Method and apparatus for simulating oxidation process of superalloy

Abstract

The disclosure provides a high-temperature alloy oxidation process simulation method, belonging to the technical field of material numerical simulation. The high-temperature alloy oxidation process simulation method can include the following steps: based on thermodynamics, classical oxidation kinetics and statics, an oxidation mechanics-chemistry coupling model of the high-temperature alloy is established. According to the coupling model, a finite element model of the oxidation mechanics-chemistry of the high-temperature alloy is determined. According to the finite element model, the oxidation process of the high-temperature alloy is simulated. In the oxidation simulation process of the high-temperature alloy, various data in the oxidation process of the high-temperature alloy can be obtained without experiments. And since the simulation method is based on the finite element model of the oxidation mechanics-chemistry of the high-temperature alloy, the workload of researchers can be reduced, the calculation efficiency can be improved, and the oxidation process of the high-temperature alloy can be simulated completely and accurately.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of material numerical simulation, and particularly relates to a simulation method and device for an oxidation process of a high-temperature alloy. BACKGROUND

[0002] The high-temperature alloy is a key material of an aero-engine and is commonly used for manufacturing turbine blades. Simulating the oxidation process of the high-temperature alloy is of great significance for the optimized design of the turbine blade material of the aero-engine.

[0003] At present, the oxidation behavior data of the high-temperature alloy are mainly obtained through oxidation tests, and then the oxidation process of the high-temperature alloy is analyzed. However, for the oxidation test, it is extremely difficult to obtain the oxidation data of the high-temperature alloy in a high-temperature environment, and it is even more difficult to obtain the material transformation data such as microstructure evolution and oxidation layer thickness in the oxidation process of the high-temperature alloy, and thus the oxidation process of the high-temperature alloy cannot be accurately and completely simulated.

[0004] The above information disclosed in the background section is only for the purpose of enhancing the understanding of the background of the present disclosure, and therefore it can include information that does not constitute the prior art known to those of ordinary skill in the art. SUMMARY

[0005] The present disclosure aims to provide a simulation method and device for an oxidation process of a high-temperature alloy, which can completely and accurately simulate the oxidation process of the high-temperature alloy without simulation tests.

[0006] To achieve the above-mentioned purpose of the present disclosure, the present disclosure adopts the following technical solutions:

[0007] According to a first aspect of the present disclosure, a simulation method for an oxidation process of a high-temperature alloy is provided, and the simulation method comprises:

[0008] a coupled model of oxidation mechanics-chemistry of the high-temperature alloy is established based on thermodynamics, classical oxidation kinetics and statics;

[0009] a finite element model of oxidation mechanics-chemistry of the high-temperature alloy is determined according to the coupled model;

[0010] the oxidation process of the high-temperature alloy is simulated according to the finite element model.

[0011] In an exemplary embodiment of the present disclosure, the coupled model of oxidation mechanics-chemistry of the high-temperature alloy is established based on thermodynamics, classical oxidation kinetics and statics, and comprises:

[0012] a first equation set is established based on thermodynamics, classical oxidation kinetics and statics, and the first equation set comprises a constitutive equation of a displacement field and a constitutive equation of a concentration field;

[0013] The constitutive equation of the displacement field is:

[0014]

[0015] The constitutive equation of the concentration field is:

[0016]

[0017] where σ ij is stress, D ijk1 is stiffness coefficient, ε k1 is strain tensor, subscripts i, j, k, l are free indices, subscript s is metal ion and oxygen ion, subscript p is oxide, Δ is gradient operator, η s is chemical expansion coefficient of metal ion and oxygen ion, c s is concentration of metal ion and oxygen ion, η p is chemical expansion coefficient of oxide, c p is concentration of oxide, δ k1 is Kronecker symbol, J s is diffusion channel of metal ion and oxygen ion, D s is diffusion coefficient of metal ion and oxygen ion, F s is constant, tr(ε) is trace of strain, is partial derivative, ε is strain, X is displacement gradient factor, J is ion diffusion channel.

[0018] In an exemplary embodiment of the present disclosure, the η s is determined by a first preset formula, and the first preset formula is:

[0019]

[0020] The F s is determined by a second preset formula, and the second preset formula is:

[0021]

[0022] where v m is molar volume, is molar volume of metal ion and oxygen ion, E is elastic modulus, ν is Poisson's ratio, R is Boltzmann constant, and T is temperature.

[0023] In an exemplary embodiment of the present disclosure, according to the coupling model, determining the oxidation mechanics-chemistry finite element model of the high-temperature alloy further comprises:

[0024] establishing a weak form of a first basic equation according to the constitutive equation of the displacement field, the control equation of the displacement field, and the boundary condition of the force;

[0025] A weak form of the second governing equation is determined according to the weak form of the first governing equation and the weak form of the second governing equation.

[0026] A weak form of the second governing equation is determined according to the weak form of the first governing equation and the weak form of the second governing equation.

[0027] In an exemplary embodiment of the present disclosure, the governing equation of the displacement field is:

[0028] σ ij,j +f i = 0.

[0029] The boundary condition of the force is:

[0030] σ ij n j -t i = 0.

[0031] A weak form of the first governing equation is:

[0032]

[0033] where v is a unit cell region to be solved, f i is a body force, s is a unit cell surface, t i is a surface force, n j is an external normal of the unit cell surface, δ is a variation symbol, d is a differential, u is a unit node displacement, and t is time.

[0034] In an exemplary embodiment of the present disclosure, the governing equation of the concentration field is:

[0035]

[0036]

[0037] The boundary condition of the concentration field is:

[0038] q = -n · J.

[0039] A weak form of the second governing equation is:

[0040]

[0041] where q is a mass flux through the surface, R P is an oxidation reaction rate, and n is an external normal of the surface.

[0042] In an exemplary embodiment of the present disclosure, determining the finite element model according to the weak form of the first governing equation and the weak form of the second governing equation includes:

[0043] According to the weak form of the first basic equation and the weak form of the second basic equation, a second equation set is established, and the second equation set is:

[0044]

[0045]

[0046] wherein I u is an unbalanced force caused by displacement change, is an unbalanced force caused by concentration change of metal ions and oxygen ions, N u is a displacement field shape function matrix, N c is a concentration field shape function matrix, B u is a displacement field strain matrix, B c is a concentration field strain matrix, C is concentration, and a superscript T represents a transpose of a matrix.

[0047] In an exemplary embodiment of the present disclosure, determining the finite element model according to the weak form of the first basic equation and the weak form of the second basic equation further includes:

[0048] According to the second equation set, a finite element model is established, and the finite element model is:

[0049]

[0050]

[0051] wherein, is an unbalanced force caused by concentration change of metal ions, is an unbalanced force caused by concentration change of oxygen ions, is an unbalanced force caused by concentration change of oxides, Δu is a displacement increment, Δc A is a metal ion concentration increment, Δc O is an oxygen ion concentration increment, Δc P is an oxide concentration increment, Δt is a time increment, C A is a metal ion concentration, C O is an oxygen ion concentration, C P is an oxide concentration, K uu , are sub-matrices of an element stiffness matrix, respectively.

[0052] In an exemplary embodiment of the present disclosure, simulating the oxidation process of the high-temperature alloy according to the finite element model further includes:

[0053] According to the finite element model, a user-defined element subroutine is established;

[0054] acquiring analysis data according to the user-defined unit program;

[0055] simulating the oxidation process of the high-temperature alloy according to the analysis data.

[0056] According to a second aspect of the present disclosure, there is provided an oxidation process simulation device of a high-temperature alloy, applied to the oxidation process simulation method described above, characterized in that the oxidation process simulation device comprises:

[0057] a building module, configured to build a high-temperature alloy oxidation mechanics-chemistry coupling model based on thermodynamics, classical oxidation kinetics and statics;

[0058] a determining module, configured to determine a high-temperature alloy oxidation mechanics-chemistry finite element model according to the coupling model;

[0059] a simulation module, configured to simulate the oxidation process of the high-temperature alloy according to the finite element model.

[0060] The oxidation process simulation method of the high-temperature alloy according to the embodiments of the present disclosure can acquire various data in the oxidation process of the high-temperature alloy without experiments in the simulation process. Since the simulation method is based on the high-temperature alloy oxidation mechanics-chemistry finite element model, the workload of researchers can be reduced, the calculation efficiency can be improved, and the oxidation process of the high-temperature alloy can be simulated completely and accurately. BRIEF DESCRIPTION OF DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0062] Figure 1 is a flowchart of the oxidation process simulation method of the high-temperature alloy according to an embodiment of the present disclosure.

[0063] Figure 2 is a structural diagram of the initial cross-sectional morphology of the nickel-based single crystal high-temperature alloy according to an embodiment of the present disclosure.

[0064] Figure 3 is a cross-sectional morphology diagram of the nickel-based single crystal high-temperature alloy after oxidation for 1000 units of time according to an embodiment of the present disclosure.

[0065] Figure 4 is an oxygen ion distribution diagram of the nickel-based single crystal high-temperature alloy after oxidation for 1000 units of time according to an embodiment of the present disclosure.

[0066] Figure 5 Oxide distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 1000 units of time.

[0067] Figure 6 Stress distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 1000 units of time.

[0068] Figure 7 Strain distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 1000 units of time.

[0069] Figure 8 Cross-sectional morphology map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 10000 units of time.

[0070] Figure 9 Oxygen ion distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 10000 units of time.

[0071] Figure 10 Oxide distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 10000 units of time.

[0072] Figure 11 Stress distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 10000 units of time.

[0073] Figure 12 Strain distribution map of a nickel-based single crystal superalloy of an embodiment of the present disclosure after oxidation for 10000 units of time.

[0074] Figure 13 Structural schematic diagram of a high-temperature alloy oxidation process simulation device of an embodiment of the present disclosure.

[0075] The main element reference signs in the figure are explained as follows:

[0076] 1, establishment module; 2, determination module; 3, simulation module. DETAILED DESCRIPTION

[0077] Example embodiments now will be described more fully hereinafter with reference to the accompanying drawings; however, the example embodiments can be implemented in any number of ways, and are not limited to the examples described herein. Rather, applications illustrate a variety of embodiments of the present disclosure to convey the subtleties and advances to the related art, and to provide a description allowing others skilled in the art to understand how the example embodiments can be implemented. An individual feature, structure, or characteristic can be combined in any suitable way with one or more others such in an embodiment. Various representative embodiments are described below.

[0078] An individual feature, structure, or characteristic can be combined in any suitable way with one or more others such in an embodiment. Various representative embodiments are described below.

[0079] When an element or layer is referred to as being "on" another element or substrate, it can be directly on the other element or substrate or intervening elements can also be present. In contrast, when an element is referred to as being "directly on" another element or substrate, there are no intervening elements present. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled or intervening elements can be present. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items.

[0080] The singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," "includes," and "including" are intended to be open-ended terms that mean "including, but not limited to," and thus specify the presence of stated elements or integers, but do not preclude the presence or addition of one or more other elements or integers. The term "first," "second," and the like do not denote any order, quantity, or importance, but rather are used to distinguish one element from another.

[0081] Superalloy is a key material of an aero-engine, and is often used to manufacture turbine blades. Simulating the oxidation process of superalloy is of great significance for the optimization design of turbine blade materials of an aero-engine.

[0082] At present, the oxidation behavior data of superalloy are mainly obtained through oxidation tests, and then the oxidation process of superalloy is analyzed. However, for the oxidation test, it is extremely difficult to obtain the oxidation data of superalloy in a high-temperature environment, and it is even more difficult to obtain the data such as microstructure evolution and oxidation layer thickness in the oxidation process of superalloy, so that the oxidation process of superalloy cannot be accurately and completely simulated.

[0083] Provided in the embodiments of the present disclosure is a method for simulating the oxidation process of superalloy, as shown in the figure, which can include the following steps. Figure 1 The method for simulating the oxidation process of superalloy can include the following steps:

[0084] In step S100, a high-temperature alloy oxidation mechanics-chemistry coupling model is established based on thermodynamics, classical oxidation kinetics and statics.

[0085] In step S110, a high-temperature alloy oxidation mechanics-chemistry finite element model is determined according to the coupling model.

[0086] In step S120, an oxidation process of the high-temperature alloy is simulated according to the finite element model.

[0087] The high-temperature alloy oxidation process simulation method provided by the embodiment of the present disclosure can obtain various data in the oxidation process of the high-temperature alloy without experiments in the simulation process. Since the simulation method is based on the high-temperature alloy oxidation mechanics-chemistry finite element model, the workload of researchers can be reduced, the calculation efficiency can be improved, and the oxidation process of the high-temperature alloy can be completely and accurately simulated.

[0088] The steps of the high-temperature alloy oxidation process simulation method provided by the embodiment of the present disclosure are described in detail as follows:

[0089] In step S100, a high-temperature alloy oxidation mechanics-chemistry coupling model is established based on thermodynamics, classical oxidation kinetics and statics.

[0090] The high-temperature alloy can refer to a kind of metal materials based on iron, nickel and cobalt, which can work at a high temperature of 600°C or above for a long time, and can be used in an aero-engine. For example, the high-temperature alloy can be a Ni3Al-based alloy. Step S100 can include: based on thermodynamics, classical oxidation kinetics and statics, a first equation set is established, which includes a constitutive equation of a displacement field and a constitutive equation of a concentration field.

[0091] In the above equation set, σ

[0092] The constitutive equation of the displacement field is:

[0093]

[0094] The constitutive equation of the concentration field is:

[0095]

[0096] In the above equation set, σ ij is stress, D ijk1 is stiffness coefficient, and ε k1is the strain tensor, the subscripts i, j, k, 1 are free indices (the tensor uses the index notation, i, j, k, 1 take values 1, 2, 3, which represent the x, y, z three spatial directions), the subscript s is the metal ion and the oxygen ion, the subscript p is the oxide, Δ is the gradient operator, η s is the chemical expansion coefficient of the metal ion and the oxygen ion, c s is the concentration of the metal ion and the oxygen ion, η p is the chemical expansion coefficient of the oxide, c p is the concentration of the oxide, δ k1 is the Kronecker symbol, J s is the diffusion channel of the metal ion and the oxygen ion, D s is the diffusion coefficient of the metal ion and the oxygen ion, F s is a constant, tr(ε) is the trace of the strain, is the partial derivative, ε is the strain, X is the displacement gradient factor, J is the ion diffusion channel.

[0097] The above η s is determined by a first preset formula, and the first preset formula is:

[0098]

[0099] The above F s is determined by a second preset formula, and the second preset formula is:

[0100]

[0101] In the above first preset formula and second preset formula, v m is the molar volume, is the molar volume of the metal ion and the oxygen ion, E is the elastic modulus, v is the Poisson's ratio, R is the Boltzmann constant, and T is the temperature.

[0102] In step S110, according to the coupling model, the oxidation mechanics-chemistry finite element model of the high-temperature alloy further comprises the following steps:

[0103] Step S200, according to the constitutive equation of the displacement field, the control equation of the displacement field, and the boundary condition of the force, a weak form of the first basic equation is established.

[0104] Step S210, according to the constitutive equation of the concentration field, the control equation of the concentration field, and the boundary condition of the concentration field, a weak form of the second basic equation is established.

[0105] Step S220, the finite element model is determined according to the weak form of the first basic equation and the weak form of the second basic equation.

[0106] Optionally, in step S200, the governing equation for the displacement field is:

[0107] σ ij,j +f i =0;

[0108] The boundary conditions for the force are:

[0109] σ ij n j -t i =0;

[0110] Specifically, the equivalent integral weak form of the displacement field differential equation can be determined based on the governing equation of the displacement field and the boundary conditions of the forces. The weak form of the first fundamental equation can then be determined based on the equivalent integral weak form of the displacement field differential equation and the constitutive equation of the displacement field. The detailed steps are as follows:

[0111] The weighting functions of the governing equations of the displacement field and the boundary conditions of the forces are derived from the variational δu of the fundamental variables. i And its boundary values ​​(taking negative values), then the third preset formula can be obtained, which is:

[0112] ∫ v δu i (σ ij,j +f i )dv-∫ s δu i (σ ij -t i ds = 0;

[0113] Based on the deformation compatibility conditions of elasticity, a fourth pre-defined formula can be obtained. This fourth pre-defined formula is as follows:

[0114]

[0115] Integrating by parts of the fourth preset formula yields the fifth preset formula, which is:

[0116]

[0117] Substituting the fifth preset formula into the third preset formula yields the sixth preset formula, which is the equivalent weak integral form of the displacement field differential equation. The sixth preset formula is as follows:

[0118] ∫ v (-εε ij σ ij +δu i f i )dv+∫ s δu i t i ds = 0;

[0119] The matrix form of the sixth preset formula is a seventh preset formula, which is:

[0120] ∫ v σ:δεdv=∫ s t·δuds+∫ v f·δudv;

[0121] Substituting the constitutive equation of the displacement field into the seventh preset formula, a weak form of the first basic equation can be obtained, which is:

[0122]

[0123] In the weak form of the first basic equation, v is the unit cell region to be solved, f i is the body force, s is the unit cell surface, t i is the surface force, n j is the outer normal of the unit cell surface, δ is the variation symbol, d is the differential, u is the unit node displacement, and t is the time.

[0124] Optionally, in the weak form of the first basic equation, the body force or the acceleration effect can be ignored. That is, f = 0, and the eighth preset formula can be obtained, which is:

[0125]

[0126] Optionally, in step S210, the control equation of the concentration field is:

[0127]

[0128]

[0129] The boundary condition of the concentration field is:

[0130] q = -n·J;

[0131] Wherein, the weak form of the second basic equation can be determined according to the control equation of the concentration field and the boundary condition of the concentration field, and the detailed steps are as follows:

[0132] For the control equation of the concentration field and the boundary condition of the concentration field, the weight function takes the differential δc s of the basic variable and its boundary value (taking negative value) to obtain the ninth preset formula, which is:

[0133]

[0134] The partial integral of the ninth preset formula can obtain the tenth preset formula, which is:

[0135]

[0136] Applying divergence theorem to the tenth preset formula can obtain an eleventh preset formula, which is:

[0137]

[0138] Substituting the constitutive equation of the concentration field into the eleventh preset formula can obtain a weak form of the second basic equation, which is:

[0139]

[0140] Wherein, q is the mass flux through the surface, R P is the oxidation reaction rate, and n is the outer normal of the surface.

[0141] Optionally, for the concentration of the oxide, if only the oxidation reaction is considered, according to the weak form of the second basic equation, a twelfth preset formula can be obtained, which is:

[0142]

[0143] In step S220, determining the finite element model according to the weak form of the first basic equation and the weak form of the second basic equation further includes:

[0144] According to the weak form of the first basic equation and the weak form of the second basic equation, a second equation set is established, which is:

[0145]

[0146]

[0147] In the above second equation set, I u is the unbalanced force caused by displacement change, is the unbalanced force caused by concentration change of metal ions and oxygen ions, N u is the shape function matrix of the displacement field, N c is the shape function matrix of the concentration field, B u is the strain matrix of the displacement field, B c is the strain matrix of the concentration field, and C is the concentration, and the superscript T represents the transpose of the matrix.

[0148] The establishment of the above second equation set will be described in detail in the manner of an embodiment, specifically:

[0149] First, for the displacement field, interpolation is performed on the virtual displacement to obtain a thirteenth preset formula, which is:

[0150]

[0151] In the above thirteenth preset formula, represents the displacement at the unit node.

[0152] According to the thirteenth preset formula, the corresponding virtual strain can be determined, and the virtual strain is as follows:

[0153]

[0154] In addition, trε can be determined by a fourteenth preset formula, and the fourteenth preset formula is as follows:

[0155]

[0156] According to the fourteenth preset formula, a fifteenth preset formula can be determined, and the fifteenth preset formula is as follows:

[0157]

[0158] Interpolating the weak form of the above first basic equation, a discrete form of the fifteenth preset formula can be obtained:

[0159]

[0160] It is worth noting that, due to the arbitrariness of According to the fifteenth preset formula, a sixteenth preset formula can be obtained, and the sixteenth preset formula is as follows:

[0161]

[0162] Then, for the concentration field, interpolating the virtual concentration can obtain a seventeenth preset formula, and the seventeenth preset formula is as follows:

[0163]

[0164] According to the seventeenth preset formula, the corresponding virtual concentration gradient can be determined:

[0165]

[0166] Interpolating the weak form of the second basic equation, a discrete form thereof can be obtained, and the discrete form is as follows:

[0167]

[0168] Due to the arbitrariness of According to the above discrete form, an eighteenth preset formula can be obtained, and the eighteenth preset formula is as follows:

[0169] ​

[0170] Thus, the above-mentioned sixteenth preset formula and eighteenth preset formula can constitute a second equation group, and a detailed process of establishing the second equation group according to a weak form of the first basic equation and a weak form of the second basic equation has been deduced.

[0171] Optionally, based on the eighteenth preset formula, for a time differential problem, an implicit Euler time integration method is used for solving, and then a nineteenth preset formula at a time t+Δt can be determined, the nineteenth preset formula being:

[0172]

[0173] In the above-mentioned nineteenth preset formula, c s is a concentration at a current time, and c is a concentration at a previous time.

[0174] Wherein, dt can be determined through a twentieth preset formula, the twentieth preset formula being:

[0175] dt=t n+1 -t n ;

[0176] Optionally, since for an oxide, a differential equation form is simple, and a value depends on a metal ion concentration and an oxygen ion concentration, a derivation process is omitted here, and an integral equation is determined by a twenty-first preset formula, the twenty-first preset formula being:

[0177]

[0178] Optionally, in the step S220, a finite element model can also be established according to the second equation group, the finite element model being:

[0179]

[0180]

[0181] Wherein, f is an unbalanced force caused by a metal ion concentration change, is an unbalanced force caused by an oxygen ion concentration change, is an unbalanced force caused by an oxide concentration change, Δu is a displacement increment, Δc A is a metal ion concentration increment, Δc O is an oxygen ion concentration increment, Δc P is an oxide concentration increment, and Δt is a time increment, C A is a metal ion concentration, C O is an oxygen ion concentration, and C P is an oxide concentration, and K uu, are sub-matrices of the unit stiffness matrix respectively.

[0182] In the finite element model described above, K uu 、 The third equation group can be determined by the eighteenth preset formula, the nineteenth preset formula and the twenty-first preset formula. The third equation group is established by taking the differential of the basic variables on the eighteenth preset formula, the nineteenth preset formula and the twenty-first preset formula.

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] In step S120, simulating the oxidation process of the high-temperature alloy according to the finite element model further comprises the following steps:

[0197] Step S300, establishing a user-defined element subroutine according to the finite element model.

[0198] Step S310, obtaining analysis data according to the user-defined element subroutine.

[0199] Step S320, simulating the oxidation process of the high-temperature alloy according to the analysis data.

[0200] Optionally, before step S300, the following step can be further included:

[0201] Step S400: Determine the model input file based on the finite element model.

[0202] Step S410: Determine the model modification file based on the model input file.

[0203] Specifically, in step S400, a simulation model is established in finite element analysis software using a nickel-based single-crystal superalloy as the simulation object. This finite element analysis software can be ABAQUS, CAE (Computer-Aided Engineering), ANSYS (analysis-system), etc. The simulation model is established based on the material characteristics of the nickel-based single-crystal superalloy, fully considering its two-phase structure, and dividing the two-dimensional shell into a CAE model with a γ / γ' two-phase structure, such as... Figure 1 As shown. In the finite element software, the analysis step is selected as a temperature-displacement coupled analysis step, where the total analysis step time is the total time of the oxidation simulation. Boundary conditions are defined, where a predefined field needs to be set in the initial analysis step to assign different temperatures to the two-phase structures divided in the previous step. The temperature settings are based on the material properties and represent the Al content in the γ phase and γ' phase, respectively. The mesh is generated, and an INP (Input, input model file) is generated. Finally, the concentration field replaces the temperature field in the temperature-displacement coupled analysis step in ABAQUS.

[0204] In step S410, the model input file in step S400 is modified to meet the needs of the oxidation simulation of nickel-based single-crystal superalloys. Based on the requirements of the oxidation simulation model, the input file is modified according to the usage rules of user-defined element subroutines and the coupled model, including custom element types, number of nodes, simulation parameters, state variables, and node degrees of freedom numbers, where degrees of freedom include displacement and temperature.

[0205] Next, the output model file is modified according to the phase-field model simulation requirements. Obtaining the modified model file also includes: creating a layer of virtual elements and mapping the calculation results of the actual calculation units onto the virtual elements, so that post-processing can be performed directly in the finite element analysis software. The virtual elements and the actual calculation units correspond one-to-one, differing only in element numbering.

[0206] UEL subroutine in the user manual of ABAQUS. For example, the UMAT subroutine is applied more in practice, and the user can tell the software to use the user-defined material properties in the calculation in the property module of ABAQUS. However, when the user uses the UEL subroutine, the software cannot be told to use the user-defined element type in the calculation in the Mesh module of ABAQUS, and the software must be told to use the user-defined element type in the calculation by modifying the INP file. This is the first reason why the INP file must be modified when using the UEL subroutine, and it is also an important rule for using the UEL subroutine. In addition, since the UEL subroutine cannot be directly post-processed, the method of post-processing implemented by the present disclosure is to map the results of the UEL subroutine calculation to a layer of "virtual" elements, so a layer of "virtual" elements needs to be defined in the INP file, which is the second reason why the INP file needs to be modified in the present disclosure.

[0207] The interface of the user-defined element in the INP file is as follows:

[0208] *User element, nodes=4, type=U1001, properties=0, coordinates=2, VARIABLES=52

[0209] Wherein, *User element is a keyword, indicating that the subsequent element is a user-defined element, such as nodes=4 indicating that the element is a four-node element, type=U1001 indicating that the element type is U1001, properties=0 indicating that the element parameter has 0 (the material parameter can be defined in the INP file or directly defined in the program, and the example is directly defined in the program), coordinates=2 indicating that the calculation model is a 2D model, and VARIABLES=52 indicating that each element has 52 state variables.

[0210] Since the UEL subroutine cannot be directly post-processed, this method needs to establish a layer of "virtual elements" to map the results of the calculation elements to the "virtual elements" for direct post-processing on ABAQUS in the later stage. The specific method is to define "virtual elements" after the element information generated by the INP file, and the virtual elements are the self-contained elements in the element library of ABAQUS. The virtual elements and the actual calculation elements correspond one by one, and only the element number is different. As follows:

[0211] *Element, type=U1001

[0212] 1, 1, 66, 873, 92

[0213] 2,66,67,874,873

[0214] 3,67,68,875,874

[0215] 4,68,2,876,875

[0216] …

[0217] *Element, type=CPE4

[0218] 3137,1,66,873,92

[0219] 3138,66,67,874,873

[0220] 3139,67,68,875,874

[0221] 3140,68,2,876,875

[0222] …

[0223] Since the temperature-displacement coupling analysis step is selected, the degrees of freedom of at least one element in the model are both displacement and temperature, such as CPE4T. The specific definition is as follows:

[0224] *Node

[0225] 999996,0.0,0.0

[0226] 999997,0.01,0.0

[0227] 999998,0.01,0.01

[0228] 999999,0.0,0.01

[0229] *Nset, nset=extraElement

[0230] 999996,999997,999998,999999

[0231] *Element, Type=CPE4T

[0232] 999999,999996,999997,999998,999999

[0233] In order to avoid errors, the node number and element number must be distinguished from the previous element and cannot be repeated.

[0234] In step S300, the user-defined element subroutine can be established according to the finite element model by the following steps:

[0235] According to the finite element model, three arrays of RHS, AMATRX, and SVARS are determined, where RHS is the right-hand side matrix of the finite element model, AMATRX is the element stiffness matrix of the finite element model, and SVARS is the state variable of the finite element model.

[0236] The Fortran subroutine interface of the UEL subroutine is given below in an embodiment, where the two arrays of RHS and AMATRX are two arrays that must be defined, and other arrays are defined according to actual needs, for example, the ENERGY array is defined if the model needs to calculate energy, and is not defined if not. The SVARS array is used in the present disclosure to store and transfer various state variables, such as displacement, stress, and concentration.

[0237] The Fortran subroutine interface of the UEL subroutine is given below in an embodiment, where the two arrays of RHS and AMATRX are two arrays that must be defined, and other arrays are defined according to actual needs, for example, the ENERGY array is defined if the model needs to calculate energy, and is not defined if not. The SVARS array is used in the present disclosure to store and transfer various state variables, such as displacement, stress, and concentration.

[0238] The UEL subroutine is written, and ABAQUS provides a fixed format subroutine interface for the user, and the user must write the program according to the format of the interface, and the subroutine interface is as follows:

[0239]

[0240] Where RHS is the right-hand side matrix of the finite element model, which can be denoted as Re, AMATRX is the element stiffness matrix of the finite element model, which can be denoted as ke, and SVARS is the state variable. It should be noted that the boundary conditions of the concentration field also need to be defined in the UEL program, and in the present embodiment, the boundary conditions are as follows:

[0241]

[0242] In the UEL, a UVARM subroutine also needs to be added for post-processing of the results, and the FORTRAN interface provided by ABAQUS is as follows:

[0243]

[0244] In step S310, the analysis data obtained according to the user-defined element subroutine is obtained through the following steps:

[0245] The working module submits the model modification file obtained in step S410 and analyzes the user-defined unit subroutine established in step S300, obtaining the result file. Based on the model modification file, the results calculated by the user-defined unit subroutine are passed to the user-defined output variable subroutine for calculation to obtain analysis data.

[0246] For example, in the JOB module, the modified INP file from step one and the user-defined unit subroutine written in step two are submitted for analysis. After the calculation is complete, post-processing can begin. Because the INP file has been modified, it cannot be imported into the ABAQUS pre-processing. Therefore, the modified INP file is directly selected in the model file of the ABAQUS JOB module, the debugged subroutine is called, and the calculation is submitted.

[0247] In step S310, simulating the oxidation process of a high-temperature alloy based on the analysis data includes post-processing the analysis data using the post-processing module of the finite element analysis software to obtain the oxidation process of the high-temperature alloy.

[0248] The following describes step S310 of this disclosure in more detail with reference to an embodiment.

[0249] Taking the oxidation process of a nickel-based single-crystal superalloy over 10,000 time units as an example, the specific parameter settings depend on the material. Figure 2 The image shows the initial cross-sectional morphology of a nickel-based single-crystal superalloy after oxidation; as shown... Figure 3 , Figure 4 , Figure 5 The figures shown are cross-sectional morphology, oxygen ion distribution, and oxide distribution of a nickel-based single-crystal superalloy after oxidation over 1000 unit time periods; Figure 6 , Figure 7 The figures shown are the stress and strain distributions of a nickel-based single-crystal superalloy after oxidation over 1000 unit time periods; Figure 8 , Figure 9 The figures shown are cross-sectional morphology, oxygen ion distribution, and oxide distribution of a nickel-based single-crystal superalloy after oxidation over 10,000 time units; Figure 10 , Figure 11 The figures shown are the stress and strain distributions of nickel-based single-crystal superalloys after oxidation over 10,000 unit time periods.

[0250] The above only shows some calculation data of the nickel-based single crystal superalloy at three different times. It can be seen that the simulation method of the oxidation process of the superalloy can well simulate the oxidation process of the nickel-based single crystal superalloy, and can simulate the evolution process of the microstructure of the nickel-based single crystal superalloy, the growth of the oxidation layer, and the stress and strain distribution in the oxidation process. In this way, the shortcomings in the oxidation process test can be well made up, so as to provide a theoretical reference for the design of the material, especially for the material design of the turbine blade.

[0251] The embodiment also provides a simulation device of an oxidation process of a superalloy. The simulation device is applied to the simulation method of the oxidation process of the superalloy, and can include an establishing module 1, a determining module 2, and a simulation module 3. Figure 13

[0252] The establishing module 1 is used to establish a coupling model of the oxidation mechanics-chemistry of the superalloy based on thermodynamics, classical oxidation kinetics, and statics. The determining module 2 is used to determine a finite element model of the oxidation mechanics-chemistry of the superalloy according to the coupling model. The simulation module 3 is used to simulate the oxidation process of the superalloy according to the finite element model.

[0253] The simulation device of the oxidation process of the superalloy in the embodiment of the present disclosure can obtain various data in the oxidation process of the superalloy without test during the simulation. Since the simulation module 3 is based on the simulation method, and the simulation method is based on the finite element model of the oxidation mechanics-chemistry of the superalloy, the workload of the researchers can be reduced, the calculation efficiency can be improved, and the oxidation process of the superalloy can be completely and accurately simulated.

[0254] It should be noted that although the steps of the method in the present disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in this specific order, or that all the steps shown must be performed to achieve the desired results. Additional or alternative, some steps can be omitted, a plurality of steps can be combined into one step, and / or one step can be divided into a plurality of steps, etc., which should be considered as part of the present disclosure.

[0255] ​It should be appreciated that the present disclosure is not limited to the details of construction and arrangement of parts set forth in the specification. The present disclosure is capable of other embodiments and of being practiced or being carried out in various ways. Variations and modifications of the foregoing are within the scope of the present disclosure. It should be understood that the present disclosure fully encompasses all combinations of two or more individual features set forth herein and / or in the appended claims. All these different combinations are considered to be within the scope of the present disclosure. The embodiments of the present disclosure as described are to be used as illustrative examples only and are not intended to limit the scope of the present disclosure in any way.

Claims

1. A method of simulating an oxidation process of a high-temperature alloy, characterized by, The oxidation process simulation method comprises: a high-temperature alloy oxidation mechanics-chemistry coupling model is established based on thermodynamics, classical oxidation kinetics and statics; a high-temperature alloy oxidation mechanics-chemistry finite element model is determined according to the coupling model; an oxidation process of the high-temperature alloy is simulated according to the finite element model; wherein the high-temperature alloy oxidation mechanics-chemistry coupling model is established based on thermodynamics, classical oxidation kinetics and statics, and comprises: a first equation set is established based on thermodynamics, classical oxidation kinetics and statics, and the first equation set comprises a displacement field constitutive equation and a concentration field constitutive equation; the displacement field constitutive equation is: the concentration field constitutive equation is: wherein, is the stress, is the stiffness coefficient, is the strain tensor, the indices i, j, k, 1 are free indices, the index s is for metal ions and oxygen ions, and the index p is for oxides, is the gradient operator, is the vector form of the conversion of the chemical expansion coefficient of the metal ions and oxygen ions, is the concentration of the metal ions and oxygen ions, is the vector form of the conversion of the chemical expansion coefficient of the oxides, is the concentration of the oxides, is the diffusion path of the metal ions and oxygen ions, is the diffusion coefficient of the metal ions and oxygen ions, is a constant, is the trace of the strain, is the partial derivative, is the strain, X is the displacement gradient factor, is the ion diffusion path; wherein the high-temperature alloy oxidation mechanics-chemistry finite element model is determined according to the coupling model, and further comprises: a weak form of a first basic equation is established according to the displacement field constitutive equation, a displacement field control equation and force boundary conditions; a weak form of a second basic equation is established according to the concentration field constitutive equation, a concentration field control equation and concentration field boundary conditions; the finite element model is determined according to the weak form of the first basic equation and the weak form of the second basic equation.

2. The oxidation process simulation method according to claim 1, characterized by, The is determined by a first preset formula, which is: ； The is determined by a second preset formula, which is wherein, is the molar volume, is the molar volume of the metal ion and the oxygen ion, E is the modulus of elasticity, is the Poisson's ratio, R is the Boltzmann constant, and T is the temperature.

3. The oxidation process simulation method according to claim 1, characterized by, the displacement field control equation is: ； the force boundary conditions are: ； the weak form of the first basic equation can be expressed as a vector: where v is the unit cell region to be solved, is the body force, s is the unit cell surface, is the surface force, is the outward normal to the unit cell surface, is the variational symbol, is the differential, is the unit node displacement.

4. The oxidation process simulation method according to claim 3, characterized in that, the concentration field control equation is: ； ； the concentration field boundary conditions are: ； the weak form of the second basic equation is: ； wherein, is the flux of the substance through the surface, is the rate of the oxidation reaction, is the outward normal to the surface, t is time.

5. The oxidation process simulation method according to claim 4, characterized in that, the finite element model is determined according to the weak form of the first basic equation and the weak form of the second basic equation, and comprises: a second equation set is established according to the weak form of the first basic equation and the weak form of the second basic equation, and the second equation set is: wherein is the unbalanced force due to the displacement variation, is the unbalanced force due to the concentration variation of the metal ions and oxygen ions, is the displacement field shape function matrix, is the concentration field shape function matrix, is the displacement field strain matrix, is the concentration field strain matrix, and the superscript T denotes the transpose of the matrix.

6. The oxidation process simulation method according to claim 5, wherein, the finite element model is determined according to the weak form of the first basic equation and the weak form of the second basic equation, and further comprises: a finite element model is established according to the second equation set, and the finite element model is: ； ; wherein, is an imbalance force caused by a change in metal ion concentration, is an imbalance force caused by a change in oxygen ion concentration, is an imbalance force caused by a change in oxide concentration, is a displacement increment, is a metal ion concentration increment, is an oxygen ion concentration increment, is an oxide concentration increment, is a time increment, is a metal ion concentration, is an oxygen ion concentration, is an oxide concentration, , , , , , , , , , , , , , , , are sub-matrices of the element stiffness matrix, respectively.

7. The oxidation process simulation method of claim 1, wherein, the oxidation process of the high-temperature alloy is simulated according to the finite element model, and further comprises: a user-defined element subroutine is established according to the finite element model; analysis data is obtained according to the user-defined element subroutine; the oxidation process of the high-temperature alloy is simulated according to the analysis data.

8. An apparatus for simulating an oxidation process of a high-temperature alloy, which is applied to the method for simulating an oxidation process according to any one of claims 1 to 7, characterized by, The oxidation process simulation device comprises: a establishing module configured to establish a high-temperature alloy oxidation mechanics-chemistry coupling model based on thermodynamics, classical oxidation kinetics and statics; a determining module configured to determine a high-temperature alloy oxidation mechanics-chemistry finite element model according to the coupling model; a simulation module configured to simulate an oxidation process of the high-temperature alloy according to the finite element model.

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