Extreme environment facing hfcsilc coating ablation process- force coupling behavior prediction method

Abstract

The application discloses an extreme environment-oriented HfC / SiC coating ablation process-force coupling behavior prediction method, and belongs to the technical field of numerical simulation of C / C composite material ultra-high temperature ceramic coating ablation behavior; the method comprises the following steps: respectively establishing differentiated force-chemical coupling control equation groups; adopting a partial constraint strategy at the coating interface, applying multi-point constraints on displacement and oxygen diffusion concentration to ensure the continuity of cross-layer physical fields, and allowing the independent evolution of the chemical reaction degree of each material layer; realizing the synchronous solution of stress field, damage field and component field through an Abaqus user-defined unit subroutine, dynamically updating material property parameters according to the chemical reaction degree in the solving process, and finally outputting the damage variable field, the component concentration field and the stress distribution field. The application can quantitatively predict the cracking and peeling behavior of the HfC / SiC double coating in the ablation process, and lays a foundation for the on-demand optimization design and real service life evaluation of the C / C composite material ablation-resistant coating.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of ablation behavior of ultra-high temperature ceramic coatings of C / C composite materials, specifically involving a chemical-force coupling behavior prediction method for the ablation process of HfC / SiC coatings in extreme environments. Background Technology

[0002] To address the oxidation susceptibility of C / C composites in extreme service environments, surface protection using ultra-high temperature ceramic coatings is crucial. HfC / SiC dual-coatings, with their low linear ablation rate, have become one of the most promising thermal protection solutions for C / C composites in recent years. During service, the oxidative expansion and cracking of the HfC outer layer and the active oxidation consumption of the SiC inner layer are coupled. This chemical-mechanical coupling effect, involving "composition evolution-structural loosening-microcrack propagation," directly determines the reliability and lifespan of the dual-coating. Therefore, predicting the ablation failure behavior of HfC / SiC dual-coatings from a multi-field coupling perspective is of significant engineering importance for ensuring the safe service of C / C composite hot-end components.

[0003] Currently, domestic and international research on ablation simulation of ultra-high temperature ceramic materials mainly focuses on silicon carbide-based materials. For example, a published numerical simulation method combining diffusion kinetics and airflow scouring effects predicts the ablation behavior of nozzle surfaces by solving for the ablation retreat and changes in surface oxide film thickness. This method primarily focuses on boundary retreat and mass loss on the material surface, providing valuable reference for evaluating the ablation depth of single SiC systems.

[0004] However, existing technologies cannot characterize the mismatch stress induced by HfC oxidative expansion within the coating, nor have they established the mechanical relationship between SiC consumption and stiffness degradation, making it difficult to predict the cracking and spalling behavior during the ablation process of dual-coating systems. Therefore, there is an urgent need for a chemical-mechanical coupling behavior prediction method for the ablation process of HfC / SiC coatings in extreme service environments, in order to achieve accurate quantitative assessment of the aforementioned failure evolution laws and provide technical support for the optimized design and life assessment of C / C composite ablation-resistant coating systems. Summary of the Invention

[0005] The technical problem to be solved: To overcome the shortcomings of existing technologies, this invention provides a chemical-mechanical coupling behavior prediction method for the ablation process of HfC / SiC coatings in extreme environments. Different chemical-mechanical coupling control equations are established for the mechanisms of oxidative expansion cracking in the outer HfC layer and oxidative degradation in the inner SiC layer. A partial constraint strategy is employed to ensure cross-layer continuity of displacement and oxygen diffusion concentration while allowing independent evolution of chemical reaction levels. The finite element method is used to simultaneously solve for composition, stress, and damage, and material properties are dynamically updated to predict coating cracking and spalling behavior. This method overcomes the limitation of existing models that only focus on surface ablation behavior. For the distinctly different failure mechanisms of the inner and outer layers, chemical-mechanical coupling control equations are constructed for the outer HfC layer and the inner SiC layer respectively, enabling the prediction of the spatiotemporal evolution of composition, stress, and damage during the coating ablation process.

[0006] The technical solution of this invention is: a method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments, comprising the following steps: Step 1: Construct a coating geometry model of the two-material stack, define the physical field degrees of freedom of each material layer unit node, and apply boundary conditions under service environment to the coating geometry model; Step 2: At the junction of adjacent material layers in the coating geometry model, establish multi-point constraint equations for displacement and oxygen diffusion concentration for the matched node pairs to achieve cross-layer continuity constraint of displacement field and oxygen diffusion concentration field at the junction; at the same time, the degree of chemical reaction in each material layer evolves independently and no cross-layer constraint is applied. Step 3: For different failure mechanisms of different material layers during the ablation process, establish independent control equation sets for each material layer. The control equation sets include oxygen transport control equations, oxidation reaction kinetic control equations, and stress balance control equations that take into account the influence of chemical evolution. Step 4: Iteratively solve the governing equations of each material layer using the finite element method, and dynamically update the material property parameters of each material layer according to the current degree of chemical reaction during the solution process; Step 5: Output the multiphysics variable distribution of each material layer; the multiphysics variables include the damage variable field, the component concentration field and the stress distribution field, which are used to evaluate the damage state and component evolution of the coating under a given ablation environment.

[0007] A further technical solution of the present invention is: in step 1, the coating geometric model of the dual-material stack consists of an outer layer of HfC and an inner layer of SiC. The outer layer of HfC and the inner layer of SiC are geometrically assembled so that the geometric contours at the junction of the two are completely fitted to form an overall geometric model of the dual coating. The physical field degrees of freedom include those characterizing macroscopic mechanical deformation. x Directional displacement ux and y Directional displacement u y Oxygen diffusion concentration, characterizing gas transport γ And the degree of chemical reaction characterizing the evolution of material components. r ; The boundary conditions include: applying a constant oxygen diffusion concentration boundary condition at the top of the overall geometry of the double-coated model to simulate the continuous oxygen supply of the external flow field; applying a zero diffusion flux boundary condition on both sides; and applying a boundary condition at the bottom. y Directional displacement constraints and zero diffusion flux boundary conditions.

[0008] A further technical solution of the present invention is as follows: In step 2, the specific implementation of the cross-layer continuity constraint is as follows: extract the spatial coordinate data of the nodes at the interface between the HfC outer layer and the SiC inner layer, identify the upper and lower interface node pairs with the closest spatial positions based on the nearest neighbor matching algorithm, and establish an independent node set for each successfully matched node pair; for each node pair set, establish a multi-point constraint equation for displacement and oxygen diffusion concentration point by point, the specific form of which includes: right x The multi-point constraint equation for directional displacement is expressed as follows:

[0009] right y The multi-point constraint equation for directional displacement is expressed as follows:

[0010] The multi-point constraint equation for constraining oxygen diffusion concentration is expressed as follows:

[0011] Among them, superscript and These represent the first and second matching numbers, respectively. n The node numbers of the upper and lower interfaces of each node pair; The above multi-point constraint equations ensure the physical continuity of the displacement at the interface and the oxygen diffusion concentration during the solution process; at the same time, different attribute labels jtype are assigned to each material layer element.

[0012] A further technical solution of the present invention is: in step 3, the process of constructing the governing equations of the HfC outer layer includes: Step 3.1.1. Oxygen transport control equation: Introduce equivalent damage variables d The effective oxygen diffusion coefficient of the HfC outer layer is constructed, and the effective oxygen diffusion coefficient of the HfC outer layer varies with the equivalent damage variable. d Increases with size; establishes oxygen transport control equations for coupled damage based on Fick's law and the law of conservation of mass; Step 3.1.2. Oxidation reaction kinetic governing equation: based on the degree of chemical reaction r I Characterizing the oxidation reaction progress of the HfC outer layer, the remaining molar concentration of HfC varies with the degree of chemical reaction of the HfC outer layer. r I Increase and decrease; based on Arrhenius's law, establish the governing equation for the oxidation reaction kinetics jointly controlled by oxygen concentration and residual HfC concentration; Step 3.1.3. Stress balance governing equation considering the influence of chemical evolution: determined by the degree of chemical reaction of the outer layer of HfC. r I The chemical expansion strain tensor induced by the oxidation reaction from HfC to HfO2 was calculated. Based on the definition of the effective stress tensor in continuum damage mechanics, a dual damage initiation criterion of tensile and shear was established, triggering damage when the effective stress exceeds the strength of HfC. The tensile damage variables and shear damage variables were calculated separately using the exponential softening law and then combined into an equivalent damage variable. d ; through equivalent damage variables d By reducing the effective stress and substituting it into the Cauchy equilibrium equation, we obtain the stress balance control equation that takes into account oxidation expansion and microcrack evolution.

[0013] A further technical solution of the present invention is: in step 3, the governing equations of the outer layer of HfC include: Oxygen transport control equation for coupled damage:

[0014] In the formula, This represents the rate of change of oxygen diffusion concentration in the outer layer of HfC over time. Denotes the divergence operator, This represents the equivalent oxygen diffusion coefficient of the outer layer of HfC. This represents the diffusion coefficient of oxygen in air. The oxygen diffusion concentration gradient within the outer layer of HfC; Oxidation reaction kinetic governing equation:

[0015] In the formula, This indicates the rate of change of the degree of chemical reaction in the outer layer of HfC over time. This indicates the oxygen diffusion concentration inside the outer layer of HfC. The pre-exponential factor representing the oxidation reaction of HfC. R represents the activation energy of the HfC oxidation reaction, and R represents the ideal gas constant. T Indicates temperature. This indicates the current remaining molar concentration of HfC; Stress equilibrium governing equations considering the effects of chemical evolution:

[0016] In the formula, This represents the initial elastic stiffness matrix of the outer layer of HfC. This represents the total strain tensor of the outer layer of HfC. The coefficient of chemical expansion of the outer layer of HfC is represented by I, and I represents the second-order unit tensor. r I Indicates the degree of chemical reaction in the outer layer of HfC; A further technical solution of the present invention is: in step 3, the process of constructing the governing equations of the SiC inner layer includes: Step 3.2.1. Kinetic governing equation for active oxidation reaction: Introducing the degree of chemical reaction r II Characterizing the local oxidation behavior of the SiC inner layer, the current remaining molar concentration of SiC varies with the degree of chemical reaction in the SiC inner layer. r II The value decreases as the value increases; the governing equation for the active oxidation reaction kinetics of SiC is established based on the Arrhenius law; Step 3.2.2. Oxygen Transport Control Equation: Define the relative consumption of material in the SiC inner layer as the ratio of the molar concentration of consumed SiC to the initial molar concentration of SiC before ablation; introduce the relative consumption of material to construct the equivalent oxygen diffusion coefficient of the SiC inner layer, which increases with the increase of the relative consumption of material in the SiC inner layer; establish the oxygen transport control equation of the SiC inner layer according to Fick's first law. Step 3.2.3. Stress balance control equation considering the influence of chemical evolution: Introduce the relative material consumption degree as a phenomenological damage parameter characterizing the degree of SiC material degradation, define the effective elastic stiffness matrix considering material consumption, the effective elastic stiffness matrix decreases as the relative material consumption degree increases; determine the stress tensor of the SiC inner layer based on the effective elastic stiffness matrix, and substitute it into the Cauchy motion equilibrium equation to obtain the stress balance control equation considering SiC consumption. A further technical solution of the present invention is: in step 3, the governing equations of the SiC inner layer include: Kinetic governing equation for active oxidation reaction:

[0017] In the formula, This indicates the rate of change of the degree of chemical reaction in the inner layer of SiC over time. This indicates the oxygen diffusion concentration within the inner layer of SiC. The pre-exponential factor representing the active oxidation reaction of SiC This represents the activation energy of the active oxidation reaction of SiC, where R represents the ideal gas constant. T Indicates temperature. This indicates the current remaining molar concentration of SiC; The governing equation for oxygen transport consumed by the coupling material:

[0018] In the formula, This represents the rate of change of oxygen diffusion concentration in the inner layer of SiC over time. Denotes the divergence operator, This represents the intrinsic oxygen diffusion coefficient of the inner layer of SiC. This represents the stoichiometric coefficient of SiC. This indicates the initial molar concentration of SiC before ablation occurred; r II Indicates the degree of chemical reaction in the inner layer of SiC. This represents the diffusion coefficient of oxygen in air. This represents the oxygen diffusion concentration gradient within the inner layer of SiC. Stress equilibrium governing equations considering the effects of chemical evolution:

[0019] In the formula, This represents the total strain tensor of the SiC inner layer. This represents the initial elastic stiffness matrix of the SiC inner layer.

[0020] A further technical solution of the present invention is: in step 4, the iterative solution is implemented through a user-defined unit subroutine, specifically including: During the calculation process, the material layer to which the current element belongs is dynamically identified based on its attribute tag jtype. When jtype is the first preset value, it is processed as an HfC outer element. The residual is calculated according to the control equations of the HfC outer element in step 3, and the corresponding Jacobian matrix is ​​obtained by taking the partial derivative of the residual with respect to the nodal degrees of freedom. When jtype is the second preset value, it is processed as an inner SiC unit. The residual is calculated according to the control equations of the inner SiC unit in step 3, and the corresponding Jacobian matrix is ​​obtained by taking the partial derivative of the residual with respect to the nodal degrees of freedom. The residuals and Jacobian matrices of all elements are returned to the finite element master solver, and the Newton-Raphson method is used for nonlinear iterative solution.

[0021] A further technical solution of the present invention is: in step 4, dynamically updating the material property parameters includes: The extent of chemical reaction on the outer layer of HfC r IThe current molar concentration of HfO2 is calculated, and the current remaining molar concentration of HfC is obtained by subtracting the already reacted molar concentration from the initial molar concentration of HfC. Based on this, the incompletely oxidized outer layer of HfC is regarded as a two-phase mixture of HfC and HfO2. According to the proportional mixing rule, the equivalent elastic modulus, equivalent strength, and equivalent oxygen diffusion coefficient of the outer layer of HfC at the current moment are calculated respectively, so as to realize the real-time updating of the material properties of the outer layer of HfC as the oxidation reaction progresses.

[0022] A further technical solution of the present invention is: in step 5, the multi-physics field variables specifically include: the tensile damage variable field, shear damage variable field, and component concentration field of the HfC outer layer, as well as the component concentration field and stress distribution field of the SiC inner layer; The multiphysics variables are used to quantitatively evaluate the damage state and compositional evolution of the HfC / SiC dual coating under a given ablation environment, thereby providing a quantitative basis for its service reliability assessment.

[0023] Beneficial effects The beneficial effects of this invention are as follows: 1. This invention proposes an interface node decoupling strategy based on multi-point constraint equations. By applying constraint equations with corresponding degrees of freedom to the matching node pairs at the HfC / SiC double-coating interface, macroscopic deformation coordination and oxygen transport continuity are ensured while allowing the inner and outer layers to evolve independently according to their respective chemical reaction mechanisms. This strategy effectively solves the computational distortion problem caused by full constraint of the degrees of freedom of heterogeneous interface nodes and provides a reference for service behavior modeling of multilayer ablation-resistant coating systems.

[0024] 2. This invention addresses the complex ablation failure mechanism within double-coated layers by establishing a chemical-mechanical coupled control equation system that includes equivalent damage variables. This enables dynamic interaction modeling between material damage, gas transport, and component evolution, overcoming the shortcomings of existing methods in the quantitative description of oxidation-damage coupling within coatings.

[0025] 3. Compared to the costly and difficult-to-observe in-situ observation of internal microscopic damage in ultra-high temperature ablation experiments, this invention provides a high-fidelity prediction method. Traditional HfC / SiC coating ablation resistance assessment relies on energy-intensive equipment such as oxy-acetylene flame ablation machines. From coating preparation to testing, a single sample takes over 48 hours and costs over 1000 yuan. This invention, by establishing and solving differentiated chemical-mechanical coupling control equations, can reproduce the ablation failure process on a conventional computer (Intel(R) Xeon(R) Platinum 8375C CPU @ 2.90GHz), with a total modeling and solving time of no more than 12 hours. This invention not only outputs the damage evolution process of coatings under extreme service environments but also effectively reduces the research and development cycle. Attached Figure Description

[0026] Figure 1 This is an overall flowchart of a method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the overall geometric model and mesh division of the HfC / SiC dual coating in an embodiment of the present invention; Figure 3 This is a schematic diagram of node matching and multi-point constraint equation application at the interface of the overall geometric model of the HfC / SiC dual coating in an embodiment of the present invention; Figure 4 This is a flowchart of a single nonlinear iterative solution based on a user-defined unit subroutine in an embodiment of the present invention; Figure 5 This is a graph showing the calculated molar concentration of HfO2 generated on the outer layer of HfC in an embodiment of the present invention; Figure 6 The diagram shows the calculation results of the damage evolution of the outer layer of HfC in the embodiment of the present invention; where (a) represents shear damage and (b) represents tensile damage. Figure 7 This is a graph showing the calculated molar concentration of remaining SiC in the inner layer of SiC in an embodiment of the present invention; Figure 8 This is a diagram showing the calculated stress distribution of the SiC inner layer in an embodiment of the present invention; wherein, (a) is x Directional stress components, (b) are y Directional stress component, (c) is shear stress component; Figure 9 This is a verification result of the ablation depth predicted by the HfC / SiC dual-coating ablation model in this embodiment of the invention; Figure 10 This is a comparison of the HfC outer layer composition and damage distribution of double-coated layers with different inner and outer layer thicknesses after 60 seconds of ablation in this embodiment of the invention; Figure 11 This is a comparison of the composition and stress distribution of the inner layer of SiC double-coated layers with different inner and outer layer thicknesses after 60 seconds of ablation in this embodiment of the invention. Detailed Implementation

[0027] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0028] To address the shortcomings of existing technologies and simulate the ablation failure process of HfC / SiC dual-coatings, which involves the coupling of component evolution, microcrack propagation, and material consumption, this invention establishes a global geometric model of the dual-coatings based on a finite element analysis framework. At the interface between the outer HfC layer and the inner SiC layer, multi-point constraint equations are applied to ensure the cross-layer continuity of displacement and oxygen diffusion concentration, while allowing the inner and outer layers to undergo independent chemical reaction evolution. Based on this, an oxidation-damage control equation set is established for the outer HfC layer, coupling oxidation reactions, volume expansion, and microcrack evolution; and a control equation set describing active oxidation and material property degradation is established for the inner SiC layer. User-defined element subroutines are used to iteratively solve these control equation sets, dynamically updating component concentrations and material properties based on the degree of chemical reaction in each material layer during the solution process, thereby achieving accurate prediction of the ablation failure behavior of the HfC / SiC dual-coating.

[0029] The above technical solution will be further analyzed below with reference to the accompanying drawings and examples: In an exemplary embodiment, an oxy-acetylene flame ablation experiment of a C / C composite HfC / SiC dual-coated layer is used as the engineering background. The HfC / SiC dual-coated sample is prepared according to the following steps: Step 1: Pretreatment of C / C composite matrix; Before coating preparation, select a size of Φ A 30 mm × 10 mm C / C composite material was used as the deposition matrix. First, the matrix surface was polished to remove surface processing marks and contaminants. Then, the cleaned matrix was ultrasonically cleaned in distilled water for no less than 15 min. Finally, the cleaned matrix was dried in an oven at 70°C for 12 hours to obtain the pretreated C / C composite material sample.

[0030] Step 2: Preparation of the SiC inner layer; The pretreated C / C composite sample was suspended in the central reaction zone of a chemical vapor deposition furnace. Argon gas was introduced as a protective atmosphere, and the furnace temperature was raised to a reaction temperature of 1100–1300°C at a heating rate of 5°C / min. After reaching the preset temperature, an MTS (CH3SiCl3)-H2-Ar precursor system was introduced for SiC deposition. The MTS supply rate was maintained at 0.1–0.4 g / min, the H2 and Ar flow rates were controlled at 20–500 mL / min and 10–200 mL / min, respectively, and the deposition time was 4 hours. After deposition, the sample was cooled to room temperature in the furnace under Ar atmosphere protection to obtain a C / C composite sample with a SiC inner layer.

[0031] Step 3: Preparation of the HfC outer layer; Using a SiC-coated C / C composite sample as the matrix, an HfC outer layer was directly deposited on the SiC inner layer surface using an HfCl4-CH4-H2-Ar precursor system. The SiC-coated C / C composite sample was placed in the central reaction zone of the deposition furnace, with argon gas introduced as a protective atmosphere, and the deposition temperature controlled at 1300–1400°C. After reaching the preset temperature, HfCl4, CH4, H2, and Ar reaction gases were simultaneously introduced. The supply rate of HfCl4 was controlled at 0.5–5 g / min, and the flow rates of CH4, H2, and Ar were controlled at 10–50 mL / min, 50–400 mL / min, and 50–300 mL / min, respectively. The deposition time was 2.5 hours. After deposition, the sample was cooled to room temperature in the furnace under Ar atmosphere protection to obtain a C / C composite sample with a double HfC / SiC coating.

[0032] According to the Shaanxi Provincial C / C Composite Materials Engineering Technology Research Center standard (Q / NPU-CC-02-08), an OA-Ⅲ type oxy-acetylene flame ablation machine was used for ablation testing. During the test, the flow rates of oxygen and acetylene were controlled at 0.42 L / s and 0.31 L / s, respectively. The inner diameter of the oxy-acetylene flame nozzle tip was 2 mm. Both the steel tank for fixing the sample and the oxy-acetylene flame tube were water-cooled. During the ablation test, the sample was fixed in the water-cooled steel tank, and a dual-color infrared thermometer (Raytek MR1SCSF) was used to measure the surface temperature of the sample during the ablation process. The infrared thermometer showed that the temperature at the center of the sample stabilized at 2373 K during the ablation process. Five independent repeated measurements were performed on the ablation center region of the test sample surface using a thickness gauge. The arithmetic mean of these measurements was taken as the final ablation depth value and quantitatively compared with the output results of the model of this invention.

[0033] In one exemplary embodiment, reference is made to Figure 1 As shown, a method for predicting the ablation failure behavior of HfC / SiC dual-coating based on chemical-mechanical coupling is provided. This method is implemented in the commercial finite element software Abaqus and its user-defined element subroutine framework, and specifically includes the following steps: Step 1: Create the overall geometric model of the HfC / SiC dual coating, define the degrees of freedom of the element nodes, and apply boundary conditions: Step 1.1 Establish a two-dimensional geometric model with double coating: Combination Figure 2 As shown, to achieve a balance between geometric fidelity and computational efficiency, this embodiment approximates the roughness of the actual coating surface as a cosine profile. First, the surface roughness of the coating before ablation is measured using a 3D profilometer. Ra ,get Ra =6μm. According to... Ra Amplitude of the cosine curve AConversion relationship between The surface profile function of the double-coated layer is determined as follows: y =9.4cos(2π x / T p ),cycle T p The value is set to 40. Further, the thickness data of the double coating was obtained through scanning electron microscopy image analysis, setting the average thickness of the HfC outer layer to 20 μm and the average thickness of the SiC inner layer to 19 μm. Based on the above morphology and thickness parameters, the HfC outer layer and the SiC inner layer were respectively established in the Abaqus preprocessing module. The two were then geometrically assembled to ensure complete fit of the geometric contours at the interface, forming a two-dimensional geometric model of the double coating with a width of 80 μm.

[0034] Step 1.2 Define the degrees of freedom of the element nodes: The two-dimensional geometric model with double coating is divided into quadrilateral meshes, and the element size at the upper and lower interfaces is set to 0.2μm to ensure that the upper and lower interfaces generate node pairs with one-to-one spatial coordinates.

[0035] The nodal degrees of freedom (i.e., the principal variables to be solved) of the element are defined as follows: x Directional displacement u x (Assigned as 1 degree of freedom in the inp file); y Displacement in direction u y (Assigned as 2 degrees of freedom in the inp file); Oxygen diffusion concentration γ (Assigned as 11 degrees of freedom in the inp file); Degree of chemical reaction r (Assigned as 12 degrees of freedom in the inp file).

[0036] Step 1.3 Assign initial material parameters and apply boundary conditions: Initial intrinsic material parameters of HfC and SiC were assigned to the outer and inner layers, respectively. A constant oxygen diffusion concentration boundary condition of 5.8 × 10⁻⁶ was applied to the top of the overall two-dimensional geometric model of the double-coated layer. -5 mol / mm 3 To simulate a continuous oxygen supply provided by an external flow field, zero diffusion flux boundary conditions were applied to both sides of the double-coated two-dimensional geometric model, and a boundary condition was applied to the bottom of the double-coated two-dimensional geometric model. y Directional displacement constraints and zero diffusion flux boundary conditions. The initial displacement, initial oxygen diffusion concentration, and initial chemical reaction degree of the double-coated two-dimensional geometric model are all zero.

[0037] Step 2: Nodal freedom constraints at the junction of the double-coated 2D geometric model: Step 2.1 Extract and match pairs of overlapping nodes at the boundary: Combination Figure 3 As shown, the spatial coordinate data of the nodes at the interface between the HfC outer layer and the SiC inner layer are extracted. A nearest neighbor matching algorithm based on spatial Euclidean distance is used to identify the nearest upper and lower interface node pairs. The first successfully matched node is recorded as... n Among the nodes, the outer node of HfC is numbered as follows: The SiC inner layer node number is For each pair of nodes, establish a separate set of nodes (e.g., ...). Figure 3 The Set-HfC-point-n and Set-SiC-point-n in the model are used to implement point-by-point physical field constraints at the boundary.

[0038] Step 2.2 Apply translayer continuity constraints on displacement and oxygen diffusion concentration: For the set of boundary node pairs established above, multi-point constraint equations are applied point by point in the inp file. Equation), constraining the displacement of the matched node pairs with the oxygen diffusion concentration. For the first... n For nodes (HfC outer layer) and (SiC inner layer), the applied constraint conditions are: (1) (2) (3) Wherein, equations (1) and (2) respectively represent the... x direction and y The multi-point constraint equation constrained by directional displacement, equation (3) represents the multi-point constraint equation constraining the oxygen diffusion concentration. (Superscript) and These represent the first and second matching numbers, respectively. n The node numbers of the upper and lower interfaces of each node pair.

[0039] Reference Figure 3 As shown, u x and u y Corresponding to degrees of freedom 1 and 2 respectively, γ The corresponding degree of freedom is 11. The specific implementation format of the above constraint equations in the inp file is as follows: Figure 3 As shown in the figure. The figure is represented by the first... n Taking nodes as an example, the following is given The three constraint entries under the Equation keyword. The treatment scheme at the interface of the above double coatings ensures the continuity of interface deformation and oxygen diffusion concentration. The degree of chemical reaction (corresponding to degree of freedom 12) is not constrained, thus preserving the independent chemical reaction behavior of the HfC outer layer and the SiC inner layer.

[0040] Step 3: Establish the oxidation-damage coupling control equations for the outer layer of HfC: During the ablation process, the HfC outer layer continuously oxidizes to form HfO2 solid oxide, accompanied by significant volume expansion and coating cracking. To address this failure mechanism, the following set of governing equations is constructed for the HfC outer layer unit.

[0041] Step 3.1 Establish the oxygen transport control equation: During service, the initiation and propagation of microcracks in the outer layer of HfC provide a rapid pathway for oxygen transport inward. To accurately describe this physical phenomenon, an equivalent damage variable is introduced. d Construct an effective oxygen diffusion coefficient for the HfC outer layer that takes into account the influence of microcracks. : (4) In the formula, The diffusion coefficient of oxygen in air is taken as 230 mm. 2 / s; Equivalent oxygen diffusion coefficient of the outer layer of HfC The update is dynamic as the components evolve; specific update rules are detailed in step 5.1. Equivalent damage variable. d See step 3.3 for the definition.

[0042] According to Fick's first law, the oxygen diffusion flux inside the damaged coating... J It can be represented as: (5) In the formula, Let be the oxygen diffusion concentration gradient within the outer layer of HfC. Combining the law of conservation of mass, the oxygen transport control equation for coupled damage is established: (6) in, This represents the rate of change of oxygen diffusion concentration in the outer layer of HfC over time. This represents the divergence operator.

[0043] Step 3.2 Establish the governing equations for the oxidation reaction kinetics: The chemical reaction equation for hafnium carbide and oxygen is: (7) In the oxidation process of the outer layer of HfC, to uniformly describe the consumption and generation of each participating component, a definition is defined.r I For any component molar concentration change Its corresponding stoichiometric coefficient in the chemical reaction equation The ratio: (8) In the formula, r I It indicates the degree of chemical reaction in the outer layer of HfC; the stoichiometric coefficients of reactants are defined as negative, and the stoichiometric coefficients of products are defined as positive.

[0044] definition The initial molar concentration of HfC before ablation occurs. This is the stoichiometric number of the outer layer of HfC (taken as -1). Therefore, the current remaining molar concentration of HfC is... Depending on the degree of chemical reaction of the outer layer of HfC r I The calculation formula is: (9) In this embodiment, at any given calculation time, the current remaining molar concentration of HfC is... Depending on the degree of chemical reaction of the outer layer of HfC r I The calculation formula is: (10) In the formula, the initial molar concentration of HfC before ablation occurs. 9.4×10 -6 mol / mm 3 The specific calculation method is as follows: molar concentration = density / molar mass, where the density and molar mass of HfC are both 1.79 g / cm³. 3 And 190.5 g / mol.

[0045] Based on Arrhenius's law, the kinetic equation for the oxidation reaction, jointly controlled by the oxygen supply and the current remaining HfC concentration, is established: (11) In the formula, The rate of change of the degree of chemical reaction of the outer layer of HfC over time. This represents the oxygen diffusion concentration within the outer layer of HfC, and the pre-exponential factor for the oxidation reaction of HfC. and activation energy 27mm respectively 3 / mol / s and 100 kJ / mol, the ideal gas constant R is 8.314 J / mol / K, temperature T It is 2373K.

[0046] Step 3.3 Establish the stress balance governing equations considering the effects of chemical evolution: During oxidation, the formation of HfO2 products leads to localized volume expansion. This expansion depends on the degree of chemical reaction on the outer layer of HfC. r I Calculate the chemical expansion strain caused by oxidation reaction. : (12) In the formula, the chemical expansion coefficient of the outer layer of HfC is... It is 6.8×10 3 mm 3 / mol, where I is the second-order unit tensor.

[0047] Based on the theory of continuous damage mechanics, the effective stress tensor of the HfC outer layer in the undamaged state is defined. for: (13) In the formula, Here is the initial elastic stiffness matrix of the outer layer of HfC. is the total strain tensor of the HfC outer layer.

[0048] Tensile damage initiation criteria are established separately in the effective stress space. and shear damage initiation criteria : (14) In the formula, Indicates Macauley brackets, For the maximum principal effective stress, For the maximum effective shear stress, and These are the tensile strength and shear strength of the HfC outer layer, respectively, which are dynamically updated as the composition evolves. The specific update rules are detailed in step 5.1. and These are the tensile and shear damage threshold variables that track historical maximum load states, and their dynamic update rules are as follows: and , and These represent the maximum tensile and shear stress ratios experienced throughout the entire loading history, respectively. The formulas for calculating the tensile and shear stress ratios are as follows: and .

[0049] Damage initiation is triggered when the local effective stress first exceeds the HfC outer layer strength (i.e., the corresponding stress ratio exceeds 1). Based on the exponential softening law, tensile damage variables are calculated separately. dt With shear damage variables d s : (15) In the formula, This represents the element feature length of the finite element mesh, taken as 0.0002 mm. This represents the elastic modulus of the corresponding stress mode (Young's modulus for the tensile mode and shear modulus for the shear mode). It is dynamically updated as the components evolve during the solution process. The specific update rules are shown in step 5.1. and The critical strain energy release rates for tensile and shear failure modes are represented respectively, both taken as 2 kJ / mm. 2 subscript k =t or s, where... k =t indicates stretching. k =s indicates shearing.

[0050] To describe the degradation of material mechanical properties under multiaxial complex stress states, an equivalent damage variable is defined based on tensile and shear damage variables. d : (16) In the formula, d t and d s These are the tensile and shear damage variables, respectively.

[0051] Finally, the equivalent damage variable is introduced. d By reducing the effective stress and based on Cauchy's equilibrium equations (ignoring body forces and inertial forces), the stress balance governing equations considering oxidation expansion and microcrack evolution are obtained: (17) Step 4: Establish the active oxidation-property degradation governing equations for the SiC inner layer: The inner layer of SiC undergoes active oxidation under high temperature and low oxygen partial pressure conditions. The oxidation products are all gaseous, leading to a decrease in material stiffness and an increase in the oxygen diffusion coefficient. Based on this mechanism, the following set of governing equations is constructed for the SiC inner layer unit.

[0052] Step 4.1 Establish the governing equation for the active oxidation reaction: The chemical equation for the active oxidation of the inner layer of SiC is: (18) The extent of chemical reaction introduced into the SiC inner layer r II To characterize the local oxidation behavior of the SiC inner layer. Let... The initial molar concentration of SiC before ablation occurs. This represents the stoichiometric coefficient of SiC in the active oxidation reaction (taken as -1). Based on this, the current remaining molar concentration of SiC is... The calculation formula is: (19) In this embodiment, the current remaining molar concentration of SiC The calculation formula is: (20) In the formula, the initial molar concentration of SiC before ablation occurs. 1.8×10 5 mol / mm 3 The specific calculation method is as follows: molar concentration = density / molar mass, where the density and molar mass of SiC are both 0.72 g / cm³. 3 And 40.1 g / mol. Based on Arrhenius's law, the governing equation for the active oxidation reaction of the SiC inner layer is established: (twenty one) In the formula, This represents the rate of change of the degree of chemical reaction in the inner layer of SiC over time. This represents the oxygen diffusion concentration within the inner layer of SiC, and is the pre-exponential factor for the active oxidation reaction of SiC. and activation energy 232 mm respectively 3 / mol / s and 110 kJ / mol, the ideal gas constant R is 8.314 J / mol / K, temperature T It is 2373K.

[0053] Step 4.2 Establish the oxygen transport control equation: During the active oxidation process of the inner layer of SiC, the solid-phase SiC undergoes a chemical reaction and transforms into all-gaseous products. The continuous consumption of SiC leads to a loose material structure, which reduces the resistance to oxygen transport to the interior, resulting in an increase in the local oxygen diffusion coefficient.

[0054] To quantitatively describe the impact of material consumption on gas transport properties, the relative material consumption rate of the SiC inner layer is defined. This is the ratio of the molar concentration of SiC consumed to the initial molar concentration of SiC that has not undergone ablation. It also considers the degree of chemical reaction on the inner layer of SiC. r II By definition, this consumption level can be expressed as: (twenty two) In the formula, the initial molar concentration of SiC before ablation occurs. 1.8×10 5 mol / mm 3 . The value range of is 0 to 1, where =0 indicates a completely unresponsive state. =1 indicates that the SiC in this local area has been completely consumed.

[0055] Relative material consumption of SiC inner layers Construct the equivalent oxygen diffusion coefficient of the SiC inner layer considering SiC consumption. : (twenty three) In the formula, the intrinsic oxygen diffusion coefficient of the SiC inner layer is... 1.6×10 6 mm 2 / s, the diffusion coefficient of oxygen in air 230 mm 2 / s.

[0056] According to Fick's first law, the final governing equation for oxygen transport in the inner SiC layer is obtained: (twenty four) In the formula, This represents the rate of change of oxygen diffusion concentration in the inner layer of SiC over time. This represents the oxygen diffusion concentration gradient within the inner layer of SiC.

[0057] Step 4.3 Establish the stress balance governing equations considering SiC consumption: During the active oxidation process of the SiC inner layer, the solid-phase material is converted into gaseous products and escapes without generating volume expansion strain. However, the continuous consumption of material leads to structural porosity, resulting in significant stiffness degradation. To quantitatively describe this chemical-mechanical coupling behavior, the relative material consumption rate of the SiC inner layer as defined in step 4.2 is used. .

[0058] Will As a phenomenological damage parameter characterizing the degree of degradation of SiC materials, an effective elastic stiffness matrix considering material consumption is defined. : (25) In the formula, Let be the initial elastic stiffness matrix of the SiC inner layer, and its Young's modulus be 448 GPa.

[0059] Based on the above stiffness degradation rule, the stress tensor of the SiC inner layer can be expressed as: Under quasi-static conditions that neglect body forces and inertial forces, substituting into the Cauchy equations of motion, we obtain the stress balance governing equations considering the wear and tear on the SiC inner layer: (26) In the formula, This represents the total strain tensor of the SiC inner layer.

[0060] Step 5: Solve the control equations based on the user-defined unit subroutine and output the results: Step 5.1 Dynamic update of HfC outer layer material properties: Based on the degree of chemical reaction of the outer layer of HfC r I The molar concentration of HfO2 is calculated as follows: (27) In the formula, The stoichiometric coefficient of HfO2 is taken as 1. In this embodiment, the molar concentration of HfO2 is: ; The current molar concentration of HfC is calculated as follows: (28) in, This indicates the initial molar concentration of HfC before ablation occurred.

[0061] During the ablation process, the incompletely oxidized outer layer of HfC is actually a mixture of HfC and HfO2. Based on the proportional mixing rule, the equivalent elastic modulus of the HfC outer layer is calculated as follows: (29) The equivalent strength of the HfC outer layer is calculated as follows: (30) The equivalent oxygen diffusion coefficient of the outer layer of HfC is calculated as follows: (31) In the formula, subscript k =t or s, where... k =t indicates stretching. k =s indicates shear; Young's modulus of HfC shear modulus Tensile strength Shear strength and oxygen diffusion coefficient The values ​​were 340.5 GPa, 136.2 GPa, 86.2 MPa, 172.4 MPa, and 6 × 10⁻⁶ MPa, respectively. -6 mm 2 / s. Young's modulus of HfO2 shear modulus Tensile strength Shear strength and oxygen diffusion coefficient The values ​​were 71.7 GPa, 28.7 GPa, 43.1 MPa, 86.2 MPa, and 1.0 × 10⁻⁶, respectively. -5 mm 2 / s, as shown in Table 1. Based on the above update rules, the properties of the HfC outer layer material are updated in real time as the composition evolves.

[0062] Table 1 Material parameters of HfC and HfO2

[0063] Step 5.2 Nonlinear Iterative Solution: Reference Figure 4 As shown, in this embodiment, the solution of the governing equations in steps 3 and 4 is implemented through a user-defined element subroutine in the Abaqus / Standard solver. During the calculation, the coating to which the current element belongs is dynamically identified based on the attribute parameter jtype: when jtype=1, it is treated as an HfC outer layer element, and when jtype=2, it is treated as a SiC inner layer element.

[0064] For the HfC outer layer unit (jtype=1), the residuals are calculated based on the oxygen transport control equation, oxidation reaction kinetic control equation, and stress balance control equation containing damage evolution from step 3. : (32) in, Represents the integration field. , and These correspond to the oxygen diffusion concentration, chemical reaction degree, and displacement residuals in the outer layer of HfC, respectively. N and B Let them represent the shape function matrix and the shape function gradient matrix, respectively. N T and B T These represent the transposes of the shape function matrix and the shape function gradient matrix, respectively.

[0065] For the SiC inner layer unit (jtype=2), the residuals are calculated based on the oxygen transport control equation, the active oxidation reaction control equation, and the stress balance control equation considering SiC consumption from step 4. : (33) in, , and These correspond to the oxygen diffusion concentration, chemical reaction degree, and displacement residuals of the SiC inner layer, respectively.

[0066] Furthermore, the Jacobian matrix is ​​obtained by taking the partial derivative of the residual with respect to the nodal degrees of freedom.

[0067] For HfC outer elements, their Jacobian matrix K HfC include: (34) (35) (36) In the formula, , and They represent The partial derivatives with respect to displacement, degree of chemical reaction, and oxygen diffusion concentration, , and They represent The partial derivatives with respect to oxygen diffusion concentration, displacement, and degree of chemical reaction, , and They represent The partial derivatives with respect to the degree of chemical reaction, oxygen diffusion concentration, and displacement, Indicates the time step. This represents the displacement vector of the outer layer of hafnium carbide.

[0068] For SiC inner layer units, their Jacobian matrix K SiC include: (37) (38) (39) In the formula, , and They represent The partial derivatives with respect to displacement, degree of chemical reaction, and oxygen diffusion concentration, , and They represent The partial derivatives with respect to oxygen diffusion concentration, displacement, and degree of chemical reaction, , and They represent The partial derivatives with respect to the degree of chemical reaction, oxygen diffusion concentration, and displacement.

[0069] Finally, the residuals and Jacobian matrices of all elements are returned to the Abaqus master solver, and the Newton-Raphson method is used for nonlinear iterative solution.

[0070] Step 5.3 Output of multiphysics results for HfC / SiC dual coating: After the solution process in step 5.2 is completed, the following multiphysics variables are extracted from the result database using the finite element post-processing module: stress field, component molar concentration field, and damage variable field. Specifically, the output includes: the molar concentration field of HfO2 generated on the outer layer of HfC during the ablation process (…). Figure 5 ), tensile and shear damage variable fields of the HfC outer layer ( Figure 6 ), the residual SiC concentration field in the inner layer of SiC ( Figure 7 ) and the stress distribution field of the SiC inner layer ( Figure 8 The aforementioned multiphysics variables can be used to quantitatively evaluate the damage state and compositional evolution of the HfC / SiC dual coating under a given ablation environment, thereby providing a basis for its service reliability assessment.

[0071] To further verify the accuracy of the prediction method of this invention, the numerical prediction results were compared with experimental measurement data from oxy-acetylene flame ablation under the same operating conditions (as shown in Table 2). This embodiment set three comparison times: one comparison after 40 seconds of ablation, and two comparisons after 60 seconds of ablation (corresponding to different samples). At each comparison time, by dynamically tracking the spatiotemporal evolution of the damage field, the total area of ​​the tensile and shear damage regions was extracted and divided by the width of the two-dimensional geometric model of the double-coated layer to obtain the corresponding predicted average ablation depth. (Refer to...) Figure 9 As shown, the comparison results indicate that the ablation depth predicted by the model of this invention has good consistency with the measured ablation depth at the center of the sample, with an average prediction error of 13.7%, proving the effectiveness of this method in engineering applications.

[0072] Table 2 Comparison of experimental and predicted values ​​of ablation depth after oxy-acetylene flame ablation

[0073] Reference Figure 10 and 11 As shown, under the premise that the service environment parameters and the total thickness of the double coating remain unchanged, the study explores the different inner and outer layer thicknesses (hafnium carbide outer layer thickness). H HfC The corresponding SiC inner layer thicknesses are set to 10μm, 20μm, and 30μm, respectively. H SiC The differences in ablation failure behavior of the double-coated layers (29 μm, 19 μm, and 9 μm, respectively) are shown in the figure. It can be observed that the smaller the thickness of the HfC outer layer, the larger the internal shear damage area and peak value.

[0074] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for predicting the chemical-force coupling behavior of HfC / SiC coatings during ablation in extreme environments, characterized in that, Includes the following steps: Step 1: Construct a geometric model of the dual-material stack coating, define the physical degrees of freedom of each material layer unit node, and apply service environment boundary conditions to the coating geometric model. The dual-material stack coating geometric model consists of an HfC outer layer and a SiC inner layer. The HfC outer layer and the SiC inner layer are geometrically assembled so that the geometric contours at their interface are completely fitted, forming the overall geometric model of the dual-coating system. The physical degrees of freedom include those characterizing macroscopic mechanical deformation. x Directional displacement u x and y Directional displacement u y Oxygen diffusion concentration, characterizing gas transport γ And the degree of chemical reaction characterizing the evolution of material components. r ; The boundary conditions include: applying a constant oxygen diffusion concentration boundary condition at the top of the overall geometry of the double-coated model to simulate the continuous oxygen supply of the external flow field; applying a zero diffusion flux boundary condition on both sides; and applying a boundary condition at the bottom. y Directional displacement constraints and zero diffusion flux boundary conditions; Step 2: At the junction of adjacent material layers in the coating geometry model, establish multi-point constraint equations for displacement and oxygen diffusion concentration for the matched node pairs to achieve cross-layer continuity constraint of displacement field and oxygen diffusion concentration field at the junction; at the same time, the degree of chemical reaction in each material layer evolves independently and no cross-layer constraint is applied. Step 3: For different failure mechanisms of different material layers during the ablation process, establish independent control equation sets for each material layer. The control equation sets include oxygen transport control equations, oxidation reaction kinetic control equations, and stress balance control equations that take into account the influence of chemical evolution. Step 4: Iteratively solve the governing equations for each material layer using the finite element method, and dynamically update the material property parameters based on the current degree of chemical reaction of each material layer during the solution process; the dynamic update of material property parameters includes: the degree of chemical reaction through the HfC outer layer. r I The current molar concentration of HfO2 is calculated, and the current remaining molar concentration of HfC is obtained by subtracting the already reacted molar concentration from the initial molar concentration of HfC. Based on this, the incompletely oxidized outer layer of HfC is regarded as a two-phase mixture of HfC and HfO2. According to the proportional mixing rule, the equivalent elastic modulus, equivalent strength, and equivalent oxygen diffusion coefficient of the outer layer of HfC at the current moment are calculated respectively, so as to realize the real-time updating of the material properties of the outer layer of HfC as the oxidation reaction progresses. Step 5: Output the multiphysics variable distribution of each material layer; the multiphysics variables include the damage variable field, component concentration field, and stress distribution field, which are used to evaluate the damage state and component evolution degree of the coating under a given ablation environment; the multiphysics variables specifically include: the tensile damage variable field, shear damage variable field, and component concentration field of the HfC outer layer, and the component concentration field and stress distribution field of the SiC inner layer; the multiphysics variables are used to quantitatively evaluate the damage state and component evolution degree of the HfC / SiC dual coating under a given ablation environment, thereby providing a quantitative basis for its service reliability assessment.

2. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 1, characterized in that: In step 2, the specific implementation of the cross-layer continuity constraint is as follows: extract the node spatial coordinate data at the junction of the HfC outer layer and the SiC inner layer, identify the upper and lower interface node pairs with the closest spatial positions based on the nearest neighbor matching algorithm, and establish an independent node set for each successfully matched node pair. For each set of node pairs, a multi-point constraint equation is established point-by-point for displacement and oxygen diffusion concentration. Its specific form includes: right x The multi-point constraint equation for directional displacement is expressed as follows: right y The multi-point constraint equation for directional displacement is expressed as follows: The multi-point constraint equation for constraining oxygen diffusion concentration is expressed as follows: Among them, superscript and These represent the first and second matching numbers, respectively. n The node numbers of the upper and lower interfaces of each node pair; The above multi-point constraint equations ensure the physical continuity of the displacement at the interface and the oxygen diffusion concentration during the solution process; at the same time, different attribute labels jtype are assigned to each material layer element.

3. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 2, characterized in that: In step 3, the process of constructing the governing equations of the outer HfC layer includes: Step 3.1.

1. Oxygen transport control equation: Introduce equivalent damage variables d The effective oxygen diffusion coefficient of the HfC outer layer is constructed, and the effective oxygen diffusion coefficient of the HfC outer layer varies with the equivalent damage variable. d Increases with size; establishes oxygen transport control equations for coupled damage based on Fick's law and the law of conservation of mass; Step 3.1.

2. Oxidation reaction kinetic governing equation: based on the degree of chemical reaction r I Characterizing the oxidation reaction progress of the HfC outer layer, the remaining molar concentration of HfC varies with the degree of chemical reaction of the HfC outer layer. r I Increase and decrease; based on Arrhenius's law, establish the governing equation for the oxidation reaction kinetics jointly controlled by oxygen concentration and residual HfC concentration; Step 3.1.

3. Stress balance governing equation considering the influence of chemical evolution: determined by the degree of chemical reaction of the outer layer of HfC. r I The chemical expansion strain tensor induced by the oxidation reaction from HfC to HfO2 was calculated. Based on the definition of the effective stress tensor in continuum damage mechanics, a dual damage initiation criterion of tensile and shear was established, triggering damage when the effective stress exceeds the strength of HfC. The tensile damage variables and shear damage variables were calculated separately using the exponential softening law and then combined into an equivalent damage variable. d ; through equivalent damage variables d By reducing the effective stress and substituting it into the Cauchy equilibrium equation, we obtain the stress balance control equation that takes into account oxidation expansion and microcrack evolution.

4. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 3, characterized in that: In step 3, the governing equations of the outer HfC layer include: Oxygen transport control equation for coupled damage: In the formula, This represents the rate of change of oxygen diffusion concentration in the outer layer of HfC over time. Denotes the divergence operator, This represents the equivalent oxygen diffusion coefficient of the outer layer of HfC. This represents the diffusion coefficient of oxygen in air. The oxygen diffusion concentration gradient within the outer layer of HfC; Oxidation reaction kinetic governing equation: In the formula, This indicates the rate of change of the degree of chemical reaction in the outer layer of HfC over time. This indicates the oxygen diffusion concentration inside the outer layer of HfC. The pre-exponential factor representing the oxidation reaction of HfC. R represents the activation energy of the HfC oxidation reaction, and R represents the ideal gas constant. T Indicates temperature. This indicates the current remaining molar concentration of HfC; Stress equilibrium governing equations considering the effects of chemical evolution: In the formula, This represents the initial elastic stiffness matrix of the outer layer of HfC. This represents the total strain tensor of the outer layer of HfC. The coefficient of chemical expansion of the outer layer of HfC is represented by I, and I represents the second-order unit tensor. r I This indicates the degree of chemical reaction on the outer layer of HfC.

5. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 3, characterized in that: In step 3, the process of constructing the governing equations for the SiC inner layer includes: Step 3.2.

1. Kinetic governing equation for active oxidation reaction: Introducing the degree of chemical reaction r II Characterizing the local oxidation behavior of the SiC inner layer, the current remaining molar concentration of SiC varies with the degree of chemical reaction in the SiC inner layer. r II The value decreases as the value increases; the governing equation for the active oxidation reaction kinetics of SiC is established based on the Arrhenius law; Step 3.2.

2. Oxygen Transport Control Equation: Define the relative consumption of material in the SiC inner layer as the ratio of the molar concentration of consumed SiC to the initial molar concentration of SiC before ablation; introduce the relative consumption of material to construct the equivalent oxygen diffusion coefficient of the SiC inner layer, which increases with the increase of the relative consumption of material in the SiC inner layer; establish the oxygen transport control equation of the SiC inner layer according to Fick's first law. Step 3.2.

3. Stress balance control equation considering the influence of chemical evolution: Introduce the relative material consumption degree as a phenomenological damage parameter characterizing the degree of SiC material degradation, define the effective elastic stiffness matrix considering material consumption, the effective elastic stiffness matrix decreases as the relative material consumption degree increases; determine the stress tensor of the SiC inner layer based on the effective elastic stiffness matrix, and substitute it into the Cauchy motion equilibrium equation to obtain the stress balance control equation considering SiC consumption.

6. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 5, characterized in that: In step 3, the governing equations for the SiC inner layer include: Kinetic governing equation for active oxidation reaction: In the formula, This indicates the rate of change of the degree of chemical reaction in the inner layer of SiC over time. This indicates the oxygen diffusion concentration within the inner layer of SiC. The pre-exponential factor representing the active oxidation reaction of SiC This represents the activation energy of the active oxidation reaction of SiC, where R represents the ideal gas constant. T Indicates temperature. This indicates the current remaining molar concentration of SiC; The oxygen transport control equation for the coupling material consumption: In the formula, This represents the rate of change of oxygen diffusion concentration in the inner layer of SiC over time. Denotes the divergence operator, This represents the intrinsic oxygen diffusion coefficient of the inner layer of SiC. This represents the stoichiometric coefficient of SiC. This indicates the initial molar concentration of SiC before ablation. r II Indicates the degree of chemical reaction in the inner layer of SiC. This represents the diffusion coefficient of oxygen in air. This represents the oxygen diffusion concentration gradient within the inner layer of SiC. Stress equilibrium governing equations considering the effects of chemical evolution: In the formula, This represents the total strain tensor of the SiC inner layer. This represents the initial elastic stiffness matrix of the SiC inner layer.

7. The method for predicting the chemical-force coupling behavior of HfC / SiC coating ablation process in extreme environments according to claim 6, characterized in that: In step 4, the iterative solution is implemented through a user-defined unit subroutine, specifically including: During the calculation process, the material layer to which the current element belongs is dynamically identified based on its attribute tag jtype. When jtype is the first preset value, it is processed as an HfC outer element. The residual is calculated according to the control equations of the HfC outer element in step 3, and the corresponding Jacobian matrix is ​​obtained by taking the partial derivative of the residual with respect to the nodal degrees of freedom. When jtype is the second preset value, it is processed as an inner SiC unit. The residual is calculated according to the control equations of the inner SiC unit in step 3, and the corresponding Jacobian matrix is ​​obtained by taking the partial derivative of the residual with respect to the nodal degrees of freedom. The residuals and Jacobian matrices of all elements are returned to the finite element master solver, and the Newton-Raphson method is used for nonlinear iterative solution.

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