A numerical simulation method for creep behavior of metals under high temperature oxidation

Abstract

The application discloses a numerical simulation method of creep behavior of metal under high-temperature oxidation, comprising the following steps: establishing a constitutive relation of oxidation-creep coupling of metal under high-temperature environment; establishing a mechanical-chemical coupling model of high-temperature oxidation-creep of metal based on thermodynamics, classical oxidation kinetics and statics; determining a finite element model of high-temperature oxidation-creep coupling of metal according to the coupling model; and simulating the creep behavior of metal under high-temperature oxidation according to the finite element model. The numerical simulation method of creep behavior of metal under high-temperature oxidation can obtain various data in the creep behavior of metal under high-temperature oxidation without experiments in the simulation process. Since the simulation method is based on the mechanical-chemical finite element model of high-temperature oxidation-creep of metal, the workload of researchers can be reduced, the calculation efficiency can be improved, and the creep behavior of metal under high-temperature oxidation can be simulated completely and accurately.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for metallic materials, and in particular to a numerical simulation method for the creep behavior of metals under high-temperature oxidation. Background Technology

[0002] Metals often operate in complex and harsh environments, typically under high temperatures and high loads, making them highly susceptible to oxidation and affecting their mechanical properties. Therefore, simulating the creep behavior of metals and alloys under high-temperature oxidizing conditions is crucial for the optimized design of practical engineering materials. Currently, high-temperature creep tests are primarily used to obtain data on the creep behavior of metals under high-temperature conditions, thereby analyzing their mechanical properties. However, obtaining creep data for metals under high-temperature conditions is challenging, and data on material transformations during oxidation, including microstructure evolution and oxide layer thickness, is even more difficult to acquire. This makes it impossible to accurately and completely describe the creep behavior of metals and to clarify the interaction between oxidation and creep. Summary of the Invention

[0003] The purpose of this invention is to provide a numerical simulation method for the creep behavior of metals under high-temperature oxidation, which can completely and accurately simulate the creep behavior of metals under high-temperature oxidation environment without simulation experiments.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] A numerical simulation method for the creep behavior of metals under high-temperature oxidation includes:

[0006] Establish constitutive relations of oxidation-creep coupling in metals under high-temperature conditions.

[0007] Based on thermodynamics, classical oxidation kinetics, and statics, a mechanical-chemical coupling model for high-temperature oxidation-creep of metals is established.

[0008] Based on the coupling model, a finite element model for high-temperature oxidation-creep coupling of metals is determined;

[0009] The creep behavior of metals under high-temperature oxidation was simulated using the finite element model.

[0010] In an exemplary embodiment of the present invention, a constitutive relation for oxidation-creep coupling of metals under high-temperature conditions is established, wherein the constitutive relation is:

[0011]

[0012] Where dσ is the stress increment, dt is the time increment, and D is the elasticity matrix. The total strain rate, The mismatch strain rate, denoted as creep rate.

[0013] In an exemplary embodiment of the present invention, a coupled mechanical-chemical model of high-temperature oxidation-creep of metals is established based on thermodynamics, classical oxidation kinetics, and statics, including:

[0014] Based on thermodynamics, classical oxidation kinetics, and statics, a first set of equations is established, which includes constitutive equations for the displacement field and constitutive equations for the concentration field.

[0015] The constitutive equation for the displacement field is:

[0016]

[0017] The constitutive equation for the concentration field is:

[0018]

[0019] Where, σ ij Let D be the stress tensor. ijk1 Let ε be the elastic modulus tensor. kl Let (ε) be the total strain tensor. k1 ) c The creep strain tensor is defined by subscripts i, j, k, and 1, which represent free indices, respectively; subscript s represents metal ions and oxygen ions; subscript p represents oxides; Δ is the gradient operator; and η is the creep strain tensor. s c is the chemical expansion coefficient of metal ions and oxygen ions. s η represents the concentrations of metal ions and oxygen ions. p c is the chemical expansion coefficient of the oxide. p δ represents the concentration of the oxide. kl J is the Kronecker symbol. s D serves as a diffusion channel for metal ions and oxygen ions. s F is the diffusion coefficient of metal ions and oxygen ions. s Let ε be a constant, and tr(ε) be the trace of strain. ε is the partial derivative, X is the strain, J is the displacement gradient factor, and J is the ion diffusion channel.

[0020] In one exemplary embodiment of the present invention, the η s Determined by a first preset formula, the first preset formula is:

[0021]

[0022] The F s Determined by a second preset formula, the second preset formula is:

[0023]

[0024] Among them, v m For molar volume, Let be the molar volume of the metal ion and oxygen ion, E be the elastic modulus, v be the Poisson's ratio, R be the Boltzmann constant, and T be the temperature.

[0025] In an exemplary embodiment of the present invention, determining the mechanical-chemical finite element model of high-temperature oxidation-creep of metals according to the coupling model further includes:

[0026] A weak form of the first fundamental equation is established based on the constitutive equation of the displacement field, the governing equation of the displacement field, and the boundary conditions of the forces.

[0027] Based on the constitutive equation of the concentration field, the governing equation of the concentration field, and the boundary conditions of the concentration field, a weak form of the second fundamental equation is established.

[0028] The finite element model is determined based on the weak forms of the first and second fundamental equations.

[0029] In an exemplary embodiment of the present invention, the governing equation of the displacement field is:

[0030] σ ij,j +f i =0;

[0031] The boundary condition for the force is:

[0032] σ ij n j -t i =0;

[0033] The weak form of the first fundamental equation is:

[0034]

[0035] Where v is the element region to be solved, f i Let s be the body force, s be the surface area of ​​the unit cell, and t be the surface area of ​​the unit cell. i For surface force, n j δ represents the outward normal to the surface of the element, d represents the variational sign, d represents the differential, u represents the nodal displacement of the element, and t represents time.

[0036] In an exemplary embodiment of the present invention, the governing equation of the concentration field is:

[0037]

[0038]

[0039] The boundary conditions for the concentration field are:

[0040] q = -n·J;

[0041] The weak form of the second fundamental equation is:

[0042]

[0043] Where q is the mass flux through the surface, and R P Let n be the oxidation reaction rate, and n be the outward normal of the surface.

[0044] In an exemplary embodiment of the present invention, determining the finite element model based on the weak form of the first fundamental equation and the weak form of the second fundamental equation includes:

[0045] Based on the weak forms of the first and second fundamental equations, a second system of equations is established, which is as follows:

[0046]

[0047]

[0048] Among them, I u The unbalanced force caused by displacement change The unbalanced force caused by changes in the concentrations of metal ions and oxygen ions, N u Let N be the displacement field shape function matrix. c Let B be the shape function matrix of the concentration field. u B is the displacement field strain matrix. c Let C be the concentration field strain matrix, where C is the concentration, and the superscript T indicates the transpose of the matrix.

[0049] In an exemplary embodiment of the present invention, determining the finite element model based on the weak form of the first fundamental equation and the weak form of the second fundamental equation further includes:

[0050] A finite element model is established based on the second set of equations. The finite element model is as follows:

[0051]

[0052]

[0053] in, This is the unbalanced force caused by changes in metal ion concentration. The unbalanced force caused by changes in oxygen ion concentration. The unbalanced force caused by the change in oxide concentration, Δu is the displacement increment, and Δc is the displacement increment. A Δc represents the increase in metal ion concentration. O Δc represents the increase in oxygen ion concentration.P C is the oxide concentration increment, Δt is the time increment, and C A C represents the concentration of metal ions. O For oxygen ion concentration, C P K represents the oxide concentration. uu ,

[0054] These are submatrices of the element stiffness matrix.

[0055] In an exemplary embodiment of the present invention, the simulation of the creep behavior of the metal under high-temperature oxidation based on the finite element model further includes:

[0056] Establish a user-defined element subroutine based on the finite element model;

[0057] The analysis data is obtained based on the user-defined unit subroutine;

[0058] The analysis data was used to simulate the creep behavior of metals under high-temperature oxidation.

[0059] The present invention also provides a numerical simulation system for creep behavior of metals under high-temperature oxidation, used in the aforementioned numerical simulation method for creep behavior of metals under high-temperature oxidation, comprising:

[0060] A module is established to create a coupled mechanical-chemical model of high-temperature oxidation-creep of metals based on thermodynamics, classical oxidation kinetics, and statics.

[0061] The module determines the finite element equations of the mechanical and chemical processes of high-temperature oxidation-creep of metals based on the coupling model.

[0062] The simulation module simulates the creep behavior of metals under high-temperature oxidation based on the finite element equation.

[0063] The present invention also provides a computer-readable storage medium comprising a stored program, wherein the program, when executed, performs the above-described numerical simulation method for creep behavior of metals under high-temperature oxidation.

[0064] The present invention also provides an electronic device, including a memory and a processor, characterized in that the memory stores a computer program, and the processor is configured to execute the aforementioned numerical simulation method for creep behavior of metals under high-temperature oxidation through the computer program.

[0065] The numerical simulation method for creep behavior of metals under high-temperature oxidation according to embodiments of the present invention can obtain various data on creep behavior of metals under high-temperature oxidation without conducting experiments during the simulation process. Furthermore, since this simulation method is based on a finite element model of the mechanics and chemistry of metal high-temperature oxidation-creep, it can reduce the workload of researchers, improve computational efficiency, and thus completely and accurately simulate the creep behavior of metals under high-temperature oxidation. Attached Figure Description

[0066] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0067] Figure 1 This is a flowchart of a numerical simulation method for creep behavior of metals under high-temperature oxidation, according to one embodiment of the present invention.

[0068] Figure 2 This is a finite element model diagram of the creep behavior of metal under high-temperature oxidation according to one embodiment of the present invention;

[0069] Figure 3 This is a growth evolution diagram of the oxide layer of a nickel-based superalloy according to one embodiment of the present invention, where UVARM11 represents the oxide concentration.

[0070] Figure 4 This is a creep curve of a nickel-based superalloy under different external loads according to one embodiment of the present invention. The vertical axis in the figure represents creep strain.

[0071] Figure 5 This is the cross-sectional stress distribution of a nickel-based superalloy after 100 hours of high-temperature oxidation loading, according to one embodiment of the present invention. In the figure, UVARM11 represents the oxide concentration. Detailed Implementation

[0072] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a full understanding of embodiments of the invention.

[0073] The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention can be practiced without one or more of the specific details described, or other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring the main technical concept of the invention.

[0074] When a structure is "on" other structures, it may mean that the structure is integrally formed on other structures, or that the structure is "directly" set on other structures, or that the structure is "indirectly" set on other structures through another structure.

[0075] The terms “a,” “one,” and “the” are used to indicate the existence of one or more elements / components / etc.; the terms “including” and “having” are used to indicate an open-ended inclusion and that other elements / components / etc. may exist in addition to those listed. The terms “first” and “second” are used only as markers and are not a limitation on the number of objects.

[0076] Metals often operate in complex and harsh environments, typically under high temperatures and high loads, where they are highly susceptible to oxidation, affecting their mechanical properties. Therefore, simulating the creep behavior of metals and alloys in high-temperature oxidizing environments is of great significance for the optimized design of practical engineering materials.

[0077] Currently, high-temperature creep tests are mainly used to obtain data on the creep behavior of metals under high-temperature environments, thereby analyzing the mechanical properties of metals under high-temperature oxidation conditions. However, for creep tests, obtaining creep data of metals under high-temperature environments is quite difficult. Furthermore, data on material transformations during the oxidation process of metals or alloys, including microstructure evolution and oxide layer thickness, are even more difficult to obtain. This makes it impossible to accurately and completely describe the creep behavior of metals and to clarify the interaction between oxidation and creep.

[0078] This invention provides a method for simulating the creep behavior of metals under high-temperature oxidation, such as... Figure 1 As shown, the method for simulating the oxidation process of the metal may include steps S100, S110, S120, and S130, wherein:

[0079] Step S100: Establish the constitutive relationship of oxidation-creep coupling of metal under high temperature environment (i.e., the stress-strain relationship of the material).

[0080] Step S110: Based on thermodynamics, classical oxidation kinetics, and statics, establish a coupled mechanical-chemical model of high-temperature oxidation-creep of metals.

[0081] Step S120: Determine the finite element model of the oxidation mechanics-chemistry of metals based on the coupling model.

[0082] Step S130: Simulate the creep behavior of metal under high-temperature oxidation based on the finite element model.

[0083] The numerical simulation method for creep behavior of metals under high-temperature oxidation according to embodiments of the present invention can obtain various data on creep behavior of metals under high-temperature oxidation without conducting experiments during the simulation process. Furthermore, since this simulation method is based on a finite element model of the mechanics and chemistry of metal high-temperature oxidation-creep, it can reduce the workload of researchers, improve computational efficiency, and thus completely and accurately simulate the creep behavior of metals under high-temperature oxidation.

[0084] The following is a detailed description of each step in the numerical simulation method for creep behavior of metals under high-temperature oxidation provided by the embodiments of the present invention:

[0085] In step S100, a constitutive relation for the oxidation-creep coupling of a metal under high-temperature conditions is established. This metal can refer to a class of high-temperature alloy materials based on iron, nickel, or cobalt, capable of long-term operation at temperatures above 600°C, and which can be used in aero-engines. For example, this high-temperature alloy can be a Ni3Al-based alloy. The constitutive relation for step S100 is as follows:

[0086]

[0087] Where dσ is the stress increment, dt is the time increment, and D is the elasticity matrix. The total strain rate, The mismatch strain rate, denoted as creep rate.

[0088] Step S110 may include: establishing a first set of equations based on thermodynamics, classical oxidation kinetics, and statics, which includes constitutive equations for the displacement field and constitutive equations for the concentration field.

[0089] in:

[0090] The constitutive equation for the displacement field is:

[0091]

[0092] The constitutive equation for the concentration field is:

[0093]

[0094] In the above system of equations, σ ij For stress, D ijk1 ε is the stiffness coefficient. k1 For the strain tensor, the subscripts i, j, k, and 1 represent the free indices (the tensor uses a subscript notation method, with i, j, k, and l taking values ​​of 1, 2, and 3 to represent the three spatial directions x, y, and z), the subscript s represents metal ions and oxygen ions, the subscript p represents oxides, Δ is the gradient operator, and η... s c is the chemical expansion coefficient of metal ions and oxygen ions. s η represents the concentrations of metal ions and oxygen ions. p c is the chemical expansion coefficient of the oxide. p δ represents the concentration of the oxide. k1 J is the Kronecker symbol. s D serves as a diffusion channel for metal ions and oxygen ions. s F is the diffusion coefficient of metal ions and oxygen ions. s Let ε be a constant, and tr(ε) be the trace of strain. ε is the partial derivative, X is the strain, J is the displacement gradient factor, and J is the ion diffusion channel.

[0095] The above η s This is determined by a first preset formula, which is:

[0096]

[0097] The above F s Determined by a second preset formula, the second preset formula is:

[0098]

[0099] In the first and second preset formulas mentioned above, v m For molar volume, Let be the molar volume of the metal ion and oxygen ion, E be the elastic modulus, v be the Poisson's ratio, R be the Boltzmann constant, and T be the temperature.

[0100] In step S120, determining the metal high-temperature oxidation-creep mechanics-chemical coupled finite element model based on the coupling model further includes the following steps:

[0101] Step S200: Establish the weak form of the first fundamental equation based on the constitutive equation of the displacement field, the governing equation of the displacement field, and the boundary conditions of the displacement field.

[0102] Step S210: Based on the constitutive equation of the concentration field, the governing equation of the concentration field, and the boundary conditions of the concentration field, establish the weak form of the second fundamental equation.

[0103] Step S220: Determine the finite element model based on the first and second fundamental equations.

[0104] Optionally, in step S200, the governing equation for the displacement field is:

[0105] σ ij,j +f i =0;

[0106] The boundary conditions for the force are:

[0107] σ ij n j -t i =0;

[0108] Based on the governing equations and boundary conditions of the displacement field, as well as the constitutive equations of the displacement field, the weak form of the first fundamental equation is obtained using the Galerkin method. The weak form of the first fundamental equation is as follows:

[0109]

[0110] In the weak form of the first fundamental equation, v is the unit volume region to be solved, and f i Let s be the body force, s be the surface area of ​​the unit cell, and t be the surface area of ​​the unit cell. i For surface force, n j δ represents the outward normal to the surface of the element, d represents the variational sign, d represents the differential, u represents the nodal displacement of the element, and t represents time.

[0111] Optionally, in step S210, the governing equation for the concentration field is:

[0112]

[0113]

[0114] The boundary conditions for the concentration field are:

[0115] q = -n·J;

[0116] Based on the governing equations and boundary conditions of the concentration field, the weak form of the second fundamental equation is obtained using the Galerkin method. The weak form of this second fundamental equation is as follows:

[0117]

[0118] Where q is the mass flux through the surface, and R P Let n be the oxidation reaction rate, and n be the outward normal of the surface.

[0119] In step S220, determining the finite element model based on the weak forms of the first and second fundamental equations further includes:

[0120] Based on the weak forms of the first and second fundamental equations, a second system of equations is established, which is as follows:

[0121]

[0122]

[0123] In the second system of equations above, I u The unbalanced force caused by displacement change The unbalanced force caused by changes in the concentrations of metal ions and oxygen ions, N u Let N be the displacement field shape function matrix. c Let B be the shape function matrix of the concentration field. u B is the displacement field strain matrix. c Let C be the concentration field strain matrix, where C is the concentration, and the superscript T indicates the transpose of the matrix.

[0124] Optionally, based on the second fundamental equations, for the time differential problem, the implicit Euler time integration method can be used to determine the third pre-defined formula at time t+Δt. This third pre-defined formula is as follows:

[0125]

[0126] In the third preset formula mentioned above, c s The concentration at the current moment, and This represents the concentration at that location at the previous moment.

[0127] Wherein, dt can be determined by a fourth preset formula, which is:

[0128] dt=t n+1 -t n ;

[0129] Optionally, since the differential equation for oxides is simple in form and its value depends on the concentrations of metal and oxygen ions at that location, its derivation is omitted here. The integral equation is determined by the fifth pre-defined formula, which is:

[0130]

[0131] Optionally, step S220 may further include establishing finite element equations based on the second set of equations, wherein the finite element equations are:

[0132]

[0133]

[0134] in, This is the unbalanced force caused by changes in metal ion concentration. The unbalanced force caused by changes in oxygen ion concentration. The unbalanced force caused by the change in oxide concentration, Δu is the displacement increment, and Δc is the displacement increment. A Δc represents the increase in metal ion concentration. O Δc represents the increase in oxygen ion concentration. P C is the oxide concentration increment, Δt is the time increment, and C A C represents the concentration of metal ions. O For oxygen ion concentration, C P K represents the oxide concentration. uu , These are submatrices of the element stiffness matrix.

[0135] In the above finite element model, K uu , This can be determined through a third-party program. The third-party program is:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] In step S130, simulating the creep behavior of metals under high-temperature oxidation based on the finite element model also includes the following steps:

[0150] Step S300: Establish a user-defined element subroutine based on the finite element model.

[0151] Step S310: Obtain analysis data based on user-defined unit subroutines.

[0152] Step S320: Simulate creep behavior of metal under high temperature environment based on analysis data.

[0153] Optionally, before step S300, the following steps may also be included:

[0154] Step S400: Determine the model input file based on the finite element model.

[0155] Step S410: Determine the model modification file based on the model input file.

[0156] Specifically, in step S400, a simulation model is established in finite element analysis software, using a nickel-based 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 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 2 As shown, all γ′ phases are square, the volume fraction of γ′ in the model is 66.6%, and all γ phases are uniformly distributed. In the finite element software, the analysis step is selected as the 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, representing the Al content in the γ phase and γ′ phase, respectively. Specifically, in this embodiment, the aluminum concentrations of the simulated nickel-based superalloy γ′ phase and γ phase are 0.13 and 0.057, respectively. Therefore, the predefined temperature fields for the corresponding γ′ phase and γ phase are set to 0.13 and 0.057 in the ABAQUS / CAE interface, or can be directly modified in the INP file. The mesh is generated, and the INP (Input, input model file) is generated. Finally, the concentration field replaces the temperature field in the temperature-displacement coupled analysis step in ABAQUS. The temperature field settings in the INP file are as follows:

[0157] **Name:Predefined Field-1 Type:Temperature

[0158] *Initial Conditions,type=TEMPERATURE

[0159] Part-1-1.Set-1,0.13,0,0

[0160] **Name:Predefined Field-2 Type:Temperature

[0161] *Initial Conditions,type=TEMPERATURE

[0162] Part-1-1.Set-2,0.057,0,0

[0163] In step S410, the model input file in step S400 is modified to simulate the creep behavior of nickel-based superalloys under high-temperature oxidation. 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. This includes custom element types, number of nodes, simulation parameters, state variables, and node degrees of freedom numbers, where degrees of freedom include displacement and temperature.

[0164] Next, the output model file is modified according to the numerical simulation requirements. Obtaining the modified model file also includes: creating a layer of virtual elements, mapping the results of the computational 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 computational units correspond one-to-one, differing only in element numbering.

[0165] The interface of the user-defined unit in the INP file is as follows:

[0166] *User

[0167] element,nodes=4,type=U1001,properties=0,coordinates=2,

[0168] VARIABLES = 520;

[0169] Among them, *User element is a keyword, indicating that the subsequent element is a custom element. For example, nodes=4 indicates that the element is a four-node element, type=U1001 indicates that the element type is U1001, properties=0 indicates that there are 0 element parameters (material parameters can be defined in the INP file or directly in the program. In this example, they are defined directly in the program), coordinates=2 indicates that the calculation model is a two-dimensional model, and VARIABLES=520 indicates that each element has 520 state variables.

[0170] Since post-processing cannot be directly performed when using UEL subroutines, this method requires creating a layer of "virtual cells" to map the results of the computational units to these "virtual cells," allowing subsequent post-processing to be performed directly in ABAQUS. Specifically, "virtual cells" are defined after the cell information generated in the INP file. These virtual cells are built into the ABAQUS cell library, and each virtual cell corresponds one-to-one with an actual computational unit, differing only in its cell number. See below:

[0171] *Element,type = U1001

[0172] 1,1,66,873,92

[0173] 2,66,67,874,873

[0174] 3,67,68,875,874

[0175] 4,68,2,876,875

[0176] ...

[0177] *Element,type = CPE4

[0178] 3137,1,66,873,92

[0179] 3138,66,67,874,873

[0180] 3139,67,68,875,874

[0181] 3140,68,2,876,875

[0182] ...

[0183] Because a temperature-displacement coupled analysis step was selected, at least one element type in the model must have degrees of freedom that simultaneously include displacement and temperature, such as CPE4T. The specific definition is as follows:

[0184] *Node

[0185] 999996, 0.0, 0.0

[0186] 999997, 0.01, 0.0

[0187] 999998, 0.01, 0.01

[0188] 999999, 0.0, 0.01

[0189] *Nset, nset = extraElement

[0190] 999996, 999997, 999998, 999999

[0191] *Element, Type = CPE4T

[0192] 999999, 999996, 999997, 999998, 999999

[0193] To avoid errors, the node number and cell number must be distinct from the preceding cell number and cannot be duplicated.

[0194] In step S300, the user-defined element subroutine based on the finite element model can be established through the following steps:

[0195] Based on the finite element equations, a UEL subroutine is written to simulate the creep behavior of metals under high-temperature oxidation. The UEL subroutine includes a UMAT subroutine, which is used to calculate the creep strain and regeneration stress of the alloy under high-temperature oxidation.

[0196] The Fortran subroutine interface of the UEL subroutine is given below as an example. The RHS and AMATRX arrays are two mandatory arrays. Other arrays are defined according to actual needs; for example, the ENERGY array is defined if the model needs to calculate energy, and not if not. This invention uses the SVARS array to store and transmit various state variables, such as displacement, stress, and concentration.

[0197] To write UEL subroutines, ABAQUS provides a fixed-format subroutine interface. Users must write programs according to the interface format. The subroutine interface is as follows:

[0198]

[0199] Where RHS is the right-hand side matrix of the finite element model, which can be denoted as R e AMATRX is the element stiffness matrix of the finite element model, which can be denoted as k. e SVARS are state variables. It is important to note that the boundary conditions for the concentration field also need to be defined in the UEL program; in this embodiment, they are:

[0200]

[0201] In UEL, oxidation-creep coupling is achieved by calling UMAT through UEL. The specific implementation method is as follows:

[0202] Before entering the UMAT subroutine, the stress, strain, and strain increment for the current increment step must be pre-defined in UEL. This strain does not include creep strain. Before entering UMAT, the mismatch strain caused by metal oxidation is calculated in the UEL subroutine, which is used to calculate the viscoelastic creep of the metal. In addition to updating the stress and defining the elastic matrix, the creep damage factor calculated in the UMAT subroutine also needs to be passed to UEL and stored in UEL's state variables. It is important to note that both UMAT and UEL subroutines contain state variables, whose main purpose is to store user-defined variables such as creep strain and cumulative damage factor. These are passed as known quantities at the beginning of the subroutine and updated and stored at the end of the program. However, there are some differences between the two: the state variable array in the UEL subroutine is SVARS, while in UMAT it is STATEV. When using the UEL subroutine to call UMAT for oxidation-creep simulation calculations of nickel-based single-crystal alloys, the UMAT state variable values ​​are also included in the UEL state variables. At the start of the incremental step, the accumulated damage factor, creep strain, and other known quantities are stored as state variables in the UEL's state variable array SVARS. The number of state variables is user-defined, calculated as the product of the number of states at a single Gaussian integration point and the number of Gaussian integration points themselves. In this paper, the element has 520 state variables, defined in the INP file as follows:

[0203] *User element,

[0204] nodes=4,properties=2,coordinates=2,variables=520

[0205] 1,2,11,12,13

[0206] At the beginning of the UEL subroutine, the data stored in the state variable array SVARS needs to be read first, and then the data in this array is evenly distributed to each Gaussian point. Data related to creep strain and creep damage calculations, as well as material parameters, are passed to the STATEV array in the UMAT subroutine. The number of STATEV arrays is defined in the UEL subroutine, and the corresponding arrays are calculated and updated in the UMAT subroutine. Before the UMAT subroutine ends, the data in the state variables needs to be returned to UEL and stored in the state variable SVARS of the UEL subroutine.

[0207] In UEL, the UVARM subroutine also needs to be added for post-processing of the calculation results. The FORTRAN interface provided by ABAQUS is as follows:

[0208] SUBROUTINE UVARM(UVAR,DIRECT,T,TIME,DTIME,CMNAME,ORNAME,

[0209] 1NUVARM,NOEL,NPT,NLAYER,NSPT,KSTEP,KINC,

[0210] 2NDI,NSHR,COORD,JMAC,JMATYP,MATLAYO,LACCFLG)

[0211] INCLUDE'ABA_PARAM.INC'

[0212] CHARACTER*80CMNAME,ORNAME

[0213] DIMENSION UVAR(*),TIME(2),DIRECT(3,3),T(3,3),COORD(*),JMAC(*),

[0214] 1JMATYP(*)

[0215] CUSER DEFINED DIMENSION STATEMENTS

[0216] CHARACTER*3FLGRAY(15)

[0217] DIMENSION ARRAY(15),JARRAY(15)

[0218] In step S310, the analysis data is obtained according to the user-defined unit subroutine through the following steps:

[0219] 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.

[0220] 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.

[0221] In step S320, simulating the creep behavior of metals under high temperature conditions 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.

[0222] The following describes step S320 of the present invention in more detail with reference to an embodiment.

[0223] Taking the simulation of creep behavior of nickel-based superalloys under 100 hours of oxidation as an example, the specific parameter settings vary depending on the material. For example... Figure 3 The figure shows the cross-sectional oxide layer morphology calculated at different times. Figure 4 The creep strain curves are shown under different applied loads. Figure 5 The stress distribution of the cross section at 100h.

[0224] The above only shows the calculated data of creep behavior of some nickel-based superalloys under high-temperature oxidation environment under certain working conditions. It can be seen that the simulation method of the creep behavior of metals under high-temperature oxidation of the present invention can well simulate the creep behavior of nickel-based superalloys, including the growth of the oxide layer of nickel-based superalloys and the stress-strain distribution of the cross section at any time. This can effectively make up for the deficiencies in high-temperature creep tests, thereby providing theoretical reference for material design, especially for the material design of turbine blades.

[0225] This invention provides a numerical simulation method for the creep behavior of metals under high-temperature oxidation. During the simulation, various data on the creep of metals under high-temperature oxidation can be obtained without conducting experiments. Furthermore, since this simulation method is based on the finite element method, it reduces the workload of researchers, improves computational efficiency, and thus enables a complete and accurate simulation of the creep behavior of metals under high-temperature oxidation.

[0226] The present invention also provides a numerical simulation system for creep behavior of metals under high-temperature oxidation, used in the aforementioned numerical simulation method for creep behavior of metals under high-temperature oxidation, comprising:

[0227] A module is established to create a coupled mechanical-chemical model of high-temperature oxidation-creep of metals based on thermodynamics, classical oxidation kinetics, and statics.

[0228] The module determines the finite element equations of the mechanical and chemical processes of high-temperature oxidation-creep of metals based on the coupling model.

[0229] The simulation module simulates the creep behavior of metals under high-temperature oxidation based on the finite element equation.

[0230] The present invention also provides a computer-readable storage medium comprising a stored program, wherein the program, when executed, performs the above-described numerical simulation method for creep behavior of metals under high-temperature oxidation.

[0231] The present invention also provides an electronic device, including a memory and a processor, characterized in that the memory stores a computer program, and the processor is configured to execute the numerical simulation method for creep behavior of metals under high-temperature oxidation through the computer program.

[0232] It should be noted that although the steps of the method in this invention are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps, such as omitting certain steps, combining multiple steps into one step, and / or breaking down one step into multiple steps, should all be considered part of this invention.

[0233] It should be understood that the application of this invention is not limited to the detailed structure and arrangement of the components presented in this specification. The invention can have other embodiments and can be implemented and performed in various ways. The foregoing variations and modifications fall within the scope of this invention. It should be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more individual features mentioned or apparent in the text and / or drawings. All these different combinations constitute multiple alternative aspects of the invention. The embodiments described in this specification illustrate the best known mode for carrying out the invention and will enable those skilled in the art to utilize the invention.

Claims

1. A numerical simulation method for the creep behavior of metals under high-temperature oxidation, characterized in that, The simulation method for the high-temperature oxidation creep behavior of metals includes: Establish constitutive relations of oxidation-creep coupling in metals under high-temperature conditions; Based on thermodynamics, classical oxidation kinetics, and statics, a coupled mechanical-chemical model of metal oxidation-creep is established. Based on the coupling model, the finite element model of oxidation mechanics-chemistry of high-temperature alloys is determined; The creep behavior of the alloy under high-temperature oxidation was simulated based on the finite element model. Establishing constitutive relations for oxidation-creep coupling in metals at high temperatures includes: ； in, For stress increment, dt For time increments, D For the elasticity matrix, The total strain rate, The mismatch strain rate, The creep rate; Based on thermodynamics, classical oxidation kinetics, and statics, a mechanical-chemical coupling model for high-temperature oxidation-creep of metals is established, including: Based on thermodynamics, classical oxidation kinetics, and statics, a first set of equations is established, which includes constitutive equations for the displacement field and constitutive equations for the concentration field. The constitutive equation for the displacement field is: ； The constitutive equation for the concentration field is: ； in, For stress tensor, For the elastic modulus tensor, For the total strain tensor, For creep strain tensor, subscript i, j, k, 1 These represent the free index, with the subscript 's' indicating metal ions and oxygen ions, respectively. p It is an oxide. For gradient operators, denoted as the chemical expansion coefficient of metal ions and oxygen ions. The concentrations of metal ions and oxygen ions. The coefficient of chemical expansion of the oxide is denoted as . The concentration of oxides, The symbol for Kronecker. It serves as a diffusion channel for metal ions and oxygen ions. denoted as the diffusion coefficient between metal ions and oxygen ions. It is a constant. For the traces of response, For partial derivatives, In response ，X For displacement gradient factor, It serves as an ion diffusion channel; The Determined by a first preset formula, the first preset formula is: ； The Determined by a second preset formula, the second preset formula is: ； in, For molar volume, Let be the molar volume of the metal ion and oxygen ion, and E be the elastic modulus. Poisson's ratio, R Boltzmann's constant, T For temperature.

2. The numerical simulation method for creep behavior of metals under high-temperature oxidation according to claim 1, characterized in that, Based on the aforementioned coupling model, the finite element model for the mechanical-chemical coupling of high-temperature oxidation-creep in metals further includes: A weak form of the first fundamental equation is established based on the constitutive equation of the displacement field, the governing equation of the displacement field, and the boundary conditions of the forces. Based on the constitutive equation of the concentration field, the governing equation of the concentration field, and the boundary conditions of the concentration field, a weak form of the second fundamental equation is established. The finite element model is determined based on the weak form of the first fundamental equation and the weak form of the second fundamental equation. The governing equation for the displacement field is: ； The boundary condition for the force is: ； The weak form of the first fundamental equation is: ； in, v For the unit volume region to be solved, For physical strength, s For the surface of the unit cell, For surface force, The outer normal to the surface of the unit cell. For variational notation, For differential, For element node displacements, For time; The governing equation for the concentration field is: ； ； The boundary conditions for the concentration field are: ； The weak form of the second fundamental equation is: ； in, The flux of matter through the surface. The oxidation reaction rate, The surface normal is denoted by .

3. The numerical simulation method for creep behavior of metals under high-temperature oxidation according to claim 2, characterized in that, Determining the finite element model based on the weak forms of the first and second fundamental equations includes: Based on the weak forms of the first and second fundamental equations, a second system of equations is established, which is as follows: ； ； in, The unbalanced force caused by displacement change The unbalanced force is caused by changes in the concentrations of metal ions and oxygen ions. The displacement field shape function matrix, The shape function matrix of the concentration field. The displacement field strain matrix, Here is the concentration field strain matrix. For concentration, superscript T This represents the transpose of a matrix.

4. The numerical simulation method for creep behavior of metals under high-temperature oxidation according to claim 3, characterized in that, Determining the finite element model based on the weak forms of the first and second fundamental equations further includes: A finite element model is established based on the second set of equations. The finite element model is as follows: ； ； in, This is the unbalanced force caused by changes in metal ion concentration. The unbalanced force caused by changes in oxygen ion concentration. The unbalanced force caused by the change in oxide concentration. For displacement increment, This represents the increase in metal ion concentration. This represents the increase in oxygen ion concentration. For the increase in oxide concentration, For time increments, This refers to the concentration of metal ions. This refers to the oxygen ion concentration. The concentration of oxides, , , , , , , , , , , , , , , , These are submatrices of the element stiffness matrix.

5. The numerical simulation method for creep behavior of metals under high-temperature oxidation according to claim 1, characterized in that, The simulation of the oxidation process of the high-temperature alloy based on the finite element equation also includes: Establish a user-defined element subroutine based on the finite element model; The analysis data is obtained based on the user-defined unit subroutine; The analysis data was used to simulate the creep behavior of the metal under high-temperature oxidation.

6. A numerical simulation system for creep behavior of metals under high-temperature oxidation, used in the numerical simulation method for creep behavior of metals under high-temperature oxidation as described in any one of claims 1 to 5, characterized in that... include: A module is established to create a coupled mechanical-chemical model of high-temperature oxidation-creep of metals based on thermodynamics, classical oxidation kinetics, and statics. The module determines the finite element equations of the mechanical and chemical processes of high-temperature oxidation-creep of metals based on the coupling model. The simulation module simulates the creep behavior of metals under high-temperature oxidation based on the finite element equation.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein the program, when executed, performs the numerical simulation method for creep behavior of metals under high-temperature oxidation as described in any one of claims 1 to 5.

8. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to execute the numerical simulation method for creep behavior of metals under high-temperature oxidation as described in any one of claims 1 to 5 through the computer program.

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