A prediction method for coating thermal stress and residual stress based on cross-scale integrated calculation

Abstract

The present invention relates to the technical field of prediction of coating service thermal stress, and particularly relates to a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation, including calculating the relationships between various thermophysical properties and mechanical properties of each layer of material in the coating varying with temperature respectively by using first-principles based on the microscale, and calculating the service thermal stress and residual stress of the coating by using finite element simulation based on the macroscale. The present invention obtains the thermophysical properties and mechanical properties of each layer of material in the coating based on first-principles on the microscale, uses them as input data for finite element simulation on the macroscale, simulates the temperature field of the coating system in the real service environment, and further obtains the corresponding stress field and residual stress distribution, solves the problems of lack of data in single finite element modeling and difficulty in quantitatively testing coating thermal stress, and quickly and efficiently predicts the service thermal stress and residual stress of the coating.

Description

Technical Field

[0001] The present invention relates to the technical field of prediction of thermal stress during coating service, and particularly relates to a method for predicting thermal stress and residual stress of a coating based on cross-scale integrated calculation. Background Art

[0002] Thermal barrier coatings, oxidation-resistant coatings, etc. are mostly used in the aerospace field, where the service conditions are harsh. There are mismatches in elastic modulus, thermal conductivity, thermal expansion coefficient, etc. between coatings. During the repeated heating and cooling process, large thermal stresses are generated inside the coatings. With the increase of service time, stress concentration is caused, leading to the initiation and propagation of cracks, and ultimately resulting in the spalling failure of the coatings. Experimental studies generally use observing microcracks or adopting the indentation fracture mechanics theoretical model to indirectly evaluate thermal stress, and cannot directly obtain the thermal stress distribution varying with temperature. Finite element can be used to evaluate the stress of a material system caused by a thermal field. For the input data of the corresponding part in finite element simulation, including density, heat capacity, Poisson's ratio, thermal conductivity, Young's modulus, thermal expansion coefficient, etc., it is mainly obtained through experimental research. For extremely harsh service environments, it is difficult to obtain these input parameters, and some materials lack relevant experimental data. Summary of the Invention

[0003] The present invention aims to provide a method for predicting thermal stress and residual stress of a coating based on cross-scale integrated calculation, so as to solve the problems of lack of data in single finite element modeling and difficulty in quantitatively testing the thermal stress of the coating, and quickly and efficiently predict the service thermal stress and residual stress of the coating.

[0004] The method for predicting thermal stress and residual stress of a coating based on cross-scale integrated calculation according to the present invention includes S1: calculating the relationships between various mechanical properties of each layer of material in the coating and temperature respectively, specifically as follows:

[0005] S101: Obtain the crystal structures of each layer of material in the coating. For the crystal structure of each material, perform full optimization relaxation to complete convergence respectively using the first principles based on the microscopic scale, and then perform relaxation with variable volume and fixed volume to complete convergence.

[0006] S102: For each layer of material in the coating, calculate the mechanical properties of the crystal structures at different volumes, and perform polynomial fitting on the mechanical properties and volume to obtain the analytical formula of the mechanical properties and volume.

[0007] S103: For each layer of material in the coating, use the quasi-harmonic approximation QHA method to calculate the relationships between thermophysical properties and temperature, including volume, thermal expansion coefficient, and heat capacity, to obtain the relationships between thermal expansion coefficient, heat capacity and temperature and the analytical formula of volume varying with temperature. Then substitute the analytical formula of volume and temperature into the analytical formula of volume and mechanical properties to obtain the relationship between mechanical properties and temperature.

[0008] S2: Based on the finite element simulation at the macroscopic scale, calculate the service thermal stress and residual stress of the coating as follows:

[0009] S201: Establish a finite element model of the coating;

[0010] S202: Perform polynomial fitting on the numerical values of various thermophysical properties and mechanical properties with temperature in S1 to obtain analytical expressions, and input the obtained analytical expressions into the finite element simulation software respectively;

[0011] S203: Mesh the finite element model to obtain a network model, and import the network model into the finite element simulation software;

[0012] S204: Set the initial conditions and boundary conditions for the service thermal stress simulation, calculate the temperature field of the finite element model in S201 under these initial conditions, apply the temperature field to the coating under steady-state operation, and simulate and calculate the service thermal stress of the coating;

[0013] S205: Set the initial condition for the residual stress simulation as the entire coating being in a same temperature field, which gradually cools from a high temperature to room temperature at a fixed cooling rate, and set the boundary conditions the same as those for the service thermal stress. When the temperature stabilizes at room temperature, perform finite element simulation to obtain the residual stress.

[0014] The beneficial effects of the present invention are as follows: For the simulation of the coating thermal stress, the present invention obtains the relationship between the thermophysical properties and mechanical properties of each coating material with temperature through the first-principles calculation based on the microscopic scale, solves the problems of lack of data in single finite element modeling and difficulty in quantitatively testing the coating thermal stress, quickly and efficiently predicts the service thermal stress and residual stress of the coating, and realizes large-scale, process-based, and automated coating structure design and coating material system screening on the premise of low cost and short R & D cycle, providing guiding opinions and technical support for industrial production.

[0015] The preferred embodiment of the present invention is as follows: In S202: The analytical expression is y = a + bx + cx 2 , where a, b, and c are fitting parameters, y is the corresponding thermophysical property or mechanical property, and x is the temperature. The beneficial effect is that using polynomial fitting to obtain the analytical expression changes the data from numerical fitting to analytical fitting, and unknown data can be predicted according to the analytical expression.

[0016] In the present invention, a finite element model can be established using the geometric structures of different coatings, or a finite element model can be further established through the following method.

[0017] The preferred embodiment of the present invention is as follows: In S201: Establish a finite element model through the following method:

[0018] a. Obtain the microstructure morphology of the coating using SEM and save it as a digital image;

[0019] b. Use Photoshop to adjust the depth of field of the digital image and remove the parts with large errors;

[0020] c. Use VECTOR MAGIC to convert the digital image into a vector graph and smooth the coating interface;

[0021] d. Convert the vector graph into a format compatible with finite element software in AutoCAD.

[0022] The beneficial effect is that when modeling the coating, digital image technology is used to process the real microstructure of the coating, and the real microstructure is mapped into the finite element model.

[0023] The preferred embodiment of the present invention is that the upper surface temperature of the coating is set as the first type of boundary condition, that is, T hot = aK, and the cooling gas with T cool = bK is used at the lower end of the substrate, where the temperature a > the temperature b, and the resulting is the service thermal stress; the initial condition for the simulation of the residual stress is set that the entire coating is in a same temperature field, and this temperature field gradually cools from a high temperature to room temperature at a fixed cooling rate, and the residual stress is simulated at room temperature; the boundary conditions for the simulation of the service thermal stress and the residual stress are both set that the x-axis direction and the y-axis direction at the lower left corner are both fixed, and only the x-axis direction at the lower right corner is fixed.

[0024] The main difference between the simulation of the service thermal stress and the residual thermal stress lies in the different initial conditions and boundary conditions; for the service thermal stress, the temperatures at the hot end and the cold end can change, and it is necessary to ensure that the hot end temperature a is greater than the cold end temperature b.

[0025] The coating described in the present invention includes a thermal barrier coating, an oxidation-resistant coating, a stealth coating, and a coating or structure composed of any several solid heterogeneous materials.

[0026] The preferred embodiment of the present invention is that the coating is a thermal barrier coating, and the materials of each layer of the thermal barrier coating include a ceramic thermal insulation layer GdTaO4, an oxidation layer Al2O3, a metal bonding layer NiCoCrAlY, and a Ni-based superalloy.

[0027] The preferred embodiment of the present invention is that the analytical formula of the bulk modulus B and the volume of the ceramic thermal insulation layer GdTaO4 is y2 = 659.355 - 1.37y1 - 9.540×10 -4 y1 2 ; the analytical formula of the shear modulus G and the volume is; y3 = -640.417 + 5.538y1 - 0.0105y1 2 .

[0028] In a preferred embodiment of the present invention: In S103, the relationship between volume and temperature is obtained by the QHA method and then polynomial fitting is performed on it to obtain an analytical form. The analytical formula for the change in the volume of the ceramic thermal insulation layer GdTaO4 with temperature is y1 = 308.6 + 0.0071x + 8.493×10 -7 x 2 , and the relationship between the bulk modulus B and temperature is: for GdTaO4: y2 = 145.583 - 0.0139x - 1.74987×10 -6 x 2 ; the relationship between the shear modulus G and temperature is: y3 = 68.631 - 0.0064x - 1.74769×10 -6 x 2 .

[0029] Specification: The Young's modulus and Poisson's ratio can be calculated based on B and G. Just by obtaining the relationships between B, G and temperature, the relationships between the Young's modulus, Poisson's ratio and temperature can be obtained.

[0030] In a preferred embodiment of the present invention: In S204, the upper surface temperature of the thermal barrier coating is set as the first type of boundary condition, i.e., T hot = 1773K, and the lower end of the substrate uses a cooling gas with T cool = 873K, and the surface convective heat transfer coefficient is set as 1900W / m 2 / K; the boundary conditions are set such that both the x-axis direction and the y-axis direction at the lower left corner of the finite element model are fixed, and only the x-axis direction at the lower right corner is fixed.

[0031] In a preferred embodiment of the present invention: The simulation calculation of residual stress is as follows:

[0032] The initial condition is set such that the entire thermal barrier coating is at a temperature of 2000K and is gradually cooled from 2000K to 300K at a cooling rate of 5K / s; the boundary conditions are set such that both the x-axis direction and the y-axis direction at the lower left corner of the finite element model are fixed, and only the x-axis direction at the lower right corner is fixed. When the system temperature stabilizes at 300K, finite element simulation is performed to obtain the residual stress.

[0033] First-principles: The first-principles calculation method, namely ab initio, is widely used in fields such as chemistry, physics, life science and materials science. Its basic idea is to regard a system composed of multiple atoms as a system composed of multiple electrons and atomic nuclei, and perform the most "non-empirical" processing of the problem according to the basic principles of quantum mechanics. It only requires 5 basic constants (m0 (electron mass), e (elementary charge), h (Planck constant), c (speed of light), k B(Boltzmann constant), the physical properties such as the energy and electronic structure of the system can be calculated. First-principles calculations can determine the structure and basic properties of known materials and achieve precise atomic-level control. It is a powerful tool for solving experimental and theoretical problems and predicting the structural properties of new materials at the present stage. Moreover, first-principles calculations do not require real experiments, greatly saving experimental costs.

[0034] Finite element simulation: Finite element simulation refers to using mathematical approximation methods to simulate real physical systems. By using simple and interacting elements, i.e., units, a real system with an infinite number of unknowns can be approximated with a finite number of unknowns. Brief Description of the Drawings

[0035] Figure 1 It is a flowchart of the first embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention;

[0036] Figure 2 It is a finite element model diagram in the first embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention;

[0037] Figure 3 It is a temperature field diagram obtained by simulation in the first embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention;

[0038] Figure 4 It is a thermal stress field diagram obtained by simulation in the first embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention;

[0039] Figure 5 It is a crystal structure diagram of Ni-based superalloy obtained by modeling in the first embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention;

[0040] Figure 6 It is a finite element model of the metal Ta and IrAl oxidation-resistant coating system in the second embodiment of a method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to the present invention. Detailed Embodiments

[0041] The following describes the preferred embodiments of the present invention with reference to the accompanying drawings. It should be understood that the described preferred embodiments are only used to explain the present invention and do not limit the protection scope of the present invention.

[0042] Embodiment 1

[0043] As shown in the appendix Figure 1As shown in the figure, a method for predicting the thermal stress and residual stress of a coating based on cross-scale integrated calculation in this embodiment includes S1: calculating the relationships between the mechanical properties of each layer of material in the coating and temperature respectively, as follows:

[0044] S101: Obtain the crystal structures of each layer of material in the coating. For the crystal structure of each material, perform full optimization relaxation to complete convergence respectively using the first principles based on the microscale, and then perform relaxation with variable volume and fixed volume to complete convergence.

[0045] S102: For each layer of material in the coating, calculate the mechanical properties of the crystal structures at different volumes, and perform polynomial fitting of the mechanical properties and volume to obtain the analytical formula of the mechanical properties and volume.

[0046] S103: For each layer of material in the coating, use the quasi-harmonic approximation (QHA) method to calculate the relationships between its thermophysical properties and temperature, including volume, thermal expansion coefficient, and heat capacity, to obtain the relationships between the thermal expansion coefficient, heat capacity and temperature and the analytical formula of volume with respect to temperature. Then, substitute the analytical formulas of volume and temperature into the analytical formulas of volume and mechanical properties respectively to obtain the relationships between the mechanical properties and temperature.

[0047] S2: Based on the finite element simulation at the macroscale, simulate and calculate the service thermal stress and residual stress of the coating, as follows:

[0048] S201: Establish a finite element model of the coating.

[0049] S202: Perform polynomial fitting on the numerical values of the mechanical properties changing with temperature in S1 to obtain analytical formulas, and input the obtained analytical formulas into the finite element simulation software respectively.

[0050] S203: Perform mesh division on the finite element model to obtain a network model, and import the network model into the finite element simulation software.

[0051] S204: Set the initial conditions and boundary conditions for the service thermal stress simulation, simulate and calculate the temperature field of the finite element model in S201 under these initial conditions, apply the temperature field to the coating under steady-state operation, and simulate and calculate the service thermal stress of the coating.

[0052] S205: Set the initial condition for the residual stress simulation as the entire coating being in a same temperature field, which gradually cools from a high temperature to room temperature at a fixed cooling rate, and set the boundary conditions the same as those for the service thermal stress. When the temperature stabilizes at room temperature, perform finite element simulation to obtain the residual stress.

[0053] The beneficial effects are as follows: For the simulation of coating thermal stress, the present invention obtains the relationship between the thermophysical properties and mechanical properties of each coating material with temperature through first-principles calculations based on the microscopic scale, solves the problems of lack of data in single finite element modeling and difficulty in quantitatively testing coating thermal stress, quickly and efficiently predicts the service thermal stress and residual stress of the coating, and realizes large-scale, process-based, and automated coating structure design and coating material system screening on the premise of low cost and short R & D cycle, providing guiding opinions and technical support for industrial production.

[0054] In this embodiment, the upper surface temperature of the coating is set as the first type of boundary condition, that is, T hot = aK, and the lower end of the substrate uses T cool = bK cooling gas, where the temperature a > the temperature b; the initial condition for residual stress simulation is set such that the entire coating is in a same temperature field, and this temperature field gradually cools from a high temperature to room temperature at a fixed cooling rate, and the residual stress is simulated at room temperature; the boundary conditions for service thermal stress and residual stress simulation are both set such that the x-axis and y-axis directions at the lower left corner are fixed, and only the x-axis direction at the lower right corner is fixed.

[0055] The coating described in this embodiment includes a thermal barrier coating, an oxidation-resistant coating, a stealth coating, and a coating or structure composed of any several solid heterogeneous materials.

[0056] Taking the GdTaO4, Al2O3, NiCoCrAlY, and Ni-based superalloy thermal barrier coating system as an example in this embodiment, other coating systems are also within the protection scope of the present invention.

[0057] A method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation disclosed in this embodiment specifically includes the following content:

[0058] S1: Calculate the relationship between the mechanical properties of GdTaO4, Al2O3, NiCoCrAlY, and Ni-based superalloy with temperature respectively, specifically including the following content:

[0059] S101: Download the crystal structures of GdTaO4, Al2O3, and NiCoCrAlY from the crystallographic database ICSD and / or materials project. The crystallographic database mentioned in this embodiment refers to ICSD. Here, ICSD refers to the Inorganic Crystal Structure Database (abbreviated as ICSD). It is jointly run by The Gmelin Institute (Frankfurt) in Germany and FIZ (Fachinformationszentrum Karlsruhe). It only collects and provides crystal structure information of all inorganic compounds except metals and alloys and those without C–H bonds. Materials project is an existing open-source materials database.

[0060] As shown in the appendix Figure 5 Using the SQS (Special Quasi-Random Structure Model) to model the crystal structure of the Ni-based superalloy. Use the first-principles software VASP based on the microscopic scale to fully optimize and relax the crystal structures of GdTaO4, Al2O3, NiCoCrAlY, and the Ni-based superalloy to complete convergence respectively, and then relax to complete convergence after changing the volume and fixing the volume. Specifically, first perform full relaxation (relax both the atomic positions and the unit cell structure) to complete convergence, then change the volume, and perform atomic position relaxation with a fixed volume to complete convergence. Some parameters in the VASP calculation are selected as follows: Use the Projector-augmented wave method (PAW) to describe the interaction between the ion core and the valence electrons; Use the Perdew Burke Ernzerhof (PBE) functional in the Generalized gradient approximation (GGA) to handle the interaction between electrons; Set the plane wave cutoff energy in the reciprocal space to 400 - 520 eV; Use the k-point Monkorst-Park grid in all calculation processes; Set the energy convergence (EDIFF) and the interatomic force (EDIFFG) that meet the calculation accuracy requirements during the relaxation process. The convergence criteria are EDIFF = 1*10-6~1*10-8 and EDIFFG = -0.01~-0.001 respectively.

[0061] S102: For GdTaO4, Al2O3, NiCoCrAlY, and Ni-based superalloys, the mechanical properties of the crystal structures at different volumes are calculated using the stress-strain method, including Young's modulus E, bulk modulus B, shear modulus G, and Poisson's ratio. The mechanical properties are polynomially fitted with the volume to obtain the analytical expressions of the mechanical properties with respect to the volume.

[0062] Specifically: The analytical expression of the bulk modulus B with respect to the volume: GdTaO4: y2 = 659.355 - 1.37y1 - 9.540*10 -4 y1 2 ; Al2O3: y2 = 170.208 + 7.060y1 - 0.0719y1 2 ; NiCoCrAlY: y2 = 793.673 - 10.765y1 + 0.042y1 2 ; Ni-based superalloy: y2 = -5587.06 + 38.93y1 - 0.0654y1 2 . The analytical expression of the shear modulus G with respect to the volume: GdTaO4: y3 = -640.417 + 5.538y1 - 0.0105y1 2 ; Al2O3: y3 = 486.331 - 3.812y1 - 0.00254y1; NiCoCrAlY: y3 = 1208.867 - 23.687y1 + 0.122y1 2 ; Ni-based superalloy: y3 = -5252.680 + 35.617y1 - 0.059y1 2 .

[0063] Young's modulus E and Poisson's ratio ν can be obtained from the bulk modulus B and shear modulus G. Only the relationships between the bulk modulus B, shear modulus G, and temperature need to be given

[0064] The formulas for Young's modulus E and Poisson's ratio ν are Formula 1 and Formula 2 respectively:

[0065]

[0066]

[0067] S103: For GdTaO4, Al2O3, NiCoCrAlY, and Ni-based superalloys, the thermal properties of the crystal structures at different volumes are calculated using the quasi-harmonic approximation (QHA) method to obtain the analytical expressions of the volume change with temperature. GdTaO4: y1 = 308.628 + 0.007x + 8.49287*10 -7 x 2 ; Al2O3: y1 = 83.58 + 0.052x - 4.032*10 -5 x2 ; NiCoCrAlY: y1 = 84.7 + 0.024x - 1.2*10 -5 x 2 ; Nickel-based superalloy: y1 = 308 + 0.013x + 2*10 -6 x 2 。For GdTaO4, Al2O3, NiCoCrAlY, and nickel-based superalloys, the analytical expressions for volume and mechanical properties are respectively substituted into the analytical expressions for volume and temperature to obtain the relationship between mechanical properties and temperature. Specifically: For the bulk modulus B of GdTaO4: y2 = 145.583 - 0.0139x - 1.74987*10 -6 x 2 ; Shear modulus G: y3 = 68.631 - 0.0064x - 1.74769*10 -6 x 2 。For the bulk modulus B of Al2O3: y2 = 264.667 - 0.032x + 5.333*10 -6 x 2 ; Shear modulus G: y3 = 167.667 - 0.018x - 2.667*10 -6 x 2 。For the bulk modulus B of NiCoCrAlY: y2 = 183 - 0.036x - 3.64*10 -6 x 2 ; Shear modulus G: y3 = 79 - 0.021x - 1.048*10 -6 x 2 。For the bulk modulus B of nickel-based superalloys: y2 = 185 - 0.012x - 8*10 -6 x 2 ; Shear modulus G: y3 = 97.8 - 0.015x - 4*10 -7 x 2 。

[0068] The thermal conductivities of GdTaO4, Al2O3, NiCoCrAlY, and nickel-based superalloys are obtained using the Slack model. The formula for the Slack model is as follows:

[0069]

[0070] Where is the average atomic mass, δ 3 is the average volume per atom, θ D is the Debye temperature, n is the number of atoms in the unit cell, γ is the Grüneisen constant, and A is a coefficient related to γ. Among them, the formulas for θ D and γ are as follows:

[0071]

[0072] h is Planck's constant, k B is the Boltzmann constant, vm is the speed of sound, which is related to the elastic modulus.

[0073]

[0074] v is the Poisson's ratio.

[0075] S2: Based on the finite element simulation at the macroscopic scale, taking the use of COMSOL software as an example in this embodiment, it includes the following contents:

[0076] S201: Establish finite element models of these four materials by using the geometric structures of GdTaO4, Al2O3, NiCoCrAlY and Ni-based superalloy, as Figure 2 shown.

[0077] In this embodiment, when modeling the thermal barrier coatings of GdTaO4, Al2O3, NiCoCrAlY and Ni-based superalloy, the coating is processed by digital image technology with the real microstructure, and the real microstructure is mapped into the finite element model.

[0078] Taking the electron microscope image obtained by SEM as an example, it is established into a finite element input model by the following method:

[0079] a. Use SEM to obtain the microstructure morphology of the thermal barrier coatings of GdTaO4, Al2O3, NiCoCrAlY and Ni-based superalloy, and save it as a digital image;

[0080] b. Use photoshop to adjust the depth of field of the digital image and remove the parts with large errors;

[0081] c. Use VECTOR MAGIC to convert the digital image into a vector graph and smooth the coating interface;

[0082] d. Convert the vector graph into a format compatible with the finite element software in AutoCAD.

[0083] S202: For GdTaO4, Al2O3, NiCoCrAlY and Ni-based superalloy respectively, perform polynomial fitting on the numerical values of the mechanical properties obtained by the first-principles method in S1 with respect to the temperature change, obtain the analytical formula, and input the obtained analytical formulas into COMSOL respectively. The form of the analytical formula is y = a + bx + cx 2, where a, b, and c are fitting parameters (calculated from known mechanical property values and corresponding known temperature values), y is the corresponding mechanical property value, and x is the temperature value. Since the changes in the obtained mechanical properties with temperature are discrete, in order to extrapolate to higher or lower temperatures and generate continuous data, the form is changed from numerical fitting to analytical fitting. According to the analytical formula, unknown data can be predicted and the data range can be expanded.

[0084] S203: Mesh the finite element model established in S201, and use the mapping method to generate a large number of finite element meshes. For the NiCoCrAlY layer, GdTaO4, and Al2O3 layers which are relatively thin, in order to ensure the accuracy of the calculation results, the meshes in this area are refined to form a network model, and the network model is imported into the finite element simulation software COMSOL.

[0085] S204: Set the initial conditions and boundary conditions for the service thermal stress simulation. Set the upper surface temperature of GdTaO4, Al2O3, NiCoCrAlY, and the Ni-based superalloy thermal barrier coating (hereinafter referred to as the coating) as the first type of boundary condition, that is, T hot = 1773K, and use the cooling gas with T cool = 873K at the lower end of the substrate. The surface convective heat transfer coefficient is set to 1900W / m 2 / K; the boundary conditions are set to be fixed in both the x-axis direction and the y-axis direction at the lower left corner of the finite element model, and only the x-axis direction is fixed at the lower right corner.

[0086] Simulate and calculate the temperature field of the finite element model in S201 under these initial conditions, as shown in Figure 3 . Apply the temperature field to the coating under steady-state operation, and simulate and calculate the service thermal stress of the coating, as shown in Figure 4 .

[0087] S205: Residual stress simulation. The initial conditions are set such that the entire coating system is at a temperature of 2000K and gradually cools from 2000K to 300K at a cooling rate of 5K / s; the boundary conditions are the same as those for the service thermal stress simulation. When the system temperature stabilizes at 300K (close to room temperature), perform finite element simulation to obtain the residual stress.

[0088] Example Two

[0089] In this example, a Ta metal substrate is combined with an IrAl coating to form an oxidation-resistant coating system, and other coating systems are also within the protection scope of the present invention.

[0090] A method for predicting the thermal stress and residual stress of a coating based on cross-scale integrated calculation disclosed in this example specifically includes the following content:

[0091] S1: Calculate the relationships between the mechanical properties of metallic Ta and IrAl alloy and temperature change respectively, which specifically include the following:

[0092] S101: Download the crystal structures of metallic Ta and IrAl alloy from the crystallographic database ICSD and / or materials project. The crystallographic database described in this embodiment refers to ICSD. Here, ICSD refers to the Inorganic Crystal Structure Database (abbreviated as ICSD). It is jointly run by The Gmelin Institute (Frankfurt) in Germany and FIZ (Fachinformationszentrum Karlsruhe). It only collects and provides crystal structure information of all inorganic compound crystals except metals and alloys and without C–H bonds. Materials project is an existing open-source materials database.

[0093] Use the first-principles software VASP based on the microscopic scale to perform full optimization relaxation on the crystal structures of the above metallic Ta and IrAl alloy until complete convergence, and then perform relaxation with fixed volume after changing the volume until complete convergence. Specifically, first perform full relaxation (relaxing both atomic positions and unit cell structures) until complete convergence, and then change the volume and perform relaxation of atomic positions at other volumes until complete convergence. Some parameters in the VASP calculation are selected as follows: Use the Projector-augmented wave method (PAW) to describe the interaction between ion cores and valence electrons; use the Perdew Burke Ernzerhof (PBE) functional in the Generalized gradient approximation (GGA) to handle the interaction between electrons; set the plane wave cutoff energy in the reciprocal space to 400 - 520 eV; use the k-point Monkorst-Park grid in all calculation processes; set the energy convergence (EDIFF) and the interatomic force (EDIFFG) convergence criteria that meet the calculation accuracy requirements during the relaxation process to EDIFF = 1*10 -6 ~1*10 -8 、EDIFFG = -0.01~-0.001.

[0094] S102: For metals Ta and IrAl alloy, the mechanical properties of crystal structures at different volumes are calculated using the stress-strain method, including Young's modulus E, bulk modulus B, shear modulus G, and Poisson's ratio. The mechanical properties are polynomially fitted with volume to obtain the analytical expressions of mechanical properties versus volume. Specifically, the analytical expression of bulk modulus B versus volume: Ta: y2 = 628.242 - 4.266y1 - 0.0202y1 2 ; IrAl: y2 = 15937.76 - 130.591y1 + 0.269y1 2 。The analytical expression of shear modulus G versus volume: Ta: y3 = 243.855 - 3.441y1 + 0.0121y1 2 ; IrAl: y3 = 1244.182 - 4.311y1 - 3.73*10 -3 y1 2 。

[0095] Young's modulus E and Poisson's ratio v can be obtained from the bulk modulus B and shear modulus G, and only the relationships between the bulk modulus B, shear modulus G and temperature need to be given.

[0096] The formulas for Young's modulus E and Poisson's ratio v are Formula 1 and Formula 2 respectively:

[0097]

[0098]

[0099] S103: For metals Ta and IrAl alloy, the thermal properties of crystal structures at different volumes are calculated using the quasi-harmonic approximation (QHA) method to obtain the analytical expressions of volume versus temperature: Ta: y1 = 75 + 6.84*10 -3 x + 1.6*10 - 7 x 2 ; IrAl: y1 = 219.84 + 0.0076x + 2.4*10 -6 x 2 。For metals Ta and IrAl alloy, the relationships between mechanical properties and temperature are obtained by substituting the analytical expressions of volume and mechanical properties into the analytical expressions of volume and temperature: Ta bulk modulus: y2 = 195 - 0.021x - 3.12*10 -5 x 2 ; Shear modulus G: y3 = 53.8 - 9.24*10 -3 x - 1.56*10 -6 x 2 。IrAl bulk modulus B: y2 = 229 - 0.0997x + 3.4*10 -6 x2 ; Shear modulus G: y3 = 116 - 0.0452x - 1.4744*10 -5 x 2 .

[0100] The thermal conductivities of metals Ta and IrAl alloy are obtained using the slack model respectively. The formula of the slack model is as follows:

[0101]

[0102] where is the average atomic mass, δ 3 is the average volume per atom, θ D is the Debye temperature, n is the number of atoms in the unit cell, γ is the Grüneisen constant, and A is a coefficient related to γ. Among them, the formulas for θ D and γ are as follows:

[0103]

[0104] h is Planck's constant, k B is the Boltzmann constant, v m is the sound velocity, which is related to the elastic modulus.

[0105]

[0106] v is the Poisson's ratio.

[0107] S2: Based on the finite element simulation at the macroscopic scale, in this embodiment, taking the use of COMSOL software as an example, it includes the following contents:

[0108] S201: Establish a finite element model of the material using the geometric structures of metals Ta and IrAl alloy, as Figure 6 shown.

[0109] S202: For metals Ta and IrAl alloy respectively, perform polynomial fitting on the numerical values of the mechanical properties obtained by the first-principles method in S1 with respect to the temperature change, obtain the analytical expressions, and input the obtained analytical expressions into COMSOL respectively. The form of the analytical expression is y = a + bx + cx 2 , where a, b, and c are fitting parameters (calculated from the known mechanical property values and the corresponding known temperature values), y is the corresponding mechanical property value, and x is the temperature value. Since the changes of the obtained mechanical properties with temperature are discrete, in order to extend to higher or lower temperatures and generate continuous data, the form is changed from numerical fitting to analytical fitting. According to the analytical expression, unknown data can be predicted and the data range can be expanded.

[0110] S203: Mesh the finite element model established in S201, and generate a large number of finite element meshes using the mapping method. Since the IrAl alloy layer is relatively thin, in order to ensure the accuracy of the calculation results, the meshes in this area are refined to form a network model, and the network model is imported into the finite element simulation software COMSOL.

[0111] S204: Set the initial conditions and boundary conditions for the service thermal stress simulation. Set the upper surface temperature of the metal Ta and the IrAl alloy oxidation-resistant coating (hereinafter referred to as the coating) as the first type of boundary condition, that is, T hot = 1773K, and use a cooling gas with T cool = 873K at the lower end of the substrate. The surface convective heat transfer coefficient is set to 1900W / m 2 / K; the boundary conditions are set to be fixed in both the x-axis and y-axis directions at the lower left corner of the finite element model, and only the x-axis direction is fixed at the lower right corner.

[0112] Simulate and calculate the temperature field of the finite element model in S201 under these initial conditions. Apply the temperature field to the coating under steady-state operation, and simulate and calculate the service thermal stress of the coating.

[0113] S205: Residual stress simulation. The initial condition is set that the entire coating system is at a temperature of 2000K and gradually cools from 2000K to 300K at a cooling rate of 5K / s; the boundary conditions are the same as those for the service thermal stress simulation. When the system temperature stabilizes at 300K (close to room temperature), perform a finite element simulation to obtain the residual stress.

[0114] The preferred embodiments of the present application are described in detail above in conjunction with the accompanying drawings. The typical well-known structures and common general knowledge technologies in the preferred embodiments are not described in detail here. Those of ordinary skill in the art can, under the inspiration given by this embodiment, improve and implement the technical solution of the present invention in combination with their own capabilities. Some typical well-known structures, well-known methods, or common general knowledge technologies should not be an obstacle for those of ordinary skill in the art to implement the present application.

[0115] The scope of protection required by the present application shall be subject to the content of its claims, and the content recorded in the invention content, specific implementation manners, and the drawings of the specification is used to interpret the claims.

[0116] Within the scope of the technical concept of the present application, several deformations can also be made to the specific implementation manners of the present application, and these deformed specific implementation manners should also be regarded as within the scope of protection of the present application.

Claims

1. A method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation, characterized in that Including S1: Calculate the relationships between various thermophysical properties and mechanical properties of each layer of material in the coating as they vary with temperature, specifically as follows: S101: Obtain the crystal structures of each layer of material in the coating. For the crystal structure of each material, perform full optimization relaxation to complete convergence using first principles based on the microscopic scale, and then perform relaxation with variable volume followed by fixed volume to complete convergence. S102: For each layer of material in the coating, calculate the mechanical properties of the crystal structures at different volumes, and perform polynomial fitting of the mechanical properties against volume to obtain the analytical expression of the mechanical properties versus volume. S103: For each layer of material in the coating, use the quasi-harmonic approximation (QHA) method to calculate the relationship between thermophysical properties and temperature, obtain the analytical expression of volume versus temperature, and then substitute the analytical expressions of volume and temperature into the analytical expression of volume and mechanical properties to obtain the relationship between mechanical properties and temperature. S2: Based on finite element simulation at the macroscopic scale, simulate and calculate the service thermal stress and residual stress of the coating, specifically as follows: S201: Establish a finite element model of the coating. S202: Perform polynomial fitting on the numerical values of the various thermophysical properties and mechanical properties varying with temperature in S1 to obtain analytical expressions, and input the obtained analytical expressions into the finite element simulation software respectively. S203: Perform mesh division on the finite element model to obtain a mesh model, and import the mesh model into the finite element simulation software. S204: Set the initial conditions and boundary conditions for the service thermal stress simulation, calculate the temperature field of the finite element model in S201 under these initial conditions, apply the temperature field to the coating under steady-state operation, and simulate and calculate the service thermal stress of the coating. S205: Set the initial conditions for the residual stress simulation such that the entire coating is in a uniform temperature field, which gradually cools from a high temperature to room temperature at a fixed cooling rate. The boundary conditions are set the same as those for the service thermal stress. When the temperature stabilizes at room temperature, perform finite element simulation to obtain the residual stress.

2. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 1, characterized in that In S202: The form of the analytical formula is y = a + bx + cx 2 , where a, b, and c are fitting parameters, y is the corresponding value of thermophysical property or mechanical property, and x is the temperature value.

3. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 1 or 2, characterized in that In S201: The finite element model is established by the following method: a. Use SEM to obtain the microscopic tissue morphology of the coating and save it as a digital image. b. Use Photoshop to adjust the depth of field of the digital image and remove parts with large errors. c. Use VECTOR MAGIC to convert the digital image into a vector graph and smooth the coating interface. d. Convert the vector graph into a format compatible with the finite element software in AutoCAD.

4. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 1 or 2, characterized in that, Set the upper surface temperature of the coating as the first type of boundary condition, i.e., T hot = aK, and use cooling gas with T cool = bK at the lower end of the substrate, where temperature a > temperature b; the initial condition for residual stress simulation is set such that the entire coating is in a same temperature field, and this temperature field gradually cools from a high temperature to room temperature at a fixed cooling rate, and the residual stress is simulated at room temperature; the boundary conditions for service thermal stress and residual stress simulation are both set such that the x-axis and y-axis directions at the lower left corner are fixed, and only the x-axis direction is fixed at the lower right corner.

5. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 1 or 2, characterized in that The coating described includes a thermal barrier coating, an oxidation-resistant coating, a stealth coating, and a coating or structure composed of any several solid heterogeneous materials.

6. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 5, wherein The coating is a thermal barrier coating, including a ceramic thermal insulation layer GdTaO4, an oxidation layer Al2O3, a metal bonding layer NiCoCrAlY, and a Ni-based superalloy.

7. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 6, wherein, The analytical formula of the bulk modulus B and volume of the ceramic thermal insulation layer GdTaO4 is y2 = 659.355 - 1.37y1 - 9.540*10 -4 y1 2 ; the analytical formula of the shear modulus G and volume is; y3 = -640.417 + 5.538y1 - 0.0105y1 2 .

8. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 7, wherein In S103: The relationship between volume and temperature is obtained by the QHA method, and then it is polynomially fitted to obtain an analytical form. The analytical formula for the change in the volume of the ceramic thermal insulation layer GdTaO4 with temperature is y1 = 308.6 + 0.0071x + 8.493*10 - 7 x 2 , and the relationship between the bulk modulus B and temperature is: for GdTaO4: y2 = 145.583 - 0.0139x - 1.74987*10 -6 x 2 ; the relationship between the shear modulus G and temperature is: y3 = 68.631 - 0.0064x - 1.74769*10 -6 x 2 .

9. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 8, wherein Simulation calculation of service thermal stress, in S204: Set the upper surface temperature of the thermal barrier coating as the first type of boundary condition, i.e., T hot = 1773 K, and use cooling gas with T cool = 873 K at the lower end of the Ni-based superalloy matrix. Set the surface convective heat transfer coefficient as 1900 W / m 2 / K; Set the boundary condition as fixed in both the x-axis and y-axis directions at the lower left corner of the finite element model, and only fixed in the x-axis direction at the lower right corner.

10. The method for predicting coating thermal stress and residual stress based on cross-scale integrated calculation according to claim 9, characterized in that The simulation calculation of the residual stress is specifically as follows: The initial conditions are set such that the entire thermal barrier coating is at a temperature of 2000 K and is gradually cooled from 2000 K to 300 K at a cooling rate of 5 K / s; the boundary conditions are set such that both the x-axis and y-axis directions at the lower left corner of the finite element model are fixed, and only the x-axis direction at the lower right corner is fixed. When the system temperature stabilizes at 300 K, finite element simulation is performed to obtain the residual stress.

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