Finite element simulation method for phase change of thermal growth oxide of environmental barrier coating
By introducing a secondary development program and a linear phase transition dynamics model into the finite element simulation, the problem of insufficient consideration of TGO phase transition was solved, the accuracy of stress field prediction was improved, and a scientific basis for coating design and optimization was provided.
Patent Information
- Application Number
- CN202511782704.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-30
- Publication Date
- 2026-02-06
AI Technical Summary
Existing finite element simulation software fails to adequately consider the volume changes caused by the thermally grown oxide (TGO) phase transformation in environmental barrier coating systems, resulting in inaccurate stress field simulations and an inability to effectively predict coating failure risks.
By introducing a secondary development program into the finite element simulation, the material properties and phase transformation behavior of the TGO layer are defined, including non-thermal strain and thermal strain. The mesh generation is refined, especially at the interface between the TGO layer and the ceramic layer, to simulate the volume change and strain during the TGO phase transformation process. A linear phase transformation dynamics model is adopted, and a geometric model is established in combination with the real morphology.
It improves the accuracy of stress field prediction, and can effectively predict the phase transformation behavior of coatings in high temperature and corrosive environments and its impact on coating performance, providing a scientific basis for coating design and optimization, and adapting to different material systems and service conditions.
Smart Images
Figure CN121480191A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of simulation of thermal barrier coating systems of aero-engines, and particularly relates to a finite element simulation method for phase transition of thermal growth oxide of environmental barrier coating. BACKGROUND
[0002] Environmental barrier coating (EBC) is a key material system for ensuring long-term stable operation of high-temperature components such as aero-engines and gas turbines in extreme environments. During high-temperature service, the bond layer in the coating reacts with the gas in the environment to form a layer of thermal growth oxide (TGO), the main component of which is SiO2. During temperature changes (especially temperature rise and fall), TGO will undergo phase transition. For example, β-SiO2 at high temperature changes into α-SiO2 at low temperature, accompanied by significant volume contraction (about 4-5%). The volume change caused by this phase transition will generate significant local stress in the coating system, thereby inducing the initiation and propagation of microcracks, ultimately leading to coating spalling and failure, which is one of the key factors of thermal failure of high-temperature components.
[0003] At present, the finite element simulation research on environmental barrier coating systems mainly focuses on thermal stress, growth stress, etc., and the simulation of the key physical process of TGO phase transition is still insufficient. Although the existing general finite element calculation software provides powerful multi-physical field coupling analysis and nonlinear solution capabilities, its built-in material model library cannot directly consider the volume strain caused by material phase transition, especially the lack of pertinence in dealing with complex interfaces and topography.
[0004] Therefore, there is an urgent need in the art for a finite element modeling method that can accurately characterize the phase transition behavior of TGO, in order to more realistically predict the stress evolution and failure risk of environmental barrier coating during long-term service, and to provide a theoretical basis for the optimized design and life assessment of the coating.
[0005] After a search of the prior art, no simulation research on the stress field in the TGO phase transition process in the environmental barrier coating system with complex interfaces of actual topography has been found. SUMMARY
[0006] The purpose of the present application is to provide a finite element simulation method for phase transition of thermal growth oxide of environmental barrier coating, which has high simulation accuracy and practicality, and can effectively predict the phase transition behavior of the coating under high temperature and corrosive environment and its influence on the performance of the coating, thereby providing a scientific basis for the design and optimization of the coating.
[0007] The present application provides a finite element simulation method for phase transition of thermal growth oxide of environmental barrier coating, and the steps of the method are as follows: (1) Geometric model establishment: a geometric model of the environmental barrier coating system including the substrate, the bonding layer, the thermally grown oxide (TGO) layer and the ceramic layer is established using a modeling module; (2) Material property definition and secondary development program integration: the material properties of the substrate, the bonding layer, the TGO layer and the ceramic layer such as the elastic modulus, the Poisson's ratio and the thermal expansion coefficient are defined in the material module, and the secondary development program is integrated into the TGO layer through the self-defined material option for calculating the non-thermal strain increment of the TGO layer according to the current temperature and the increment step time and the like, and the non-thermal strain is executed according to the phase change kinetics model; (3) Analysis step and boundary condition setting: the analysis step is set to simulate the response of the environmental barrier coating system in the phase change process; the mechanical boundary condition is set to constrain the rigid body displacement of the model, and the thermal boundary condition is defined through the amplitude curve or the temperature gradient function to simulate the service temperature environment of the coating system; (4) Mesh division; (5) Calculation solving and result analysis: the finite element software is submitted for calculation, the secondary development program is called for solving, the stress field and the strain field distribution are obtained, and the dangerous area of the environmental barrier coating system is predicted.
[0008] The finite element simulation method for the thermal growth oxide phase change of the environmental barrier coating provided by the application, in the geometric model establishment process, the geometric shape of each layer of the environmental barrier coating is obtained through a cross-sectional image of a scanning electron microscope (SEM), and after gray processing, threshold segmentation and smoothing processing by an image processing software, a sketch format recognizable by the finite element software is generated.
[0009] The finite element simulation method for the thermal growth oxide phase change of the environmental barrier coating provided by the application, in the secondary development program, the strain of the TGO layer in the phase change temperature interval is composed of non-thermal strain and thermal strain, wherein: ① the non-thermal strain is determined by the phase change volume strain, the current temperature and the phase change temperature interval, each non-thermal strain increment is determined by the total thermal strain and the increment step time, and the non-thermal strain increment is the product of the total non-thermal strain and the increment step time; ② the thermal strain increment is determined by the thermal expansion coefficients of the two phases before and after the phase change obtained through linear interpolation and the temperature difference before and after the increment step, and the thermal strain increment is the product of the thermal expansion coefficients obtained through linear interpolation and the temperature difference.
[0010] The finite element simulation method for the thermal growth oxide phase change of the environmental barrier coating provided by the application, when the secondary development program is used to calculate the non-thermal strain increment of the TGO layer, the volume change in the phase change process, the isotropy of the strain and the influence of the increment step time are considered.
[0011] The application provides a finite element simulation method for phase transition of a thermal growth oxide of an environmental barrier coating.
[0012] The application provides a finite element simulation method for phase transition of a thermal growth oxide of an environmental barrier coating, and the mesh division further refines the interface part between the TGO layer and the ceramic layer, so that the calculation accuracy of the stress field and the strain field distribution in the region is improved.
[0013] The application has the beneficial effects that: the application introduces the volume strain caused by the TGO phase transition in the finite element model through a secondary development program, the influence of the phase transition is included in the traditional thermal stress analysis, and the prediction result of the stress field is closer to the actual situation. The method is based on a general finite element calculation platform, and the phase transition process can be simply and effectively simulated by calling the secondary development program, and the method has strong practicability. The flexibility of the method is also reflected in that the transition from the beta phase to the alpha phase in the cooling process and the transition from the alpha phase to the beta phase in the heating process can be simulated at the same time, so that the simulation of the stress field in the thermal cycle process is facilitated. Meanwhile, the user can easily simulate different types of phase transition behaviors by modifying the temperature interval, the strain increment and other parameters in the secondary development program, and the method is suitable for different material systems and service conditions. BRIEF DESCRIPTION OF DRAWINGS
[0014] Figure 1 It is a flowchart of the finite element simulation method for phase transition of a thermal growth oxide of an environmental barrier coating. Figure 2 It is a geometric model based on a real topography and a mesh division schematic diagram, wherein (a) is a geometric model of each layer of the coating and the substrate, (b) is a combined geometric model, and (c) is a finite element model after mesh division. Figure 3 It is a schematic diagram of the mechanical and thermal boundary condition setting of the finite element model of the environmental barrier coating. Figure 4 It is a schematic diagram of the TGO phase transition process and the phase transition implementation mode under the cooling condition. Figure 5 It is a stress nephogram along the x direction near the interface of the EBC layer before and after the phase transition under the cooling condition. Figure 6 It is a schematic diagram of the TGO phase transition process and the phase transition implementation mode under the heating condition. Figure 7 It is a stress nephogram along the x direction near the interface of the EBC layer before and after the phase transition under the heating condition. Figure 8 It is an interface damage condition after the TGO phase transition. DETAILED DESCRIPTION
[0015] The application will be further described in detail below with reference to examples, but the embodiments of the application are not limited thereto.
[0016] In the examples, an environmental barrier coating system based on real topography is selected as the research object, a finite element analysis model thereof is established, and stress field and interface damage changes caused by TGO phase transition during temperature rising and falling are analyzed.
[0017] Assumed conditions: 1. Each layer of coating and the substrate is uniform and isotropic; 2. A linear elastic model is adopted; 3. The mechanical and thermal responses under small deformation are simulated.
[0018] Example 1 The flow of the finite element simulation method of this example is shown in Figure 1 , including the following steps: (1) Geometric model establishment: ① Obtain the coating cross-sectional topography: obtain the cross-sectional topography of the coating to be studied through a scanning electron microscope (SEM) and save it in a digital image format. Use image processing software to perform gray scale processing, threshold segmentation and smoothing processing to obtain the gray scale images of each layer of the coating. Then, use a plane design software to extract the gray scale image contour and export it as a sketch format recognizable by the finite element software; ② Establish the environmental barrier coating (EBC) model: import the sketch obtained in step ① into the finite element calculation software and use the modeling module to establish the environmental barrier coating (EBC) model, denoted as model A; ③ Establish the thermal growth oxide layer (TGO) model: also in the modeling module of the finite element calculation software, use the sketch contour to establish the thermal growth oxide layer (TGO) model, denoted as model B; ④ Establish the bonding layer (BC) model: use the sketch contour in the finite element software to establish the bonding layer (BC) model, denoted as model C; ⑤ Establish the substrate (SUB) model: use the sketch contour in the finite element software to establish the substrate (SUB) model, denoted as model D.
[0019] (2) Secondary processing of the geometric model Import each model A, B, C and D established in step (1) into the secondary assembly processing module of the finite element software: ① Perform a tangent Boolean operation on models A and B to obtain the geometric models of EBC and TGO, denoted as EBC and TGO, respectively; ② Perform a tangent Boolean operation on models B and C to obtain the geometric model of BC, denoted as BC; ③ Boolean operation of model C and D is performed to get the geometric model of SUB, denoted as SUB, the coating and substrate model after Boolean operation is shown in Figure 2 (a); ④ Merge operation of EBC, TGO, BC and SUB is performed to get the geometric model with different layers, denoted as component 1; ⑤ Size scaling is performed on component 1 to make it conform to the actual size of the topography to get the final geometric model Coatings-SUB, the model after merge operation is shown in Figure 2 (b).
[0020] (3) Material property assignment Material properties are assigned to EBC, TGO, BC and SUB layers respectively. The TGO layer is processed using a secondary development program, assuming that the volume change and strain during the phase transition are isotropic. The material properties of each layer are shown in Table 1.
[0021] Table 1 Material properties of coating and substrate layers (4) Boundary condition setting
[0022] The mechanical and thermal boundary conditions of the model are set according to existing literature. The mechanical boundary conditions are set as follows: the left side is a symmetric boundary, the bottom is constrained y=0 to avoid rigid body displacement, and the right side is set as an equation constraint to ensure that the nodes on the rightmost column have the same x displacement (as shown in Figure 3 ). The overall temperature field is applied to the model by predefining the field, and the temperature change is set using the amplitude curve, from 1350 ℃ to 25 ℃, as shown in Figure 4 .
[0023] (5) Meshing: meshing is performed on the model, and meshing is performed on the interface, as shown in Figure 2 (c).
[0024] (6) Create analysis step: set the analysis step and use implicit algorithm for solution.
[0025] (7) TGO phase transition secondary development program writing: ① Determine the TGO phase transition temperature range between temperature 1 and temperature 2; ② Calculate the volume change and corresponding strain of TGO phase transition: the density of α-SiO2 is 2.31 g / cm 3 , the density of β-SiO2 is 1.97 g / cm 3 , the molar volume ratio V α : V β= 0.8528, the volume strain of phase transition is 0.1726, the linear strain is 0.0575, the volume strain of phase transition from β to α is -0.1472, the linear strain is -0.0491, the strain application process is as shown in Figure 4 ; 3) Linear model is used to process the phase transition trend of TGO, assuming that the volume of TGO gradually changes at the beginning temperature in the phase transition temperature interval, and the phase transition is completely completed at the end temperature; 4) The elastic modulus, Poisson's ratio and thermal expansion coefficient of the α and β phases of TGO are different, and the linear interpolation method is used to calculate the property parameters changing with temperature during the phase transition; For example, the modulus of the β phase is 71 GPa, the modulus of the α phase is 30 GPa, and the phase transition temperature is between temperature 1 and temperature 2, then the relationship between the modulus and the temperature is obtained by fitting a linear function, so as to obtain the modulus value at different temperatures in the phase transition temperature interval. Poisson's ratio and thermal expansion coefficient are also interpolated in this way.
[0026] 5) In addition to the strain caused by phase transition, thermal strain should also be considered. Before the phase transition temperature, define TGO as the β phase, and its thermal expansion coefficient is the thermal expansion coefficient of the β phase; after the phase transition temperature, define TGO as the α phase, and its thermal expansion coefficient is the thermal expansion coefficient of the α phase. The thermal expansion coefficient in the phase transition temperature interval is interpolated by the interpolation method in step 4. The thermal strain increment is the thermal expansion coefficient multiplied by the temperature difference.
[0027] Through the above steps, the secondary development program of the TGO phase transition process is completed, which is suitable for phase transition simulation in the cooling and heating processes.
[0028] (8) Calculation and result analysis: submit the completed model to the finite element calculation solver for calculation, and call the secondary development program during the calculation process. After the calculation is completed, the stress and strain field of the coating is extracted, the stress concentration is analyzed and the dangerous area of the coating is identified, and the influence of thermal mismatch and TGO phase transition on the coating failure behavior is evaluated. As shown in Figure 5 , it is the stress nephogram near the EBC layer interface before and after the phase transition.
[0029] Example 2: The flow chart of the finite element simulation method of this example is as shown in Figure 1 , which includes the following steps, wherein steps (1) to (3) are the same as those of example 1 except for step (4): (1) Geometric model establishment: (2) Secondary processing of geometric model (3) Material property assignment Material properties are assigned to the EBC, TGO, BC and SUB layers, respectively. The TGO layer is processed using a user-defined program, assuming that the volume change and strain during phase transformation are isotropic. The material properties of each layer are shown in Table 1 in Example 1.
[0030] (4) Setting boundary conditions.
[0031] The mechanical and thermal boundary conditions of the model are set according to the existing literature. The mechanical boundary conditions are set as follows: the left side is a symmetric boundary, the bottom is constrained at y = 0 to avoid rigid body displacement, and the right side is set as an equation constraint to ensure that the nodes in the rightmost column have the same x displacement (as shown in Figure 3 The overall temperature field is applied to the model by predefining the field, and the temperature change is set using the amplitude curve, which increases from 25 °C to 1350 °C, as shown in Figure 6
[0032] (5) Meshing.
[0033] (6) Creating analysis steps: setting analysis steps and solving using implicit algorithm.
[0034] (7) TGO phase transformation user-defined program: the same program as in Example 1 is used, which can be used in both cooling and heating processes.
[0035] (8) Calculation and result analysis: submit the set model to the finite element calculation solver for calculation, and call the user-defined program during the solving process. After the calculation is completed, the stress and strain fields of the coating are extracted, the stress concentration is analyzed, the dangerous areas of the coating are identified, and the effects of thermal mismatch and TGO phase transformation on the coating failure behavior are evaluated. As shown in Figure 7 , the stress contour near the EBC layer interface before and after phase transformation.
[0036] Example 3: The flowchart of the finite element simulation method in this example is shown in Figure 1 , which includes the following steps, except for steps (3) and (6), which refer to Example 1: (1) Geometric model establishment: (2) Secondary processing of geometric model (3) Material property assignment Material properties are assigned to the EBC, TGO, BC and SUB layers, respectively. The TGO layer is processed using a user-defined program, assuming that the volume change and strain during phase transformation are isotropic. The material properties of each layer are shown in Table 1 in Example 1.
[0037] In addition, the properties required to establish the cohesive element are established, where the element modulus is 1000 GPa, the critical contact stress is 20 MPa, and the fracture energy is 30 J / m2 .
[0038] (4) Setting boundary conditions.
[0039] (5) Meshing.
[0040] (6) Creation of cohesive elements at the interface. In this embodiment, a layer of zero-thickness cohesive elements is inserted at the EBC / TGO interface to simulate the damage of the interface.
[0041] (7) Creation of analysis steps: setting analysis steps and using implicit algorithm for solving.
[0042] (8) Writing of secondary development program for TGO phase transition, using the same program as in Example 1.
[0043] (9) Calculation and result analysis: submitting the set model to the finite element calculation solver for calculation, calling the secondary development program during the solving process. After the calculation is completed, the damage of the interface after the TGO phase transition is extracted, as shown in FIG. 4. Figure 8
[0044] In addition, the present application is not only suitable for simulating the stress field and interface damage of environmental barrier coating systems, but also can be used together with other simulation required programs (such as the surface of the EBC layer being corroded), introducing the TGO phase transition factor for multi-physical field coupling analysis, simulating the stress and fracture failure behavior of the coating.
Claims
1. A method for finite element modeling of thermal growth oxide phase transition for environmental barrier coating, characterized by: The method steps are as follows: (1) Geometric model establishment: a geometric model of the environmental barrier coating system including the substrate, the bonding layer, the thermally grown oxide (TGO) layer and the ceramic layer is established using a modeling module; (2) Material property definition and secondary development program integration: the material properties such as the elastic modulus, the Poisson's ratio and the thermal expansion coefficient of the substrate, the bonding layer, the TGO layer and the ceramic layer are defined in the material module, and the secondary development program is integrated into the TGO layer through the self-defined material option for calculating the non-thermal strain increment of the TGO layer according to the current temperature and the increment step time and the like, and the non-thermal strain is executed according to the phase change kinetics model; (3) Analysis step and boundary condition setting: the analysis step is set to simulate the response of the environmental barrier coating system in the phase change process; the mechanical boundary condition is set to constrain the rigid body displacement of the model, and the thermal boundary condition is defined through the amplitude curve or the temperature gradient function to simulate the service temperature environment of the coating system; (4) Mesh division; (5) Calculation solving and result analysis: the finite element software is submitted for calculation, the secondary development program is called for solving, the stress field and the strain field distribution are obtained, and the dangerous area of the environmental barrier coating system is predicted.
2. The finite element modeling method for environmental barrier coating thermally grown oxide phase transformation according to claim 1, wherein: In the geometric model establishment process, the geometric shapes of the layers of the environmental barrier coating are obtained through the cross-sectional images of a scanning electron microscope (SEM), and after gray processing, threshold segmentation and smoothing processing by an image processing software, a sketch format recognizable by the finite element software is generated.
3. The finite element modeling method for environmental barrier coating thermally grown oxide phase transformation of claim 1, wherein: In the secondary development program, the strain of the TGO layer in the phase change temperature interval is composed of non-thermal strain and thermal strain, wherein: ① the non-thermal strain is determined by the phase change volume strain, the current temperature and the phase change temperature interval, each non-thermal strain increment is determined by the total thermal strain and the increment step time, and the non-thermal strain increment is the product of the total non-thermal strain and the increment step time; ② the thermal strain increment is determined by the thermal expansion coefficients of the two phases before and after the phase change obtained through linear interpolation and the temperature difference before and after the increment step, and the thermal strain increment is the product of the thermal expansion coefficients obtained through linear interpolation and the temperature difference.
4. The finite element modeling method for environmental barrier coating thermally grown oxide phase transformation according to claim 1 or 3, characterized in that: When the secondary development program is used to calculate the non-thermal strain increment of the TGO layer, the volume change in the phase change process, the isotropy of the strain and the influence of the increment step time are considered.
5. The finite element modeling method for environmental barrier coating thermally grown oxide phase transformation of claim 1, wherein: The phase change kinetics model is a linear model, that is, the phase change volume strain is linearly distributed in the phase change temperature interval, and is completely applied at the end of the phase change.
6. The finite element modeling method for environmental barrier coating thermally grown oxide phase transformation of claim 1, wherein: The mesh division further refines the interface part between the TGO layer and the ceramic layer to improve the calculation accuracy of the stress field and the strain field distribution in this region.