Simulation test method for ceramic sintering stress and method for reducing ceramic sintering stress

Abstract

The invention discloses a simulation test method for ceramic sintering stress and a method for reducing the ceramic sintering stress. The simulation test method comprises the following steps: 1, measuring the grain size, the relative density and the geometric size before and after sintering; 2, establishing a ceramic geometry by using Abaqus, and constructing a transient heat conduction model; 3, establishing a viscoelastic constitutive equation of sintering shrinkage deformation of the zirconia ceramic, and constructing a sintering shrinkage model; and 4, sequentially coupling the transient heat conduction model and the sintering shrinkage model, and implementing joint simulation of solid-phase sintering simulation to obtain a sintering stress simulation result of the ceramic. The method for reducing the ceramic sintering stress comprises the following steps: 5, establishing a ceramic sintering shrinkage finite element model with grain sizes distributed in proportion, and calculating average sintering stress distribution of the grain size proportion distribution model; and 6, comparing the average sintering stress of the sintering shrinkage models with different grain size proportions, and determining a method for reducing the sintering stress. The ceramic sintering quality and the production efficiency are improved.

Description

Technical Field

[0001] The invention relates to a ceramic material preparation technology, and in particular to a ceramic sintering stress simulation test method and a method for reducing the ceramic sintering stress. Background Art

[0002] Ceramic materials are usually produced using printing technology to manufacture complex structures, especially light-curing printing, which is widely used due to its advantages such as short preparation cycle and low mold requirements. However, after the ceramic material is printed, there are often 20%-30% of resin and other organic components inside it, which affects the normal performance of the ceramic structure. In order to make the ceramic meet the performance requirements, the resin and other organic substances need to be removed as much as possible through the degreasing process, and then the sintering process is used to form a ceramic structure with a higher degree of densification.

[0003] During the sintering process, ceramics will shrink and deform greatly due to densification. The sintering stress is regarded as the driving force of sintering shrinkage deformation. The greater the sintering stress during the sintering process, the greater the sintering shrinkage deformation, that is, the greater the possibility of cracking due to excessive shrinkage. Therefore, reducing the sintering stress can avoid excessive shrinkage deformation at key parts of the printed structure, thereby avoiding external defects such as cracks at key locations of the printed structure and improving the sintering quality and production efficiency of the printed structure.

[0004] During the sintering process of ceramics, grains generally go through two stages: the first stage is the initial stage of sintering. Due to the low temperature, the grains are mainly aggregated by surface diffusion. However, the sintering temperature is low at this time, and the energy provided is insufficient to support the growth of the grains. The pore shape between the grains will gradually move with the movement of the grains, but the volume of the pores has not changed. Therefore, the degree of densification of the ceramic will not be greatly improved at this stage, and the shrinkage deformation of the ceramic is small. At this time, the expansion deformation of the ceramic is mainly the main factor. In the second stage, as the sintering temperature continues to rise, when the critical temperature is reached, the diffusion between the ceramic grains will gradually shift from surface diffusion to grain boundary diffusion. A large amount of energy promotes the adhesion and aggregation between the grains, and the grain boundaries begin to gradually form. At the same time, the grains begin to grow gradually. As the sintering process continues, entering the late stage of sintering, the degree of densification inside the ceramic reaches a relatively high degree, the larger the grain boundaries, the faster the grains grow, and the greater the shrinkage deformation of the ceramic. In the second stage of sintering, the sintering stress is regarded as a force that promotes shrinkage deformation caused by the growth movement of the grains. Therefore, it can be reasonably inferred that reasonable grain size and coordinated shrinkage deformation during sintering are effective ways to reduce sintering stress.

[0005] In actual production, the slurry ratio, powder particle size, sintering temperature, heating rate, etc. are often changed by trial and error to reduce the cracking tendency of ceramics during sintering, reduce sintering shrinkage deformation of key parts and prevent defects. This method is costly and has a long cycle. Therefore, the present invention establishes a finite element model, adjusts different grain ratios, and analyzes the influence of different grain size ratios on sintering stress by numerical simulation without changing the existing sintering process, so as to improve the ceramic sintering production efficiency and guide the ceramic production process. Summary of the invention

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

[0007] In order to solve the above technical problems, the technical solution of the present invention is:

[0008] On the one hand, the present invention provides a method for simulating and testing ceramic sintering stress, comprising the following steps:

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

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

[0011] Step 3, establishing the viscoelastic constitutive equation of sintering shrinkage deformation of zirconia ceramics and constructing a sintering shrinkage model;

[0012] Step 4: sequentially couple the transient heat conduction model with the sintering shrinkage model, implement a joint simulation of the solid phase sintering simulation, and obtain the sintering stress simulation results of the ceramic.

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

[0014] Step 5, establishing a ceramic sintering shrinkage finite element model with proportional distribution of grain size, and calculating the average sintering stress distribution of the grain size proportional distribution model;

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

[0016] The technical effects of the present invention are:

[0017] The simulation test method of ceramic sintering stress of the present invention uses a finite element numerical simulation method to simulate the sintering shrinkage deformation of zirconia ceramics. Compared with the existing finite element model, the grain growth dynamics process is taken into account, and a finite element model that can accurately simulate the ceramic sintering process is established, and the sintering stress of the shrinkage deformation during the sintering process is calculated.

[0018] The method of reducing ceramic sintering stress of the present invention achieves reduction of sintering stress by controlling the distribution ratio of grain size in the ceramic structure without changing the sintering process and thus affecting the final sintering densification degree of the ceramic, thereby reducing the tendency of ceramic structure cracking caused by excessive shrinkage during the sintering shrinkage densification process of the model. The simulation method is simple and has a short experimental cycle, which can meet the use requirements of the ceramic sintering preparation process industry and has a relatively broad application prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The accompanying drawings of the present invention are as follows:

[0020] Figure 1 is a flow chart of the present invention;

[0021] Figure 2 is the sintering curve of zirconia ceramics;

[0022] Figure 3 The sintering stress distribution diagram of the finite element model with uniform grain size distribution;

[0023] Figure 4 This is the sintering stress distribution diagram of the grain size ratio distribution finite element model;

[0024] Figure 5 The figure is a comparison diagram of the sintering stress corresponding to the sintering process of the finite element model with two different grain size distribution ratios. DETAILED DESCRIPTION

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

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

[0027] like Figure 1 As shown, this embodiment takes zirconia ceramic sintering as an example, and the ceramic sintering stress simulation test method of this embodiment includes the following steps:

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

[0029] The zirconia ceramics after 3D printing are degreased and sintered. The degreasing process removes excess resin inside the ceramics, and sintering makes the material more dense.

[0030] Determination of the ceramic grain size before and after sintering: Using a scanning electron microscope (SEM), the ceramic grain size and grain distribution before and after sintering were measured at different magnifications.

[0031] Determination of relative density: using Archimedes drainage method.

[0032] Relative density refers to the ratio of the density of a material to the density of a reference material. When the relative density reaches 1, it is considered that the entire material has been completely densified and there are no pores inside.

[0033] Determine the geometric dimensions of ceramics before and after sintering: use a vernier caliper.

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

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

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

[0037] The input performance parameters of the transient heat conduction model are density (ρ), thermal conductivity (k), specific heat capacity (c p ); when setting the analysis step, select the transient heat conduction analysis step; the control equation of transient heat conduction is:

[0038]

[0039] Where T is temperature; Q is the heat released by the heat source per unit time and per unit area; x, y, z are the three-dimensional coordinates of the geometric body. Define the sintering curve in the amplitude curve of the temperature boundary condition and call it in the load; select the discrete grid type as DC3D8 (8-node three-dimensional heat conduction unit).

[0040] In the Abaqus software property module, input material parameters. The specific parameters to be set are: thermal conductivity (Conductivity), specific heat (Specific Heat), density (Density). In the Abaqus software load module, define the sintering curve by the amplitude curve in the temperature boundary condition. The sintering curve is obtained from the experiment, such as Figure 2 As shown, the sintering line is described by Kelvin temperature because absolute zero needs to be defined in the finite element method.

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

[0042] The temperature boundary conditions are set according to the sintering curve, such as Figure 2 As shown, the initial temperature is 0°C, the heating rate is 5°C / min, the temperature is raised to 1500°C, kept at this temperature for 2h, and then cooled with the furnace.

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

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

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

[0046] According to the literature "Performance, Validation, and Modifications to the SOVS Continuum Constitutive Model in a Nonlinear Large-Deformation Finite Element Code [J]", Arguello, Jose Guadalupe, Reiterer, Markus W. Ewsuk, Kevin G. Verification, JOURNAL OF THE AMERICAN CERAMIC SOCIETY, 2009, 92, (7): 1442-1449. DOI: 10.1111 / j.1551-2916.2009.03008.x. ("Performance, Validation, and Modifications to the SOVS Continuum Constitutive Model in a Nonlinear Large-Deformation Finite Element Code", Arguello, Jose Guadalupe, Reiterer, Markus W. Ewsuk, Kevin G. Verification, Journal of the American Ceramic Society") and the literature "Numerical simulation of sintering for 3D-printed ceramics via SOVS model[J]”, Safonov, Alexander, Chugunov, Svyatoslav, Tikhonov, Andrey.etal, CERAMICS INTERNATIONAL, 2019, 45, (15): 19027-19035. DOI: 10.1016 / j.ceramint.2019.06.144. (“Numerical simulation of sintering of 3D printed ceramics based on SOVS model”, Safonov, Alexander, Chugunov, Svyatoslav, Tikhonov, Andrey, International Ceramics) records: The viscoelastic sintering constitutive equation for shrinkage deformation of ceramic sintering is:

[0047]

[0048] in, is the elastic strain rate, is the thermal strain rate, Creep strain rate;

[0049] The expression for elastic strain rate is:

[0050]

[0051] Where C is the elasticity matrix, is the Cauchy stress tensor;

[0052] The expression of thermal strain rate is:

[0053]

[0054] Where α is the thermal expansion coefficient of zirconia ceramics, Δ is the Hamiltonian vector differential operator, is the temperature change rate;

[0055] The expression of creep strain rate is:

[0056]

[0057] Where σ' is the deviatoric stress tensor, is the shear viscosity modulus, σ h is the hydrostatic pressure, σ s is the sintering stress, ηψ is the bulk viscosity modulus, and I is the unit 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]

[0060] in is the creep incremental strain, is the creep expansion strain;

[0061] The creep amount after time integration of formula (5) is:

[0062]

[0063] 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).

[0064] n is the deviatoric stress potential, defined as:

[0065]

[0066] is the Mises equivalent deviatoric stress, defined as:

[0067]

[0068] The deviatoric stress devσ is defined as follows:

[0069] devσ=σ-p (11)

[0070] From equations (10) and (11), the deviatoric stress potential n can be obtained as:

[0071]

[0072] The definition formula of shear viscosity modulus and bulk viscosity modulus is:

[0073]

[0074] Where η is the Newtonian viscosity inside the ceramic material, and θ is the porosity of the material;

[0075] The viscosity term in ceramic materials is defined by the Arrhenius equation as follows:

[0076]

[0077] Where η0 is the pre-exponential coefficient of the viscosity term of the material and is a function of temperature T, Q v is the viscous flow activation energy, R is the universal gas constant, T abs is the absolute temperature at the current temperature;

[0078] The porosity θ and relative density ρ have the following relationship:

[0079] θ=1-ρ (16)

[0080] Among them, the relative density ρ is derived from the relationship of mass conservation as follows:

[0081]

[0082] ρ0 is the initial relative density of the material before sintering;

[0083] In formula (5), σ s Sintering stress is the driving force for the shrinkage and densification of materials during the sintering process, and its expression is as follows:

[0084]

[0085] Among them, γ s is the specific surface energy of the material, g is the average grain size inside the ceramic;

[0086] The growth kinetics of grain g is expressed as:

[0087]

[0088] Where D is the pre-exponential coefficient of the internal grain size growth term of zirconia ceramics, Q G is the activation energy of grain growth inside the ceramic.

[0089] In the Abaqus subroutine, the above equations (2) to (19) are written in Fortran to establish a 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.

[0090] The input performance parameters of the sintering shrinkage model are: density, specific heat capacity, thermal conductivity, Young's elastic modulus, Poisson's ratio, thermal expansion coefficient, creep, and creep expansion; the analysis step selects the viscous analysis step, and turns on the large geometric deformation (the large geometric deformation is inherent in the analysis step module in Abaqus); the transient heat conduction model analysis result file .ODB file is called as a predefined temperature field in the load step, and the vertical gravity load of the sintering shrinkage model is defined. A center point fixed constraint is applied to the bottom surface. Since the ceramic is placed on a smooth crucible during the sintering process, the friction effect is ignored; the discrete grid type is selected as C3D8R (8-node three-dimensional stress unit).

[0091] It should be noted that when selecting the transient heat conduction analysis step and the viscosity analysis step of sintering shrinkage, the total time of the analysis step module should be set to the completion time of the sintering process curve. Since the Abaqus Creep subroutine is inlined when the sintering shrinkage model calls the transient heat transfer model, this step requires additional definition when inputting performance parameters: non-independent variables.

[0092] In the Abaqus property module, input density, specific heat capacity, thermal conductivity, Young's modulus of elasticity, Poisson's ratio, thermal expansion coefficient, creep, and creep expansion. The physical parameters of ceramic sintering shrinkage in this embodiment are as follows:

[0093] Elastic modulus (Elasticity option in the Properties module): 220.2 GPa;

[0094] Poisson's ratio (Elasticity option in the Properties module): 0.32;

[0095] Thermal expansion coefficient (Expansion option in the Properties module): 8-11x10^-6 / ℃ (100℃-1100℃);

[0096] Specific heat capacity (Thermal option in the Properties module): 0.4-0.6 J / (g*K) (20℃—1700℃);

[0097] Thermal conductivity (Thermal option in the Properties module): 1.5-2.0 W / (m*K) (20℃—1500℃);

[0098] Density (General option in the Properties module): 6.05 g / cm 3 ;

[0099] The definitions of density, specific heat capacity, and thermal conductivity are the same as those used for transient heat conduction;

[0100] Creep (Plasticity option in the Property Module): Since the Creep subroutine will be called later, just select User Defined and no specific value needs to be assigned.

[0101] Creep expansion (Plasticity option in the Property Module): Since the Creep subroutine will be called later, just select User Defined and there is no need to assign a specific value.

[0102] The boundary conditions are set as follows: constrain the vertical degrees of freedom of the bottom surface and fix the center point of the bottom surface.

[0103] Step 4: Sequentially or directly couple the transient heat conduction model with the sintering shrinkage model, implement a joint simulation of the solid phase sintering simulation, and obtain the sintering stress simulation results of the ceramic.

[0104] In this step, there are two ways to solve the thermal coupling of finite element analysis: the first is direct coupling: select the temperature-displacement coupling analysis step in the analysis step module, and then define both thermal boundary conditions (temperature, heat flow) and displacement boundary conditions (freedom constraints in different directions) in the load module. The second is sequential coupling: first perform a heat conduction analysis, and then call the obtained temperature field result file (.ODB) in the predefined field in the subsequent load module of mechanics (in this embodiment, shrinkage deformation analysis). There is no obvious difference between the two methods.

[0105] When using sequential coupling for calculation, even if the subsequent sintering shrinkage model calculation reports an error, the analysis result file output by the transient heat conduction model can still be obtained normally, so sequential coupling is selected. The joint simulation of sequential coupling is: the transient heat conduction model analysis result file .ODB file is called as a predefined temperature field in the load module of the sintering shrinkage model as the temperature input of the shrinkage deformation, and the previously defined Creep subroutine is called in the job file of the shrinkage deformation to perform shrinkage deformation finite element analysis and realize mechanical and thermal joint simulation. The sintering stress simulation results of 0.15μm grain ceramics are shown in the figure. 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.

[0106] During the operation, the load module in the Abaqus software calls 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.

[0107] The method for reducing ceramic sintering stress of this embodiment uses the above-mentioned ceramic sintering stress simulation test method, and also includes the following steps:

[0108] Step 5: Establish a finite element model of ceramic sintering shrinkage with proportional grain size distribution, and calculate the average sintering stress distribution of the grain size proportional distribution model.

[0109] Based on the ceramic sintering shrinkage finite element model established with uniform grain size, the unit numbers corresponding to different positions in the finite element model are taken out and replaced with different grain sizes. For example, a part of 0.15μm grains are taken out and replaced with 0.25μm grains. In order to configure the grain size ratio for the newly created finite element model, the order of the taken unit numbers is shuffled in MATLAB, and the taken unit numbers are re-assigned according to different grain size ratios. In the Creep subroutine of Abaqus, the grain size of each unit is defined according to the configured ratio according to the unit number.

[0110] The definition of grain size can only be achieved through the Creep subroutine. In the Creep subroutine, any user-defined external variable must be defined in the unit or node of the model grid before the subsequent call calculation of this additional variable can be realized. Therefore, the grain size is corresponding to the unit, one unit one grain size. If MATLAB disrupts the order of unit numbers, the order of grain size distribution will be disrupted.

[0111] In order to reduce the overall sintering stress of experimental ceramics, after the finite element model is meshed, the uniform grain size distribution model unit and node related information are extracted, the unit number information of the finite element model is input into MATLAB for scrambling, and extracted according to the corresponding proportion to generate a .txt text file. Finally, the file is called in the Creep subroutine to establish the grain size ratio distribution finite element model, and the average sintering stress distribution of the grain size ratio distribution model is calculated on the Abaqus finite element software, as shown in the figure. Figure 4 As shown, the sintering stress distribution is uneven and the sintering stress of the model with larger grains is smaller.

[0112] from Figure 3 and Figure 4 By comparison: Figure 3 In the figure, the sintering stress corresponding to the uniform grain size has no obvious difference in the values ​​on the right side of the cloud chart, which can be considered that the sintering stress is uniformly distributed. Figure 4 In the figure, the values ​​on the right side of the cloud diagram of grain size ratio distribution are quite different, and the uneven distribution of sintering stress on the cloud diagram is very significant, so the uneven grain size corresponds to the uneven sintering stress.

[0113] Step 6: Compare the average sintering stress of the sintering shrinkage models with different grain size ratios, determine the correlation between grain size distribution and sintering stress, and determine the method to reduce the sintering stress.

[0114] like Figure 5 As shown in the figure, by changing the grain size ratio, the average sintering stress of the sintering shrinkage model with different grain size ratios is compared through the newly created finite element model calculation. It can be found that Figure 2 Under the sintering process conditions, the sintering was carried out at 1500℃ and kept for 2h. The sintering stress was different. As the proportion of large-size grains in the ceramic increased, the average sintering stress corresponding to the sintering shrinkage model would also decrease.

[0115] It can be seen from step 6 that the presence of large grains inside the zirconia ceramic can reduce the sintering stress of the ceramic, so it is concluded that reducing the sintering stress of zirconia ceramics is to mix large grains into key parts of the ceramic, that is, to add coarse particles of zirconia powder when mixing the powder so that large grains are contained inside the ceramic.

Claims

1. A method for simulating and testing ceramic sintering stress, characterized in that: The following steps are involved: Step 1, determining the physical parameters of the ceramic, including grain size, relative density and geometric dimensions before and after sintering; Step 2: Use Abaqus to build the ceramic geometry and construct a transient heat conduction model; Step 3, establishing the viscoelastic constitutive equation of sintering shrinkage deformation of zirconia ceramics and constructing a sintering shrinkage model; Step 4: sequentially couple the transient heat conduction model with the sintering shrinkage model, implement a joint simulation of the solid phase sintering simulation, and obtain the sintering stress simulation results of the ceramic.

2. The ceramic sintering stress simulation test method according to claim 1 or 2, characterized in that: In step 1, the 3D printed ceramics are degreased and sintered, and a scanning electron microscope (SEM) is used to measure the grain size and grain distribution of the ceramics before and after sintering at different magnifications.

3. The ceramic sintering stress simulation test method according to claim 1 or 2, characterized in that: In step 2, the input performance parameters of the transient heat conduction model are density ρ, thermal conductivity k, specific heat capacity c p ; Select the transient heat conduction analysis step. The control equation of transient heat conduction is: In formula (1), T is temperature; Q is the heat released by the heat source per unit time and per unit area; x, y, and z are the three-dimensional coordinates of the geometric body; the sintering process curve used in the sintering experiment is defined in the amplitude curve in the temperature boundary condition and called in the load; the discrete grid type is selected as DC3D8.

4. The ceramic sintering stress simulation test method according to claim 3 is characterized in that: In step 3, The viscoelastic constitutive equation of ceramic sintering shrinkage deformation is defined in the Creep subroutine of Abaqus; The input performance parameters of the sintering shrinkage model are: density, specific heat capacity, thermal conductivity, Young's elastic modulus, Poisson's ratio, thermal expansion coefficient, creep, creep expansion; the analysis step selects the viscosity analysis step and opens the 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 gravity load in the vertical direction of the sintering shrinkage model is defined, and a center point fixed constraint is applied to the bottom surface; the discrete grid type is selected as C3D8R.

5. The ceramic sintering stress simulation test method according to claim 4 is characterized in that: The viscoelastic sintering constitutive equation is: In formula (2), is the elastic strain rate, is the thermal strain rate, Creep strain rate; The expression for elastic strain rate is: In formula (3), C is the elastic matrix, is the Cauchy stress tensor; The expression of thermal strain rate is: In formula (4), α is the thermal expansion coefficient of zirconia ceramics, Δ is the Hamiltonian vector differential operator, is the temperature change rate; The expression of creep strain rate is: In formula (5), σ' is the deviatoric stress tensor, is the shear viscosity modulus, σ h is the hydrostatic pressure, σ s is the sintering stress, ηψ is the bulk viscosity modulus, and I is the unit matrix when the material is isotropic; The creep strain rate in formula (5) is It is represented by the following two incremental strains: In formula (6) and formula (7), is the creep incremental strain, is the creep expansion strain; The creep amount after time integration of formula (5) is: n is the deviatoric stress potential, defined as: is the Mises equivalent deviatoric stress, defined as: The deviatoric stress devσ is defined as follows: devσ=σ-p (11) From equations (10) and (11), the deviatoric stress potential n can be obtained as: The definition formula of shear viscosity modulus and bulk viscosity modulus is: In formula (13) and formula (14), η is the Newtonian viscosity inside the ceramic material, and θ is the porosity of the material; The viscosity term in ceramic materials is defined by the Arrhenius equation as follows: In formula (15), η0 is the pre-exponential coefficient of the viscosity term of the material and is a function of temperature T, Q v is the viscous flow activation energy, R is the universal gas constant, T abs is the absolute temperature at the current temperature; The porosity θ and relative density ρ have the following relationship: θ=1-ρ (16) In formula (16), the relative density ρ is derived from the following relationship based on the law of mass conservation: In formula (17), ρ0 is the initial relative density of the material before sintering; In formula (5), σ s Sintering stress is the driving force for the shrinkage and densification of materials during the sintering process, and its expression is as follows: In formula (18), γ s is the specific surface energy of the material, g is the average grain size inside the ceramic; The growth kinetics of grain g is expressed as: In formula (19), D is the pre-exponential coefficient of the internal grain size growth term of zirconia ceramics, Q G is the activation energy of grain growth inside the ceramic.

6. A method for reducing ceramic sintering stress, characterized in that: The method for simulating the testing of ceramic sintering stress according to any one of claims 1 to 5 further comprises: Step 5, establishing a ceramic sintering shrinkage finite element model with proportional distribution of grain size, and calculating the average sintering stress distribution of the grain size proportional distribution model; Step 6: Compare the average sintering stress of the sintering shrinkage models with different grain size ratios, determine the correlation between grain size distribution and sintering stress, and determine the method to reduce the sintering stress.

7. The method for reducing ceramic sintering stress according to claim 6 is characterized in that: In step 5, based on the ceramic sintering shrinkage finite element model with uniform grain size, the unit numbers corresponding to different positions inside the finite element model are taken out and replaced with different grain sizes. The order of the taken out unit numbers is shuffled in MATLAB, and they are re-matched with the taken out unit numbers according to different grain size ratios; in the Creep subroutine of Abaqus, the grain size of each unit with the configured proportion is defined according to the unit number; and the average sintering stress distribution of the grain size ratio distribution model is calculated on the Abaqus finite element software.

8. The method for reducing ceramic sintering stress according to claim 7, characterized in that: Coarse-grained ceramic powder is doped into key parts of the ceramic so that large grains are contained inside the ceramic.

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