CN114372387A

CN114372387A - Finite element method of nickel-based single crystal alloy microstructure evolution phase field model

Info

Publication number: CN114372387A
Application number: CN202111464488.XA
Authority: CN
Inventors: 王心美; 李磊; 岳珠峰; 惠煜中; 余志远
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2021-12-03
Filing date: 2021-12-03
Publication date: 2022-04-19

Abstract

The invention provides a finite element method of a microstructure evolution phase field model of a nickel-based single crystal alloy, which comprises the following steps: establishing a phase field model through finite element analysis software to obtain an output model file; modifying the output model file according to the simulation requirements of the phase field model to obtain a model modified file; establishing a user-defined unit subprogram and a user-defined output variable subprogram of finite element analysis software; submitting and analyzing the model modification file, the user-defined unit subprogram and the user-defined output variable subprogram through a working module to obtain analysis data; and post-processing the analysis data through a post-processing module of the finite element analysis software. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model provided by the invention greatly reduces the programming and debugging work of programs in the nickel-based single crystal alloy microstructure evolution phase field simulation, and improves the scientific research efficiency.

Description

Finite element method of nickel-based single crystal alloy microstructure evolution phase field model

Technical Field

The invention relates to the technical field of numerical simulation of materials, in particular to a finite element method of a microstructure evolution phase field model of a nickel-based single crystal alloy.

Background

The phase field model belongs to a phenomenological model and has excellent characteristics in researching the influence of different driving forces on the microstructure evolution in a system. Since the phase field model is applied to research on microstructure evolution of alloys, many researchers have researched microstructure evolution in the phase transition process by means of the phase field model.

The phase field model is solved by three methods, namely Fourier transform, finite difference and finite element. However, at present, there is no more sophisticated software for phase-field simulation, and therefore, a large amount of code needs to be written for solving the model and performing later visualization, which undoubtedly increases the workload of researchers and reduces the work efficiency.

It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present invention and therefore may include information that does not constitute prior art known to a person of ordinary skill in the art.

Disclosure of Invention

The embodiment of the invention aims to provide a finite element method of a nickel-based single crystal alloy microstructure evolution phase field model, which greatly reduces the programming and debugging work of a program in the nickel-based single crystal alloy microstructure evolution phase field simulation and improves the scientific research efficiency.

According to an aspect of an embodiment of the present invention, there is provided a finite element method of a microstructure evolution phase field model of a nickel-based single crystal alloy, the finite element method of the microstructure evolution phase field model of the nickel-based single crystal alloy including:

establishing a phase field model through finite element analysis software to obtain an output model file;

modifying the output model file according to the simulation requirements of the phase field model to obtain a model modified file;

establishing a user-defined unit subprogram and a user-defined output variable subprogram of finite element analysis software;

submitting and analyzing the model modification file, the user-defined unit subprogram and the user-defined output variable subprogram through a working module to obtain analysis data;

and post-processing the analysis data through a post-processing module of the finite element analysis software.

In an exemplary embodiment of the present disclosure, establishing a phase field model by finite element analysis software, obtaining an output model file, includes:

establishing a model in finite element analysis software according to the simulation object;

the analysis step selects a temperature-displacement coupling analysis step, divides grids, defines boundary conditions and generates an output model file.

In an exemplary embodiment of the present disclosure, modifying an output model file according to a phase-field model simulation requirement, and obtaining a model modification file includes:

and modifying the output model file according to the phase field model simulation requirement and the user-defined unit subprogram using rule and the solution model, wherein the modification comprises defining unit node freedom, unit type, model parameter and model initial value.

In an exemplary embodiment of the present disclosure, the degrees of freedom of the cell type include displacement and temperature.

In an exemplary embodiment of the present disclosure, modifying an output model file according to a phase-field model simulation requirement, and obtaining a model modified file further includes:

and establishing a layer of virtual unit, and mapping the result calculated by the calculation unit to the virtual unit so that the post-processing can be directly carried out on finite element analysis software.

In an exemplary embodiment of the present disclosure, the virtual units and the actual computing units correspond one-to-one, and only the unit numbers are different.

In an exemplary embodiment of the disclosure, a user-defined element subroutine and a custom output variable subroutine of finite element analysis software are created, comprising:

establishing a user-defined unit subprogram according to the right-end item matrix, the unit stiffness matrix and the state variable;

and establishing a custom output variable subprogram behind the user-defined unit subprogram, and transmitting the calculation result in the user-defined unit subprogram to a custom output variable array in the custom output variable subprogram.

In an exemplary embodiment of the present disclosure, the cell stiffness matrix is:

in an exemplary embodiment of the present disclosure, obtaining analysis data by submitting and analyzing the model modification file, the user-defined unit subprogram, and the custom output variable subprogram through a work module includes:

calculating by adopting the user defined unit subprogram according to the model modification file;

and transmitting the result of the user-defined unit subprogram calculation to a user-defined output variable subprogram for calculation to obtain analysis data.

In an exemplary embodiment of the present disclosure, the phase field equation is:

the method establishes the ABAQUS-based phase field model solving method, on one hand, the workload of scientific research personnel can be reduced to a great extent by means of the ABAQUS/CAE module for preliminary modeling; on the other hand, the computing speed is improved to a great extent by means of the excellent nonlinear computing performance of the ABAQUS software. Finally, a new method is provided for phase field simulation involving the Cahn-Hilliard equation.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:

FIG. 1 is a finite element method flow diagram of a microstructure evolution phase field model of a nickel-based single crystal alloy according to an embodiment of the disclosure;

FIGS. 2A-2D illustrate the effect of intrinsic strain on microstructure evolution in an AM decomposition single grain model provided by an embodiment of the present disclosure;

fig. 3A-3F are diagrams illustrating the evolution of the microstructure of an am decomposition multi-grain model under intrinsic strain according to an embodiment of the present disclosure.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art.

Furthermore, 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 provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, devices, steps, and so forth. In other instances, well-known methods, devices, implementations or operations have not been shown or described in detail to avoid obscuring aspects of the invention.

The block diagrams shown in the figures are functional entities only and do not necessarily correspond to physically separate entities. I.e. these functional entities may be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different networks and/or processor means and/or microcontroller means.

The flow charts shown in the drawings are merely illustrative and do not necessarily include all of the contents and operations/steps, nor do they necessarily have to be performed in the order described. For example, some operations/steps may be decomposed, and some operations/steps may be combined or partially combined, so that the actual execution sequence may be changed according to the actual situation.

The inventors found that, there are researchers who solve the Allen-Chan phase field model by using the finite element software ABAQUS (finite element analysis software) for studying crack propagation, and they use a length sequence parameter to represent the phase field variable and all use the UEL subroutine (user defined unit subroutine) to solve the phase field control equation.

However, there are no degrees of freedom in the model other than displacement, nor are there any references to solving the Chan-Hilliard equations, but there is provided a way to solve the Chan-Hilliard equations using the UEL subroutine, i.e. the evolution of the simulated concentration field in the ABAQUS can be implemented by the UEL subroutine, and the appropriate degrees of freedom are assigned to the calculation units according to the specific problems to which the model refers.

In view of the above technical problems, the present disclosure provides a finite element method for a phase field model of microstructure evolution of a nickel-based single crystal alloy, which can be used for phase field simulation of martensite phase transformation, spinodal decomposition, grain growth, etc. in the field of materials, as shown in fig. 1, the finite element method includes:

s100, establishing a phase field model through finite element analysis software, and acquiring an output model file;

s200, modifying the output model file according to the phase field model simulation requirement to obtain a model modification file;

step S300, establishing a user-defined unit subprogram and a user-defined output variable subprogram of finite element analysis software;

step S400, submitting and analyzing the model modification file, the user-defined unit subprogram and the user-defined output variable subprogram through a working module to obtain analysis data;

and S500, post-processing the analysis data through a post-processing module of the finite element analysis software.

In the following, each step in the finite element method of the microstructure evolution phase field model of the nickel-based single crystal alloy provided by the present disclosure will be described in detail.

In step S100, a phase field model is established by finite element analysis software, and an output model file is obtained.

Specifically, a model is established in finite element analysis software (ABAQUS/CAE) according to a simulation object; the analysis step selects a temperature-displacement coupling analysis step, divides grids, defines boundary conditions and generates an output model file (INP file). And (3) realizing concentration evolution in the phase field model by using the temperature freedom degree in the temperature-displacement coupling analysis step in the ABAQUS.

In step S200, the output model file is modified according to the phase-field model simulation requirement, and a model modification file is obtained.

Specifically, according to the simulation requirements of the phase field model, the output model file is modified according to the use rules of the user-defined unit subprogram and the solution model, and the modification comprises the definition of unit node freedom, unit type, model parameters and model initial values. Wherein the degrees of freedom of the cell type include displacement and temperature.

Wherein, modify the output model file according to the simulation requirement of the phase field model, obtain the model and modify the file, still include: and establishing a layer of virtual unit, and mapping the result calculated by the calculation unit to the virtual unit so that the post-processing can be directly carried out on finite element analysis software. The virtual units correspond to the actual computing units one by one, and only the unit numbers are different.

Illustratively, the INP generated in step S100 is modified according to the UEL subroutine using rules and solution models, including defining unit node degrees of freedom, unit types, model parameters, model initial values, and the like.

Among them, the user manual of ABAQUS has a rule and a method for using the UEL subprogram. For example, the UMAT subroutine is more versatile in practice, and the user can tell the software in the property module of ABAQUS that the user-defined material properties are to be used in the calculation; but when the user uses the UEL subprogram, the Mesh module of the ABAQUS cannot tell the software to use the user-defined unit type in the calculation, and the software must tell the user-defined unit type to be used in the calculation by modifying the INP file. This is the first reason that the INP file must be modified when using the UEL subprogram, which is also an important rule used by the UEL subprogram. In addition, since post-processing cannot be directly performed by using the UEL subprogram, the method for implementing post-processing in the present disclosure is to map the result calculated by the UEL subprogram onto a layer of "virtual" unit, so a layer of "virtual" unit needs to be defined in the INP file, which is the second reason that the INP file needs to be modified in the present invention.

The solving model is actually used for simulating which physical phenomena, amplitude modulation decomposition, film instability or phase separation and the like, although control equations of the phenomena are Chan-Hilliard equations, parameters in the equations in each phenomenon are different, and driving forces in the evolution process are different.

The interfaces of the user definition unit in the INP file are as follows:

*User element，nodes＝4，type＝U1，properties＝3，coordinates＝2，VARIABLES＝40。

user elements indicate that software in calculation is to perform calculation according to unit parameters defined later, for example, nodes ═ 4 indicates a 4-node unit, type ═ U1 indicates that the unit type is U1, properties ═ 3 indicates that the unit parameters are 3, coordinatates ═ 2 indicates that the calculation model is a 2-dimensional model, and VARIABLES ═ 40 indicates that each unit has 40 VARIABLES.

Since direct post-processing cannot be performed when the UEL subroutine is used, the method needs to establish a layer of "virtual unit" and map the result calculated by the calculation unit to the "virtual unit" so that the post-processing at a later stage can be performed directly on the ABAQUS. The specific method is that after the unit information generated by the INP file, a 'virtual unit' is defined, the virtual unit corresponds to the actual calculation unit one by one, and only the unit number is different. As follows:

*Element，type＝U1

……

*Element，type＝CPE4

……

because the temperature-displacement coupling analysis step is chosen, the freedom of the cell type of at least one cell in the model is both displacement and temperature, such as CPE 4T. The specific definition is as follows:

*Node

999996，0.0，0.0

999997，0.01，0.0

999998，0.01，0.01

999999，0.0，0.01

*Nset，nset＝extraElement

999996，999997，999998，999999

*Element，Type＝CPE4T

999999，999996，999997，999998，999999

in order to avoid error reporting, the node number and the element number must be distinguished from the previous element and cannot be repeated.

In step S300, a user-defined element subroutine and a custom output variable subroutine of the finite element analysis software are created.

Specifically, a user-defined unit subprogram is established according to the right-end item matrix, the unit stiffness matrix and the state variable; and establishing a custom output variable subprogram behind the user-defined unit subprogram, and transmitting the calculation result in the user-defined unit subprogram to a custom output variable array in the custom output variable subprogram.

In an example, a finite element solution derivation is performed on a phase field equation controlled by a Chan-Hilliard equation as follows:

where c denotes concentration, r and t denote position and time, respectively, M denotes diffusion coefficient, and F denotes free energy function.

Introducing an intermediate variable mu, reducing the order,

wherein f represents chemical free energy, w represents elastic strain energy, k represents gradient coefficient, omega represents boundary condition, two equations are respectively multiplied by potential functions eta and xi to obtain weak situation,

where V represents the solution area, then discretized,

wherein N represents the nth solution step and is a shape function N_iAnd N_jObtaining the right end instead of the potential functionItem (1):

wherein the content of the first and second substances,

referred to as residual phase, i.e. the right-hand term, T represents the transpose of the matrix, the mechanical equilibrium equation can also be used to obtain the right-hand term in the same process,

wherein, B^eRepresents the cell strain matrix and σ represents the stress.

And (3) respectively solving partial derivatives of the displacement u, the reduced variable mu and the concentration c for the three right-end items, so as to obtain a unit stiffness matrix as follows:

wherein the content of the first and second substances,

respectively, a sub-matrix of the cell stiffness matrix.

The UEL subroutine is written according to theoretical derivation, wherein three arrays of RHS, AMATRX, SVARS are mainly defined, wherein RHS is a right-end item matrix, AMATRX is a cell stiffness matrix, and SVARS is a state variable.

The Fortran subroutine interface of the UEL subroutine is given below, where two arrays, RHS and AMATRX, are two arrays that must be defined, and the other arrays are defined according to actual requirements, such as the ENERGY array, if the model requires computing ENERGY, then it is defined, and if it does not need defining. SVARS arrays are used in this disclosure to store and communicate various state variables such as displacement, stress, concentration, etc.

The UEL subprogram is written, and the UEL Fortran subprogram interface of ABAQUS is as follows:

SUBROUTINE UEL(RHS，AMATRX，SVARS，ENERGY，NDOFEL，NRHS，NSVARS，

1 PROPS，NPROPS，COORDS，MCRD，NNODE，U，DU，V，A，JTYPE，TIME，DTIME，

2 KSTEP，KINC，JELEM，PARAMS，NDLOAD，JDLTYP，ADLMAG，PREDEF，NPREDF，

3 LFLAGS，MLVARX，DDLMAG，MDLOAD，PNEWDT，JPROPS，NJPROP，PERIOD)

C

INCLUDE'ABA_PARAM.INC'

C

DIMENSION RHS(MLVARX，*)，AMATRX(NDOFEL，NDOFEL)，PROPS(*)，

1 SVARS(*)，ENERGY(8)，COORDS(MCRD，NNODE)，U(NDOFEL)，

2 DU(MLVARX，*)，V(NDOFEL)，A(NDOFEL)，TIME(2)，PARAMS(*)，

3 JDLTYP(MDLOAD，*)，ADLMAG(MDLOAD，*)，DDLMAG(MDLOAD，*)，

4PREDEF(2，NPREDF，NNODE)，LFLAGS(*)，JPROPS(*)

user coding to define RHS，AMATRX，SVARS，ENERGY，and PNEWDT

RETURN

END

wherein RHS is a matrix of right-hand terms

AMATRX is a matrix of cell stiffness

SVARS is a state variable.

The UVARM subprogram is written behind the UEL subprogram, and the UVARM Fortran subprogram interface of ABAQUS is as follows:

SUBROUTINE UVARM(UVAR，DIRECT，T，TIME，DTIME，CMNAME，ORNAME，

1 NUVARM，NOEL，NPT，LAYER，KSPT，KSTEP，KINC，NDI，NSHR，COORD，

2 JMAC，JMATYP，MATLAYO，LACCFLA)

INCLUDE'ABA_PARAM.INC'

C

CHARACTER*80 CMNAME，ORNAME

CHARACTER*3 FLGRAY(15)

DIMENSION UVAR(NUVARM)，DIRECT(3，3)，T(3，3)，TIME(2)

DIMENSION ARRAY(15)，JARRAY(15)，JMAC(*)，JMATYP(*)，COORD(*)

C The dimensions of the variables FLGRAY，ARRAY and JARRAY

C must be set equal to or greater than 15.

user coding to define UVAR

RETURN

END

and (3) transmitting each state variable (namely SVARS array) obtained by calculation in the UEL to a UVAR array in the UVARM, and combining the virtual units in the first step to perform post-processing.

In step S400, the work module submits analysis using the model modification file, the user-defined unit subprogram, and the user-defined output variable subprogram, and obtains analysis data.

Specifically, calculating by adopting the user-defined element subprogram according to the model modification file; and transmitting the result of the user-defined unit subprogram calculation to a user-defined output variable subprogram for calculation to obtain analysis data.

For example, the first modified INP file and the second written subroutine are used in the JOB module to submit and analyze, and post-processing is performed after calculation is completed; (1) because the INP file is modified, the modified file cannot be imported in the preprocessing of the ABAQUS, so that the modified INP file is directly selected from the model file of the JOB module of the ABAQUS, a debugged subprogram is called, and calculation is submitted.

In step S500, the analysis data is post-processed by a post-processing module of the finite element analysis software.

Specifically, after the calculation is completed, the analysis data is post-processed by a post-processing module of the finite element analysis software.

The present invention will be further described with reference to the following examples.

As shown in fig. 2A-2D, the initial microtopography, the microtopography of the concentration field distribution after phase equilibrium regardless of intrinsic strain and intrinsic strain intensity of 0.01 and 0.05, respectively, is shown. It can be seen from the figure that the single-grain gamma' phase grows continuously driven by chemical energy and interfacial energy and remains as round grains until equilibrium, without taking into account intrinsic strain; however, when the intrinsic strain is considered, the gamma 'phase of a single particle gradually evolves from a circular shape to a square particle with rounded corners under the combined action of chemical energy, interfacial energy and elastic strain energy, and the gamma' phase changes more than usual to equilibrium as the intrinsic strain intensity is higher. This is because the nickel-based single crystal superalloy is a cubic anisotropic material having an anisotropy coefficient of about 3, and has elastic soft directions of 10 and 01 in the presence of intrinsic strain. Under the push of the integral potential energy of the system, the chemical energy and the interface energy promote the grains to grow continuously until the grains are balanced, and due to the existence of intrinsic strain, in order to relax the elastic energy and reduce the system energy, the gamma ' phase preferentially grows along two elastic soft directions, and finally when the gamma ' phase evolves to a balanced state, the final shape of the gamma ' phase is a square. The greater the intrinsic strain strength, the more elastic energy in the system needs to relax and the greater the extent to which the particles grow in both soft directions.

As shown in fig. 3A-3F, the evolution of the am decomposition multi-particle model concentration field over time is shown. FIG. 3A is the initial microstructure before the intrinsic strain is added, where smaller particles are precipitated under the action of chemical energy and gradient energy to show a decreasing trend, and larger particles are interconnected with neighboring particles. After the intrinsic strain is added, the particles are connected to each other and grow continuously in the directions of yellow arrows and black arrows in fig. 3B, respectively, under the action of elastic strain energy, and the smaller γ' phase gradually disappears. Furthermore, as the evolution progresses, the tendency of coarsening along the direction of the light-colored arrow is greater than that of the dark-colored arrow, the γ 'phase in the direction of the light-colored arrow becomes thicker, and the γ' phase in the direction of the dark-colored arrow becomes thinner. The elastic strain energy also has a certain influence on the equilibrium concentration of the gamma 'phase, and under the action of the elastic strain energy, the equilibrium concentration of the gamma' phase is firstly reduced to 0.993 from the initial 1.071 and then is increased to 1.019 along with the progress of evolution. The concentration of the gamma matrix phase appears negative under the effect of the elastic strain energy, which may occur depending on the choice of the boundary conditions of the model.

The invention relates to a finite element method of a nickel-based single crystal alloy microstructure evolution phase field model based on an ABAQUS user defined element subprogram (UEL), which aims at the phase change process (such as amplitude modulation decomposition, phase separation caused by uneven elasticity and external stress, and film instability) controlled by a Cahn-Hilliard equation or the phase change process (grain growth and martensite phase change) controlled by an Allen-Cahn equation, and the like, initially models a CAE interface preprocessed by an ABAQUS/Stardand solver, and modifies an obtained INP file to complete modeling, wherein the solution of a control equation is realized by the user defined element subprogram (UEL), and the solution method of a partial differential equation is the finite element method. And finally, combining a simple subprogram and a post-processing module to realize post-processing of the simulation working condition. The method for solving the phase field model based on the ABAQUS is established, on one hand, the workload of scientific researchers can be reduced to a great extent by means of the initial modeling of the ABAQUS/CAE module; on the other hand, the computing speed is improved to a great extent by means of the excellent nonlinear computing performance of the ABAQUS software. Finally, a new method is provided for phase field simulation involving the Cahn-Hilliard equation.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams or flowchart illustration, and combinations of blocks in the block diagrams or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein may be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solution according to the embodiment of the present invention can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to execute the method according to the embodiment of the present invention.

Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

It will be understood that the invention is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the invention is limited only by the appended claims.

Claims

1. A finite element method of a microstructure evolution phase field model of a nickel-based single crystal alloy is characterized by comprising the following steps:

2. The finite element method of the phase field model of the nickel-based single crystal alloy microstructure evolution according to claim 1, wherein the phase field model is established by finite element analysis software, and the obtaining of the output model file comprises:

3. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 1, wherein the modifying the output model file according to the simulation requirement of the phase field model to obtain the model modified file comprises:

4. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 3, wherein the degrees of freedom of the cell type include displacement and temperature.

5. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 3, wherein the output model file is modified according to the simulation requirement of the phase field model to obtain a model modified file, further comprising:

6. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 5, wherein the virtual units correspond to the actual calculation units one by one, and only the unit numbers are different.

7. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 1, wherein the establishing of the user-defined element subprogram and the custom output variable subprogram of the finite element analysis software comprises:

8. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 7, wherein the unit stiffness matrix is:

9. the finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 1, wherein the obtaining of the analysis data by submitting the model modification file, the user-defined element subprogram and the custom output variable quantum program to analysis through a working module comprises:

10. The finite element method of the nickel-based single crystal alloy microstructure evolution phase field model as claimed in claim 1, wherein the phase field equation is: