Grain boundary stress concentration factor calculation method, device, medium, and program

Abstract

The application discloses a kind of grain boundary stress concentration factor calculation method, equipment, medium and program, method is applied to a grain boundary stress concentration factor calculation device, method includes: based on the grain size and grain orientation information of material, establish finite element model;The stress-strain curve of material is fitted by crystal plastic finite element model, and the critical starting stress value of deformation mode and hardening parameter of material at room temperature is determined;Based on finite element model, the critical starting stress value of deformation mode and hardening parameter, obtain the shear stress of each grain in finite element model on slip system or twinning system;Eshelby model is fitted based on the shear stress of different positions of grain boundary, and the grain boundary stress concentration factor is obtained.This application requires low, and the difficulty of calculation is low, can accurately calculate the stress concentration factor of each grain boundary of material, can quantitatively evaluate the ability of each grain boundary in material to hinder deformation transmission and crack initiation, provide criterion for material service performance evaluation.

Description

Technical Field

[0001] This invention relates to the field of grain boundary stress concentration factor calculation for high-performance materials, and particularly to a method, apparatus, medium, and program for calculating grain boundary stress concentration factor. Background Technology

[0002] Grain boundaries, as an inherent microstructure of polycrystalline materials, are widely present in metallic materials and have a significant impact on their mechanical, corrosion, and metallurgical properties. Grain boundaries effectively hinder dislocation movement, and dislocation pile-up at grain boundaries induces the formation of local stress concentrations.

[0003] Both microscopic plastic deformation and macroscopic mechanical properties of materials are related to grain boundary stress concentration, including the formation of Lüders bands, the formation and propagation of deformation twins, the fine-grain strengthening effect, and the initiation and propagation of fatigue cracks. Therefore, quantitative analysis of grain boundary stress distribution can provide criteria for a deeper understanding of various plastic deformation behaviors, fracture mechanisms, and the control of macroscopic mechanical properties.

[0004] In the process of implementing the technical solutions of the embodiments of this application, the inventors of this application have discovered at least the following technical problems in the prior art:

[0005] Traditional methods for obtaining stress distribution near grain boundaries using EBSD data analysis determine lattice strain by comparing diffraction patterns in undeformed regions and deformed regions within the grain. This process relies on high-resolution, high-quality diffraction patterns. Therefore, it requires high-quality sample surfaces and very high electron doses, resulting in slow analysis speeds, large data acquisition volumes, and unsuitability for samples with significant deformation. Consequently, obtaining stress concentration factors near grain boundaries using EBSD suffers from drawbacks such as difficult sample preparation and large data acquisition volumes. Furthermore, this method can only obtain the stress distribution on the sample surface and is insufficient for analyzing deformation information within the material.

[0006] In summary, existing technologies suffer from technical problems such as the high difficulty and high requirements in calculating stress concentration factors, and the inability to analyze deformation information inside materials. Summary of the Invention

[0007] This application provides a method, device, medium, and program for calculating grain boundary stress concentration factor, which solves the technical problems of existing stress concentration factor calculation methods being difficult, demanding, and unable to analyze deformation information inside materials.

[0008] This application provides a method for calculating grain boundary stress concentration factor, applied to a grain boundary stress concentration factor calculation device. The method includes: establishing a finite element model based on the grain size and grain orientation information of the material; fitting the stress-strain curve of the material through a crystal plastic finite element model to determine the critical initiation stress value and hardening parameter of the material at room temperature for the deformation mode; obtaining the shear stress on the slip system or twin system of each grain in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameter; and obtaining the grain boundary stress concentration factor by fitting an Eshelby model based on the shear stress at different positions of the grain boundary.

[0009] Optionally, the step of establishing a finite element model based on the grain size and grain orientation information of the material specifically involves: establishing a finite element model based on the grain size of the material and at least 800 grain orientation information, wherein the finite element model contains more than 9,000 meshes and the increment step must be less than 0.001.

[0010] Optionally, before establishing the finite element model based on the grain size and grain orientation information of the material, the method further includes: physically grinding the material until the surface is smooth; and performing photochemical polishing on the material.

[0011] Optionally, the step of fitting the stress-strain curve of the material using a crystal plastic finite element model to determine the critical initiation stress value and hardening parameters of the material at room temperature specifically involves: using a periodic boundary condition constraint model, fitting the stress-strain curve of the material using a crystal plastic finite element model to determine the critical initiation stress value and hardening parameters of the material at room temperature.

[0012] Optionally, obtaining the shear stress on the slip system or twin system of each grain in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters specifically includes: obtaining the slip system or twin system initiated within each grain in the finite element model during plastic deformation based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters; and obtaining the shear stress on the slip system or twin system of each grain in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, the hardening parameters, and the slip system or twin system within each grain.

[0013] Optionally, obtaining the shear stress of each grain on the slip system or twin system in the finite element model specifically involves: determining the slip surface and slip direction of each grain in the finite element model under different strain values, which are used to extract the shear stress corresponding to each slip system or twin system; and extracting at least 50 shear stresses at different locations for each grain.

[0014] Optionally, after obtaining the grain boundary stress concentration factor, the method further includes: comparing the relationship between the grain boundary stress concentration factor and the Hall-Petch slope.

[0015] On the other hand, embodiments of this application also provide a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a method for calculating grain boundary stress concentration factor.

[0016] This application also provides a computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the steps of a method for calculating grain boundary stress concentration factor.

[0017] This application also provides a computer program product, including a computer program, characterized in that, when the computer program is executed by a processor, it implements the steps of a method for calculating grain boundary stress concentration factor.

[0018] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0019] Based on the grain size and orientation information of the material, a finite element model is established. The stress-strain curve of the material is fitted using a crystal plasticity finite element model to determine the critical initiation stress value and hardening parameters of the deformation mode at room temperature. Based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. The grain boundary stress concentration factor is obtained by fitting an Eshelby model based on the shear stress at different grain boundary locations. This application does not require a high-quality sample surface, thus having low requirements. The data acquisition volume is small, and the computational difficulty is low. The reliability of the results for each grain boundary stress concentration factor mainly depends on the accuracy of the obtained stress distribution near the grain boundary. Through crystal plasticity finite element simulation (CPFEM), the stress distribution near the grain boundary can be accurately obtained, the stress concentration factor at each grain boundary can be accurately measured, and the grain refinement strengthening orientation dependence can be analyzed. By adjusting the loading direction and strain in the crystal plasticity model after fitting the stress-strain curve of the material using a finite element model, the influence of loading conditions and strain on grain boundary stress distribution can be analyzed. This allows for the accurate calculation of the stress concentration factor at each grain boundary, enabling a quantitative assessment of the ability of grain boundaries within the material to hinder deformation propagation and crack initiation. Both the microscopic plastic deformation behavior and macroscopic mechanical properties of materials are related to grain boundary stress concentration. Quantitatively calculating the grain boundary stress concentration factor provides a criterion for evaluating the service performance of materials.

[0020] Furthermore, the establishment of a finite element model based on the material's grain size and orientation information specifically involves: establishing a finite element model based on the material's grain size and at least 800 grain orientation information points. The finite element model contains a mesh size greater than 9000, and the increment step must be less than 0.001. If the number of grain orientation information points is less than 800, the orientation information is insufficient to reflect the macroscopic orientation information of the sample; if the number of mesh points is less than 9000, the simulation results will not converge, and increasing the mesh size will lead to changes in stress distribution; if the increment step is greater than 0.001, the simulation results will not converge, and decreasing the increment step will also lead to changes in stress distribution.

[0021] Furthermore, before establishing the finite element model based on the material's grain size and orientation information, the method further includes: physically grinding the material until its surface is smooth; and performing photochemical polishing on the material. This is beneficial for obtaining the material's grain size and orientation information.

[0022] Furthermore, the determination of the critical initiation stress value and hardening parameters of the material at room temperature by fitting the stress-strain curve of the material using a crystal plasticity finite element model specifically involves: using a periodic boundary condition constraint model to fit the stress-strain curve of the material using a crystal plasticity finite element model to determine the critical initiation stress value and hardening parameters of the material at room temperature. Without using a periodic boundary condition constraint model, the stress distribution at the model boundaries would be significantly different; using a periodic boundary condition constraint model can reduce the influence of the model boundaries on the simulation results.

[0023] Furthermore, obtaining the shear stress on the slip system or twin system of each grain in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters specifically includes: obtaining the slip system or twin system initiated within each grain in the finite element model during plastic deformation based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters; and obtaining the shear stress on the slip system or twin system of each grain in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, the hardening parameters, and the slip system or twin system within each grain. This is beneficial for obtaining the shear stress.

[0024] Furthermore, obtaining the shear stress of each grain on the slip system or twin system in the finite element model specifically involves: determining the slip surface and slip direction corresponding to each grain in the finite element model under different strain values, which are used to extract the shear stress corresponding to each slip system or twin system; extracting at least 50 shear stress values ​​at different locations for each grain. If fewer than 50 shear stress values ​​are obtained within a grain, the curve fitting results will have a larger error.

[0025] Furthermore, after obtaining the grain boundary stress concentration factor, the method further includes comparing the relationship between the grain boundary stress concentration factor and the Hall-Petch slope. This verifies the accuracy of the calculation results. Attached Figure Description

[0026] Figure 1 This is a flowchart of a method for calculating grain boundary stress concentration factor in one embodiment of this application;

[0027] Figure 2 This is a schematic diagram of a finite element model in one embodiment of this application;

[0028] Figure 3 This is a stress distribution diagram at different locations from the grain boundary in one embodiment of this application;

[0029] Figure 4 This is a plot of grain boundary stress concentration factors under different strain variables in one embodiment of this application. Detailed Implementation

[0030] This application provides a method, device, medium, and program for calculating grain boundary stress concentration factor, which solves the technical problems of existing stress concentration factor calculation methods being difficult, demanding, and unable to analyze deformation information inside materials.

[0031] The technical solution of one embodiment of the present invention is to solve the above-mentioned problems, and the overall idea is as follows:

[0032] Based on the grain size and orientation information of the material, a finite element model is established. The stress-strain curve of the material is fitted using a crystal plasticity finite element model to determine the critical initiation stress value and hardening parameters for the deformation mode at room temperature. Based on the finite element model, the critical initiation stress value for the deformation mode, and the hardening parameters, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. The grain boundary stress concentration factor is obtained by fitting the Eshelby model based on the shear stress at different grain boundary locations. This application does not require a high-quality sample surface, thus having low requirements. The data acquisition volume is small, and the computational difficulty is low. The reliability of the results for each grain boundary stress concentration factor mainly depends on the accuracy of the obtained stress distribution near the grain boundary. Through crystal plasticity finite element simulation (CPFEM), the stress distribution near the grain boundary can be accurately obtained, the stress concentration factor at each grain boundary can be accurately measured, and the grain refinement strengthening orientation dependence can be analyzed. By adjusting the loading direction and strain in the crystal plasticity model after fitting the stress-strain curve of the material using a finite element model, the influence of loading conditions and strain on grain boundary stress distribution can be analyzed. This allows for the accurate calculation of the stress concentration factor at each grain boundary, enabling a quantitative assessment of the ability of grain boundaries within the material to hinder deformation propagation and crack initiation. Both the microscopic plastic deformation behavior and macroscopic mechanical properties of materials are related to grain boundary stress concentration. Quantitatively calculating the grain boundary stress concentration factor provides a criterion for evaluating the service performance of materials.

[0033] To better understand the above technical solutions, a detailed description of the solutions will be provided below in conjunction with the accompanying drawings and specific embodiments. Obviously, the embodiments described in this invention are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0034] Theoretical calculations show that the local stress near the grain boundary varies with the distance from the grain boundary. This local stress variation with distance (x) from the grain boundary can be written as: τ=τ0+F(x) -1 / This equation is commonly referred to as the Eshelby model. Here, τ represents the shear stress in the slip system, τ0 is the critical initiation stress for free sliding of dislocations, and F is the stress concentration factor. This value reflects the hindering effect of grain boundaries on deformation propagation; a larger F value indicates a greater hindering effect of grain boundaries on deformation propagation between adjacent grains, and a stronger grain refinement strengthening effect. Therefore, the stress concentration factor of each grain boundary can be obtained by analyzing the stress distribution near the grain boundaries.

[0035] Recent studies have shown that HR-EBSD (high-resolution electron backscatter diffraction) can successfully obtain the stress distribution near grain boundaries, and that this local stress distribution is consistent with the stress distribution predicted by the Eshelby model. Therefore, combining HR-EBSD and the Eshelby model can yield the stress concentration factor at each grain boundary within the material. However, obtaining stress concentration near grain boundaries using HR-EBSD has drawbacks such as difficult sample preparation and large data acquisition volume. Furthermore, this method can only obtain the stress distribution on the sample surface, making it difficult to analyze deformation information within the material. In fact, the reliability of the results of analyzing the stress concentration factor at each grain boundary using a combination of HR-EBSD and the Eshelby model largely depends on the accuracy of the obtained stress distribution near the grain boundaries. If other methods, such as crystal plasticity finite element simulation (CPFEM), can accurately obtain the stress distribution near grain boundaries, then the stress concentration factor at each grain boundary can also be accurately measured, and the grain refinement strengthening orientation dependence can be analyzed. CPFEM is an effective method for analyzing the deformation behavior of micro-regions in materials. The local deformation behavior and local stress distribution predicted by CPFEM are consistent with the results of digital image correlation (DIC), EBSD analysis, and three-dimensional synchrotron radiation experiments. Therefore, combining CPFEM and the Eshelby model allows for the quantitative calculation of the stress concentration factor at each grain boundary.

[0036] The method for calculating the grain boundary stress concentration factor in this application combines the CPFEM and Eshelby models to quantitatively calculate the stress concentration factor of each grain boundary.

[0037] This embodiment provides a method for calculating grain boundary stress concentration factor, which is applied to a grain boundary stress concentration factor calculation device.

[0038] The grain boundary stress concentration factor calculation method provided in this embodiment can be applied to metallic materials, and can include, but is not limited to, magnesium alloys, titanium alloys, copper alloys, and zirconium alloys.

[0039] Please refer to Figure 1 The present invention provides a detailed description of a method for calculating grain boundary stress concentration factor in an embodiment of the present invention.

[0040] Step 101: Establish a finite element model based on the grain size and grain orientation information of the material;

[0041] Step 102: Fit the stress-strain curve of the material using a crystal plastic finite element model to determine the critical initiation stress value and hardening parameters of the material at room temperature for the deformation mode;

[0042] Step 103: Based on the finite element model, the critical starting stress value of the deformation mode, and the hardening parameters, obtain the shear stress of each grain on the slip system or twin system in the finite element model;

[0043] Step 104: Based on the shear stress at different locations of the grain boundary, fit the Eshelby model to obtain the grain boundary stress concentration factor.

[0044] The following will describe in detail the process of calculating the grain boundary stress concentration factor in the embodiments of this application, taking magnesium alloy as an example.

[0045] Once the preparation work for calculating the grain boundary stress concentration factor is completed, step 101 is executed: establishing a finite element model based on the grain size and grain orientation information of the material.

[0046] In specific implementation, for example, EBSD (electron backscatter diffraction) technology is used to obtain grain size and orientation information of magnesium alloy materials. The orientation data of the magnesium alloy materials are acquired using electron backscatter diffraction (EBSD) technology on a scanning electron microscope (SEM; TESCAN MIRA3) equipped with an HKL-EBSD system. A finite element model is constructed based on the EBSD data (including grain size and orientation information), containing 1×100×100 = 10000 three-dimensional elements. The texture characteristics of the established finite element model are similar to those of the macroscopic texture.

[0047] Specifically, the recognition rate of EBSD data needs to be better than 90% to improve the accuracy of grain orientation information in the EBSD data. Conversely, when the recognition rate of EBSD data is low, the grain orientation information in the EBSD data will be inaccurate.

[0048] Next, proceed with step 102: fit the stress-strain curve of the material using a crystalline plastic finite element model to determine the critical initiation stress value and hardening parameters of the material's deformation mode at room temperature.

[0049] In the specific implementation process, for example: importing the finite element model into ABAQUS software, the finite element model is as follows: Figure 2 As shown. By fitting the stress-strain curves of magnesium alloys using a crystalline plastic finite element model, the deformation modes that are easily initiated under room temperature deformation conditions in magnesium alloys ({110} in body-centered cubic metals) are determined. <111> Slip system, face-centered cubic metal is {111} <110> Slip system, with close-packed hexagonal metals as the basal plane slip. Cylindrical slip tapered surface Slip <c+a> Slip and twins Critical starting stress value and hardening parameters.

[0050] Next, we begin step 103: based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, we obtain the shear stress of each grain on the slip system or twin system in the finite element model.

[0051] In specific implementation, for example, based on the finite element model, the critical starting stress value of the deformation mode and the hardening parameters, the local stress is distributed to the slip system / twin system according to Schmidt's law, so as to obtain the shear stress of each grain on the slip system or twin system.

[0052] Next, we begin step 104: based on the shear stress at different locations of the grain boundary, we fit the Eshelby model to obtain the grain boundary stress concentration factor.

[0053] In the specific implementation process, for example: Figure 3As shown, the stress distribution varies depending on the distance from the grain boundary. The shear stress at different distances from the grain boundary is extracted, and the formula τ=τ0+F(x) is fitted in Origin software. -1 / This equation is commonly referred to as the Eshelby model. Here, τ is the shear stress in the slip system, τ0 is the critical initiation stress for dislocation free sliding, and F is the stress concentration factor, which is obtained for each grain boundary. Each grain contains more than 100 units.

[0054] In order to ensure that the grain orientation information can reflect the macroscopic orientation information of the sample and to make the simulation results converge, step 101 establishes a finite element model based on the grain size and grain orientation information of the material. Specifically, a finite element model is established based on the grain size of the material and at least 800 grain orientation information. The finite element model contains more than 9,000 meshes and the increment step must be less than 0.001.

[0055] In specific implementation, for example, EBSD data needs to contain orientation information of more than 800 grains. If the number of grains is small, the orientation information in EBSD data is insufficient to reflect the macroscopic orientation information of the sample.

[0056] The finite element model contains more than 9000 meshes, and the increment step must be less than 0.001. If the number of meshes is less than 9000, the simulation results will not converge. Increasing the number of meshes will cause changes in the stress distribution. When the increment step is greater than 0.001, the simulation results will not converge. Decreasing the increment step will also cause changes in the stress distribution.

[0057] In order to facilitate the acquisition of grain size and grain orientation information of the material, before establishing the finite element model based on the grain size and grain orientation information of the material in step 101, the following steps are also included: physically grinding the material until the surface is smooth; and photochemical polishing the material.

[0058] In the specific implementation process, for example, before conducting the EBSD test, the magnesium alloy material is first polished with SiC sandpaper until the surface is smooth and free of scratches, and then electrochemical polishing is performed with AC2 electrolyte at a voltage of 20V and a temperature of -20℃.

[0059] To reduce the influence of model boundaries on simulation results, step 102 uses a crystal plastic finite element model to fit the stress-strain curve of the material and determine the critical initiation stress value and hardening parameters of the deformation mode at room temperature. Specifically, a periodic boundary condition constraint model is used to fit the stress-strain curve of the material using a crystal plastic finite element model to determine the critical initiation stress value and hardening parameters of the deformation mode at room temperature.

[0060] In practical implementation, for example, periodic boundary condition constraint models are used in simulations. Figure 1As shown, the constraints applied to boundaries BC and AC are:

[0061]

[0062]

[0063] u i This is the displacement along the i-th direction (i = x, y). Meanwhile, the constraints in equations (1) and (2) above do not include nodes O, A, B, and C. The constraints on these four nodes can be described as:

[0064]

[0065] Node B is fixed in the y-direction, node A is fixed in the x-direction, and node O cannot move in the x, y, and z directions. During the simulation, the applied strain is applied at node A.

[0066] To facilitate the acquisition of shear stress, step 103, based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, obtains the shear stress of each grain in the finite element model on the slip system or twin system. Specifically, this includes: obtaining the slip system or twin system initiated within each grain in the finite element model during plastic deformation based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters; and obtaining the shear stress of each grain in the finite element model on the slip system or twin system based on the finite element model, the critical initiation stress value of the deformation mode, the hardening parameters, and the slip system or twin system within each grain.

[0067] In the specific implementation process, for example: importing the finite element model into ABAQUS software, the finite element model is as follows: Figure 2 As shown. By fitting the stress-strain curves of magnesium alloy materials, the parameters of the crystal plastic constitutive model are adjusted, and then the plastic deformation modes of each grain are analyzed. The local stress near the grain boundary is then assigned to the slip system or twin system. The model after fitting the stress-strain curves of magnesium alloy to the finite element model is the crystal plastic constitutive model. The crystal plastic constitutive model is called, and the model parameters are adjusted by fitting the stress-strain curves of magnesium alloy materials under normal tension, deviation from the normal of the plate at 45°, and deviation from the normal of the plate at 90°. In the simulation, it is assumed that the plastic deformation of magnesium alloys with different orientations is all due to basal slip. Cylindrical slip tapered surface Slip <c+a> Slip and twins To coordinate, the parameters of each deformation mode in the model are shown in the table below.

[0068]

[0069]

[0070] To minimize the error in the curve fitting results, step 104 obtains the shear stress of each grain on the slip system or twin system in the finite element model. Specifically, this involves determining the slip surface and slip direction of each grain in the finite element model under different strain values, which are used to extract the shear stress corresponding to each slip system or twin system. At least 50 shear stresses at different locations are extracted for each grain.

[0071] In specific implementation, for example, the initiation activity under different strains for each deformation mode within the grain can be extracted using the ABAQUS software post-processing module. Figure 4 The figure shows the distribution of grain boundary stress concentration factors under different strain values. Due to the non-uniformity of deformation within grains, it is necessary to collect the average value of the deformation mode activity at ten different locations within a single grain to represent the deformation behavior within that grain.

[0072] Analyze the six local stress tensors of each grain, namely σ 11 σ 22and σ 33 The three normal stress components and σ 12 σ 13 and σ 23 The three shear stress components determine the strain components that cause local stress concentration, and the local stress is sheared onto the slip system / twin system.

[0073] Extracting more than 50 shear stresses from different locations within the grain leads to a larger error in the curve fitting results when fewer than 50 shear stresses are obtained within the grain.

[0074] To verify the accuracy of the calculation results, after obtaining the grain boundary stress concentration factor by fitting the Eshelby model based on the shear stress at different locations of the grain boundary in step 104, the following steps are also included: comparing the relationship between the grain boundary stress concentration factor and the Hall-Petch slope.

[0075] In practical implementation, for example, the numerical relationship between the grain boundary stress concentration factor and the Hall-Petch slope (k) is as follows: N is the number of grain boundaries, k is the Hall-Petch slope, F is the grain boundary stress concentration factor, and M... i The Schmitt factor for each grain.

[0076] Based on the numerical relationship between grain boundary stress concentration factor and Hall-Petch slope (k), the Hall-Petch slope (k) of magnesium alloys with different textures was calculated, and the accuracy of the calculation results was verified.

[0077] As shown in the table below, the predicted average k values ​​for magnesium alloy materials under tension along the normal direction, at a deviation of 45° from the normal direction, and at a deviation of 90° from the normal direction are 209 MPa mm. 1 / 2 149MPa mm 1 / 2 and 381MPa mm 1 / 2 The experimentally determined k-values ​​of magnesium alloy materials under loading in different directions were: 227 MPa mm. 1 / 2 158MPa mm 1 / 2 and 411MPa mm 1 / 2 This indicates that finite element simulation based on crystal plasticity can accurately calculate the grain boundary stress concentration factor of magnesium alloys.

[0078]

[0079] The number of grain boundaries analyzed should be greater than 20. Analyzing too few grain boundaries will result in a large error in the results.

[0080] Another embodiment of the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a method for calculating grain boundary stress concentration factor.

[0081] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a method for calculating grain boundary stress concentration factor.

[0082] Another embodiment of the present invention provides a computer program product, including a computer program, wherein when the computer program is executed by a processor, it implements the steps of a method for calculating grain boundary stress concentration factor.

[0083] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0084] Based on the grain size and orientation information of the material, a finite element model is established. The stress-strain curve of the material is fitted using a crystal plasticity finite element model to determine the critical initiation stress value and hardening parameters for the deformation mode at room temperature. Based on the finite element model, the critical initiation stress value for the deformation mode, and the hardening parameters, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. The grain boundary stress concentration factor is obtained by fitting the Eshelby model based on the shear stress at different grain boundary locations. This application does not require a high-quality sample surface, thus having low requirements. The data acquisition volume is small, and the computational difficulty is low. The reliability of the results for each grain boundary stress concentration factor mainly depends on the accuracy of the obtained stress distribution near the grain boundary. Through crystal plasticity finite element simulation (CPFEM), the stress distribution near the grain boundary can be accurately obtained, the stress concentration factor at each grain boundary can be accurately measured, and the grain refinement strengthening orientation dependence can be analyzed. By adjusting the loading direction and strain in the crystal plasticity model after fitting the stress-strain curve of the material using a finite element model, the influence of loading conditions and strain on grain boundary stress distribution can be analyzed. This allows for the accurate calculation of the stress concentration factor at each grain boundary, enabling a quantitative assessment of the ability of grain boundaries within the material to hinder deformation propagation and crack initiation. Both the microscopic plastic deformation behavior and macroscopic mechanical properties of materials are related to grain boundary stress concentration. Quantitatively calculating the grain boundary stress concentration factor provides a criterion for evaluating the service performance of materials.

[0085] Furthermore, a finite element model is established based on the material's grain size and grain orientation information. Specifically, a finite element model is established based on the material's grain size and at least 800 grain orientation information points. The finite element model contains more than 9000 meshes, and the increment step must be less than 0.001. When there are fewer than 800 grain orientation information points, the orientation information is insufficient to reflect the macroscopic orientation information of the sample; when the number of meshes is less than 9000, the simulation results do not converge, and increasing the number of meshes will lead to changes in stress distribution; when the increment step is greater than 0.001, the simulation results do not converge, and decreasing the increment step will also lead to changes in stress distribution.

[0086] Furthermore, before establishing a finite element model based on the material's grain size and orientation information, the method also includes: physically grinding the material until the surface is smooth; and performing photochemical polishing on the material. This is beneficial for obtaining the material's grain size and orientation information.

[0087] Furthermore, by fitting the stress-strain curve of the material using a crystalline plasticity finite element model, the critical initiation stress value and hardening parameters of the deformation mode at room temperature are determined. Specifically, a periodic boundary condition constraint model is used, and the stress-strain curve of the material is fitted using a crystalline plasticity finite element model to determine the critical initiation stress value and hardening parameters of the deformation mode at room temperature. Without the periodic boundary condition constraint model, the stress distribution at the model boundaries would be significantly different; using the periodic boundary condition constraint model can reduce the influence of the model boundaries on the simulation results.

[0088] Furthermore, based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. Specifically, this includes: obtaining the slip system or twin system initiated within each grain in the finite element model during plastic deformation based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters; and obtaining the shear stress of each grain on the slip system or twin system in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, the hardening parameters, and the slip system or twin system within each grain. This is beneficial for obtaining the shear stress.

[0089] Furthermore, the shear stresses of each grain on the slip system or twin system in the finite element model are obtained. Specifically, the slip planes and slip directions corresponding to each grain under different strains are determined in the finite element model, which are used to extract the shear stresses corresponding to each slip system or twin system. At least 50 shear stresses at different locations are extracted for each grain. If fewer than 50 shear stress values ​​are obtained within the grain, the curve fitting results will have a large error.

[0090] Furthermore, after obtaining the grain boundary stress concentration factor, the calculation also includes comparing the relationship between the grain boundary stress concentration factor and the Hall-Petch slope. This verifies the accuracy of the calculation results.

[0091] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.

[0092] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0093] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0094] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0095] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating grain boundary stress concentration factor, applied to a grain boundary stress concentration factor calculation device, characterized in that, The method includes: A finite element model is established based on the grain size and grain orientation information of the material. By fitting the stress-strain curve of the material using a crystalline plastic finite element model, the critical initiation stress value and hardening parameters of the material at room temperature for deformation mode were determined. Based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. The grain boundary stress concentration factor is obtained by fitting the Eshelby model to the shear stress at different locations of the grain boundary. Specifically, obtaining the shear stress of each grain on the slip system or twin system in the finite element model based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters includes: Based on the finite element model, the critical initiation stress value of the deformation mode, and the hardening parameters, the slip system or twin system initiated in each grain in the finite element model during plastic deformation is obtained. Based on the finite element model, the critical initiation stress value of the deformation mode, the hardening parameters, and the slip system or twin system within each grain, the shear stress of each grain on the slip system or twin system in the finite element model is obtained. Specifically, obtaining the shear stress of each grain on the slip system or twin system in the finite element model involves: The slip planes and slip directions of each grain in the finite element model under different strains are determined, which are used to extract the shear stress corresponding to each slip system or twin system; At least 50 different shear stresses were extracted from each grain; In this study, the loading direction and loading strain in the crystal plasticity model after fitting the stress-strain curve of the material by the finite element model were adjusted, and then the influence of loading conditions and strain on grain boundary stress distribution was analyzed.

2. The method as described in claim 1, characterized in that, The finite element model is established based on the grain size and grain orientation information of the material, specifically as follows: A finite element model is established based on the grain size of the material and at least 800 grain orientation information. The finite element model contains more than 9,000 meshes and the increment step must be less than 0.

001.

3. The method as described in claim 1, characterized in that, Before establishing the finite element model based on the material's grain size and grain orientation information, the method further includes: The material is physically polished until the surface is smooth; The material is subjected to photochemical polishing.

4. The method as described in claim 1, characterized in that, The process of fitting the stress-strain curve of the material using a crystalline plastic finite element model to determine the critical initiation stress value and hardening parameters of the material at room temperature is as follows: A periodic boundary condition constraint model was used, and the stress-strain curve of the material was fitted by a crystal plastic finite element model to determine the critical initiation stress value and hardening parameters of the deformation mode at room temperature.

5. The method as described in claim 1, characterized in that, After obtaining the grain boundary stress concentration factor, the method further includes: Compare the relationship between the grain boundary stress concentration factor and the Hall-Petch slope.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method described in any one of claims 1-5.

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