A dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics

Abstract

The present invention discloses a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, which belongs to the field of advanced ceramic analysis technology. First, an RVE model is constructed to calculate microscale mechanical properties such as average fracture strength, fracture energy, elastic modulus and Poisson's ratio at the microscale, and simultaneously calculate thermal conductivity, heat capacity and thermal expansion coefficient; then a three-point bending model with a single-edge crack is established at the macroscale, and performance data is input to calculate the macroscopic fracture toughness; a thermal shock model with a single-edge crack is established at the macroscale to calculate the relationship between the thermal stress intensity factor and the temperature difference; finally, the critical damage temperature difference is evaluated by combining the thermal stress intensity factor and the fracture toughness, and the relationship between the material microstructure parameters and the macroscopic thermal shock damage resistance is established. The present invention adopts the above-mentioned dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics to provide a basis for microscopic regulation and performance prediction in design applications in the research and development of high-strength and excellent thermal shock resistance ceramic materials.

Description

Technical Field

[0001] The present invention relates to the field of advanced ceramic analysis technology, and in particular to a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics. Background Art

[0002] As we all know, pores are common microstructural components in ceramic materials and have a significant impact on their structural and functional integration. Pores reduce the density of ceramic materials, giving them thermal insulation properties while retaining high temperature resistance and chemical stability, making them widely used in fields such as metallurgy, chemical industry, and aerospace, with significant commercial value and military potential. However, the inherent brittleness of ceramic materials makes them sensitive to defects, and pores significantly reduce the fracture toughness of ceramics. The microstructural differences caused by different preparation processes make the influence of microstructural parameters on fracture toughness unclear. The high elastic modulus, low thermal conductivity and large thermal expansion coefficient of ceramic materials are prone to induce thermal stress at extreme temperatures. In particular, the addition of pores makes cracks more likely to deflect and bifurcate under thermal stress, making crack monitoring and size measurement more difficult, increasing the difficulty of evaluating and predicting the performance of porous ceramics, and affecting the research and development and application of high-strength and toughness ceramic materials. Summary of the Invention

[0003] The purpose of the present invention is to provide a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, combining the thermal stress intensity factor and fracture toughness to evaluate the critical damage temperature difference, and provide a basis for micro-control in the research and development of high-strength and high-toughness ceramic materials with excellent thermal shock resistance and performance prediction in design applications.

[0004] To achieve the above objectives, the present invention provides a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, comprising the following steps:

[0005] S1. Construct an RVE model containing microscopic features of grains, grain boundaries, and pores, and calculate microscale mechanical properties such as average fracture strength, fracture energy, elastic modulus, and Poisson's ratio at the microscale, while also calculating thermal conductivity, heat capacity, and thermal expansion coefficient.

[0006] S2, establish a three-point bending model with a single-edge crack at the macro scale, and input the micro-scale mechanical property data of S1 to calculate the macro fracture toughness;

[0007] S3. Establish a thermal shock model with a single-edge crack at the macroscale, and calculate the relationship between the thermal stress intensity factor and the temperature difference based on the microscale mechanical property data of S1;

[0008] S4. Combine the thermal stress intensity factor and fracture toughness to evaluate the critical damage temperature difference and establish the relationship between the material microstructure parameters and the macro thermal shock damage resistance.

[0009] Preferably, the establishment of the RVE model in S1 includes the following steps:

[0010] S11. Constructing RVE model of microscopic features of dense alumina using Thiessen polygons;

[0011] S12, generating randomly distributed holes, constructing rectangles of the same size, and randomly generating a second set of seed points, deleting the grains corresponding to the seed points to generate holes, and for seed points that are simultaneously in multiple polygons, deleting polygons with too many seed points, and not deleting seed points that are in boundary polygons, controlling the number of seeds each time to obtain representative volume element models with different porosities;

[0012] S13. Use Image-Pro plus 6.4 software to calculate the area ratio of pores to the entire RVE model, i.e., porosity;

[0013] S14. Use the Abaqus software to divide the microstructure model into grids, input material mechanical parameters and apply boundary conditions, and calculate the average fracture strength, fracture energy, elastic modulus and Poisson's ratio microscale mechanical properties, thermal conductivity, heat capacity and thermal expansion coefficient at the microscale.

[0014] Preferably, the establishment of the three-point bending model SEVNB containing a single-edge crack in S2 includes the following steps: using the material fracture parameters obtained during the RVE failure process for the macroscopic three-point bending model to calculate the fracture toughness under different porosity, grain size, and grain boundary strength; the material is a linear elastic constitutive material with isotropic properties, and the crack propagation process is described by the extended finite element method XFEM.

[0015] Preferably, the establishment of the thermal shock model containing a single-edge crack in S3 comprises the following steps:

[0016] S31. The lower and right surfaces of the model are at specified temperatures, while the upper and left surfaces are in adiabatic state. Based on this, the heat conduction control equation is:

[0017]

[0018] ρ is density, λ is thermal conductivity, x is x-axis coordinate, y is y-axis coordinate, t is time, and c is specific heat capacity;

[0019] The initial state of the model at time T=0 is:

[0020] T(x,y,t=0)=T0 (2)

[0021] The heat exchange between the surface of an object and the environment is divided into three categories, namely the first-class boundary condition with known temperature, the second-class boundary condition with known heat flux, and the third-class boundary condition with convective heat transfer. The macroscopic thermal shock resistance model with cracks is a first-class boundary condition with known temperature, so:

[0022] T(x,y,t)=T∞ (3)

[0023] T ∞ is the ambient temperature;

[0024] For the top and left surfaces, the boundaries are adiabatic, meaning the heat flux is zero:

[0025]

[0026] Where n represents the normal direction of the interface, which is the y direction for the upper surface and the x direction for the left surface. Solving the heat conduction control equation can obtain the temperature of each area at any time;

[0027] S32. The model uses sequential thermal-mechanical coupling to analyze the stress field. The strain caused by temperature difference is:

[0028] ε ij =αΔT(i,j) (5)

[0029] α is the thermal expansion coefficient; ΔT is the temperature difference;

[0030] According to the linear elastic constitutive relation, the stress is solved as:

[0031] σ ij =-ε ij Eδ ij (6)

[0032] Where E is the equivalent elastic modulus, δ ij is the Kronecker symbol, i is the i-th row, j is the j-th column, when i=j, δ ij is 0, when i≠j, δ ij is 1.

[0033] Preferably, the relationship between the material microstructure parameters and the macroscopic thermal shock damage resistance is established in S4 by comparing the thermal stress intensity factor and the fracture toughness. If the thermal stress intensity factor is equal to the fracture toughness, the crack is ready to expand; if the thermal stress intensity factor is greater than the fracture toughness, the crack begins to expand, and the critical temperature difference for crack expansion is determined, thereby establishing the relationship between the material microstructure parameters and the macroscopic thermal shock damage resistance.

[0034] Therefore, the present invention adopts the above-mentioned dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, which has the following beneficial effects:

[0035] (1) By establishing a dual-scale model, the relationship between microstructural parameters such as grain size, grain boundary fracture energy and porosity and the fracture toughness of porous ceramics is quantitatively analyzed. This solves the problem that traditional microscale models are difficult to evaluate the effects of microstructural parameters such as grain size, grain boundary fracture energy and porosity on fracture toughness. At the same time, it also solves the problem of the separation between the macroscopic model and the microstructure.

[0036] (2) The complex coupling effects of porosity, grain size, and grain boundary fracture energy on thermal shock resistance were quantitatively analyzed, solving the problem that after the addition of pores to ceramic materials, cracks are more likely to deflect and bifurcate under thermal stress, making crack monitoring and size measurement more difficult, and thus solving the problem of performance evaluation and prediction of porous ceramics.

[0037] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A microscopic feature model diagram including grains, grain boundaries and pores is constructed in accordance with an embodiment of a dual-scale simulation method for evaluating thermal shock resistance of porous ceramics according to the present invention;

[0039] Figure 2 This is a macroscopic model diagram of establishing a three-point bending model with a single-edge crack in an embodiment of a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics according to the present invention;

[0040] Figure 3 This is a thermal shock model diagram containing a single-edge crack in an embodiment of a dual-scale simulation method for evaluating thermal shock resistance of porous ceramics according to the present invention;

[0041] Figure 4 The present invention provides a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, which is a comparative diagram of the critical shock temperature difference versus grain boundary fracture energy for micro RVE models with grain sizes of 0.1 μm and 5 μm, and the critical shock temperature difference versus porosity for micro RVE models with grain sizes of 0.1 μm and 5 μm.

[0042] Figure 5 It is a schematic diagram of the relationship between the microstructure and macroscopic mechanical properties of an embodiment of a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics according to the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0044] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0045] The present invention provides a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, comprising the following steps:

[0046] S1. Construct an RVE model containing microscopic features of grains, grain boundaries, and pores, and calculate microscale mechanical properties such as average fracture strength, fracture energy, elastic modulus, and Poisson's ratio at the microscale, while also calculating thermal conductivity, heat capacity, and thermal expansion coefficient.

[0047] The establishment of the RVE model includes the following steps:

[0048] S11. Constructing RVE model of microscopic features of dense alumina using Thiessen polygons;

[0049] S12, generating randomly distributed holes, constructing rectangles of the same size, and randomly generating a second set of seed points, deleting the grains corresponding to the seed points to generate holes, and for seed points that are simultaneously in multiple polygons, deleting polygons with too many seed points, and not deleting seed points that are in boundary polygons, controlling the number of seeds each time to obtain representative volume element models with different porosities;

[0050] S13. Use Image-Pro plus 6.4 software to calculate the area ratio of pores to the entire RVE model, i.e., porosity;

[0051] S14. Use the Abaqus software to divide the microstructure model into grids, input material mechanical parameters and apply boundary conditions, and calculate the average fracture strength, fracture energy, elastic modulus and Poisson's ratio microscale mechanical properties, thermal conductivity, heat capacity and thermal expansion coefficient at the microscale.

[0052] S2. Establish a three-point bending model with a single-edge crack at the macro scale, and input the microscale mechanical property data of S1 to calculate the macro fracture toughness; the establishment of the three-point bending model SEVNB with a single-edge crack includes the following steps: using the material fracture parameters obtained during the RVE failure process for the macro three-point bending model, and calculating the fracture toughness under different porosity, grain size, and grain boundary strength; its material is an isotropic linear elastic constitutive model, and the crack propagation process is described by the extended finite element method XFEM.

[0053] S3. Establish a thermal shock model with a single-edge crack at the macroscale, and calculate the relationship between the thermal stress intensity factor and the temperature difference based on the microscale mechanical property data of S1;

[0054] The establishment of a thermal shock model with a single-edge crack includes the following steps:

[0055] S31. The lower and right surfaces of the model are at specified temperatures, while the upper and left surfaces are in adiabatic state. Based on this, the heat conduction control equation is:

[0056]

[0057] ρ is density, λ is thermal conductivity, x is x-axis coordinate, y is y-axis coordinate, t is time, and c is specific heat capacity;

[0058] The initial state of the model at time T=0 is:

[0059] T(x,y,t=0)=T0 (2)

[0060] The heat exchange between the surface of an object and the environment is divided into three categories, namely the first-class boundary condition with known temperature, the second-class boundary condition with known heat flux, and the third-class boundary condition with convective heat transfer. The macroscopic thermal shock resistance model with cracks is a first-class boundary condition with known temperature, so:

[0061] T(x,y,t)=T ∞ (3)

[0062] T ∞ is the ambient temperature;

[0063] For the top and left surfaces, the boundaries are adiabatic, meaning the heat flux is zero:

[0064]

[0065] Where n represents the normal direction of the interface, which is the y direction for the upper surface and the x direction for the left surface. Solving the heat conduction control equation can obtain the temperature of each area at any time;

[0066] S32. The model uses sequential thermal-mechanical coupling to analyze the stress field. The strain caused by temperature difference is:

[0067] ε ij =αΔT(i,j) (5)

[0068] α is the thermal expansion coefficient; ΔT is the temperature difference;

[0069] According to the linear elastic constitutive relation, the stress is solved as:

[0070] σ ij =-ε ij Eδ ij (6)

[0071] Where E is the equivalent elastic modulus, δ ij is the Kronecker symbol, i is the i-th row, j is the j-th column, when i=j, δ ij is 0, when i≠j, δ ij is 1.

[0072] S4. Combine the thermal stress intensity factor and fracture toughness to evaluate the critical damage temperature difference and establish the relationship between the material microstructure parameters and the macro thermal shock damage resistance.

[0073] In S4, the relationship between the material microstructure parameters and the macro thermal shock damage resistance is established by comparing the thermal stress intensity factor and the fracture toughness. If the thermal stress intensity factor is equal to the fracture toughness, the crack is ready to expand; if the thermal stress intensity factor is greater than the fracture toughness, the crack begins to expand. The critical temperature difference for crack expansion is determined, thereby establishing the relationship between the material microstructure parameters and the macro thermal shock damage resistance.

[0074] Example 1

[0075] like Figure 5 As shown, the present invention provides a dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, which uses a dual-scale model for simulation, wherein the dual-scale model includes a microstructure model and a macroscopic three-point bending model with a single-edge crack and a thermal shock model with a single-edge crack, and specifically includes the following steps:

[0076] S1. Establish a microstructure model: First, add pores to the polycrystalline RVE model and construct a micro-feature model including grains, grain boundaries and pores. Use Thiessen polygons to construct a micro-feature RVE model of dense alumina. In order to generate randomly distributed pores, rectangles of the same size are first constructed, and a second set of seed points are randomly generated (the first set is used to generate Thiessen polygons), and the grains corresponding to these seed points are deleted to form pores. For seed points that are located in multiple polygons at the same time, polygons with more seed points are deleted first. In order to maintain stress symmetry on symmetric boundaries, seed points within the boundary polygons are not deleted. By controlling the number of seeds, a representative volume element model of different porosity can be obtained. This model combines microstructural features such as grains, grain boundaries and pores, such as Figure 1 shown.

[0077] As the global mesh size of the microscopic model decreases, the mesh is gradually refined and the number of meshes increases rapidly. The model element type is a four-node bilinear plane stress quadrilateral (CPS4R), the grains are isotropic, and behave as linear elastic. Zero-thickness cohesive elements (four-node two-dimensional cohesive elements, COH2D4) are inserted inside the grains and at the grain boundaries to simulate the fracture of grains and grain boundaries. The tensile strength and shear strength of the RVE model with different mesh sizes are used to evaluate the mesh quality. As the mesh is refined, the tensile strength and shear strength decrease, and the error also decreases. When the mesh size is less than 0.09μm, the tensile strength and shear strength tend to be stable. After the mesh around the hole is refined 3 times, the tensile strength and shear strength also tend to be stable when the mesh size is less than 0.09μm, and are basically consistent with those without refinement.

[0078] S2. Establish a macro model with prefabricated cracks: Take three-point bending as an example, Figure 2 As shown in the figure, a three-point bending finite element model with a length and width of 40 mm and 4 mm was established. To investigate the effect of microstructure on fracture toughness, strength and fracture toughness were measured through three-point bending tests. Using the fracture parameters obtained during RVE failure, the fracture toughness was calculated for various porosity, grain size, and grain boundary strength. The material was assumed to be isotropic linear elastic, and the crack propagation process was described using the extended finite element method (XFEM).

[0079] S3, Figure 3 The schematic diagram of the macro thermal shock resistance model with cracks is 8 mm long and 2 mm wide. The initial temperature T0 is a relatively high temperature, and the ambient temperature is T ∞ Add a prefabricated crack on the lower boundary with an angle of 3°. 3° has almost no effect on the magnitude of the stress intensity factor and can be equivalent to a crack of the same length. The specific steps include:

[0080] Step 1: The lower and right surfaces of the model are at a specified temperature, while the upper and left surfaces are in an adiabatic state. Based on this, the heat conduction control equation is:

[0081]

[0082] ρ is density, λ is thermal conductivity, x is x-axis coordinate, y is y-axis coordinate, t is time, and c is specific heat capacity;

[0083] The initial state of the model at time T=0 is:

[0084] T(x,y,t=0)=T0 (2)

[0085] Heat exchange between an object's surface and the environment can be divided into three categories: first-class boundary conditions with known temperature, second-class boundary conditions with known heat flux, and third-class boundary conditions with known convection heat transfer. The macroscopic thermal shock resistance model with cracks is a first-class boundary condition with known temperature, so:

[0086] T(x,y,t)=T ∞ (3)

[0087] For the top and left surfaces, the boundaries are adiabatic, meaning the heat flux is zero:

[0088]

[0089] Where n represents the normal direction of the interface, which is the y-direction for the top surface and the x-direction for the left surface. Solving the governing heat conduction equations yields the temperature of each region at any given time.

[0090] Step 2: The model uses sequential thermal-mechanical coupling to analyze the stress field. The strain caused by temperature difference is:

[0091] ε ij =αΔT(i,j) (5)

[0092] α is the thermal expansion coefficient; ΔT is the temperature difference;

[0093] According to the linear elastic constitutive relation, the stress is solved as:

[0094] σ ij =-ε ij Eδ ij (6)

[0095] Where E is the equivalent elastic modulus, δ ij is the Kronecker symbol, i is the i-th row, j is the j-th column, when i=j, δ ij is 0, when i≠j, δ ij is 1.

[0096] S4. Thermal shock resistance evaluation: Figure 4 The calculated curves of critical shock temperature difference as a function of grain boundary fracture energy and the curves of critical shock temperature difference as a function of porosity for the micro RVE model with grain sizes of 0.1μm and 5μm. Figure 4 (a) is the curve of the critical shock temperature difference of the micro RVE model with a diameter of 0.1 μm and the change of grain boundary fracture energy. Figure 4 (b) is the curve of the critical shock temperature difference of the 5μm micro RVE model versus the grain boundary fracture energy. Figure 4 (c) shows the critical shock temperature difference as a function of porosity for micro-RVE models with grain sizes of 0.1μm and 5μm. The results show that fracture toughness increases with increasing grain boundary energy. However, for models with larger grain sizes and higher grain boundaries, the fracture toughness decreases more significantly with increasing porosity. Compared to fine-grained ceramics and models with lower porosity, the critical shock temperature difference for coarse grains and higher porosity decreases with increasing grain boundary fracture energy, and even stops increasing substantially when the porosity reaches 30%.

[0097] Therefore, the present invention adopts the above-mentioned dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, and quantitatively analyzes the influence of microstructure on thermal shock resistance through a dual-scale model, overcoming the problem that cracks in thermal shock resistance test of ceramic materials are more susceptible to deflection and bifurcation under thermal stress, and crack monitoring and size measurement are difficult. At the same time, it also overcomes the problem of separation between macro model and microstructure, provides a solution for the connection between microstructure and macro performance, and provides a rapid evaluation method for ceramic materials with high strength and excellent thermal shock resistance, which saves time and effort, and is fast, efficient and accurate.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics, characterized by: The following steps are involved: S1. Construct an RVE model containing microscopic features of grains, grain boundaries, and pores, and calculate the microscale mechanical properties of average fracture strength, fracture energy, elastic modulus, and Poisson's ratio at the microscale, as well as thermal conductivity, heat capacity, and thermal expansion coefficient; S2, establish a three-point bending model with a single-edge crack at the macro scale, and input the micro-scale mechanical property data of S1 to calculate the macro fracture toughness; S3. Establish a thermal shock model with a single-edge crack at the macroscale, and calculate the relationship between the thermal stress intensity factor and the temperature difference based on the microscale mechanical property data of S1; The establishment of the thermal shock model containing a single-edge crack in S3 includes the following steps: S31. The lower and right surfaces of the model are at specified temperatures, while the upper and left surfaces are in adiabatic state. Based on this, the heat conduction control equation is: （1） is the density, is the thermal conductivity, is the x-axis coordinate, is the y-axis coordinate, For time, is the specific heat capacity; The initial state of the model at time T=0 is: （2） The heat exchange between the surface of an object and the environment is divided into three categories, namely the first-class boundary condition with known temperature, the second-class boundary condition with known heat flux, and the third-class boundary condition with convective heat transfer. The macroscopic thermal shock resistance model with cracks is a first-class boundary condition with known temperature, so: （3） is the ambient temperature; For the top and left surfaces, the boundaries are adiabatic, meaning the heat flux is zero: （4） in Indicates the normal direction of the interface, and for the upper surface Direction, for the left surface Direction, solve the heat conduction control equation to get the temperature of each area at any time; S32. The model uses sequential thermal-mechanical coupling to analyze the stress field. The strain caused by temperature difference is: （5） is the coefficient of thermal expansion, is the temperature difference; According to the linear elastic constitutive relation, the stress is solved as: （6） in E is the equivalent elastic modulus, is the Kronecker symbol, For the OK, For the Column, when hour, is 0, when hour, is 1; S4. Combine the thermal stress intensity factor and fracture toughness to evaluate the critical damage temperature difference and establish the relationship between the material microstructure parameters and the macro thermal shock damage resistance.

2. A dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics according to claim 1, characterized in that: The establishment of the RVE model in S1 includes the following steps: S11. Constructing RVE model of microscopic features of dense alumina using Thiessen polygons; S12, generating randomly distributed holes, constructing rectangles of the same size, and randomly generating a second set of seed points, deleting the grains corresponding to the seed points to generate holes, and for seed points that are simultaneously in multiple polygons, deleting polygons with too many seed points, and not deleting seed points that are in boundary polygons, controlling the number of seeds each time to obtain representative volume element models with different porosities; S13. Use Image-Pro plus 6.4 software to calculate the area ratio of pores to the entire RVE model, i.e., porosity; S14. Use the Abaqus software to divide the microstructure model into grids, input material mechanical parameters and apply boundary conditions, and calculate the average fracture strength, fracture energy, elastic modulus and Poisson's ratio microscale mechanical properties, thermal conductivity, heat capacity and thermal expansion coefficient at the microscale.

3. The dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics according to claim 1, characterized in that: The establishment of the three-point bending model SEVNB containing a single-edge crack in S2 includes the following steps: using the material fracture parameters obtained during the RVE failure process for the macroscopic three-point bending model to calculate the fracture toughness under different porosities, grain sizes, and grain boundary strengths; the material is an isotropic linear elastic constitutive model, and the crack propagation process is described by the extended finite element method XFEM.

4. The dual-scale simulation method for evaluating the thermal shock resistance of porous ceramics according to claim 1, characterized in that: In said S4, the relationship between the material microstructure parameters and the macro thermal shock damage resistance is established by comparing the thermal stress intensity factor and the fracture toughness. If the thermal stress intensity factor is equal to the fracture toughness, the crack is ready to propagate; If the thermal stress intensity factor is greater than the fracture toughness, the crack begins to propagate, and the critical temperature difference for crack propagation is determined, thereby establishing the relationship between the material microstructure parameters and the macroscopic thermal shock damage resistance.

Images