Residual stress and density numerical value prediction method based on modified Drucker-Prager Cap model

Abstract

The invention discloses a residual stress and density numerical value prediction method based on a corrected Drucker-Prager Cap model, and the method comprises the steps: obtaining a parameter relation according to the corrected Drucker-Prager Cap model and theoretical analysis, and selecting a parameter variable; training the initial residual stress and density numerical value prediction model by using the selected parameter variables and different set temperatures to obtain a residual stress and density numerical value prediction model; and obtaining a target residual stress and density value, and inputting the residual stress and density value prediction model to obtain a prediction result. According to the method, actual engineering is converted into a visual model, and the processes of compression molding and sinter molding of the neodymium iron boron powder are observed, so that trial and error can be effectively reduced, and the success rate of ideal samples is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of residual stress and density numerical prediction, and in particular relates to a residual stress and density numerical prediction method based on a modified Drucker-Prager Cap model. Background Art

[0002] NdFeB permanent magnet materials are widely used in many fields due to their excellent magnetic properties and low cost. The preparation process of NdFeB magnets includes bonding process, sintering process and hot pressing process. Hot pressing process is a hot forming technology that has been developed and applied earlier in powder metallurgy. However, the magnets prepared by hot pressing process have problems such as uneven density and stress concentration, which have a serious impact on the forming performance and magnetic properties of the magnets. Therefore, multiple trials and errors are required in the preparation process to obtain a more ideal effect. Problems such as long test cycle and waste of resources caused by multiple trials and errors need to be solved urgently. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a numerical prediction method for residual stress and density based on the modified Drucker-Prager Cap model, adopts finite element simulation technology to solve the limitations of the relative density, temperature field and stress field of actual engineering that are difficult to predict, and converts the actual engineering into a visual model. By observing the pressing and sintering process of NdFeB powder, it can effectively reduce trial and error and improve the success rate of ideal samples.

[0004] To achieve the above object, the present invention provides a numerical prediction method for residual stress and density based on a modified Drucker-Prager Cap model, comprising:

[0005] According to the modified Drucker-Prager Cap model and theoretical analysis, the parameter relationship is obtained and the parameter variables are selected;

[0006] The initial residual stress and density numerical prediction model is trained by selecting parameter variables and setting different temperatures to obtain the residual stress and density numerical prediction model;

[0007] Obtain target residual stress and density values, input the residual stress and density numerical prediction model, and obtain prediction results.

[0008] Optionally, the basis for selecting the porosity parameter in the green compaction stage in the theoretical analysis includes:

[0009] E=c 0 +c 1 exp(c 2 ρ),

[0010]

[0011] Among them, c 0 、c 1 、c 2 is the coefficient of data fitting; ρ 0 is the volume density of the material, ρ is the material density, E is the elastic modulus, and p is the porosity.

[0012] Optionally, the basis for selecting the porosity parameter in the sintering stage in the theoretical analysis includes:

[0013] Q=mcΔT,

[0014] Where c is the specific heat capacity, Q is the amount of heat absorbed or released by the object, m is the mass of the object, and ΔT is the change in the object's temperature;

[0015]

[0016] Where q is the heat flux, S is the unit area, λ is the thermal conductivity, ΔT is the temperature difference between the upper surface and the center, and d is the sample thickness.

[0017] Optionally, the numerical prediction model for initial residual stress and density includes: a punch and a blank, wherein the size of the blank is the same as the actual engineering size, i.e., a diameter of 10 mm and a height of 5 mm, and the diameter of the punch is 10 mm and the height is 20 mm; the punch applies a pressure of 60 MPa and moves downward, and the blank is pressed downward into shape, and the boundary conditions are set to U1, U2 direction is fixed, and U3 direction is displaced, and the bottom of the blank is set to be completely fixed to simulate the wrapping effect of the outer wall on the blank, and at the same time, the contact surface between the punch and the blank is set to be master-slave surface binding.

[0018] Optionally, training the initial residual stress and density numerical prediction model by selecting parameter variables and setting different temperatures includes:

[0019] According to the selected parameter variables, simulation calculations are performed before sintering, and the pressing stress cloud map, initial residual stress and density numerical prediction model of NdFeB powder before sintering are constructed, and the stress cloud map results are obtained by simulating the powder pressing experiment;

[0020] According to the stress cloud map results, different temperatures are set for simulation calculation to obtain the cloud map changes of temperature field and stress field during the sintering process and after cooling to room temperature after sintering. At the same time, the results are compared and analyzed using actual engineering experiments to complete the training of the initial residual stress and density numerical prediction model.

[0021] Optionally, obtaining the cloud map changes of the temperature field and the stress field during the sintering process and after the sintering is completed and cooled to room temperature includes:

[0022] In the heating stage, the equivalent stress values ​​on the powder surface vary significantly, and are arranged in a step-by-step manner from small to large from the center point to the edge position. At the same time, it is observed that the maximum stress value is found in the area where the center of the bottom surface and the side surface of the blank is connected, which corresponds to the stress situation analyzed in the temperature field simulation.

[0023] During the insulation stage, the temperature inside the green body reaches equilibrium, the stress distribution gradually becomes uniform, and the relative density also gradually becomes uniform;

[0024] When the temperature drops to room temperature, the stress trend on the upper surface does not change, while the area of ​​side stress concentration shifts to the four corners where the upper surface and the side surface are connected.

[0025] Optionally, simulation calculations before sintering based on selected parameter variables include:

[0026] Perform pre-processing based on the physical problems involved and create ABAQUS input files;

[0027] Use ABAQUS / CAE graphical interface to create models or directly edit text files; use ABAQUS / Standard to perform numerical solutions based on the model established in pre-processing;

[0028] The computational output includes the display of field variables and physical properties, which are stored in binary files;

[0029] After the simulation calculation and analysis are completed, post-processing begins. ABAQUS / CAE or other post-processing tools are used to read the binary output database file for result analysis and visualization.

[0030] Optionally, setting different temperatures for simulation calculation according to the stress cloud map result includes:

[0031] According to the parameters of the green body model before sintering, while keeping the mesh quality, unit characteristics, material data, load and boundary conditions, analysis type and output requirements unchanged in the pre-processing step, add the simulation calculation of sintering in the "Step" module, set the "Time period" to be greater than or equal to the required sintering time, input the preset incremental step size, and set the amplitude parameters of the synchronous change of temperature and time in the "Amplitudes" module in ABAQUS by changing the temperature amplitude. Simulate and analyze the changes of the green body under three sintering temperatures to predict the effect of temperature on green body densification.

[0032] Technical effect of the invention: The invention discloses a numerical prediction method for residual stress and density based on a modified Drucker-Prager Cap model. Based on the modified Drucker-Prager Cap model, the parameters are modified to increase the porosity and friction to make it more suitable for actual engineering. Previous studies predicted the stress distribution problem related to the pressing of green body powder before sintering. This work proposes the stress distribution problem in the sintering process and the prediction of the influence of different sintering temperatures and stresses on the material densification process, which effectively helps the sintering molding of the material (green body cracking problem and densification) and provides relevant parameter guidance. The stress is concentrated at the edge of the green body pressing. In actual engineering, the lubrication problem of the inner wall of the mold should be considered to reduce friction. Within a certain temperature range, the higher the sintering temperature, the more friendly it is to the stress concentration problem and densification of the green body. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0034] Figure 1 It is a flow chart of a numerical prediction method of residual stress and density based on a modified Drucker-Prager Cap model according to an embodiment of the present invention;

[0035] Figure 2 The stress cloud diagrams during the simulated powder pressing experiment of the embodiment of the present invention are shown in FIG. 1 , wherein (a) is the stress cloud diagram after correction in the prior art, and (b) is the stress cloud diagram obtained in the present invention;

[0036] Figure 3 These are NdFeB samples at different sintering temperatures in the embodiments of the present invention;

[0037] Figure 4 The temperature field cloud diagrams at three time points during the heating stage of the sintering process at 780°C in the embodiment of the present invention are shown, wherein (a) is the temperature field cloud diagram at the initial stage of heating, (b) is the temperature field cloud diagram when the temperature reaches the highest point, and (c) is the temperature field cloud diagram at the insulation stage;

[0038] Figure 5 The stress cloud diagram of the upper surface of the green body after sintering at 780°C in the embodiment of the present invention, wherein (a) is the stress cloud diagram when the sintering temperature reaches the highest, (b) is the stress cloud diagram when the temperature is kept at a constant temperature and pressure, and (c) is the stress cloud diagram when the temperature drops to room temperature after sintering.

[0039] Figure 6 It is a point location diagram of the upper surface of an embodiment of the present invention;

[0040] Figure 7 The three-point stress band error bar diagram of the upper surface at different temperatures of the embodiment of the present invention;

[0041] Figure 8 The temperature field cloud diagrams at different time points during the sintering heating stage of 850°C and 940°C of the embodiment of the present invention are shown, wherein (a) is the temperature field cloud diagram when the sintering temperature reaches a maximum of 850°C, (b) is the temperature field cloud diagram during the heat preservation stage; (c) is the temperature field cloud diagram when the sintering temperature reaches a maximum of 940°C, and (d) is the temperature field cloud diagram during the heat preservation stage;

[0042] Fig. 9 The stress cloud diagrams of the upper surface of the green body after sintering at 850°C and 940°C in the embodiment of the present invention are shown, wherein (a) is the stress cloud diagram when the sintering temperature reaches a maximum of 850°C, (b) is the stress cloud diagram when the temperature is kept at a constant temperature and pressure, and (c) is the stress cloud diagram when the temperature is reduced to room temperature after sintering; (d) is the stress cloud diagram when the sintering temperature reaches a maximum of 940°C, (e) is the stress cloud diagram when the temperature is kept at a constant temperature and pressure, and (f) is the stress cloud diagram when the temperature is reduced to room temperature after sintering;

[0043] Fig.10 Schematic diagram of the initial residual stress and density numerical prediction model constructed for the embodiment of the present invention, wherein (a) is the powder side boundary condition setting, (b) is the powder bottom boundary condition setting, and (c) is the powder constraint setting on the contact surface of the indenter. DETAILED DESCRIPTION

[0044] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0045] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0046] like Figure 1 As shown, this embodiment provides a numerical prediction method for residual stress and density based on a modified Drucker-Prager Cap model, including:

[0047] According to the modified Drucker-Prager Cap model and theoretical analysis, the parameter relationship is obtained and the parameter variables are selected;

[0048] The initial residual stress and density numerical prediction model is trained by selecting parameter variables and setting different temperatures to obtain the residual stress and density numerical prediction model;

[0049] Obtain target residual stress and density values, input the residual stress and density numerical prediction model, and obtain prediction results.

[0050] Furthermore, the selection basis of the porosity parameters in the green compaction stage in the theoretical analysis includes:

[0051] E=c 0 +c 1 exp(c 2 ρ),

[0052]

[0053] Among them, c 0 、c 1 、c 2 is the coefficient of data fitting; ρ 0 is the volume density of the material, ρ is the material density, E is the elastic modulus, and p is the porosity.

[0054] Furthermore, the selection basis of the porosity parameters in the sintering stage in the theoretical analysis includes:

[0055] Q=mcΔT,

[0056] Where c is the specific heat capacity, Q is the amount of heat absorbed or released by the object, m is the mass of the object, and ΔT is the change in the object's temperature;

[0057]

[0058] Where q is the heat flux, S is the unit area, λ is the thermal conductivity, ΔT is the temperature difference between the upper surface and the center, and d is the sample thickness;

[0059] λ∝c-τ 1 p,

[0060] p∝c-τ 0 ρ 0 ,

[0061] ρ 0 ∝λ,

[0062] The porosity parameter should be considered in both the compacting and sintering stages. The initial porosity of this model is set to 0.3, and the final simulation results are more accurate.

[0063] Further, such as Fig.10 The numerical prediction model of initial residual stress and density is shown in Fig.10 (a) is the boundary condition setting of the powder side. Fig.10 (b) is the boundary condition setting for the powder bottom. Fig.10(c) is the constraint setting of the powder on the contact surface of the indenter; the numerical prediction model of initial residual stress and density includes: an indenter and a green body, wherein the green body size is the same as the actual engineering size, which is 10 mm in diameter and 5 mm in height, and the indenter has a diameter of 10 mm and a height of 20 mm; the indenter applies a pressure of 60 MPa to move downward, and the green body is pressed downward into shape, and the boundary conditions are set to U1, U2 direction is fixed, and U3 direction is displaced. The bottom of the green body is set to be completely fixed to simulate the wrapping effect of the outer wall on the green body, and at the same time, the contact surface between the indenter and the green body is set to be bound by the master and slave surfaces.

[0064] Furthermore, the selected parameter variables and different temperatures are set to train the initial residual stress and density numerical prediction model, including:

[0065] According to the selected parameter variables, simulation calculations are performed before sintering, and the pressing stress cloud map, initial residual stress and density numerical prediction model of NdFeB powder before sintering are constructed, and the stress cloud map results are obtained by simulating the powder pressing experiment;

[0066] According to the stress cloud map results, different temperatures are set for simulation calculations to obtain the cloud map changes of temperature field and stress field during the sintering process and after cooling to room temperature after sintering. At the same time, the results are compared and analyzed using actual engineering experiments to complete the training of the initial residual stress and density numerical prediction model.

[0067] Furthermore, the cloud map changes of the temperature field and stress field during the sintering process and after the sintering is completed and cooled to room temperature include:

[0068] In the heating stage, the equivalent stress values ​​on the powder surface vary significantly, and are arranged in a step-by-step manner from small to large from the center point to the edge position. At the same time, it is observed that the maximum stress value is found in the area where the center of the bottom surface and the side surface of the blank is connected, which corresponds to the stress situation analyzed in the temperature field simulation.

[0069] During the insulation stage, the temperature inside the green body reaches equilibrium, the stress distribution gradually becomes uniform, and the relative density also gradually becomes uniform;

[0070] When the temperature drops to room temperature, the stress trend on the upper surface does not change, while the area of ​​side stress concentration shifts to the four corners where the upper surface and the side surface are connected.

[0071] Furthermore, the simulation calculation before sintering according to the selected parameter variables includes:

[0072] Perform preprocessing based on the physical problem involved and create ABAQUS input files. You can use the ABAQUS / CAE graphical interface to create models, or you can directly edit text files for simple problems. The generated input file (such as job.inp) contains all the details of the model. The preprocessing step includes the setting of mesh quality, element properties, material data, loads and boundary conditions, analysis type, and output requirements.

[0073] According to the model established in the pre-processing, the numerical solution is performed using ABAQUS / Standard, which runs in the background. The calculation output includes the display of field variables and physical characteristics, which are stored in binary files (such as: job.res, job.i) for subsequent post-processing. The calculation time depends on the complexity of the problem and the computing resources.

[0074] After the simulation analysis is completed, the post-processing is performed, and the binary output database file is read using ABAQUS / CAE or other post-processing tools to analyze and visualize the results. There are various visualization forms, such as color contour maps, deformation shape maps, and xy plane curve maps.

[0075] Furthermore, according to the stress cloud map results, different temperatures are set for simulation calculations, including:

[0076] According to the parameters of the green body model before sintering, while the mesh quality (element type, shape, position and quantity), element characteristics, material data (providing the physical properties of the material, Young's modulus, Poisson's ratio, etc.), load and boundary conditions (defining the external forces and constraints acting on the structure, such as loads, initial conditions, contact conditions), analysis type, and output requirements (specifying the results to be calculated and output) remain unchanged in the pre-processing step, add a simulation calculation of sintering in the "Step" module, set the "Time period" to be greater than or equal to the required sintering time, enter a suitable incremental step size, and by changing the temperature amplitude, set the amplitude parameters of the synchronous change of temperature and time in the "Amplitudes" module in ABAQUS, simulate and analyze the changes of the green body at three sintering temperatures, and predict the effect of temperature on green body densification.

[0077] An application experiment example of the present invention is as follows:

[0078] After obtaining a series of parameter relationships, the powder pressing experiment was simulated based on the improved Drucker-Prager Cap model, and the following results were obtained: Figure 2 The stress cloud diagram shown is consistent with the established NdFeB powder pressing result cloud diagram before sintering. Figure 10 Similar to Figure 2 On this basis, simulation calculations at different temperatures are set to observe the changes in the temperature field and stress field cloud map after sintering, as shown in (b). Figure 2 (a) is the corrected stress cloud diagram in the prior art.

[0079] The NdFeB blocks were sintered at 780℃, 850℃ and 940℃ by plasma sintering technology. From the SEM images, it can be seen that the grain sizes are different at the three temperatures. The smaller the grain size, the higher the yield strength of the material. The NdFeB powder used in the experiment has a specification of 2000 mesh and a theoretical density of 7.4g.cm -3 The NdFeB is prepared by powder metallurgy sintering technology. The NdFeB powder is placed in a graphite mold for SPS sintering. The sintering equipment is an SPS spark plasma sintering furnace. The SPS conditions are: vacuum atmosphere 10 -3 Pa, sintering temperatures were 780℃, 850℃, 940℃, pressure was 60Mpa, heating rate was 30℃ / min, sintering holding time was 10min. Figure 3 shown.

[0080] NdFeB material is not a common material in the ABAQUS software material library, so the material parameters need to be customized. Powder molding is a complex process, which is related to factors such as the shape, particle size distribution and moisture content of the powder particles. The present invention ignores factors such as particle shape and moisture content, only considers the influence of particle size distribution, and adds the parameter of porosity. During the pressing process, the distance between powder particles will also change. It is a nonlinear, isotropic elastic model. The material parameters of NdFeB powder at room temperature are shown in Table 1. In addition, friction is also an important influencing condition that needs to be considered, and the contact coefficient between materials is shown in Table 2.

[0081] Table 1

[0082]

[0083] Table 2

[0084]

[0085] The outer wall of the mold uses boundary conditions to save computing power and time costs. The initial residual stress and density numerical prediction model includes: a punch and a blank, where the size of the blank is the same as the actual engineering size, with a diameter of 10mm and a height of 5mm, and the punch has a diameter of 10mm and a height of 20mm; the punch applies a pressure of 60Mpa and moves downward, and the blank is pressed downward into shape. The boundary conditions are set to U1, fixed in the U2 direction, and displaced in the U3 direction. The bottom of the blank is set to be completely fixed to simulate the wrapping effect of the outer wall on the blank. At the same time, the contact surface between the punch and the blank is set to be bound by the master and slave surfaces to avoid the occurrence of mold penetration.

[0086] During the sintering process, temperature plays an important role in the densification of NdFeB powder. Therefore, the present invention first analyzes the temperature field cloud diagram of the finite element model.

[0087] Figure 4 The temperature field cloud diagram at three time points during the heating stage of the sintering process. Figure 4 (a) is the initial stage of warming. Figure 4 (b) is the temperature field cloud diagram when the temperature reaches the highest point. Figure 4 (c) is the temperature field cloud diagram in the insulation stage. Figure 4 It can be seen that during the sintering heating process, there is a large temperature gradient inside and outside the powder. During the heating process, the overall temperature of the green body increases significantly, and the temperature change inside is more obvious, with a temperature difference of about 41°C. As the insulation time increases, the temperature difference inside the green body is 0°C. Long-term insulation and pressure maintenance make the temperature inside the green body reach equilibrium.

[0088] During the heating stage, the outer temperature of the powder is much higher than the inner temperature due to the heat transfer of the outer wall. The densification rate of the outer powder is much faster than that of the inner powder. When the densification rate increases, the sintering volume shrinks and the density increases. Therefore, the edge of the upper surface of the powder will be under greater pressure than the center point. As the temperature rises, the powder absorbs more heat, the temperature gradient continues to increase, and the difference in relative density continues to increase. Until the heat preservation and pressure maintenance, the internal and external temperatures of the powder gradually become uniform, the temperature gradient decreases, and the relative density gradually becomes uniform.

[0089] Since the temperature field cannot intuitively show the area where cracks may occur, the present invention combines the temperature field with the stress field to verify the correctness of the field change trend. At the same time, the densification process of the green body can be better observed in the stress field cloud map.

[0090] The source of residual stress is non-uniform deformation. In the case of powder compaction, residual stress is mainly caused by die friction and non-uniform densification.

[0091] Figure 5 This is the stress cloud diagram of the green body surface after sintering. Figure 5 (a) is the stress cloud diagram when the sintering temperature reaches the highest. Figure 5 (b) is the stress cloud diagram during heat preservation and pressure maintenance. Figure 5 (c) is the stress cloud diagram after sintering and dropping to room temperature. Figure 5 From (a), we can see that in the heating stage (71st incremental step), the equivalent stress values ​​on the powder surface vary significantly, and are arranged in a stepped manner from small to large from the center point to the edge position. At the same time, it can be observed that the stress value is the maximum in the area where the bottom surface and the side surface of the blank are connected to the center, which corresponds to the stress situation analyzed in the temperature field simulation. Figure 5(b) In the insulation stage (the 108th incremental step), as the temperature inside the blank reaches equilibrium, the stress distribution gradually becomes uniform, and the relative density also gradually becomes uniform. When the temperature drops to room temperature, Figure 5 (c) The stress trend on the upper surface has not changed, while the area of ​​side stress concentration has shifted to the four corners where the upper surface and the side surface are connected.

[0092] In order to further improve the accuracy of stress values, NdFeB powders were prepared at the same pressure and sintering temperature in actual engineering, and measured using an X-ray residual stress meter. Figure 6 As shown in Table 3, the stress values ​​at three locations on the upper surface of the blank are the center point A, the interval point B and the edge point C. The values ​​are the average values ​​of multiple measurements, as shown in Table 3. Figure 7 The three-point stress error bar diagram on the upper surface of the blank at different temperatures is used to more intuitively display the stress changes.

[0093] Table 3

[0094]

[0095]

[0096] From the above analysis, it can be seen that the stress distribution of NdFeB after sintering is quite different, which means that the overall stress of the powder is uneven during the hot pressing process. Combined with the simulation analysis of the temperature field, the speed of densification affects the stress conditions at different positions on the upper surface, making the stress on the upper surface increase from the center to the edge. Therefore, it can be inferred that the green body will be affected by the sintering temperature during the forming process, and uneven stress will occur. In the powder cylinder, the diagonal stress along the corner is too large. This change is likely to have an adverse effect on the densification of the green body, causing rupture and destroying the integrity of the green body. Therefore, it is necessary to ensure the smoothness of the mold and the holding time.

[0097] After preparing NdFeB magnets at a sintering temperature of 780°C, in order to further explore the effect of sintering temperature on the densification of NdFeB, NdFeB magnets were prepared at sintering temperatures of 850°C and 940°C under the condition that other variables remained unchanged. The temperature field and stress field values ​​at the two temperatures were simulated and calculated to obtain a cloud map, which was then compared and analyzed in combination with the data measured by the X-ray residual stress detector (summarized in Table 3).

[0098] Through the above Figure 8 , Fig. 9 The cloud data show that the temperature field and stress field trends at the three different temperatures are the same during the heating stage. However, as the sintering temperature increases, the stress distribution in the center of the green body becomes uniform, and the relative density is also more uniform, but there are areas of high stress concentration on both sides. At 940°C, the stress concentration area changes. At the highest temperature, Fig. 9 At (d) (92nd increment), the stress inside the blank is more uniform than at the previous two temperatures, and the stress concentration areas on both sides are smaller, which can effectively reduce the possibility of cracking. Fig. 9 (f) (623 increments), 940℃ compared to the lower sintering temperature (850℃) Fig. 9 (c) The stress concentration phenomenon at the four corners of the blank is relatively relieved, which is consistent with Figure 7 The stress trend of the actual engineering experiment is consistent. Therefore, it is concluded that as the sintering temperature increases, the stress inside and outside the green body becomes more uniform, the edge stress decreases, and the difference gradient of relative density decreases relatively, which is conducive to the forming of the NdFeB green body and reduces the probability of green body cracking during pressing and sintering.

[0099] Finite element simulation technology is used to solve the limitations of the actual engineering relative density, temperature field, and stress field that are difficult to predict. The actual engineering is converted into a visual model. By observing the process of NdFeB powder pressing and sintering, trial and error can be effectively reduced and the success rate of ideal samples can be improved. The accuracy of the finite element analysis results is verified by comparing with specific experiments and x-ray diffraction analyzer measurement data; in previous studies, more analysis results were obtained from pressing experiments, and there was little research on the densification process during powder hot processing, but the formation of the microstructure of NdFeB powder is closely related to the sintering densification process. ABAQUS based on the Drucker-Prager Cap model is conducive to determining the area where stress is generated before and after powder sintering to analyze its densification process.

[0100] In order to study the effect of sintering temperature on the forming and densification process of NdFeB blank, finite element analysis modeling was used to simulate the sintering densification process of NdFeB, the temperature field and stress field were calculated, and the influence of different sintering temperatures on the microstructure was analyzed. SEM, XRD, X-ray residual stress measurement and other detection techniques were used to verify and correct the finite element analysis results and improve the accuracy of the model.

[0101] The temperature field cloud diagram analysis shows that the outer temperature of the powder is much higher than the inner temperature, and the densification speed of the outer powder is much faster than that of the inner powder. Therefore, the outer edge will bear more force than the center, which corresponds to the stress field trend. The different sintering temperatures do not have much effect on the field change trend.

[0102] From the stress field cloud diagrams at three sintering temperatures, it can be seen that at different temperatures, the values ​​of the equivalent stress when heating up are arranged in a stepped manner from the center point to the edge position from small to large. At the same time, it can be observed that the area where the bottom surface and the side of the blank are connected is the area where the stress value is the largest. However, with the increase of temperature, the stress distribution becomes more uniform, and the stress concentration area in the center of the side has a significant shrinking trend until it drops to room temperature. The stress trend on the upper surface has not changed, and the area of ​​​​side stress concentration is transferred to the four corners where the upper surface and the side are connected, but the stress at the four corners becomes smaller. Therefore, it is concluded that within a certain temperature range, the higher the sintering temperature, the more uniform the stress and relative density distribution, and the lower the probability of cracks.

[0103] Compared with other constitutive models, based on the Drucker-Prager Cap model which is closely related to the relative density parameter, the simulation results of the residual stress of 3D modeling of NdFeB powder hot pressing are in good agreement with the experimental results, which verifies the accuracy of the model. It makes up for the current situation of rare research on NdFeB in the field of finite element analysis and its correction, provides a reference for the prediction of temperature field and stress field before and after pressing and sintering of NdFeB powder, and provides a solution for reducing the occurrence of cracks in the green body.

[0104] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A numerical prediction method for residual stress and density based on the modified Drucker-Prager Cap model, characterized in that: include: According to the modified Drucker-Prager Cap model and theoretical analysis, the parameter relationship is obtained and the parameter variables are selected; The initial residual stress and density numerical prediction model is trained by selecting parameter variables and setting different temperatures to obtain the residual stress and density numerical prediction model; Obtain target residual stress and density values, input the residual stress and density numerical prediction model, and obtain prediction results.

2. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 1, characterized in that: The basis for selecting the porosity parameters in the green compaction stage in the theoretical analysis includes: E=c0+c1exp(c2ρ), Among them, c0, c1, c2 are the coefficients of data fitting; ρ0 is the volume density of the material, ρ is the material density, E is the elastic modulus, and p is the porosity.

3. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 1, characterized in that: The selection basis of the porosity parameters in the sintering stage in the theoretical analysis includes: Q=mcΔT, Where c is the specific heat capacity, Q is the amount of heat absorbed or released by the object, m is the mass of the object, and ΔT is the change in the object's temperature; Where q is the heat flux, S is the unit area, λ is the thermal conductivity, ΔT is the temperature difference between the upper surface and the center, and d is the sample thickness.

4. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 1, characterized in that: The numerical prediction model for initial residual stress and density includes: a punch and a blank, where the size of the blank is the same as the actual engineering size, which is 10 mm in diameter and 5 mm in height, and the diameter of the punch is 10 mm and the height is 20 mm; the punch applies a pressure of 60 MPa and moves downward, and the blank is pressed downward into shape. The boundary conditions are set to U1, fixed in U2 direction, and displaced in U3 direction. The bottom of the blank is set to be completely fixed to simulate the wrapping effect of the outer wall on the blank. At the same time, the contact surface between the punch and the blank is set to master-slave surface binding.

5. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 1, characterized in that: The selected parameter variables and different temperatures are used to train the initial residual stress and density numerical prediction model, including: According to the selected parameter variables, simulation calculations are performed before sintering, and the pressing stress cloud map, initial residual stress and density numerical prediction model of NdFeB powder before sintering are constructed, and the stress cloud map results are obtained by simulating the powder pressing experiment; According to the stress cloud map results, different temperatures are set for simulation calculation to obtain the cloud map changes of temperature field and stress field during the sintering process and after cooling to room temperature after sintering. At the same time, the results are compared and analyzed using actual engineering experiments to complete the training of the initial residual stress and density numerical prediction model.

6. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 5, characterized in that: The cloud diagram changes of temperature field and stress field during sintering and after sintering is completed and cooled to room temperature include: In the heating stage, the equivalent stress values ​​on the powder surface vary significantly, and are arranged in a step-by-step manner from small to large from the center point to the edge position. At the same time, it is observed that the maximum stress value is found in the area where the center of the bottom surface and the side surface of the blank is connected, which corresponds to the stress situation analyzed in the temperature field simulation. During the insulation stage, the temperature inside the green body reaches equilibrium, the stress distribution gradually becomes uniform, and the relative density also gradually becomes uniform; When the temperature drops to room temperature, the stress trend on the upper surface does not change, while the area of ​​side stress concentration shifts to the four corners where the upper surface and the side surface are connected.

7. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 5, characterized in that: The simulation calculation before sintering based on the selected parameter variables includes: Perform pre-processing based on the physical problems involved and create ABAQUS input files; Use ABAQUS / CAE graphical interface to create models or directly edit text files; use ABAQUS / Standard to perform numerical solutions based on the model established in pre-processing; The computational output includes the display of field variables and physical properties, which are stored in binary files; After the simulation calculation and analysis are completed, post-processing begins. ABAQUS / CAE or other post-processing tools are used to read the binary output database file for result analysis and visualization.

8. The method for numerically predicting residual stress and density based on the modified Drucker-Prager Cap model according to claim 7, characterized in that: According to the stress cloud map results, different temperatures are set to perform simulation calculations, including: According to the parameters of the green body model before sintering, while keeping the mesh quality, unit characteristics, material data, load and boundary conditions, analysis type and output requirements unchanged in the pre-processing step, add the simulation calculation of sintering in the "Step" module, set the "Time period" to be greater than or equal to the required sintering time, input the preset incremental step size, and set the amplitude parameters of the synchronous change of temperature and time in the "Amplitudes" module in ABAQUS by changing the temperature amplitude. Simulate and analyze the changes of the green body under three sintering temperatures to predict the effect of temperature on green body densification.

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