A method for simulating and testing ceramic sintering stress and a method for reducing ceramic sintering stress.

Abstract

This invention discloses a method for simulating and testing ceramic sintering stress and a method for reducing ceramic sintering stress. The simulation and testing method includes: 1. Measuring the grain size, relative density, and geometric dimensions before and after sintering; 2. Using Abaqus to establish the ceramic geometry and construct a transient heat conduction model; 3. Establishing the viscoelastic constitutive equation for the sintering shrinkage deformation of zirconia ceramics and constructing a sintering shrinkage model; 4. Sequentially coupling the transient heat conduction model and the sintering shrinkage model to perform joint simulation of solid-state sintering, obtaining the simulation results of ceramic sintering stress. The method for reducing ceramic sintering stress includes: 5. Establishing a finite element model of ceramic sintering shrinkage with proportionally distributed grain sizes and calculating the average sintering stress distribution of the grain size proportional distribution model; 6. Comparing the average sintering stress of sintering shrinkage models with different grain size proportions to determine the method for reducing sintering stress. This invention improves ceramic sintering quality and production efficiency.

Description

Technical Field

[0001] This invention relates to ceramic material preparation technology, specifically to a method for simulating and testing ceramic sintering stress and a method for reducing ceramic sintering stress. Background Technology

[0002] Ceramic materials are often manufactured using printing technology to create complex structures, especially photopolymerization printing, which is widely used due to its advantages such as short preparation cycle and low mold requirements. However, after printing, ceramic materials often contain 20%-30% resin and other organic components, which affect the normal performance of the ceramic structure. In order to make the ceramic meet the performance requirements, it is necessary to remove as much of the resin and other organic matter as possible through a degreasing process, and then use a sintering process to form a ceramic structure with a high degree of densification.

[0003] During sintering, ceramics undergo significant shrinkage deformation due to densification. Sintering stress is considered the driving force behind this shrinkage deformation. Greater sintering stress during sintering means greater shrinkage deformation, increasing the likelihood of cracking due to excessive shrinkage. Therefore, reducing sintering stress and preventing excessive shrinkage deformation in critical areas of the printed structure can prevent external defects such as cracks, thereby improving the sintering quality and production efficiency of the printed structure.

[0004] During the sintering process of ceramics, grains generally undergo two stages: The first stage is the initial sintering phase. Due to the low temperature, grains mainly aggregate through surface diffusion. However, the low sintering temperature at this stage provides insufficient energy to support grain growth. The shape of the pores between grains gradually shifts with grain movement, but the pore volume remains unchanged. Therefore, the densification degree of the ceramic does not increase significantly in this stage, and the shrinkage deformation is small; expansion deformation is the dominant phenomenon. In the second stage, as the sintering temperature continues to rise, upon reaching the critical temperature, the diffusion between ceramic grains gradually shifts from surface diffusion to grain boundary diffusion. A large amount of energy promotes adhesion and aggregation between grains, grain boundaries begin to form, and grains begin to grow. As the sintering process continues into the later stages, the internal densification degree of the ceramic reaches a relatively high level, the grain boundaries become larger, grain growth accelerates, and the shrinkage deformation of the ceramic increases. In the second stage of sintering, sintering stress is considered a force that balances the shrinkage deformation caused by grain growth. Therefore, it can be reasonably inferred that a reasonable grain size to coordinate shrinkage deformation during sintering is an effective method to reduce sintering stress.

[0005] In actual production, methods such as adjusting slurry ratios, powder particle size, lowering sintering temperature, and reducing heating rate are often used through experimental trial and error to reduce the tendency of ceramics to crack during sintering and to reduce sintering shrinkage deformation in critical areas to prevent defects. However, this method is costly and time-consuming. Therefore, this invention establishes a finite element model and adjusts different grain ratios. Without altering existing sintering processes, it analyzes the impact of different grain size ratios on sintering stress through numerical simulation, thereby improving ceramic sintering production efficiency and guiding ceramic production processes. Summary of the Invention

[0006] To address the problems existing in the prior art, the technical problem to be solved by this invention is to provide a simulation and testing method for ceramic sintering stress. This method, by establishing a finite element model of the ceramic sintering process, can calculate the sintering stress caused by shrinkage deformation during sintering. It also provides a method for reducing ceramic sintering stress, which can solve the problem of cracking in certain key parts during sintering due to excessive shrinkage deformation without changing the sintering process and thus affecting the final densification degree of the ceramic, thereby improving ceramic sintering quality and production efficiency.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0008] On one hand, the method for simulating and testing ceramic sintering stress provided by the present invention includes the following steps:

[0009] Step 1: Measure the physical parameters of the ceramic, including grain size, relative density, and geometric dimensions before and after sintering;

[0010] Step 2: Use Abaqus to create the ceramic geometry and construct a transient heat conduction model;

[0011] Step 3: Establish the viscoelastic constitutive equation for the sintering shrinkage deformation of zirconia ceramics and construct a sintering shrinkage model;

[0012] Step 4: Couple the transient heat conduction model and the sintering shrinkage model sequentially to perform a joint simulation of solid-state sintering and obtain the simulation results of the sintering stress of the ceramic.

[0013] On the other hand, the method for reducing ceramic sintering stress provided by the present invention, using the above-mentioned simulation test method for ceramic sintering stress, further includes the following steps:

[0014] Step 5: Establish a finite element model of ceramic sintering shrinkage with proportionally distributed grain size, and calculate the average sintering stress distribution of the proportionally distributed grain size model.

[0015] Step 6: Compare the average sintering stress of sintering shrinkage models with different grain size ratios to determine the correlation between grain size ratio distribution and sintering stress, and determine the method to reduce sintering stress.

[0016] The technical effects of this invention are:

[0017] The ceramic sintering stress simulation test method of the present invention uses the finite element numerical simulation method to simulate the sintering shrinkage deformation of zirconia ceramics. Compared with the existing finite element model, it considers the grain growth kinetics process, establishes a finite element model that can accurately simulate the ceramic sintering process, and calculates the sintering stress of shrinkage deformation during the sintering process.

[0018] The method for reducing ceramic sintering stress of the present invention reduces sintering stress by controlling the distribution ratio of grain size in the ceramic structure without changing the sintering process and thus affecting the final densification degree of the ceramic. This reduces the tendency of the ceramic structure to crack due to excessive shrinkage during the sintering shrinkage densification process. Furthermore, the simulation method is simple and has a shorter experimental cycle, which can meet the needs of the ceramic sintering preparation industry and has a wide range of application prospects. Attached Figure Description

[0019] The accompanying drawings of this invention are described below:

[0020] Figure 1 This is a flowchart of the present invention;

[0021] Figure 2 The sintering curve of zirconia ceramic;

[0022] Figure 3 Sintering stress distribution diagram for a finite element model with uniform grain size distribution;

[0023] Figure 4 The sintering stress distribution diagram is shown in the finite element model of the grain size ratio distribution.

[0024] Figure 5 This is a comparison diagram of the sintering stress during the sintering process for two finite element models with different proportions of grain size distribution. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0026] The sintering stress in this application refers to the average value of the sintering stress calculated from all elements in the finite element model.

[0027] like Figure 1 As shown, this embodiment uses zirconia ceramic sintering as an example. The simulation and testing method for ceramic sintering stress in this embodiment includes the following steps:

[0028] Step 1: Determine the physical parameters of the zirconia ceramic, including grain size, relative density, and geometric dimensions before and after sintering.

[0029] The 3D-printed zirconia ceramics were degreased and sintered. The degreasing process removed excess resin from the ceramic interior, and the sintering process resulted in a high degree of material densification.

[0030] Determination of ceramic grain size before and after sintering: Scanning electron microscopy (SEM) was used to measure the ceramic grain size and grain distribution before and after sintering at different magnifications.

[0031] Relative density was determined using Archimedes' method of water displacement.

[0032] Relative density refers to the ratio of the density of a substance to the density of a reference substance. When the relative density reaches 1, the entire material is considered to be completely dense, with no pores inside.

[0033] Determine the geometric dimensions of ceramics before and after sintering using vernier calipers.

[0034] In this embodiment, the parameters of the zirconia ceramic block are as follows: Dimensions before sintering: length 5mm, width 5mm, height 1mm; Dimensions after sintering: length 4.1mm, width 4.1mm, height 0.81mm. Grain size before sintering: 0.15μm and 0.25μm; Grain size after sintering: 0.305μm and 0.42μm. Relative density before sintering: 0.447; Relative density after sintering: 0.92.

[0035] Step 2: Use Abaqus to create the ceramic geometry and construct a transient heat conduction model.

[0036] With Abaqus, you only need to create the geometry before sintering, and you can obtain the geometry after sintering through simulation.

[0037] The input performance parameters for the transient heat conduction model include density ( ), thermal conductivity ( ), specific heat capacity ( When setting the analysis step, select the transient heat conduction analysis step; the governing equation for transient heat conduction is:

[0038] (1)

[0039] in For temperature; This represents the amount of heat released by the heat source per unit time through a unit area; x, y, and z are the three-dimensional coordinates of the geometry. The sintering curve is defined in the amplitude curve of the temperature boundary condition and can be called in the load; the discrete mesh type is selected as DC3D8 (8-node three-dimensional heat conduction element).

[0040] In the Abaqus software's properties module, input material parameters, specifically setting parameters such as thermal conductivity, specific heat capacity, and density. In the Abaqus software's load module, define the sintering curve using the amplitude curve in the temperature boundary conditions. The sintering curve is obtained experimentally, such as... Figure 2 As shown, the sintering strips are described using an open temperature description because absolute zero needs to be defined in the finite element method.

[0041] The ceramic physical parameters used in this embodiment are as follows: specific heat capacity: 0.4-0.6 J / (g*K) (20℃—1700℃); thermal conductivity: 1.5-2.0 W / (m*K) (20℃—1500℃); density: 6.05 g / cm³ 3 (This density is the reference density of zirconia ceramics, that is, the density of fully densified zirconia ceramics.)

[0042] The temperature boundary conditions are set based on the sintering curve, such as... Figure 2 As shown, the initial temperature was 0℃, the heating rate was 5℃ / min, the temperature was raised to 1500℃, held for 2 hours, and then cooled with the furnace.

[0043] Step 3: Establish the viscoelastic constitutive equation for the sintering shrinkage deformation of zirconia ceramics and construct a sintering shrinkage model.

[0044] The viscoelastic constitutive equation for the shrinkage deformation of ceramics during sintering is used to establish the finite element model in this step, and transient heat conduction analysis is performed to obtain the temperature field distribution of the ceramics during the sintering process; the creep and expansion characteristics of the material are defined; and the parameters of relative density, grain size, and viscosity in the constitutive equation are calibrated based on the sintering microscopic characterization data.

[0045] The SOVS model (viscous sintering phenomenological constitutive model) includes quantitative formulas for creep strain rate, shear viscosity modulus, bulk viscosity modulus, grain growth kinetics, porosity, and sintering stress.

[0046] The viscoelastic constitutive equation for ceramic sintering shrinkage deformation is:

[0047] (2)

[0048] in, Represents elastic strain rate. Indicates thermal strain rate, Creep strain rate;

[0049] The expression for elastic strain rate is:

[0050] (3)

[0051] in, For the elasticity matrix, It is the Cauchy stress tensor;

[0052] The expression for thermal strain rate is:

[0053] (4)

[0054] in, The coefficient of thermal expansion of zirconia ceramics is given. For Hamiltonian vector differential operators, The rate of temperature change;

[0055] The expression for creep strain rate is:

[0056] (5)

[0057] in, For the deviatoric stress tensor, Shear viscosity modulus For hydrostatic pressure, For sintering stress, Bulk viscosity modulus It is the identity matrix when the material is isotropic;

[0058] In the above formula, creep strain rate It can be represented by the following two incremental strains:

[0059] (6)

[0060] (7)

[0061] in For creep incremental strain, For creep expansion strain;

[0062] The creep variable after integrating equation (5) over time is:

[0063] (8)

[0064] The two increments on the right side of equation (8) correspond to the strains of equations (6) and (7), that is, equation (8) is the total strain of equations (6) and (7).

[0065] It is a deviatoric stress potential, defined as:

[0066] (9)

[0067] The Mises equivalent deviatoric stress is defined as:

[0068] (10)

[0069] Deviatoric stress It has the following definition:

[0070] (11)

[0071] From equations (10) and (11), the deviatoric stress potential n can be obtained as:

[0072] (12)

[0073] The definitions of shear viscosity modulus and bulk viscosity modulus are as follows:

[0074] (13)

[0075] (14)

[0076] in, The Newtonian viscosity is the internal viscosity of the ceramic material. Porosity of the material;

[0077] In ceramic materials, the viscosity term is defined using the Arrhenius equation as follows:

[0078] (15)

[0079] in, The coefficient of viscosity of the material is the exponential coefficient, and it is also the coefficient of temperature. The function, It is the activation energy for viscous flow. This is the universal gas constant. The absolute temperature is the temperature at the current temperature.

[0080] Porosity With relative density The following relationship exists:

[0081] (16)

[0082] Among them, relative density The following relationship is derived based on the law of conservation of mass:

[0083] (17)

[0084] The initial relative density of the material before sintering;

[0085] In equation (5), Sintering stress is the driving force for the shrinkage and densification of materials during the sintering process, and its expression is as follows:

[0086] (18)

[0087] in, The specific surface energy of the material, The average grain size inside the ceramic;

[0088] grains The growth kinetics expression is:

[0089] (19)

[0090] in, represents the pre-exponential coefficient of the grain size growth term within zirconia ceramics. This refers to the activation energy for grain growth inside the ceramic.

[0091] In the Abaqus subroutine, the above equations (2) to (19) are written in Fortran to establish the complete viscoelastic sintering constitutive equation. The established viscoelastic constitutive equation is defined in the Creep subroutine of Abaqus to form a complete SOVS sintering constitutive model.

[0092] The input performance parameters for the sintering shrinkage model are: density, specific heat capacity, thermal conductivity, Young's modulus, Poisson's ratio, coefficient of thermal expansion, creep, and creep expansion. The analysis step is selected as the viscous analysis step, and large geometric deformation is enabled (large geometric deformation is a built-in feature of the analysis step module in Abaqus). The transient heat conduction model analysis result file (.ODB file) is used as a predefined temperature field in the load step. Simultaneously, a vertical gravity load is defined for the sintering shrinkage model, and a center-point fixed constraint is applied to the bottom surface. Since the ceramic is placed on a smooth crucible during sintering, friction is ignored. The discrete mesh type is selected as C3D8R (8-node three-dimensional stress element).

[0093] It is important to note that when selecting the transient heat conduction analysis step and the viscous analysis step for sintering shrinkage, the total time of the analysis step module should be set to the completion time of the sintering process curve. Because the sintering shrinkage model uses the Abaqus Creep subroutine inline when calling the transient heat transfer model, this step requires additional definition of non-independent variables when inputting performance parameters.

[0094] In Abaqus's properties module, input the density, specific heat capacity, thermal conductivity, Young's modulus, Poisson's ratio, coefficient of thermal expansion, creep, and creep expansion. The physical parameters of ceramic sintering shrinkage in this embodiment are as follows:

[0095] Elastic modulus (elasticity option in the properties module): 220.2 GPa;

[0096] Poisson's ratio (elasticity option in the properties module): 0.32;

[0097] Coefficient of thermal expansion (expansion option in the properties module): 8—11x10^-6 / ℃ (100℃—1100℃);

[0098] Specific heat capacity (thermal option in the properties module): 0.4-0.6 J / (g*K) (20℃—1700℃);

[0099] Thermal conductivity (thermal option in the properties module): 1.5-2.0 W / (m*K) (20℃—1500℃);

[0100] Density (General option in the Properties module): 6.05 g / cm³ 3 ;

[0101] The definitions of density, specific heat capacity, and thermal conductivity are the same as those used for transient heat conduction.

[0102] Creep (Plasticity option in the Properties module): Since the Creep subroutine will be called later, you can choose user-defined and do not need to assign a specific value;

[0103] Creep expansion (plasticity option in the properties module): Since the Creep subroutine will be called later, you can choose user-defined and do not need to assign a specific value.

[0104] The boundary conditions are set as follows: constrain the vertical degree of freedom of the bottom surface, and fix the center point of the bottom surface.

[0105] Step 4: Couple the transient heat conduction model and the sintering shrinkage model sequentially or directly to perform a joint simulation of solid-state sintering and obtain the simulation results of the sintering stress of the ceramic.

[0106] In this step, there are two solutions for the thermo-mechanical coupling in finite element analysis: The first is direct coupling: In the analysis step module, select the temperature-displacement coupling analysis step, and then define both thermal boundary conditions (temperature, heat flux) and displacement boundary conditions (degrees of freedom constraints in different directions) in the load module. The second is sequential coupling: Perform heat conduction analysis first, and then call the obtained temperature field result file (.ODB) in the predefined field of the load module in the subsequent mechanical (contraction deformation analysis in this example) analysis. There is no significant difference between the two methods.

[0107] Sequential coupling is chosen because even if subsequent sintering shrinkage model calculations fail, the analysis result file output by the transient heat conduction model can still be obtained normally. The sequential coupling co-simulation involves calling the transient heat conduction model analysis result file (.ODB file) as a predefined temperature field in the load module of the sintering shrinkage model, using it as the temperature input for shrinkage deformation. Furthermore, the previously defined Creep subroutine is called in the shrinkage deformation job file to perform finite element analysis of shrinkage deformation, achieving a combined mechanical and thermal simulation. The sintering stress simulation results for 0.15μm grain ceramics are shown below. Figure 3 As shown, from Figure 3 It can be seen that the sintering stress distribution corresponding to the uniform grain size distribution model is relatively uniform.

[0108] During operation, the load module in Abaqus software loads the analysis result file of the transient heat conduction model, the job file calls the creep subroutine, and the visualization module directly outputs the deformation results.

[0109] The method for reducing ceramic sintering stress in this embodiment, using the above-described simulation test method for ceramic sintering stress, further includes the following steps:

[0110] Step 5: Establish a finite element model of ceramic sintering shrinkage with proportionally distributed grain size, and calculate the average sintering stress distribution of the proportionally distributed grain size model.

[0111] A ceramic sintering shrinkage finite element model based on uniform grain size is established. The element numbers corresponding to different locations within the finite element model are extracted and replaced with different grain sizes; for example, some 0.15μm grains are extracted and replaced with 0.25μm grains. To configure the grain size ratio in the newly created finite element model, the extracted element numbers are shuffled in MATLAB and reassigned to different grain size ratios. In the Abaqus Creep subroutine, the grain size of each element is defined according to the configured ratio based on its element number.

[0112] Grain size can only be defined through the Creep subroutine. Any user-defined external variable within the Creep subroutine must be defined on an element or node of the model mesh before it can be called and calculated subsequently. Therefore, grain size corresponds to an element; one element, one grain size. MATLAB shuffles the element numbering order, thus shuffling the grain size distribution order.

[0113] To reduce the overall sintering stress of the experimental ceramic, after the finite element model is meshed, the uniform grain size distribution model elements and node information are extracted. The element numbering information of the finite element model is input into MATLAB for shuffling, and extracted according to the corresponding proportions to generate a .txt text file. Finally, this file is called in the Creep subroutine to establish the finite element model of the grain size distribution. The average sintering stress distribution of the grain size distribution model is then calculated in Abaqus finite element software. Figure 4 As shown, the sintering stress distribution is uneven and the larger the grains, the smaller the corresponding sintering stress in the model.

[0114] from Figure 3 and Figure 4 The comparison shows that: Figure 3 In the diagram, the sintering stress corresponding to uniform grain size shows no significant difference in value on the right side, which can be considered as a uniform distribution of sintering stress. Figure 4 In the cloud map, the values ​​on the right side of the grain size distribution are quite different, and the sintering stress distribution on the cloud map is very uneven. Therefore, the uneven grain size corresponds to the uneven sintering stress.

[0115] Step 6: Compare the average sintering stress of sintering shrinkage models with different grain size ratios to determine the correlation between grain size distribution and sintering stress, and determine the method to reduce sintering stress.

[0116] like Figure 5 As shown, by changing different grain size ratios and calculating using a newly established finite element model, the average sintering stress of the sintering shrinkage model with different grain size ratios is compared. It can be found that... Figure 2 Under the sintering process conditions, the sintering stress varies when sintered at 1500℃ for 2 hours. As the proportion of large-sized grains inside the ceramic increases, the average sintering stress corresponding to the sintering shrinkage model will also decrease.

[0117] As can be seen from step 6, the presence of large grains inside zirconia ceramics can reduce the sintering stress of ceramics. Therefore, the conclusion is that reducing the sintering stress of zirconia ceramics is achieved by incorporating large grains into the key parts of the ceramic, that is, by adding coarse-grained zirconia powder during powder mixing, so that the ceramic contains large grains.

Claims

1. A method for reducing sintering stress in ceramics, characterized in that, Includes the following steps: Step 1: Measure the physical parameters of the ceramic, including grain size, relative density, and geometric dimensions before and after sintering; Step 2: Use Abaqus to create the ceramic geometry and construct a transient heat conduction model; Step 3: Establish the viscoelastic constitutive equation for the sintering shrinkage deformation of zirconia ceramics and construct a sintering shrinkage model; The viscoelastic constitutive equation for the shrinkage deformation of ceramics during sintering is defined in the Creep subroutine of Abaqus. The viscoelastic sintering constitutive equation is: （2） In equation (2), Represents elastic strain rate. Indicates thermal strain rate, Creep strain rate; The expression for elastic strain rate is: （3） In equation (3), For the elasticity matrix, It is the Cauchy stress tensor; The expression for thermal strain rate is: （4） In equation (4), The coefficient of thermal expansion of zirconia ceramics is given. For Hamiltonian vector differential operators, The rate of temperature change; The expression for creep strain rate is: （5） In equation (5), For the deviatoric stress tensor, Shear viscosity modulus For hydrostatic pressure, For sintering stress, Bulk viscosity modulus It is the identity matrix when the material is isotropic; In equation (5), the creep strain rate It is represented by the following two incremental strains: （6） （7） In equations (6) and (7) For creep incremental strain, For creep expansion strain; The creep variable after integrating equation (5) over time is: （8） It is a deviatoric stress potential, defined as: （9） The Mises equivalent deviatoric stress is defined as: （10） Deviatoric stress It has the following definition: （11） From equations (10) and (11), the deviatoric stress potential n can be obtained as: （12） The definitions of shear viscosity modulus and bulk viscosity modulus are as follows: （13） （14） In equations (13) and (14), The Newtonian viscosity is the internal viscosity of the ceramic material. Porosity of the material; In ceramic materials, the viscosity term is defined using the Arrhenius equation as follows: （15） In equation (15), The coefficient of viscosity of the material is the exponential coefficient, and it is also the coefficient of temperature. The function, It is the activation energy for viscous flow. This is the universal gas constant. The absolute temperature is the temperature at the current temperature. Porosity With relative density The following relationship exists: （16） In equation (16), relative density The following relationship is derived based on the law of conservation of mass: （17） In equation (17), The initial relative density of the material before sintering; In equation (5), Sintering stress is the driving force for the shrinkage and densification of materials during the sintering process, and its expression is as follows: （18） In equation (18), The specific surface energy of the material, The average grain size inside the ceramic; grains The growth kinetics expression is: （19） In equation (19), represents the pre-exponential coefficient of the grain size growth term within zirconia ceramics. This refers to the activation energy for grain growth within the ceramic. Step 4: Sequentially couple the transient heat conduction model with the sintering shrinkage model to perform joint simulation of solid-state sintering and obtain the simulation results of sintering stress in ceramics. Step 5: Establish a finite element model of ceramic sintering shrinkage with proportionally distributed grain size, and calculate the average sintering stress distribution of the proportionally distributed grain size model. Based on a ceramic sintering shrinkage finite element model with uniform grain size, the element numbers corresponding to different locations within the finite element model were extracted and replaced with different grain sizes. In MATLAB, the extracted element numbers were shuffled and reassigned to the extracted element numbers according to different grain size ratios. In the Creep subroutine of Abaqus, each element was defined with a configured proportion of grain size according to its element number. The average sintering stress distribution of the grain size ratio distribution model was calculated using Abaqus finite element software. Step 6: Compare the average sintering stress of sintering shrinkage models with different grain size ratios to determine the correlation between grain size distribution and sintering stress, and determine the method to reduce sintering stress.

2. The method for reducing ceramic sintering stress according to claim 1, characterized in that: in In step 1, the 3D-printed ceramic is degreased and sintered. Scanning electron microscopy (SEM) is used to measure the ceramic grain size and grain distribution before and after sintering at different magnifications.

3. The method for reducing ceramic sintering stress according to claim 1 or 2, characterized in that: in In step 2, the input performance parameters of the transient heat conduction model include density. Thermal conductivity Specific heat capacity Select the transient heat conduction analysis step. The governing equation for transient heat conduction is: （1） In formula (1) For temperature; x represents the amount of heat released by the heat source per unit time through a unit area, and x, y, and z represent the three-dimensional coordinates of the geometry. The sintering process curve used in the sintering experiment is defined in the amplitude curve of the temperature boundary condition and can be called in the load. The discrete mesh type is selected as DC3D8.

4. The method for reducing ceramic sintering stress according to claim 3, characterized in that: in In step 3, The input performance parameters for the sintering shrinkage model are: density, specific heat capacity, thermal conductivity, Young's modulus, Poisson's ratio, coefficient of thermal expansion, creep, and creep expansion; select the viscous analysis step and enable large geometric deformation. The transient heat conduction model analysis result file (.ODB file) is called as a predefined temperature field in the load step. At the same time, the vertical gravity load of the sintering shrinkage model is defined, and the center point is fixedly constrained on the bottom surface; the discrete mesh type is selected as C3D8R.

5. The method for reducing ceramic sintering stress according to claim 4, characterized in that, Coarse-grained ceramic powder is incorporated into key parts of the ceramic, resulting in large grains within the ceramic.

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