Method for determining fastest cooling rate of ceramic material through numerical calculation

Abstract

The invention discloses a method for determining the fastest cooling rate of a ceramic material through numerical calculation. The method comprises the following steps: constructing a three-dimensional structure thermal-mechanical coupling model in the sintering cooling process of the ceramic material, and establishing a heat transfer equation and a mechanical constitutive equation; determining parameters and material attributes in the simulation process; determining boundary conditions; selecting a proper method to carry out grid division, and carrying out local adjustment; a function scanning node is adopted to solve a temperature field and a stress field under a plurality of cooling systems under a transient condition at a time, the breaking strength of the material serves as a criterion, the obtained maximum stress in the cooling process is compared with the criterion, whether the material is damaged by thermal stress or not is judged, and the fastest cooling rate is determined. According to the method, the thermal stress field caused by the temperature gradient in the sintering process of the ceramic material is simulated and predicted, the influence of the geometric shape, the material type and the cooling rate of the ceramic material is considered, reference is provided for formulating the sintering schedule of the ceramic material, and the time and energy cost in production can be reduced.

Description

Technical Field

[0001] The invention relates to the technical field of ceramic material production, and in particular to a method for determining the fastest cooling rate of a ceramic material through numerical calculation. Background Art

[0002] The study of firing curves has always been one of the important theoretical and applied research topics in the ceramic industry. The optimal firing curve generally refers to the firing curve with the best heating and cooling rate and the shortest firing time without affecting the firing quality of the product. During the cooling stage of the ceramic firing process, the ceramic material has formed a dense structure. At this time, the ceramic body has high strength and poor toughness. Excessive thermal stress may cause the body to crack. Therefore, it is necessary to focus on the influence of the cooling rate to avoid excessive temperature differences between the inside and outside. The existing temperature system design method is to calculate the fastest heating speed based on the material's flexural strength limit, such as: Among them, v is the heating / cooling rate, ℃ / h; μ is Poisson's ratio; a is the thermal conductivity of the material; σ is the elastic coefficient of the material; α is the linear expansion coefficient of the material; S is the size of the product, m; η is the shape factor. However, the shape factor in the formula needs to be determined through experiments, and it is difficult to accurately determine it for geometric bodies with complex shapes. In addition, this formula cannot take into account stress concentration, nor does it take into account the changes in material physical properties with temperature, and can only give a vague value. In order to avoid cracking caused by thermal stress, extremely low cooling rates are often used in production, and the insulation time is fully extended to prevent cracking, which reduces production efficiency.

[0003] To achieve a balance between firing quality and time / energy cost and determine the fastest firing curve, it is necessary to understand the maximum stress during the firing process. Therefore, the temperature field and stress field during the firing process can be calculated by the finite element method to determine the fastest cooling rate and improve production efficiency. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and deficiencies of the prior art and to provide a method for determining the fastest cooling rate of a ceramic material through numerical calculation.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for determining the fastest cooling rate of a ceramic material by numerical calculation comprises the following steps:

[0007] S1. Construct a three-dimensional structural thermal-mechanical coupling model of the sintering and cooling process of ceramic materials, and establish the heat transfer equation and mechanical constitutive equation;

[0008] S2. Determine the temperature regime during the simulation and the thermal and mechanical properties of the ceramic material, including thermal conductivity, density, heat capacity at constant pressure, thermal expansion coefficient, Young's modulus and Poisson's ratio;

[0009] S3, determining boundary conditions, applying convection and radiation boundary conditions to the ceramic material to achieve cooling, and applying specified displacement boundary conditions to the bottom surface of the ceramic material as a constraint;

[0010] S4, select a corresponding method to divide the grid and make local adjustments;

[0011] S5. Use the transient method to solve the temperature field and stress field, use the function scanning node to solve multiple cooling systems at one time, and use the material flexural strength σ t and the maximum thermal stress σ during the cooling process max The size relationship between them is used as the failure criterion to judge whether the material is damaged by thermal stress and determine the fastest cooling rate.

[0012] In step S1, the heat transfer equation is:

[0013] Where ρ, C p are the density and constant pressure heat capacity of the ceramic material, respectively. q is the heat flux. The heat flux in the model includes the convective heat flux q1=h(T ext -T) and radiative heat flux Q is the heat source, and in this model, Q=0.

[0014] In step S1, the mechanical constitutive equation is:

[0015] (1) Hooke’s law, σ=C:ε th , where σ is the stress tensor; ε th is the thermal strain rate; C is the elastic tensor, defined by Young's modulus and Poisson's ratio;

[0016] (2) Thermal strain rate ε th is: th =α(T)(TT ref ), where α(T) is the secant thermal expansion coefficient, T is the temperature, T ref is the volume reference temperature, that is, the temperature at which the material is unstrained.

[0017] In step S3, convection and radiation boundary conditions are applied to the ceramic material, specifically, heat conduction boundary conditions are applied to the bottom surface, and convection and radiation boundary conditions are applied to the remaining boundaries. The ambient temperature is the furnace cavity temperature, which is approximately a cooling system.

[0018] In step S4, a corresponding method is selected to divide the grid, specifically, a structured partitioning method is selected to divide regular geometric bodies, a free tetrahedron method is selected to divide irregular geometric bodies, and the grid is refined for corners and concave and convex special positions to obtain a ceramic material grid division diagram.

[0019] In step S5, the material flexural strength σ t and the maximum thermal stress σ during the cooling processmax The relationship between the magnitudes of max ≤σ t , it is believed that thermal stress will not cause damage to ceramic materials, so σ max ≤σ t The maximum cooling rate established is the fastest cooling rate for ceramic sintering.

[0020] In solid heat transfer, heat conduction boundary conditions are applied to the bottom surface of the blank, and convection and radiation boundary conditions are applied to the other boundaries. The ambient temperature is the furnace cavity temperature, which is approximately a cooling system. A specified displacement boundary condition is applied to the bottom surface of the blank, and the bottom surface displacement is specified to be 0.

[0021] For regular geometry, the structural meshing method is used for meshing. First, the bottom surface is meshed with quadrilaterals, and then the entire geometry model is meshed by sweeping. For irregular geometry, the free tetrahedron method is used for meshing, and local refinement is performed as needed.

[0022] The temperature discretization in solid heat transfer uses the "quadratic Lagrangian unit", and the displacement discretization in the solid mechanics module uses the "linear unit".

[0023] In order to control variables, when studying the influence of material type on the sintering process of ceramic materials, the shape is kept consistent; when examining the influence of shape, the material type is kept consistent.

[0024] Compared with the prior art, the present invention has the following advantages and effects:

[0025] The present invention simulates the cooling stage during the sintering process of ceramic materials by using the finite element method, and solves the temperature and stress distribution inside the brick body.

[0026] The present invention can be applied to predict the maximum stress of ceramic materials during sintering and cooling process, and can fully consider the influence of factors such as shape, size, material properties changing with temperature, etc., can ensure that thermal stress is within the allowable value range, and reduce cooling time.

[0027] The present invention can also be used for shape optimization, topology optimization, and parameter optimization to improve production efficiency. Compared with formula method and experimental method to determine the firing system, the numerical simulation method has high accuracy, low experimental cost, and is simple and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 The present invention is a flow chart of a method for determining the fastest cooling rate of ceramic materials through numerical calculation.

[0029] Figure 2 This is the three-dimensional mesh division diagram of cubic mullite brick;

[0030] Figure 3is a temperature system diagram of the ceramic material of the present invention;

[0031] Figure 4 The stress cloud diagram of cubic mullite brick

[0032] Figure 5 The maximum stress curve of cubic mullite brick under different cooling systems;

[0033] Figure 6 This is the three-dimensional mesh division diagram of the porous mullite brick;

[0034] Figure 7 The maximum stress curve of porous mullite brick under different cooling systems;

[0035] Figure 8 This is the maximum stress curve of cubic chromium oxide bricks under different cooling systems. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below in conjunction with specific embodiments.

[0037] Embodiment 1:

[0038] Taking cubic sintered mullite refractory brick as an example, the cooling process under different cooling systems is simulated by discrete coordinate method. Figure 1 A method for determining the fastest cooling rate of ceramic materials by numerical calculation is shown in FIG. The specific prediction method is as follows:

[0039] S1. Establish a three-dimensional structural model of cubic sintered mullite refractory bricks, such as Figure 2 As shown, a cube geometry with a side length of 0.6m is established;

[0040] Select the Heat Transfer in Solids and Solid Mechanics physics fields and add a Thermal Expansion node under the Multiphysics node.

[0041] S2. Determine the material properties of mullite bricks, including density, thermal conductivity, thermal expansion coefficient, constant pressure heat capacity, Young's modulus, Poisson's ratio, and surface emissivity; set Poisson's ratio = 0.24, surface emissivity = 0.68, and other material properties are functions of temperature.

[0042] Determine the model parameters: the initial temperature of the cooling process T0 = 1620°C, and the volume reference temperature T_ref = 20°C.

[0043] S3. Determine the boundary conditions, apply specified displacement conditions to the bottom surface of the mullite brick, and set the specified displacement in the z direction to 0;

[0044] During the firing process, the bottom surface of the green body is in contact with the refractory material at the bottom of the furnace. It is believed that the heat dissipation rate of the bottom is lower than that of other surfaces. For simplicity, its heat transfer coefficient is set to half of that of other surfaces, and the radiation heat transfer of the bottom is ignored.

[0045] Apply heat flux boundary conditions to the bottom surface of the mullite brick, select convection heat flux, and set the heat transfer coefficient to 4W / (m 2 ·K); add heat flux boundary conditions to all surfaces except the bottom surface, select convection heat flux, and set the heat transfer coefficient to 8W / (m 2 K); add surface-to-ambient radiation boundary conditions to all surfaces except the bottom surface, and set the surface emissivity to 0.68.

[0046] S4. For cubic mullite bricks, structured grids are used for grid division. First, the bottom surface is divided into square grids, and then the entire geometric body is grid divided by the sweep tool. The grid division diagram is shown in the figure. Figure 3 shown.

[0047] S5. The transient method is used to solve the temperature field and stress field, and the program-controlled cooling process in the range of 1620 ~ 20 °C is investigated.

[0048] Set the temperature system as Figure 4 As shown, the cooling rates are 10, 12, 14, 15, 16, and 20°C / h, and the time step sequence settings are (0h, 5h, 400h), respectively.

[0049] In the result post-processing, the maximum body stress at each time node is calculated, which is the material flexural strength σ t and the maximum thermal stress σ during the cooling process max The size relationship between them is used as the failure criterion to determine whether the material is damaged due to thermal stress.

[0050] The flexural strength of mullite brick is about 80MPa. According to the calculation results, when the cooling rates are 10, 12, 14, 15, 16, and 20℃ / h, the maximum stresses are 51, 66, 75, 80, 84, and 109MPa, respectively. Therefore, the fastest cooling rate is 14℃ / h.

[0051] Embodiment 2:

[0052] Taking the cubic sintered mullite refractory brick with through holes in the middle as an example, the cooling process under different cooling systems is simulated by discrete coordinate method. Figure 1 A method for determining the fastest cooling rate of ceramic materials by numerical calculation is shown in FIG. The specific prediction method is as follows:

[0053] S1. Establish a three-dimensional structural model of cubic sintered mullite refractory bricks, such as Figure 6As shown, a cube geometry with a side length of 0.6m is established, and there is a through hole with a diameter of 0.1m in the center of the cube;

[0054] Select the Heat Transfer in Solids and Solid Mechanics physics fields and add a Thermal Expansion node under the Multiphysics node.

[0055] S2. Determine the material properties of mullite bricks, including density, thermal conductivity, thermal expansion coefficient, constant pressure heat capacity, Young's modulus, Poisson's ratio, and surface emissivity; set Poisson's ratio = 0.24, surface emissivity = 0.68, and other material properties are functions of temperature.

[0056] Determine the model parameters: the initial temperature of the cooling process T0 = 1620°C, and the volume reference temperature T_ref = 20°C.

[0057] S3. Determine the boundary conditions, apply specified displacement conditions to the bottom surface of the mullite brick, and set the specified displacement in the z direction to 0;

[0058] During the firing process, the bottom surface of the green body is in contact with the refractory material at the bottom of the furnace. It is believed that the heat dissipation rate of the bottom is lower than that of other surfaces. For simplicity, its heat transfer coefficient is set to half of that of other surfaces, and the radiation heat transfer of the bottom is ignored.

[0059] Apply heat flux boundary conditions to the bottom surface of the mullite brick, select convection heat flux, and set the heat transfer coefficient to 4W / (m 2 ·K); add heat flux boundary conditions to all surfaces except the bottom surface, select convection heat flux, and set the heat transfer coefficient to 8W / (m 2 K); add surface-to-ambient radiation boundary conditions to all surfaces except the bottom surface, and set the surface emissivity to 0.68.

[0060] S4. For cubic mullite bricks, structured grids are used for grid division. The bottom surface is first divided into free triangle grids, and then the entire geometric body is grid divided by the sweep tool. The inner hole boundary is refined. The grid division diagram is shown in the figure. Figure 7 shown.

[0061] S5. The temperature field and stress field are solved by transient method, and the cooling process with fire in the range of 1620~20℃ is investigated.

[0062] Set the temperature system as Figure 4 The cooling rates are 5, 10, 12, 14, 15, and 16°C / h, respectively, and the corresponding time step sequence settings are (0h, 5h, 400h), respectively.

[0063] In the result post-processing, the maximum body stress at each time node is calculated, which is the material flexural strength σ t and the maximum thermal stress σ during the cooling process maxThe size relationship between them is used as the failure criterion to determine whether the material is damaged due to thermal stress.

[0064] The flexural strength of mullite refractory bricks is about 80MPa. Figure 8 It can be seen that when the cooling rates are 5, 10, 12, 14, 15, and 16°C / h, the maximum process stresses are 25, 61, 70, 73, and 82 MPa, respectively. It can be seen that the fastest cooling rate is 15°C / h.

[0065] Embodiment 3:

[0066] Taking cubic chromium oxide refractory bricks as an example, the cooling process under different cooling systems is simulated by discrete coordinate method. Figure 1 A method for determining the fastest cooling rate of ceramic materials by numerical calculation is shown as follows:

[0067] S1. Establish a three-dimensional structural model of cubic chromium oxide bricks, such as Figure 2 As shown, a cube geometry with a side length of 0.6m is established;

[0068] Select the Heat Transfer in Solids and Solid Mechanics physics fields and add a Thermal Expansion node under the Multiphysics node.

[0069] S2. Determine the material properties of chromium oxide bricks, including density, thermal conductivity, thermal expansion coefficient, constant pressure heat capacity, Young's modulus, Poisson's ratio, and surface emissivity; set Poisson's ratio = 0.24, surface emissivity = 0.68, and other material properties are functions of temperature.

[0070] Determine the model parameters: the initial temperature of the cooling process T0 = 1620°C, and the volume reference temperature T ref = 20°C.

[0071] S3, determine the boundary conditions, apply specified displacement conditions to the bottom surface of the chromium oxide brick, and specify the displacement in the z direction as 0;

[0072] During the firing process, the bottom surface of the green body is in contact with the refractory material at the bottom of the furnace. It is believed that the heat dissipation rate of the bottom is lower than that of other surfaces. For simplicity, its heat transfer coefficient is set to half of that of other surfaces, and the radiation heat transfer of the bottom is ignored.

[0073] Apply heat flux boundary conditions to the bottom surface of the chromium oxide brick, select convection heat flux, and set the heat transfer coefficient to 4W / (m 2 ·K); add heat flux boundary conditions to all surfaces except the bottom surface, select convection heat flux, and set the heat transfer coefficient to 8W / (m 2 K); add surface-to-ambient radiation boundary conditions to all surfaces except the bottom surface, and set the surface emissivity to 0.68.

[0074] S4. For the cubic chrome oxide brick, a structured grid is used for grid division. First, the bottom surface is divided into square grids, and then the entire geometric body is grid divided by the sweep tool. The grid division diagram is shown in Figure 3 shown.

[0075] S5. Use the transient method to solve the temperature field and stress field, and solve the program-controlled cooling process in the range of 1620 ~ 20 °C.

[0076] Set the temperature system as Figure 4 As shown, the cooling rates are 4, 5, 8, and 10°C / h, and the time step sequence settings are (0h, 5h, 500h), respectively.

[0077] In the result post-processing, the maximum body stress at each time node is calculated, which is the material flexural strength σ t and the maximum thermal stress σ during the cooling process max The size relationship between them is used as the failure criterion to determine whether the material is damaged due to thermal stress.

[0078] The flexural strength of chromium oxide refractory bricks is about 30MPa. Figure 8 It can be seen that when the cooling rates are 10, 9, 8, and 5°C / h, respectively, the maximum stresses of the process are 33, 29, 26, and 18 MPa, respectively. It can be seen that the fastest cooling rate is 9°C / h.

[0079] As described above, the present invention realizes the simulation prediction of the thermal stress field caused by the temperature gradient during the sintering process of ceramic materials, and takes into account the influence of the geometric shape, material type, and cooling rate of the ceramic materials, providing a reference for the formulation of the sintering system of ceramic materials, which is conducive to reducing the time and energy costs in production.

[0080] The implementation methods of the present invention are not limited to the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention shall be equivalent replacement methods and shall be included in the protection scope of the present invention.

Claims

1. A method for determining the fastest cooling rate of ceramic materials by numerical calculation, characterized in that The steps include: S1. Construct a three-dimensional structural thermal-mechanical coupling model of the sintering and cooling process of ceramic materials, and establish the heat transfer equation and mechanical constitutive equation; S2. Determine the temperature regime during the simulation and the thermal and mechanical properties of the ceramic material, including thermal conductivity, density, heat capacity at constant pressure, thermal expansion coefficient, Young's modulus and Poisson's ratio; S3, determining boundary conditions, applying convection and radiation boundary conditions to the ceramic material to achieve cooling, and applying specified displacement boundary conditions to the bottom surface of the ceramic material as a constraint; S4, select a corresponding method to divide the grid and make local adjustments; S5. Use the transient method to solve the temperature field and stress field, use the function scanning node to solve multiple cooling systems at one time, and use the material flexural strength σ t and the maximum thermal stress σ during the cooling process max The size relationship between them is used as the failure criterion to judge whether the material is damaged by thermal stress and determine the fastest cooling rate.

2. The method for determining the fastest cooling rate of ceramic materials by numerical calculation according to claim 1, characterized in that: In step S1, the heat transfer equation is: Where ρ, C p are the density and constant pressure heat capacity of the ceramic material, respectively. q is the heat flux. The heat flux in the model includes the convective heat flux q1=h(T ext -T) and radiative heat flux Q is the heat source, and in this model, Q=0.

3. The method for determining the fastest cooling rate of ceramic materials by numerical calculation according to claim 1, characterized in that: In step S1, the mechanical constitutive equation is: (1) Hooke’s law, σ=C:ε th , where σ is the stress tensor; ε th is the thermal strain rate; C is the elastic tensor, defined by Young's modulus and Poisson's ratio; (2) Thermal strain rate ε th is: th =α(T)(TT ref ), where α(T) is the secant thermal expansion coefficient, T is the temperature, T ref is the volume reference temperature, that is, the temperature at which the material is unstrained.

4. The method for determining the fastest cooling rate of ceramic materials by numerical calculation according to claim 1, characterized in that: In step S3, convection and radiation boundary conditions are applied to the ceramic material, specifically, heat conduction boundary conditions are applied to the bottom surface, and convection and radiation boundary conditions are applied to the remaining boundaries. The ambient temperature is the furnace cavity temperature, which is approximately a cooling system.

5. The method for determining the fastest cooling rate of ceramic materials by numerical calculation according to claim 1, characterized in that: In step S4, a corresponding method is selected to divide the grid, specifically, a structured partitioning method is selected to divide regular geometric bodies, a free tetrahedron method is selected to divide irregular geometric bodies, and the grid is refined for corners and concave and convex special positions to obtain a ceramic material grid division diagram.

6. The method for determining the fastest cooling rate of ceramic materials by numerical calculation according to claim 1, characterized in that: In step S5, the material flexural strength σ t and the maximum thermal stress σ during the cooling process max The size relationship between them is used as the failure criterion, specifically when σ max ≤σ t , it is believed that thermal stress will not cause damage to ceramic materials, so σ max ≤σ t The maximum cooling rate established is the fastest cooling rate for ceramic sintering.

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