoms within a cylindrical region of equal size to the target precipitation are deleted from the optimized matrix phase model. Specifically: Based on the experimentally obtained Au lattice constant of 4.0788 Å, lattice type of FCC, and relative atomic mass of 196.97, a unit cell model is established. In the Cartesian coordinate system, according to convention, the crystal orientation

[001] is aligned with the x-axis, the crystal axis [-110] is aligned with the y-axis, and the crystal axis

[110] is aligned with the z-axis.

[0025] The matrix phase model is built using Atomsk and LAMMPS. Specifically, the initial unit cell model of the face-centered cubic structure is built using the create command in Atomsk; the poly.txt file is created and edited using a text editor, and the size of the expanded model is set to 200Å×120Å×120Å. Then, the polycrystal command is used to expand the cell to obtain the Au supercell model. Finally, the dislocation is added at a specified position using the dislocation command.

[0026] Next, use text editing software to edit the atom types, set the Ag and Cu atom parameters, and then use the `set type / radio` command in LAMMPS software to replace Au atoms with a certain proportion of Ag and Cu atoms according to the target alloy composition, thus obtaining the following... Figure 4 The model shown is an initial matrix phase model containing a dislocation.

[0027] The initial matrix phase model is minimized using the min command to optimize the overall atomic distribution. Finally, the atoms in the specified cylindrical region are deleted using the remove and select commands to obtain the model Au-Ag-Cu.cfg. The resulting model is named shear1.cfg.

[0028] S2, a single cell is established using Atomsk, then the cell is expanded and atoms are replaced to establish an initial precipitate model. The model structure is optimized using energy minimization, and then atoms outside the cylindrical region of the same size as the target precipitate are deleted from the optimized precipitate model.

[0029] This step is similar to step S1, the main difference being that the composition and structure of the precipitated phase differ from the matrix phase. Specifically: Based on the lattice constants and lattice types of the precipitated phases obtained from the experiment, an Au unit cell model is first established. In the Cartesian coordinate system, according to convention, the crystal orientation

[001] is aligned with the x-axis, the crystal axis [-110] is aligned with the y-axis, and the crystal axis

[110] is aligned with the z-axis.

[0030] Create and edit the poly.txt file using a text editor, setting the expanded cell model size to 200Å × 120Å × 120Å. Then, use the polycrystal command to expand the cell to obtain a supercell model. Edit the atom types, set the Cu atom parameters, and finally, in the LAMMPS software, use the set type / radio command to replace Au atoms with a certain proportion of Cu atoms according to the target alloy composition to obtain the initial precipitate phase model.

[0031] Use the min command to minimize the energy of the model and optimize the overall atom distribution. Then use the remove and select commands to delete atoms outside the specified cylindrical region. Name the resulting model shear2.cfg.

[0032] S3: Combine the matrix phase model and precipitate phase model processed in steps S1 and S2 to obtain the dislocation / precipitate phase model. Set a shear strain rate with a uniform gradient along the z-axis to the dislocation / precipitate phase model, simulating a tangential force of magnitude τ acting on the model. Use the EAM potential function to simulate the entire motion process, and statistically analyze the critical shear stress during dislocation motion to characterize the strengthening effect of different precipitates. Obtain the law governing the age-hardening effect of the alloy as a function of precipitate size, guiding the selection of actual alloy composition. Specifically: In Atomsk, the merge command is used to merge the two models, resulting in the dislocation / precipitate model shear.lmp. Subsequent simulations are then performed in LAMMPS software. The region command is used to define the boundary conditions and strain regions, and the velocity command is used to set the positive strain direction along the positive x-axis. The strain rate is related to the z-axis coordinate value z0 of the surface, specifically 0.05 + 0.1 × (z0 ÷ 120 - 1) Å / ps.

[0033] The EAM potential function of Au-Ag-Cu was selected for simulation calculation. Atomic information and a post-processable data file dumpthermo.atom.xxxx were output using the dump command. OVITO software was used for post-processing analysis and statistical analysis of the critical shear stress during the operation to characterize the strengthening effect of the precipitated phase.

[0034] Simulations were performed on precipitates of different sizes, and the final results were obtained. Figure 5 The figure shows the critical shear stress corresponding to different precipitate sizes, with the precipitate size referring to the height of the cylinder. It can be seen from the figure that the strengthening effect of nanoscale precipitates in Au-Ag-Cu alloys increases with size, and Au-20Ag-10Cu with larger precipitate sizes exhibits better performance. Combined with the dislocation motion process in the simulation, it can be determined that this is mainly because the precipitates pin dislocations, and the pinning force is positively correlated with the precipitate size. Furthermore, in this embodiment, the method of this invention can construct microstructures such as matrix phases, precipitates, and dislocations with highly consistent structure, size, and shape with the experimental samples. Moreover, by simply changing individual parameters, molecular dynamics simulation analysis of various alloys can be achieved, thus balancing accuracy and convenience in research on related materials.

[0035] Example 2: The molecular dynamics simulation method used in this embodiment for predicting the strengthening effect of precipitated phases in materials is as follows: S1. Establish a single-cell model, then expand the cell, add dislocations, replace atoms, establish a matrix phase model containing one dislocation, optimize the model structure, and delete atoms in the cylindrical region of the same size as the target precipitation within the model. S2, establish a single-cell model, expand the cell and replace atoms to establish a precipitation phase model, optimize the model structure, and delete atoms outside the cylindrical region of the same size as the target precipitation phase in the model; S3. Combine the matrix phase model and precipitate phase model obtained in steps S1 and S2 to obtain the dislocation / precipitate phase model. Apply shear strain to the model and statistically analyze the relationship curve between the critical shear stress and the size of the cylindrical precipitate phase to guide the selection of actual alloy composition.

[0036] Example 3: Based on Example 2, in steps S1 and S2, a single-cell model is established using Atomsk, and the model structure is optimized using energy minimization.

[0037] In step S1, the initial size of the matrix phase model is set based on the target precipitate size, wherein the initial model length is ≥3 × the tangent diameter of the target precipitate orientation, and the initial model height = initial model width = dislocation length ≥1.5 × the tangent diameter of the target precipitate orientation.

[0038] Example 4: Based on Example 3, in step S2, the initial size of the precipitate model is set based on the target precipitate size, the initial model length is ≥ 2 × the directional tangent diameter of the target precipitate, and the initial model height is equal to the initial model width, which is greater than or equal to the directional tangent diameter of the target precipitate.

[0039] Example 5: Based on Example 4, in step S3, in the dislocation / precipitate model, the height of the cylindrical precipitate is perpendicular to the Burgers vector of the dislocation.

[0040] The direction of the shear strain applied in step S3 is: the coordinate system is defined according to the crystal orientation and crystal axis, and the positive direction of the strain is along the positive x-axis.

[0041] Example 6: The molecular dynamics simulation method used in this embodiment for predicting the strengthening effect of precipitated phases in materials is as follows: S1. Establish a single-cell model, then expand the cell, add dislocations, replace atoms, establish a matrix phase model containing one dislocation, optimize the model structure, and delete atoms in the cylindrical region of the same size as the target precipitation within the model. S2, establish a single-cell model, expand the cell and replace atoms to establish a precipitation phase model, optimize the model structure, and delete atoms outside the cylindrical region of the same size as the target precipitation phase in the model; S3. Combine the matrix phase model and precipitate phase model obtained in steps S1 and S2 to obtain the dislocation / precipitate phase model. Apply shear strain to the model and statistically analyze the relationship curve between the critical shear stress and the size of the cylindrical precipitate phase to guide the selection of actual alloy composition.

[0042] In steps S1 and S2, a single-cell model is established using Atomsk, and the model structure is optimized using energy minimization.

[0043] In step S1, the initial size of the matrix phase model is set based on the target precipitate size, wherein the initial model length is ≥3 × the tangent diameter of the target precipitate orientation, and the initial model height = initial model width = dislocation length ≥1.5 × the tangent diameter of the target precipitate orientation.

[0044] In step S2, the initial size of the precipitate model is set based on the target precipitate size. The initial model length is ≥ 2 × the directional tangent diameter of the target precipitate, and the initial model height is equal to the initial model width, which is greater than or equal to the directional tangent diameter of the target precipitate.

[0045] In step S3, in the dislocation / precipitate model, the height of the cylindrical precipitate is perpendicular to the Burgers vector of the dislocation.

[0046] The direction of the shear strain applied in step S3 is: the coordinate system is defined according to the crystal orientation and crystal axis, and the positive direction of the strain is along the positive x-axis.

[0047] The shear strain applied in step S3 is a uniform gradient, and the magnitude of the strain rate is related to the z-axis coordinate value z0 of the surface. The maximum value of the z-axis coordinate is denoted as z. max Strain rate = 0.05 + 0.1 × (z0 ÷ z) max -1 )Å / ps.

Claims

1. A molecular dynamics simulation method for predicting a precipitation phase strengthening effect of a material, characterized by, Specifically: S1. Establish a single-cell model, then expand the cell, add dislocations, replace atoms, establish a matrix phase model containing one dislocation, optimize the model structure, and delete atoms in the cylindrical region of the same size as the target precipitation within the model. S2, establish a single-cell model, expand the cell and replace atoms to establish a precipitation phase model, optimize the model structure, and delete atoms outside the cylindrical region of the same size as the target precipitation phase in the model; S3. Combine the matrix phase model and precipitate phase model obtained in steps S1 and S2 to obtain the dislocation / precipitate phase model. Apply shear strain to the model and statistically analyze the relationship curve between the critical shear stress and the size of the cylindrical precipitate phase to guide the selection of actual alloy composition.

2. The molecular dynamics simulation method for prediction of a precipitation phase strengthening effect of a material according to claim 1, characterized by, In steps S1 and S2, a single-cell model is established using Atomsk, and the model structure is optimized using energy minimization.

3. The molecular dynamics simulation method for prediction of a precipitation phase strengthening effect of a material according to claim 1, characterized by, In step S1, the initial size of the matrix phase model is set based on the target precipitate size, wherein the initial model length is ≥3 × the tangent diameter of the target precipitate orientation, and the initial model height = initial model width = dislocation length ≥1.5 × the tangent diameter of the target precipitate orientation.

4. The molecular dynamics simulation method for prediction of a precipitation phase strengthening effect of a material according to claim 1, characterized by, In step S2, the initial size of the precipitate model is set based on the target precipitate size. The initial model length is ≥ 2 × the directional tangent diameter of the target precipitate, and the initial model height is equal to the initial model width, which is greater than or equal to the directional tangent diameter of the target precipitate.

5. The molecular dynamics simulation method for prediction of a precipitation phase strengthening effect of a material according to claim 1, characterized by, In step S3, in the dislocation / precipitate model, the height of the cylindrical precipitate is perpendicular to the Burgers vector of the dislocation.

6. The molecular dynamics simulation method for prediction of a precipitation phase strengthening effect of a material according to claim 1, characterized by, The direction of the shear strain applied in step S3 is: the coordinate system is defined according to the crystal orientation and crystal axis, and the positive direction of the strain is along the positive x-axis.

7. The molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials according to claim 1, characterized in that, The shear strain applied in step S3 is uniformly gradiently changed, and the strain rate is related to the z-axis coordinate value z0 of the plane, and the maximum value of the z-axis coordinate is denoted as z max , and the strain rate = 0.05 + 0.1 × (z0 ÷ z max -1 ) Å / ps.

8. The molecular dynamics simulation method for predicting the strengthening effect of precipitated phases in materials according to claim 1, characterized in that, In step S3, the entire motion process is simulated and calculated using the EAM potential function. The critical shear stress of the dislocation motion process is statistically analyzed to characterize the strengthening effect of different precipitates. The law of the age strengthening effect of the alloy with the change of the cylindrical precipitate size is obtained, which guides the selection of actual alloy composition.

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