Numerical simulation method for creep behavior of metal after pre-oxidation

Abstract

The invention relates to the technical field of numerical simulation of metal materials, and discloses a numerical simulation method for creep behavior of metal after pre-oxidation, which comprises the following steps: establishing a finite element model of the creep behavior of the metal after pre-oxidation; a finite element equation of metal high-temperature oxidation simulation is established according to a mechanical-chemical coupling model of high-temperature oxidation simulation, a user-defined unit subprogram is written according to the finite element equation, and the user-defined unit subprogram is used for calculating metal high-temperature oxidation; writing a user material subprogram according to the constitutive model of metal creep, wherein the user material subprogram is used for calculating creep deformation and creep damage; and the creep behavior of the metal after pre-oxidation is simulated in a mode of calling a user material subprogram in a user-defined unit subprogram. Through numerical simulation, related data of the creep behavior of the metal after pre-oxidation can be obtained without a test, and manpower and material resources are saved.

Description

Technical Field

[0001] The invention relates to the technical field of numerical simulation of metal materials, and in particular to a numerical simulation method for creep behavior of metal after pre-oxidation. Background Art

[0002] Metals and alloys are pre-oxidized to form an initial oxide film on the surface to improve their oxidation resistance. In addition, metals are usually easily oxidized when used in high-temperature environments. At the same time, a large number of studies have shown that oxidation can also affect the mechanical properties of metals. Therefore, studying the creep behavior of metals after pre-oxidation is of great significance for the optimization design of actual engineering materials.

[0003] At present, the creep data of metals after pre-oxidation are mainly obtained through experimental means to analyze the mechanical properties of metals after pre-oxidation. However, the test is relatively costly and needs to consider the influence of multiple factors. In addition, it is difficult to obtain data on the microstructure evolution, oxide layer thickness, and creep deformation of metals and alloys under high temperature environments, making it difficult to clarify the interaction between pre-oxidation and creep. Summary of the invention

[0004] Based on the above, the purpose of the present invention is to provide a numerical simulation method for the creep behavior of metal after pre-oxidation, which can obtain relevant data on the creep behavior of metal after pre-oxidation without conducting experiments, saving manpower and material resources.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A numerical simulation method for creep behavior of metal after pre-oxidation, comprising:

[0007] Establish a finite element model of creep behavior of metals after pre-oxidation;

[0008] Establishing a finite element equation for high-temperature oxidation simulation of metals according to a mechanical-chemical coupling model for high-temperature oxidation simulation, and writing a user-defined unit subroutine according to the finite element equation, wherein the user-defined unit subroutine is used to calculate the high-temperature oxidation of the metals;

[0009] Writing a user material subroutine according to a constitutive model of metal creep, wherein the user material subroutine is used to calculate creep deformation and creep damage;

[0010] The creep behavior of metal after pre-oxidation is simulated by calling the user material subroutine in the user-defined unit subroutine.

[0011] As a preferred solution for numerical simulation of creep behavior of metal after pre-oxidation, establishing a finite element model of creep behavior of metal after pre-oxidation includes:

[0012] Generate a geometric model in the interface of the finite element software, select the temperature-displacement coupling analysis step as the analysis step, set a predefined temperature field for the model in the predefined field, where the temperature represents the metal atom concentration, and then divide the grid to generate the input model file.

[0013] As a preferred solution for a numerical simulation method of creep behavior of metal after pre-oxidation, the method of calling a user material subroutine in a user-defined unit subroutine includes:

[0014] Establishing two analysis steps in the custom unit subroutine;

[0015] The first analysis step simulates the pre-oxidation of the metal. When the current incremental step is in the first analysis step, the oxygen concentration boundary condition and the oxidized material parameters are loaded. The total time of the analysis step is determined according to the pre-oxidation time, and the oxide concentration, metal ion concentration and oxygen ion concentration of each unit are calculated.

[0016] The second analysis step simulates the creep behavior of the metal. When the current incremental step is in the second analysis step, the external load boundary condition is loaded, and the time of the analysis step is the creep time. The specific position of the current unit is determined according to the oxide concentration or the metal ion concentration in the unit, that is, the current unit is in the oxide layer or the unoxidized layer, and different creep material parameters are assigned to the unit accordingly, and the creep strain increment is calculated. The increments of the damage factors S and W are calculated according to the creep strain increment, and the damage factors D, S, and W are updated after the incremental step ends.

[0017] As a preferred solution for numerical simulation of creep behavior of metal after pre-oxidation, the finite element equations for high-temperature oxidation simulation of metal are established according to the mechanical-chemical coupling model of high-temperature oxidation simulation, including:

[0018] Based on thermodynamics, classical oxidation kinetics and statics, a first set of equations is established, wherein the first set of equations includes a constitutive equation of a displacement field and a constitutive equation of a concentration field;

[0019] The constitutive equation of the displacement field is:

[0020]

[0021] The constitutive equation of the concentration field is:

[0022]

[0023] Among them, σ ij is the stress tensor, D ijkl is the elastic modulus tensor, ε kl is the total strain tensor, subscripts i, j, k, and 1 represent free indices, subscript s represents metal ions and oxygen ions, subscript p represents oxide, Δ represents the gradient operator, and η sis the chemical expansion coefficient of metal ions and oxygen ions, c s is the concentration of metal ions and oxygen ions, η p is the chemical expansion coefficient of the oxide, c p is the concentration of oxide, δ kl is the Kronecker symbol, J s is the diffusion channel for metal ions and oxygen ions, D s is the diffusion coefficient of metal ions and oxygen ions, F s is a constant, tr(ε) is the trace of strain, is the partial derivative, ε is the strain, and X is the displacement gradient factor;

[0024] The above η s Determined by a first preset formula, the first preset formula is:

[0025]

[0026] The above F s Determined by a second preset formula, the second preset formula is:

[0027]

[0028] In the first preset formula and the second preset formula, v m is the molar volume, is the molar volume of metal ions and oxygen ions, E is the elastic modulus, v is the Poisson's ratio, R is the Boltzmann constant, and T is the temperature.

[0029] As a preferred solution for a numerical simulation method of creep behavior of metal after pre-oxidation, according to the constitutive relationship of displacement field and concentration field, force boundary conditions and concentration boundary conditions and control equations of displacement field and concentration field in the first set of equations, the equivalent integral weak form of displacement field and concentration field is obtained by using the Galerkin method, and the equivalent integral weak form is discretized by finite element to obtain the finite element equation for high temperature oxidation simulation of metal;

[0030] The governing equation of the displacement field is:

[0031] σ ij，j +f i =0;

[0032] The boundary conditions for the force are:

[0033] σ ij n j -t i =0;

[0034] The control equation of the concentration field is:

[0035]

[0036]

[0037] The boundary conditions of the concentration field are:

[0038] q=-n•J;

[0039] Among them, t i is the surface force, n j is the outer normal of the unit cell surface, q is the material flux through the surface, R P is the oxidation reaction rate, n is the external normal of the surface;

[0040] The finite element equation is:

[0041]

[0042]

[0043]

[0044] Among them, I u is the unbalanced force caused by displacement change, is the unbalanced force caused by the concentration change of metal ions and oxygen ions, is the unbalanced force caused by the change in the concentration of the generated oxide, N u is the displacement field shape function matrix, N c is the concentration field shape function matrix, B u is the displacement field strain matrix, B c is the concentration field strain matrix, C is the concentration, R P is the chemical reaction rate, and the superscript T represents the transpose of the matrix.

[0045] As a preferred solution of a numerical simulation method for creep behavior of metal after pre-oxidation, according to the finite element equation, the basic variables are differentiated to obtain the matrix formula used for simulation calculation:

[0046]

[0047]

[0048] in, is the unbalanced force caused by the change in metal ion concentration, is the unbalanced force caused by the change in oxygen ion concentration, is the unbalanced force caused by the change in oxide concentration, Δu is the displacement increment, Δc A is the metal ion concentration increment, Δc O is the oxygen ion concentration increment, ΔC Pis the oxide concentration increment, Δt is the time increment, C A is the metal ion concentration, C O is the oxygen ion concentration, C P is the oxide concentration, K uu , are sub-matrices of the element stiffness matrix respectively.

[0049] As a preferred embodiment of a numerical simulation method for creep behavior of a metal after pre-oxidation, the constitutive model of metal creep includes:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Where C is the elasticity matrix, is the total strain rate, is the creep strain rate, A is the material creep constant, n is the Norton parameter, D, S and W are the material damage factors, c, p, w and m are the temperature-related material damage parameters obtained by experimental calibration.

[0056] A numerical simulation system for creep behavior of metal after pre-oxidation, comprising:

[0057] Establish a module for establishing a finite element model of creep behavior of metals after pre-oxidation;

[0058] A user-defined unit subroutine calling module is used to call a user-defined unit subroutine;

[0059] A user material subroutine calling module, used for calling a user material subroutine;

[0060] The calculation module is used to calculate the creep behavior of metals after high temperature oxidation and pre-oxidation.

[0061] A computer-readable storage medium, the computer-readable storage medium comprising a stored program, wherein when the program is run, the numerical simulation method of the creep behavior of metal after pre-oxidation described in any of the above technical solutions is executed.

[0062] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute the numerical simulation method of creep behavior of metal under high temperature oxidation described in the above technical solution through the computer program.

[0063] The beneficial effects of the present invention are:

[0064] The present invention provides a numerical simulation method for the creep behavior of metal after pre-oxidation. By simulating the creep behavior of metal after pre-oxidation, there is no need to conduct experiments, thus saving manpower and material resources. Compared with the situation in which data such as microstructure evolution, oxide layer thickness and creep deformation are difficult to obtain under experiments, these data can be obtained through numerical simulation, which makes it easy to clarify the relationship between pre-oxidation and creep. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the contents of the embodiments of the present invention and these drawings without paying any creative work.

[0066] Figure 1 It is a flow chart of a numerical simulation method of creep behavior of metal after pre-oxidation provided by an embodiment of the present invention;

[0067] Figure 2 is a finite element program development flow chart provided by an embodiment of the present invention;

[0068] Figure 3 It is a cross-sectional aluminum oxide distribution diagram of a nickel-based high-temperature alloy after pre-oxidation for 50 hours and 100 hours provided by an embodiment of the present invention;

[0069] Figure 4 It is a creep curve of the nickel-based high-temperature alloy provided in an embodiment of the present invention at a stress level of 248 MPa after pre-oxidation at 1000° C. for 0 h, 50 h, 100 h and 200 h;

[0070] Figure 5 The present invention provides a nickel-based high-temperature alloy provided in an embodiment of the present invention, which is provided with respect to the distribution of cross-sectional stress and damage factors D, W, and S when the alloy fails due to creep damage after being pre-oxidized for 100 hours. DETAILED DESCRIPTION

[0071] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0072] Metals and alloys are pre-oxidized to form an initial oxide film on the surface to improve their oxidation resistance. In addition, metals are usually easily oxidized when used in high-temperature environments. At the same time, a large number of studies have shown that oxidation can also affect the mechanical properties of metals. Therefore, studying the creep behavior of metals after pre-oxidation is of great significance for the optimization design of actual engineering materials.

[0073] At present, the creep data of metals after pre-oxidation are mainly obtained through experimental means to analyze the mechanical properties of metals after pre-oxidation. However, the test is relatively costly and needs to consider the influence of multiple factors. In addition, it is difficult to obtain data on the microstructure evolution, oxide layer thickness, and creep deformation of metals and alloys under high temperature environments, making it difficult to clarify the interaction between pre-oxidation and creep.

[0074] like Figure 1 and Figure 2 As shown, this embodiment provides a numerical simulation method for creep behavior of metal after pre-oxidation, and the numerical simulation method for creep behavior of metal after pre-oxidation includes the following steps:

[0075] S100: Establishment of finite element model of creep behavior of metal after pre-oxidation;

[0076] S200: Establish the finite element equation for high temperature oxidation simulation of metals according to the mechanical-chemical coupling model for high temperature oxidation simulation, and write a user-defined unit subroutine according to the finite element equation. The user-defined unit subroutine is used to calculate the high temperature oxidation of metals;

[0077] S300: Write a user material subroutine based on the constitutive model of metal creep. The user material subroutine is used to calculate creep deformation and creep damage.

[0078] S400: The creep behavior of metal after pre-oxidation is simulated by calling the user material subroutine in the user-defined unit subroutine.

[0079] By simulating the creep behavior of metals after pre-oxidation, the calculation efficiency is high and the data acquisition is intuitive and convenient, which can greatly reduce the workload of scientific researchers. That is, there is no need to conduct experiments, saving manpower and material resources. Compared with the data of microstructure evolution, oxide layer thickness and creep deformation under experiments, which are difficult to obtain, they can be obtained through numerical simulation, which is convenient for clarifying the relationship between pre-oxidation and creep. At the same time, the creep life of metals after different pre-oxidation times is predicted, providing a reference for the optimal design of actual engineering materials.

[0080] Specifically, in step S100, a geometric model is generated in the interface of the finite element software, specifically a two-dimensional model is generated in the ABAQUS / CAE interface, and the temperature-displacement coupling analysis step is selected as the analysis step. A predefined temperature field is set for the model in the predefined field, and the temperature represents the metal atom concentration. Then, the grid is divided to generate an input model file (INP file). Among them, the predefined temperature field can also be defined directly in the INP file, and the specific information is as follows:

[0081] **Name:Predefined Field-1

[0082] Type:Temperature*Initial Conditions,type=TEMPERATURE

[0083] MAT1,0.06,0,0

[0084] In step S200, the finite element equations for high temperature oxidation simulation of metals are established according to the mechanical-chemical coupling model for high temperature oxidation simulation, including: establishing a first set of equations based on thermodynamics, classical oxidation kinetics and statics, the first set of equations including the constitutive equations of the displacement field and the constitutive equations of the concentration field:

[0085] The constitutive equation of the displacement field is:

[0086]

[0087] The constitutive equation of the concentration field is:

[0088]

[0089] Among them, σ ij is the stress tensor, D ijkl is the elastic modulus tensor, ε kl is the total strain tensor, subscripts i, j, k, and 1 represent free indices, subscript s represents metal ions and oxygen ions, subscript p represents oxide, Δ represents the gradient operator, and η s is the chemical expansion coefficient of metal ions and oxygen ions, c s is the concentration of metal ions and oxygen ions, η p is the chemical expansion coefficient of the oxide, c p is the concentration of oxide, δ kl is the Kronecker symbol, J s is the diffusion channel for metal ions and oxygen ions, D s is the diffusion coefficient of metal ions and oxygen ions, F s is a constant, tr(ε) is the trace of strain, is the partial derivative, ε is the strain, and X is the displacement gradient factor;

[0090] The above η s Determined by a first preset formula, the first preset formula is:

[0091]

[0092] The above F s Determined by a second preset formula, the second preset formula is:

[0093]

[0094] In the first preset formula and the second preset formula, v m is the molar volume, is the molar volume of metal ions and oxygen ions, E is the elastic modulus, v is the Poisson's ratio, R is the Boltzmann constant, and T is the temperature.

[0095] According to the constitutive relationship between the displacement field and the concentration field, the boundary conditions of the force and the concentration, and the control equations of the displacement field and the concentration field in the first set of equations, the Galerkin method is used to obtain the equivalent integral weak form of the displacement field and the concentration field, and the equivalent integral weak form is discretized by finite element to obtain the finite element equation for high temperature oxidation simulation of metals;

[0096] The governing equation for the displacement field is:

[0097] σ ij，j +f i =0;

[0098] The boundary conditions for the force are:

[0099] σ ij n j -t i =0;

[0100] The governing equation for the concentration field is:

[0101]

[0102]

[0103] The boundary conditions of the concentration field are:

[0104] q = -n·J;

[0105] Among them, t i is the surface force, n j is the outer normal of the unit cell surface, q is the material flux through the surface, R P is the oxidation reaction rate, n is the external normal of the surface;

[0106] The finite element equation is:

[0107]

[0108]

[0109]

[0110] Among them, I u is the unbalanced force caused by displacement change, is the unbalanced force caused by the concentration change of metal ions and oxygen ions, is the unbalanced force caused by the change in the concentration of the generated oxide, N u is the displacement field shape function matrix, N c is the concentration field shape function matrix, B u is the displacement field strain matrix, B c is the concentration field strain matrix, C is the concentration, R P is the chemical reaction rate, and the superscript T represents the transpose of the matrix.

[0111] According to the finite element equation, the differential of the basic variables is taken to obtain the matrix formula used for simulation calculation:

[0112]

[0113]

[0114] in, is the unbalanced force caused by the change in metal ion concentration, is the unbalanced force caused by the change in oxygen ion concentration, is the unbalanced force caused by the change in oxide concentration, Δu is the displacement increment, Δc A is the metal ion concentration increment, Δc O is the oxygen ion concentration increment, Δc P is the oxide concentration increment, Δt is the time increment, C A is the metal ion concentration, C O is the oxygen ion concentration, C P is the oxide concentration, K uu , are sub-matrices of the element stiffness matrix respectively.

[0115] It can be determined by the second set of equations. By taking the differentiation of the basic variables of the above finite element equations, we can get:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] In step S200, a user-defined unit subroutine UEL is written according to the finite element equation. ABAQUS provides users with a fixed-format subroutine interface. Users must write programs according to the format of the interface. The two arrays RHS and AMATRX are two arrays that must be defined, and other arrays are defined according to actual needs. In this embodiment, the SVARS array is used to store and transfer various state variables, such as displacement, stress, concentration, etc. The subroutine interface is as follows:

[0130]

[0131]

[0132] It should be noted that the boundary conditions of the concentration field also need to be defined in the UEL program, which are:

[0133] DO I=1,4

[0134] IF(COORDS(2,I).EQ.25)THEN

[0135] UO(I)=0.025

[0136] ENDIF

[0137] In this embodiment, according to the material properties and the use requirements of the user-defined unit subroutine, the INP file generated in step S100 needs to be modified, including the custom unit type, number of nodes, parameters required for simulation, state variables and node degree of freedom number, where the degrees of freedom include displacement and temperature.

[0138] The modification of INP files must follow the specified syntax, such as: "**" indicates comments, "*" indicates keywords define data types, and the interface of the UEL unit in the INP file is as follows (taking the plane four-node unit as an example):

[0139] *User element,nodes=4,properties=2,coordinates=2,variables=520

[0140] 1,2,11,12,13

[0141] *Element,type=U1

[0142] 1,1,2,5,4

[0143] 2,2,3,6,5

[0144] 3,4,5,8,7

[0145] 4,5,6,9,8

[0146] *Elset,elset=All,generate

[0147] 1,4,1

[0148] *Uel property,elset=All

[0149] 0.3,200e3

[0150] "*User element" indicates the start of user element definition, "nodes = 4" indicates that the element has 4 nodes, "type = U1" is the user-defined element name, "properties = 2" indicates the number of material parameters, and "variables = 520" indicates that the number of state variables of the element is 520 (the number of state variables per Gauss point × the number of Gauss points of the element). "1,2,11,12,13" specifies the degrees of freedom of the element nodes. In this embodiment, "1,2" represents the displacement in the X and Y directions, while "11,12,13" represents the concentration degrees of freedom of metal ions, oxygen ions, and oxides. The "*Element,type = U1" command line indicates that the following data lines are element information, where the type must be the same as the element name defined in the *User element, and the following four lines contain specific information for each element. After completing the definition of the unit, in order to facilitate the definition of different unit types and boundary conditions, etc., different node sets and unit sets need to be established. "*Elset,elset=All,generate" means to establish a unit set. The name of the unit set is "ALL", and the unit set contains 4 units 1-4; next, the material properties need to be defined. "*Uel property" indicates the material properties of the custom unit. The number of material parameters here is the same as the number defined by "properties".

[0151] Furthermore, in order to facilitate post-processing, the UVARM subroutine is added to the user-defined unit subroutine to complete the output of the unit results and realize the visualization of the results. The UVARM subroutine will be called at all material calculation points of the unit. The material definition of these units includes the output variables specified by the user. The UVARM subroutine is only used for result display and does not participate in the calculation. By passing the state variable value of the UEL storage data to UVARM, the calculation results can be displayed in the post-processing module. The FORTRAN interface provided by ABAQUS is:

[0152]

[0153] At the same time, the INP file also needs to be modified. Obtaining the model modification file also includes: establishing a layer of virtual units, mapping the results of the calculation unit calculation to the virtual unit, so that post-processing can be performed directly on the finite element analysis software. Among them, the virtual unit corresponds to the actual calculation unit one by one, and only the unit number is different.

[0154] When ABAQUS calls the UEL calculation, the calculation results cannot be viewed and analyzed in the post-processing module of the CAE interface. The method adopted in this embodiment is to use the UVARM subroutine to achieve its post-processing. It is necessary to add a layer of "virtual" units in the INP file to display the result cloud map with the help of virtual units. After the UEL unit definition, use the "*Element" command to define the virtual unit. The virtual unit does not participate in the calculation results, but only presents the calculation results as a carrier. The specific information of the "virtual" unit in the INP file is as follows:

[0155] *Element,type=CPE4

[0156] 5,1,2,5,4

[0157] 6,2,3,6,5

[0158] 7,4,5,8,7

[0159] 8,5,6,9,8

[0160] The unit type used by the virtual unit is the unit that comes with the ABAQUS unit library. The unit number starts from 5 to distinguish between UEL units and virtual units, and the corresponding unit nodes are the same as UEL units. In order to prevent the virtual unit from affecting the displacement field calculation of the user-defined unit, the Young's modulus of the virtual unit is as small as possible to ignore its elastic stiffness. The specific example is as follows:

[0161]

[0162] When calling UEL for mechanical-chemical coupling calculation, select the temperature-displacement coupling analysis step to add additional degrees of freedom, and use the concentration field degrees of freedom instead of the temperature degrees of freedom. In order for the program to run smoothly, it is necessary to add a temperature-displacement coupling unit, such as CPE4T, by establishing an "extra" unit to meet the conditions. The establishment of the "extra" unit is also carried out by modifying the INP file. The specific information is as follows:

[0163] *Node

[0164] 999996,0.0,0.0

[0165] 999997,.00001,0.0

[0166] 999998,.00001,.00001

[0167] 999999,0.0,.00001

[0168] *Nset,nset=extraElement

[0169] 999996,999997,999998,999999

[0170] *Element,Type=CPE4T

[0171] 999999,999996,999997,999998,999999

[0172] The role of the additional unit is only to allow the program to run smoothly, so this unit has no connection with the actual calculation unit. When assigning material parameters, in addition to requiring a small Young's modulus value like the virtual unit, its specific heat and density also need to be defined.

[0173] After completing the rewriting of the INP file and the modification of the user-defined unit subroutine, submit the INP file and call the subroutine for calculation. In addition, since the ABAQUS unit library does not contain self-edited units, the UVARM subroutine is required for post-processing display.

[0174] In step S300, the constitutive model of metal creep includes:

[0175]

[0176]

[0177]

[0178]

[0179]

[0180] Where C is the elasticity matrix, is the total strain rate, is the creep strain rate, A is the material creep constant, n is the Norton parameter, D, S and W are the material damage factors, c, p, w and m are the temperature-related material damage parameters obtained by experimental calibration.

[0181] The user material subroutine UMAT is written according to the constitutive model of metal creep. The user material subroutine calculates the creep strain and updates the stress according to the strain increment, and calculates the creep damage and updates the damage factor according to the stress.

[0182] like Figure 2 As shown, in step S400, the method of calling the user material subroutine in the user-defined unit subroutine includes:

[0183] Create two analysis steps in the custom unit subroutine;

[0184] The first analysis step simulates the pre-oxidation of the metal. When the current incremental step is in the first analysis step, the oxygen concentration boundary condition and the oxidized material parameters are loaded. The total time of the analysis step is determined according to the pre-oxidation time, and the oxide concentration, metal ion concentration, and oxygen ion concentration of each unit are calculated.

[0185] The second analysis step simulates the creep behavior of metal. When the current incremental step is in the second analysis step, the external load boundary condition is loaded. The time of the analysis step is the creep time. The specific position of the current unit is determined according to the concentration of oxides or metal ions in the unit, that is, the current unit is in the oxide layer or the unoxidized layer, and different creep material parameters are assigned to the unit accordingly. The creep strain increment is calculated, and the increment of the damage factor S and W is calculated according to the creep strain increment. After the incremental step, the damage factors D, S, and W are updated. The details are as follows:

[0186] **STEP:Step-1

[0187] *Step,name=Step-1,nlgeom=NO,inc=20000

[0188] *Coupled Temperature-displacement, creep=none, deltmx=1.

[0189] 0.01,180000,1e-05,500

[0190] **BOUNDARY CONDITIONS

[0191] **Name:BC-1Type:Displacement / rotation

[0192] *Boundary

[0193] Set-6,1,1

[0194] **STEP:Step-2

[0195] *Step,name=Step-2,nlgeom=NO,inc=20000

[0196] *Coupled Temperature-displacement, creep=none, deltmx=1.

[0197] 0.001,200,1e-05,2.

[0198] **BOUNDARY CONDITIONS

[0199] **Name:BC-1 Type:Displacement / rotation

[0200] *Boundary

[0201] Set-6,1,1

[0202] **LOADS

[0203] **Name:Load-1 Type:Concentrated force

[0204] *Cload

[0205] Set-5,1,1512.8

[0206] Specifically, at the beginning of the user-defined unit subroutine, the data stored in the state variable array SVARS is read, and then the data in the array is evenly distributed to each Gaussian point. The data will be used to calculate creep strain and creep damage; the relevant data and material parameters are passed to the STATEV array in the user material subroutine. The number of STATEV arrays is defined in the user-defined unit subroutine, and the corresponding arrays are calculated and updated in the user-defined unit subroutine. Before the end of the user material subroutine, the data in the state variables needs to be returned to the user-defined unit subroutine and stored in the state variable SVARS of the user-defined unit subroutine.

[0207] In this embodiment, a judgment process is also added to the user-defined unit subroutine, that is, when the current incremental step is in the first analysis step, the user-defined unit subroutine adds oxygen boundary conditions and various material parameters of oxidation to simulate the pre-oxidation of metals. This example program is as follows:

[0208]

[0209] When the incremental step is in the second analysis step, the program determines the specific location of the current unit according to the concentration of oxides or metal ions in the unit, that is, the oxide layer or the unoxidized layer, and assigns different creep material parameters to the unit accordingly. Add judgment criteria to the program to determine whether the unit is in the oxide layer according to the concentration of oxides, oxygen ions and metal ions, and assign different material parameters to the unit. The program of this example is as follows:

[0210]

[0211]

[0212] The present embodiment is further described in detail below in conjunction with an embodiment:

[0213] Taking the simulation of the creep of 0.3mm thick nickel-based high-temperature alloy after pre-oxidation at 1000℃ for 0h, 50h, 100h and 200h as an example, the specific parameter settings depend on different materials. Figure 3 The figure shows the distribution of aluminum oxide in the cross section after 50h and 100h of pre-oxidation. Figure 4 Creep curves of nickel-based superalloy after pre-oxidation at 1000°C for 0h, 50h, 100h and 200h at a stress level of 248MPa. Figure 5 As shown, the distribution of cross-sectional stress and damage factors D, W, and S at creep damage failure after pre-oxidation for 100 hours.

[0214] The above only shows the calculation data of 0.3 mm thick nickel-based high-temperature alloy at four different times. It can be seen that the simulation method of the creep behavior of metal after pre-oxidation in this embodiment can well simulate the creep behavior of nickel-based high-temperature alloy after pre-oxidation, and predict the creep life of the alloy after different pre-oxidation times, which can provide a theoretical reference for the optimization design of materials.

[0215] The present embodiment also provides a numerical simulation system for the creep behavior of metal after pre-oxidation, which is used for the numerical simulation method for the creep behavior of metal after pre-oxidation. The numerical simulation system for the creep behavior of metal after pre-oxidation includes an establishment module, a user-defined unit subroutine calling module, a user material subroutine calling module and a calculation module, wherein the establishment module is used to establish a finite element model of the creep behavior of metal after pre-oxidation, the user-defined unit subroutine calling module is used to call the user-defined unit subroutine; the user material subroutine calling module is used to call the user material subroutine; the calculation module is used to calculate the creep behavior of metal after high-temperature oxidation and metal after pre-oxidation. By using the above-mentioned numerical simulation system for the creep behavior of metal after pre-oxidation to simulate the creep behavior of metal after pre-oxidation, manpower and material resources can be effectively saved, no scientific researchers need to conduct experiments, and the simulation data is relatively accurate and comprehensive.

[0216] This embodiment further provides a computer-readable storage medium, which includes a stored program, wherein the program executes the above-mentioned numerical simulation method of creep behavior of metal after pre-oxidation when it is run.

[0217] This embodiment also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor is configured to execute the above-mentioned numerical simulation method of creep behavior of metal under high-temperature oxidation through the computer program.

[0218] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A numerical simulation method for creep behavior of metals after pre-oxidation. It is characterized in that include: Establish a finite element model of creep behavior of metals after pre-oxidation; Establishing a finite element equation for high-temperature oxidation simulation of metals according to a mechanical-chemical coupling model for high-temperature oxidation simulation, and writing a user-defined unit subroutine according to the finite element equation, wherein the user-defined unit subroutine is used to calculate the high-temperature oxidation of the metals; Writing a user material subroutine according to a constitutive model of metal creep, wherein the user material subroutine is used to calculate creep deformation and creep damage; The creep behavior of metal after pre-oxidation is simulated by calling the user material subroutine in the user-defined unit subroutine.

2. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 1, It is characterized in that The finite element model of creep behavior of metal after pre-oxidation includes: Generate a geometric model in the interface of the finite element software, select the temperature-displacement coupling analysis step as the analysis step, set a predefined temperature field for the model in the predefined field, where the temperature represents the metal atom concentration, and then divide the grid to generate the input model file.

3. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 1, It is characterized in that The methods of calling user material subroutines in user-defined unit subroutines include: Establishing two analysis steps in the custom unit subroutine; The first analysis step simulates the pre-oxidation of the metal. When the current incremental step is in the first analysis step, the oxygen concentration boundary condition and the oxidized material parameters are loaded. The total time of the analysis step is determined according to the pre-oxidation time, and the oxide concentration, metal ion concentration and oxygen ion concentration of each unit are calculated. The second analysis step simulates the creep behavior of the metal. When the current incremental step is in the second analysis step, the external load boundary condition is loaded, and the time of the analysis step is the creep time. The specific position of the current unit is determined according to the oxide concentration or the metal ion concentration in the unit, that is, the current unit is in the oxide layer or the unoxidized layer, and different creep material parameters are assigned to the unit accordingly, and the creep strain increment is calculated. The increments of the damage factors S and W are calculated according to the creep strain increment, and the damage factors D, S, and W are updated after the incremental step ends.

4. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 1, It is characterized in that The finite element equations for high-temperature oxidation simulation of metals are established based on the mechanical-chemical coupling model of high-temperature oxidation simulation, including: Based on thermodynamics, classical oxidation kinetics and statics, a first set of equations is established, wherein the first set of equations includes a constitutive equation of a displacement field and a constitutive equation of a concentration field; The constitutive equation of the displacement field is: The constitutive equation of the concentration field is: Among them, σ ij is the stress tensor, D ijkI is the elastic modulus tensor, ε k / is the total strain tensor, subscripts i, j, k, and 1 represent free indices, subscript s represents metal ions and oxygen ions, subscript p represents oxide, Δ represents the gradient operator, and η s is the chemical expansion coefficient of metal ions and oxygen ions, c s is the concentration of metal ions and oxygen ions, η p is the chemical expansion coefficient of the oxide, c p is the concentration of oxide, δ k / is the Kronecker symbol, J s is the diffusion channel for metal ions and oxygen ions, D s is the diffusion coefficient of metal ions and oxygen ions, F s is a constant, tr(ε) is the trace of strain, is the partial derivative, ε is the strain, and X is the displacement gradient factor; The above η s Determined by a first preset formula, the first preset formula is: The above F s Determined by a second preset formula, the second preset formula is: In the first preset formula and the second preset formula, v m is the molar volume, is the molar volume of metal ions and oxygen ions, E is the elastic modulus, v is the Poisson's ratio, R is the Boltzmann constant, and T is the temperature.

5. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 4, It is characterized in that According to the constitutive relationship between the displacement field and the concentration field, the boundary conditions of the force and the concentration, and the control equations of the displacement field and the concentration field in the first set of equations, the Galerkin method is used to obtain the equivalent integral weak form of the displacement field and the concentration field, and the equivalent integral weak form is discretized by finite element to obtain the finite element equation for high temperature oxidation simulation of metals; The governing equation of the displacement field is: s ij，j +f i =0 The boundary conditions for the force are: s ij n j -t i =0; The control equation of the concentration field is: The boundary conditions of the concentration field are: q = -n·J; Among them, t i is the surface force, n j is the outer normal of the unit cell surface, q is the material flux through the surface, R P is the oxidation reaction rate, n is the external normal of the surface; The finite element equation is: Among them, I u is the unbalanced force caused by displacement change, is the unbalanced force caused by the concentration change of metal ions and oxygen ions, is the unbalanced force caused by the change in the concentration of the generated oxide, N u is the displacement field shape function matrix, N c is the concentration field shape function matrix, B u is the displacement field strain matrix, B c is the concentration field strain matrix, C is the concentration, R P is the chemical reaction rate, and the superscript T represents the transpose of the matrix.

6. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 5, It is characterized in that According to the finite element equation, the differential of the basic variables is taken to obtain the matrix formula used for simulation calculation: in, is the unbalanced force caused by the change in metal ion concentration, is the unbalanced force caused by the change in oxygen ion concentration, is the unbalanced force caused by the change in oxide concentration, Δu is the displacement increment, is the metal ion concentration increment, is the oxygen ion concentration increment, is the oxide concentration increment, Δt is the time increment, C A is the metal ion concentration, C o is the oxygen ion concentration, C p is the oxide concentration, K uu , are sub-matrices of the element stiffness matrix respectively.

7. The numerical simulation method for creep behavior of metal after pre-oxidation according to claim 1, It is characterized in that The constitutive model of metal creep includes: Where C is the elasticity matrix, is the total strain rate, is the creep strain rate, A is the material creep constant, n is the Norton parameter, D, S and W are the material damage factors, c, p, w and m are the temperature-related material damage parameters obtained by experimental calibration.

8. A numerical simulation system for creep behavior of metals after pre-oxidation. It is characterized in that include: Establish a module for establishing a finite element model of creep behavior of metals after pre-oxidation; A user-defined unit subroutine calling module is used to call a user-defined unit subroutine; A user material subroutine calling module, used for calling a user material subroutine; The calculation module is used to calculate the creep behavior of metals after high temperature oxidation and pre-oxidation.

9. A computer-readable storage medium, It is characterized in that The computer-readable storage medium includes a stored program, wherein the program, when executed, executes the numerical simulation method for creep behavior of metal after pre-oxidation as described in any one of claims 1 to 7.

10. An electronic device comprising a memory and a processor, It is characterized in that The memory stores a computer program, and the processor is configured to execute the numerical simulation method for the creep behavior of metal under high temperature oxidation as claimed in any one of claims 1 to 7 through the computer program.

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