A method for predicting moisture-heat coupling cracking of thermal barrier coatings

Abstract

The present invention relates to a method for predicting moisture-heat coupling cracking of thermal barrier coatings, comprising: obtaining the moisture-heat-elastic coupling relationship of thermal barrier coating materials, introducing relaxation time according to the moisture-heat-elastic coupling relationship, establishing a hyperbolic parabolic moisture-heat coupling model, combining the moisture-heat-elastic response and the surface elastic constitutive relationship, and establishing a moisture-heat coupling model of thermal barrier coating materials based on phase lag; when the moisture-heat coupling model of thermal barrier coating materials is subjected to ultra-rapid moisture-heat coupling shock, combining the surface elastic model, establishing a moisture-heat coupling model of thermal barrier coatings with cracks; predicting the crack direction of thermal barrier coating materials according to the moisture-heat coupling model of thermal barrier coatings with cracks, and obtaining crack direction prediction results. The present invention studies the influence characteristics of ultra-rapid moisture-heat shock on thermal barrier coating materials, analyzes the influence law of temperature-humidity correlation on the mechanical properties of thermal barrier coating materials, establishes a moisture-heat coupling fracture model of thermal barrier coatings under ultra-rapid shock, predicts the crack direction of thermal barrier coatings, and establishes a crack evaluation mechanism for thermal barrier coatings.

Description

Technical Field

[0001] The invention relates to the technical field of crack trend prediction, and in particular to a method for predicting moisture-heat coupling cracking of a thermal barrier coating. Background Art

[0002] Ultra-rapid moisture-heat shocks caused by laser shock and humidity changes in space are inevitable technical problems in the development of aerospace technology. Thermal barrier coatings are an important technical means to increase the service life of aircraft engine turbine blades, and they are also inevitably subjected to ultra-rapid moisture-heat transient shocks in the external environment. The existing technology cannot accurately describe the moisture-heat coupling transmission mechanism of thermal barrier coatings during ultra-rapid moisture-heat shocks, and the moisture-heat coupling mechanism of microstructures is still unclear. Since thermal barrier coatings have obvious scale dependence at the micro-nano scale, the existing technology cannot accurately predict the cracking mechanism of thermal barrier coatings and the direction of cracks. Therefore, it is necessary to study the moisture-heat coupling characteristics and cracking mechanism of thermal barrier coating materials under ultra-rapid shocks. Summary of the invention

[0003] The purpose of the present invention is to provide a method for predicting the cracking of thermal barrier coatings due to moisture-heat coupling. Considering the surface elasticity theory, a non-classical theoretical moisture-heat coupling model considering the scale effect is established from the perspective of phase lag, and the cracking mechanism of thermal barrier coating materials under ultra-rapid thermal coupling shock is studied. It can more accurately describe the dependence of fracture parameters on non-Fourier, non-Fick parameters and scale factors during drastic temperature and humidity changes, reveal the distribution law of temperature field, humidity field, moisture-heat stress and strain at the crack tip or front, and clarify the influence mechanism of non-Fourier, non-Fick effect and scale effect on the interface cracking of thermal barrier coating materials, providing theoretical support for the reliability design and mechanical property evaluation of thermal barrier coating materials in extreme environments such as ultra-rapid moisture-heat coupling shock.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A method for predicting moisture-heat coupling cracking of thermal barrier coatings, comprising:

[0006] The hygrothermal-elastic coupling relationship of the thermal barrier coating material is obtained, and according to the hygrothermal-elastic coupling relationship, the relaxation time is introduced to establish a hyperbolic parabolic hygrothermal coupling model, and the hygrothermal-elastic response and the surface elastic constitutive relationship are combined to establish a hygrothermal coupling model of the thermal barrier coating material based on phase lag;

[0007] When the moisture-heat coupling model of the thermal barrier coating material is subjected to ultra-rapid moisture-heat coupling impact, a moisture-heat coupling model of the thermal barrier coating with cracks is established in combination with a surface elastic model;

[0008] The crack orientation of the thermal barrier coating material is predicted according to the moisture-heat coupling model of the cracked thermal barrier coating, and a crack orientation prediction result is obtained.

[0009] Optionally, the method for establishing the hyperbolic parabola hygrothermal coupling model is:

[0010]

[0011] Among them, q m is the heat generated by absorbing / releasing water vapor, C(r,t) is the water content per unit volume of voids, and D m is the water vapor diffusion coefficient, τ m is the relaxation time of water flow, q h is the heat flow, T(r,t) is the temperature, k is the thermal conductivity, is the spatial gradient operator, r is the spatial position, t is the time, τ h is the relaxation time of heat flow.

[0012] Optionally, establishing the phase-lag-based moisture-heat coupling model of the thermal barrier coating material includes:

[0013] Establishing an energy conservation model corresponding to temperature and a mass conservation model corresponding to humidity, and combining the hyperbolic parabola-type hygrothermal coupling model to obtain a hygrothermal coupling model;

[0014] By combining the moisture-heat coupling model with the moisture-heat elastic response and the surface elastic constitutive relationship, a moisture-heat coupling model of thermal barrier coating material considering scale effect is obtained;

[0015] Based on the thermal barrier coating material moisture-heat coupling model considering scale effect combined with equilibrium equations, geometric equations and boundary conditions, the thermal barrier coating material moisture-heat coupling model based on phase lag is obtained.

[0016] Optionally, the method for obtaining the hygrothermal elastic response is:

[0017]

[0018] Among them, λ and μ are Lame constants, δ ij is the Kronecker symbol, l=1 is the coating, l=2 is the base layer, i and j vary from 1 to 3, ΔT is the temperature change, ε is the strain, and γ is a parameter related to the coefficient of hygrothermal expansion.

[0019] Optionally, a method for obtaining the surface elastic constitutive relation is:

[0020]

[0021] in, is the surface stress, δ ij is the Kronecker symbol, is the surface strain, αs is the moisture / thermal expansion coefficient of the interface layer, σ0 is the surface residual tension in the unconstrained zero strain state, ▽ s is the surface gradient operator, μ s , s is the surface Lamé constant, ε s is the surface strain, u is the displacement, α s is the thermal expansion coefficient of the interface layer, k s is a parameter related to the surface Lamé constant, σ a s 3 is the surface stress, u 3,a is the surface displacement.

[0022] Optionally, obtaining the crack direction prediction result includes:

[0023] The crack direction of the thermal barrier coating material predicted by the thermal-wet coupling model of the cracked thermal barrier coating is converted into the initial boundary value of the time-dependent partial differential equation group, and based on the Laplace transform, the initial boundary value is converted from the time domain to the pure boundary value of the Laplace domain, and according to the boundary conditions, the pure boundary value is converted into a Fredholm integral model or a singular integral model;

[0024] The Fredholm integral model or the singular integral model is transformed to obtain a related algebraic model, the related algebraic model is calculated to obtain a calculation result, the calculation result is inversely transformed by Laplace transform to obtain crack trend parameters at the crack tip or front, the crack trend of the thermal barrier coating material is predicted according to the crack trend parameters, and a crack trend prediction result is obtained.

[0025] Optionally, the crack trend parameters include: stress intensity factor, energy release rate and J integral.

[0026] Optionally, obtaining the relevant algebraic model includes:

[0027] The unknown function in the Fredholm integral model or the singular integral model is expanded to obtain an orthogonal function, and the singularity index of the crack tip is determined. The expansion coefficient of the orthogonal function is obtained through the determined singularity index of the crack tip. Based on the expansion coefficient of the orthogonal function, the Fredholm integral model or the singular integral model is converted into a related algebraic model.

[0028] The beneficial effects of the present invention are:

[0029] The present invention proposes a phase-lag-based moisture-heat coupling model to explore the anomalous diffusion process of heat and moisture transfer inside thermal barrier coating materials under ultra-rapid moisture-heat coupling impact, and analyzes the influence of factors such as phase lag, phase change potential, and moisture-heat wave propagation velocity on moisture-heat stress.

[0030] The present invention studies the influence characteristics of ultra-rapid moisture-heat shock on thermal barrier coating materials, analyzes the influence law of temperature-humidity correlation on the mechanical properties of thermal barrier coating materials, establishes a moisture-heat coupling model of thermal barrier coatings under ultra-rapid shock, and reveals the change law of humidity-temperature-stress field.

[0031] The present invention clarifies the influence mechanism of thermal barrier coating material properties on crack propagation behavior, reveals the fracture failure mechanism of such materials in ultra-rapid moisture-heat coupling impact, and provides theoretical guidance and scientific basis for the reliability design and mechanical property evaluation of thermal barrier coating materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0033] Figure 1 A schematic diagram of an ultra-rapid heat shock test device according to an embodiment of the present invention;

[0034] Figure 2 A flow chart of a method for predicting moisture-heat coupling cracking of a thermal barrier coating according to an embodiment of the present invention;

[0035] Among them, 1. Metal shielding box, 2. Thin film resistor thermometer and hygrometer, 3. Quartz glass column, 4. Insulation material. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] like Figure 1 As shown, this embodiment discloses a method for predicting moisture-heat coupling cracking of thermal barrier coatings, comprising:

[0039] The moisture-heat-elastic coupling relationship of the thermal barrier coating material is obtained, and the relaxation time is introduced according to the moisture-heat-elastic coupling relationship to establish a hyperbolic parabolic moisture-heat coupling model. The moisture-heat-elastic response and the surface elastic constitutive relationship are combined to establish a moisture-heat coupling model of the thermal barrier coating material based on phase lag. When the moisture-heat coupling model of the thermal barrier coating material is subjected to ultra-rapid moisture-heat coupling impact, a moisture-heat coupling model of the thermal barrier coating with cracks is established in combination with the surface elastic model. The crack direction of the thermal barrier coating material is predicted according to the moisture-heat coupling model of the thermal barrier coating with cracks, and the crack direction prediction result is obtained.

[0040] Establishing a phase-lag-based moisture-heat coupling model for thermal barrier coating materials includes: establishing an energy conservation model corresponding to temperature and a mass conservation model corresponding to humidity, combining a hyperbolic parabolic moisture-heat coupling model to obtain a moisture-heat coupling model; obtaining a moisture-heat coupling model for thermal barrier coating materials that considers scale effects by combining the moisture-heat coupling model with the moisture-heat elastic response and the surface elastic constitutive relationship; obtaining a phase-lag-based moisture-heat coupling model for thermal barrier coating materials based on the moisture-heat coupling model for thermal barrier coating materials that considers scale effects, combining equilibrium equations, geometric equations and boundary conditions, specifically:

[0041] When the temperature and humidity inside the thermal barrier coating material change, the deformation of the material depends not only on the stress field, but also on the temperature and humidity field. The classical hygrothermal elastic coupling theory is only applicable to conventional situations. In order to meet its wider application field, this embodiment proposes a hyperbolic parabolic hygrothermal elastic theory model based on the classical theory. Therefore, a hyperbolic parabolic hygrothermal coupling equation is first established. For example, the classical Fourier law of heat conduction:

[0042]

[0043] Among them, q h (r, t) is the heat flow, T(r, t) is the temperature, k is the thermal conductivity, is the spatial gradient operator, r is the spatial position, and t is the time. Introduce the relaxation time τ h , then we have the following non-Fourier law:

[0044]

[0045] For the diffusion of humidity water vapor, a similar relationship holds:

[0046]

[0047] Among them, q m is the heat generated by absorbing / releasing water vapor, C(r,t) is the water content per unit volume of voids, and D m is the water vapor diffusion coefficient, τ m is the relaxation time of water flow, qh is the heat flow, T(r,t) is the temperature, k is the thermal conductivity, is the spatial gradient operator, r is the spatial position, t is the time, τ h is the relaxation time of heat flow.

[0048] Using the conservation of energy and mass:

[0049]

[0050] Among them, q h (r, t) is the heat generated by temperature change, q m (r, t) is the heat generated by humidity change, ρ is the density, is the partial differential symbol.

[0051] Considering the coupling of temperature field and humidity field, and temporarily ignoring the coupling with elastic field, the wet-heat coupling formula can be obtained from the Dufour and Soret effect and phase change potential:

[0052]

[0053] Among them, the coefficients L and D are related to the Dufour and Soret effects and the phase transition potential. From the above equations, q can be eliminated h ,q m , thus obtaining the hyperbolic parabolic hygrothermal coupling control partial differential equations. When τ h =τ m When =0, the equation degenerates into the classical model.

[0054] The hygrothermoelastic response is described by the constitutive relation:

[0055]

[0056] Among them, λ and μ are Lame constants, δ ij is the Kronecker symbol, l=1 is coating, l=2 is base layer, i and j vary from 1 to 3.

[0057] Equations (6), (7), and (8) constitute the hygrothermal coupling constitutive relationship between the coating and the substrate. Since the surface layer is regarded as a material film of zero thickness, using the surface elasticity theory, the surface elastic constitutive relationship is as follows:

[0058]

[0059] in is the surface stress, is the surface strain, α s is the moisture / thermal expansion coefficient of the interface layer, k s =2(μ s +λs ), σ0 is the surface residual tension in the unconstrained zero strain state, λ s , μ s is the surface Lamé constant, ▽ s is the surface gradient operator, and the following table ij indicates that it can only change in the two-dimensional direction of the surface tangent plane.

[0060] The hygrothermal coupling constitutive equations (6), (7) (8) of the coating and substrate materials of the thermal barrier coating and the hygrothermal elastic constitutive equations (9) and (10) of the interface layer together constitute the hygrothermal coupling theoretical constitutive relationship of the thermal barrier coating material considering the scale effect. By combining the equilibrium equation, geometric equation and boundary conditions, the hygrothermal coupling equation group of the thermal barrier coating material is formed. The transient problem is solved by certain mathematical physics methods, integral transformation method, etc., so as to obtain the transient hygrothermal coupling response of the thermal barrier coating material, such as transient temperature distribution, humidity distribution and stress-strain distribution.

[0061] Obtaining the crack direction prediction result includes: converting the crack direction of the thermal barrier coating material predicted by the thermal-wet coupling model of the cracked thermal barrier coating into the initial boundary value of the time-related partial differential equation group, based on the Laplace transform, converting the initial boundary value from the time domain to the pure boundary value of the Laplace domain, and converting the pure boundary value into a Fredholm integral model or a singular integral model according to the boundary conditions; transforming the Fredholm integral model or the singular integral model, obtaining the relevant algebraic model, calculating the relevant algebraic model, obtaining the calculation result, performing the inverse transformation of the Laplace transform on the calculation result, obtaining the crack direction parameter at the crack tip or front, predicting the crack direction of the thermal barrier coating material according to the crack direction parameter, and obtaining the crack direction prediction result; wherein, the crack direction parameters include: stress intensity factor, energy release rate and J integral.

[0062] Obtaining the relevant algebraic model includes: expanding the unknown function in the Fredholm integral model or the singular integral model, obtaining the orthogonal function, determining the singularity index of the crack tip, obtaining the expansion coefficient of the orthogonal function through the determined singularity index of the crack tip, and converting the Fredholm integral model or the singular integral model into the relevant algebraic model based on the expansion coefficient of the orthogonal function, specifically:

[0063] Study on interface cracking of thermal barrier coatings

[0064] First, a model is proposed for the crack problem. For the study of crack problems in thermal barrier coating materials, in addition to the above-mentioned control partial differential equations, the boundary conditions of the crack surface also need to be considered. For the elastic field, since the crack surface is free and cannot transmit force, but for humidity and temperature, the open crack surface can transmit part of the heat and water vapor. Therefore, the influence of cracks on temperature, humidity and even further on the stress field must be considered. The relationship can be assumed with the help of moist heat conduction and convection. The most common crack forms of thermal barrier coating materials are linear cracks and three-dimensional coin-shaped cracks. When subjected to ultra-rapid moist heat coupling impact, due to the presence of cracks, the moist heat flow produces stress concentration at the crack tip. Considering the surface effect on the crack surface, with the help of surface elasticity theory, a moist heat coupling model of thermal barrier coatings with cracks is established.

[0065] Secondly, the model is to be solved. Since the research object is ultra-rapid transient impact, it is related to time. Therefore, the corresponding problem is converted into an initial boundary value problem of a group of partial differential equations related to time. To solve such problems, the Laplace transform can be used to transform the problem from the time domain to a pure boundary value problem in the Laplace domain for solution. According to the boundary conditions, the problem can be transformed into solving Fredholm integral equations or singular integral equations. Next, the unknown function is selected to expand into a class of orthogonal functions related to Chybeshev polynomials. The singularity index of the crack tip can be determined according to the complex function technology or the characteristic expansion technology. Once the index is determined, the coefficients of the orthogonal function expansion can be further transformed into a group of related algebraic equations using the matching method or the weighted residual method. With the help of existing commercial computing tools such as Matlab and Mathematica, the problem can be solved. Finally, the stress intensity factor, energy release rate, J integral and other fracture parameters at the crack tip or front can be calculated by the inverse transformation of the Laplace transform. The influence of certain physical quantities such as relaxation time and phase change potential on fracture parameters is analyzed.

[0066] For crack problems in multi-layer composite materials such as thermal barrier coatings, it is necessary to consider that the properties of each layer of material are different, and the corresponding equations describing the internal moisture heat conduction and mass transfer will also be different. Therefore, this embodiment will analyze the relationship between temperature and humidity and material properties. And simulate the deformation and fracture of more complex multi-layer materials under moisture heat coupling conditions, including the size and direction distribution of cracks, so as to better predict the direction of cracks, and provide theoretical guidance and scientific basis for the reliability design and mechanical property evaluation of thermal barrier coating materials.

[0067] Study on the correlation between temperature and humidity of thermal barrier coating materials

[0068] First, the thermal conductivity, specific heat capacity, thermal diffusivity and other material parameters of the thermal barrier coating material are measured through conventional experiments to facilitate subsequent data analysis, and then the laser heating experiment is carried out. Build a corresponding test platform (such as Figure 2 ), based on a metal shielding box 1, a thin film resistor thermometer and hygrometer 2, a quartz glass column 3 and an insulating material 4, a short laser is used to heat the thin layer of the sample, and a miniaturized platinum thin film resistor is used to collect the temperature. The entire experimental device is sealed in a metal box to reduce external electromagnetic interference. The thin layer of the sample to be tested is laid flat on the upper surface of the quartz glass column, and foam plastics are used around it for heat and moisture insulation.

[0069] By experimentally measuring the material parameters of the coating material, substrate material and coating-substrate interface of the thermal barrier coating at different temperatures and humidities, the relationship between the material parameters and the temperature and humidity changes was obtained. Combined with the thermal barrier coating moisture-heat coupling model, the influence of temperature-humidity correlation on the moisture-heat coupling behavior of the thermal barrier coating material interface was explored.

[0070] First, the temperature and humidity correlation was determined. Taking rare earth doped thermal barrier coating (YSZ) as an example, YSZ samples were made, the changes of samples were observed using a scanning electron microscope, and the thickness and elastic modulus of the coating were measured using instruments. The data of the material properties of the thermal barrier coating substrate and each part of the coating changing with temperature and humidity under different temperatures and humidities were tested experimentally, and the relationship curve between the mechanical properties of the material and temperature and humidity was obtained by fitting.

[0071] Then, the relaxation time was measured, and a laser pulse heating platform was established to perform short pulse laser heating and temperature measurement on different specimens. The diameter of the laser spot was adjusted to completely cover the specimen. The Laplace transform was used to obtain the theoretical solution in combination with the corresponding boundary conditions and initial conditions. By comparing the experimental measurement values ​​with the theoretical solution, the phase delay time of the material under test was obtained using the least squares method.

[0072] Finally, the temperature and humidity related model is solved, and a phase-delay-based moisture-heat coupling model of thermal barrier coating materials is established and solved through experimentally measured data. Numerical simulation is performed on it to analyze the influence mechanism of the temperature and humidity correlation of the mechanical properties parameters of thermal barrier coatings on the moisture-heat coupling behavior.

[0073] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for predicting moisture-heat coupling cracking of thermal barrier coatings, characterized in that: include: The hygrothermal-elastic coupling relationship of the thermal barrier coating material is obtained. According to the hygrothermal-elastic coupling relationship, the relaxation time is introduced to establish a hyperbolic parabolic hygrothermal coupling model. The hygrothermal-elastic response and the surface elastic constitutive relationship are combined to establish a hygrothermal coupling model of the thermal barrier coating material based on phase lag: Establishing an energy conservation model corresponding to temperature and a mass conservation model corresponding to humidity, and combining the hyperbolic parabola-type hygrothermal coupling model to obtain a hygrothermal coupling model; By combining the moisture-heat coupling model with the moisture-heat elastic response and the surface elastic constitutive relationship, a moisture-heat coupling model of thermal barrier coating material considering scale effect is obtained; Based on the thermal barrier coating material moisture-heat coupling model considering scale effect combined with equilibrium equations, geometric equations and boundary conditions, a phase-delay-based moisture-heat coupling model of the thermal barrier coating material is obtained; When the moisture-heat coupling model of the thermal barrier coating material is subjected to ultra-rapid moisture-heat coupling impact, a moisture-heat coupling model of the thermal barrier coating with cracks is established in combination with a surface elastic model; The crack orientation of the thermal barrier coating material is predicted according to the moisture-heat coupling model of the cracked thermal barrier coating, and a crack orientation prediction result is obtained.

2. The method for predicting moisture-heat coupled cracking of thermal barrier coatings according to claim 1, characterized in that: The method for establishing the hyperbolic parabola hygrothermal coupling model is: Among them, q m is the heat generated by absorbing / releasing water vapor, C(r,t) is the water content per unit volume of voids, and D m is the water vapor diffusion coefficient, m is the relaxation time of water flow, q h is the heat flow, T(r,t) is the temperature, k is the thermal conductivity, is the spatial gradient operator, r is the spatial position, t is the time, h is the relaxation time of heat flow.

3. The method for predicting moisture-heat coupled cracking of thermal barrier coatings according to claim 1, characterized in that: The method for obtaining the hygrothermal elastic response is: Among them, λ and μ are Lame constants, δ ij is the Kronecker symbol, l=1 is the coating, l=2 is the base layer, i and j vary from 1 to 3, ΔT is the temperature change, ε is the strain, and γ is a parameter related to the coefficient of hygrothermal expansion.

4. The method for predicting moisture-heat coupling cracking of thermal barrier coatings according to claim 1, characterized in that: The method for obtaining the surface elastic constitutive relation is: in, is the surface stress, δ ij is the Kronecker symbol, is the surface strain, α s is the moisture / thermal expansion coefficient of the interface layer, σ0 is the surface residual tension in the unconstrained zero strain state, is the surface gradient operator, μ s , s is the surface Lamé constant, ε s is the surface strain, u is the displacement, α s is the thermal expansion coefficient of the interface layer, k s is a parameter related to the surface Lamé constant, is the surface stress, u 3,a is the surface displacement.

5. The method for predicting moisture-heat coupling cracking of thermal barrier coatings according to claim 1, characterized in that: Obtaining the crack direction prediction result includes: The crack direction of the thermal barrier coating material predicted by the thermal-wet coupling model of the cracked thermal barrier coating is converted into the initial boundary value of the time-dependent partial differential equation group, and based on the Laplace transform, the initial boundary value is converted from the time domain to the pure boundary value of the Laplace domain, and according to the boundary conditions, the pure boundary value is converted into a Fredholm integral model or a singular integral model; The Fredholm integral model or the singular integral model is transformed to obtain a related algebraic model, the related algebraic model is calculated to obtain a calculation result, the calculation result is inversely transformed by Laplace transform to obtain crack trend parameters at the crack tip or front, the crack trend of the thermal barrier coating material is predicted according to the crack trend parameters, and a crack trend prediction result is obtained.

6. The method for predicting moisture-heat coupled cracking of thermal barrier coatings according to claim 5, characterized in that: The crack trend parameters include: stress intensity factor, energy release rate and J integral.

7. The method for predicting moisture-heat coupling cracking of thermal barrier coatings according to claim 5, characterized in that: Obtaining relevant algebraic models includes: The unknown function in the Fredholm integral model or the singular integral model is expanded to obtain an orthogonal function, and the singularity index of the crack tip is determined. The expansion coefficient of the orthogonal function is obtained through the determined singularity index of the crack tip. Based on the expansion coefficient of the orthogonal function, the Fredholm integral model or the singular integral model is converted into a related algebraic model.

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