A phase field kinetic method for simulating the evolution of gamma prime phase precipitation in nickel-based superalloys under applied stress

Abstract

The present application relates to the field of metallurgical casting, in particular to a phase field dynamics method for simulating gamma prime phase precipitation evolution of nickel-based high-temperature alloy under applied stress. The method comprises the following steps: S1, obtaining thermal and dynamic information of gamma phase and gamma prime phase by using CALPHAD method according to target composition of the nickel-based high-temperature alloy; S2, constructing a strain energy term containing plastic strain, defining stress-free strain caused by lattice mismatch during gamma to gamma prime phase transition, and defining gradient energy term which can consider different slip system information; S3, establishing a phase field model, and solving phase field control equation by using Kim-Kim-Suzuki interface model at two-phase interface to obtain order parameter result value, and investigating the influence of different forms of applied stress load and different plastic strain on gamma prime phase precipitation growth; S4, visualizing the gamma prime phase precipitation evolution structure in the nickel-based high-temperature alloy, and clarifying the influence law of applied stress and plastic strain on the gamma prime phase precipitation evolution.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of metallurgical casting, in particular to a phase field dynamics method for simulating the evolution of gamma prime phase precipitation in nickel-based high-temperature alloy under applied stress. BACKGROUND

[0002] Nickel-based high-temperature alloy is a key structural material widely used in the fields of aerospace, navigation, energy and chemical industry. Among them, the nickel-based high-temperature alloy blade is the core hot end component of high-end equipment such as aircraft engines, and often faces harsh service environments such as high temperature, oxidation, hot corrosion and complex stress. Generally, under the action of stress and high temperature for a long time, the cubic gamma prime phase in the nickel-based high-temperature alloy will usually grow preferentially in a certain direction, which is called directional coarsening. According to the relationship between the applied stress and the directional coarsening direction of the gamma prime phase, the directional coarsening of the <001> oriented nickel-based high-temperature alloy gamma prime phase can be divided into two types: N type and P type. N type, the directional coarsening direction of the gamma prime phase is perpendicular to the direction of the applied stress; P type, the directional coarsening direction of the gamma prime phase is parallel to the direction of the applied stress. The directional coarsening of the gamma prime phase and the creep deformation in the nickel-based high-temperature alloy will determine the performance and service life of the engine turbine blade, which depends on the creep (temperature, stress) conditions and the microstructure (gamma prime phase size, volume fraction, gamma prime / gamma mismatch degree, etc.) of the alloy. However, in the elastic anisotropic and non-uniform system, the complexity brought by the close coupling process of the gamma / gamma prime microstructure evolution and the plastic deformation in the gamma channel has brought great difficulties to the research. Therefore, it is of great significance to characterize the gamma prime phase precipitation evolution dynamics process and predict the microstructure morphology evolution process by means of computational simulation. SUMMARY

[0003] (1) Technical problems to be solved

[0004] In order to perfect and optimize the microstructure design of nickel-based high-temperature alloy, the purpose of the present application is to provide a phase field dynamics method for simulating the evolution of gamma prime phase precipitation in nickel-based high-temperature alloy under applied stress. This method can reproduce the gamma prime phase precipitation growth process in nickel-based single crystal high-temperature alloy under applied stress, and provide an effective prediction method for the microstructure evolution law of the directional coarsening process of the gamma prime phase in the nickel-based high-temperature alloy.

[0005] (2) Technical solutions

[0006] In order to achieve the above purpose, the main technical scheme adopted by the present application is:

[0007] A phase field dynamics method for simulating the evolution of gamma prime phase precipitation in nickel-based high-temperature alloy under applied stress, comprising the following steps:

[0008] S1, according to the target composition of the nickel-based superalloy, the CALPHAD method is used to obtain the thermal and kinetic information of the gamma phase and the gamma' phase, including the free energy curve, the equilibrium composition and the atomic mobility of each component in the two phases;

[0009] S2, a strain energy term containing plastic strain is constructed, a stress-free strain caused by lattice mismatch during gamma→gamma' phase transition is defined, and a gradient energy term considering different slip system information is defined;

[0010] S3, a phase field model is established, and the Kim-Kim-Suzuki interface model is used to solve the phase field control equation to obtain the order parameter result value at the two-phase interface, and the influence of different forms of external stress load and different plastic strain on the growth of the gamma' phase is investigated;

[0011] S4, the visual processing of the gamma' phase precipitation evolution organization in the nickel-based superalloy is carried out, and the influence law of the external stress and the plastic strain on the gamma' phase precipitation evolution is clarified.

[0012] The phase field dynamics method for simulating the gamma' phase precipitation evolution in single crystal superalloy under external stress includes the following contents in step S1:

[0013] The free energy curve expression of the gamma and gamma' phase in the nickel-based single crystal superalloy at the two-phase equilibrium is simplified as:

[0014]

[0015] Wherein, f γ (X γ (r)) is the Gibbs free energy of the gamma phase, unit J / m 3 ; f γ′ (X γ′ (r)) is the Gibbs free energy of the gamma' phase, unit J / m 3 ; f0 corresponds to the second derivative of the chemical free energy near the equilibrium composition, unit J / mol; V m is the molar volume, unit m 3 / mol; X γ (r) and X γ′ (r) are the "virtual" compositions of the gamma and gamma' phases, unit at.%; based on the "virtual" composition, the composition (unit at.%) at each position in space is expressed as:

[0016] X(r)=[1-h(φ q (r))]X γ (r)+h(φ q (r))X γ′ (r)

[0017] Wherein, h(φ q (r)) is a difference function:

[0018]

[0019] where φ q (r) is the qth order structural field variable, q = 1, …, 4, dimensionless; φ q (r) = 0 represents the γ phase, φ q (r) = 1 represents the qth ordered γ' phase.

[0020] The system local chemical free energy (unit: J / m 3 ) is expressed as:

[0021] f(X(r), φ q (r)) = [1 - h(φ q (r))]f γ (X γ (r)) + h(φ q (r))f γ′ (X γ′ (r)) + ω·g(φ q (r))

[0022] where ω·g(φ q (r)) represents the energy barrier between the two phases, ω is the height of the energy barrier, unit: J / m 3 ; and g(φ q (r)) is expressed as:

[0023]

[0024] where p is a subscript different from q; the parameter θ is related to the anti-phase domain boundary energy, dimensionless.

[0025] The chemical mobility is expressed as M c = X Al X Ni (X Al M Ni + X Ni M Al ), where M c is the chemical mobility, unit: mol·m 2 / sJ; M Al and M Ni are the atomic mobilities of Al and Ni atoms, unit: mol·m 2 / sJ; X Al and X Ni are the percentages of Al and Ni atoms, unit: at. %.

[0026] The phase field dynamics method for simulating the evolution of γ' phase precipitation in single crystal superalloys under applied stress, step S2 comprises the following contents:

[0027] According to the phase field micropolar theory of Khachaturyan, under the stress control boundary condition, the total elastic strain energy of the system is written as:

[0028]

[0029] Wherein, E el is the elastic strain energy, unit J / m 3 ; p and q represent different types of γ' variants, V is the total volume of the system, unit m 3 ; n is the unit vector along the k vector direction; is the applied stress, unit MPa; The shape function is represented by θ p (k); B pq (n) is defined as:

[0030]

[0031] Wherein, C ijkl is the elastic constant tensor, unit GPa; is the stress-free strain or intrinsic strain of the pth variant, and

[0032] In addition, the stress-free strain between γ / γ' due to lattice mismatch is defined as :

[0033]

[0034] Wherein, a γ′ and a γ are the equilibrium lattice constants of γ' and γ phases, δ ij is the Kronecker symbol; the dislocation-related stress-free strain is represented by:

[0035]

[0036] Wherein, b is the Burgers vector, n is the slip plane normal vector, η α (r) is the plastic strain field, is the intrinsic plastic strain of the αth slip system;

[0037] When considering the variants, dislocations and applied stress, the strain energy term is:

[0038]

[0039] Wherein, is the Fourier transform of the function h(φ q (r)), is the Fourier transform of the plastic strain η α (r), and:

[0040]

[0041] where <B hh (n) > and <B are the average values of B hh (n) and B along different orientations, respectively; in addition,

[0042]

[0043] The energy term represents the plastic deformation work under external force loading, and the macroscopic plastic strain of the system is expressed as:

[0044]

[0045] The phase field kinetic method for simulating the evolution of γ' phase precipitation in single crystal superalloys under applied stress, the integral of the strain energy excludes the point k = 0,

[0046] The phase field kinetic method for simulating the evolution of γ' phase precipitation in single crystal superalloys under applied stress, step S3 includes the following contents:

[0047] The total free energy of the system is expressed as a functional of the field variables, including the local chemical free energy, gradient energy and strain energy, that is:

[0048]

[0049] wherein, The meanings and units of various symbols are: F represents the total free energy, unit: J / m 3 ; dV is the volume element, unit m 3 ; f(X(r), φ q (r)) is the local chemical free energy density, unit J / m 3 ; κ φ and κ η are the structure field variable and the plastic strain field gradient energy term coefficient, unit J / m; and represent the structure field variable and the plastic strain field variable gradient, unit m -1 ;

[0050] Based on the Kim-Kim-Suzuki model, the interface satisfies:

[0051] df γ (X γ (r)) / dX γ (r)=df γ′ (X γ′ (r)) / dX γ′ (r)

[0052] The evolution of the concentration field with time is controlled by the diffusion equation, usually referred to as the Cahn-Hilliard equation:

[0053]

[0054] where M c is the chemical mobility, representing the solute diffusion rate, with the unit of mol·m 2 / sJ, and the larger the value, the faster the diffusion;

[0055] The evolution of the structural and plastic strain order parameter field with time is described by the relaxation equation, usually referred to as the time-dependent Ginzburg-Landau (TDGL) equation or the Allen-Cahn equation:

[0056]

[0057] where L φ and L η are the kinetic coefficients representing the structural and plastic strain relaxation, with the unit of m 3 / J / s, and the larger the value, the faster the structural relaxation.

[0058] The design idea of the present application is: considering the limitations of the characterization tests in experimental research, fully exerting the advantages of material calculation simulation method, using the phase field dynamics method to simulate the evolution of the γ' phase precipitation process under external stress in nickel-based superalloy, and illustrating the influence law of different plastic strains on the γ' phase precipitation and growth process and different forms of external stress load on the γ' phase directional coarsening process. This simulation method lays a theoretical and methodological foundation for in-depth understanding of the formation reasons and regulation of the microstructure of the γ' phase directional coarsening in nickel-based superalloy.

[0059] (Three) beneficial effects

[0060] The advantages and beneficial effects of the present application are:

[0061] 1、Nickel-based superalloy as a key structural material, the directional coarsening of gamma prime phase and the creep deformation in the nickel-based superalloy will determine the performance and service life of the engine turbine blade, the experimental cost of deeply understanding the forming reason and the microstructure control of the directional coarsening of the gamma prime phase of the nickel-based superalloy is high, and when the solid phase transformation is transformed, the interface energy between phases, the system strain energy and the plastic deformation in the gamma channel are difficult to be characterized by experiments, and there is great limitation for investigating the microstructure evolution law of the gamma prime phase precipitation evolution process of the nickel-based superalloy. The present application uses the method of numerical simulation to study the influence law of the external stress on the microstructure evolution of the directional coarsening process of the gamma prime phase in the nickel-based superalloy at a certain temperature, which can effectively avoid the limitation of experimental research.

[0062] 2、The present application can introduce the key influencing factors such as interfacial energy between phases, system strain energy, plastic strain, temperature, stress and balanced composition of two phases at target temperature into numerical simulation, can truly reproduce the microstructure morphology of the directional coarsening of the gamma prime phase during creep deformation, and can accurately simulate the evolution process of the microstructure, so as to provide reliable information for improving and optimizing the microstructure control of the nickel-based superalloy. According to the stress state, the specific active slip system is determined, a group of dislocation density field variables are introduced according to the number of slip systems, when the plastic deformation occurs in the gamma channel, the dislocation activity from the specific slip system is characterized, and the influence law of different plastic strains on the gamma prime phase precipitation and growth process and different forms of external stress load on the directional coarsening process of the gamma prime phase can be investigated. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 The specific flow chart for the numerical model program in the present application.

[0064] Figure 2 The Gibbs free energy curve of the gamma and gamma prime phases in the nickel-based superalloy in the specific embodiment of the present application.

[0065] Figure 3 The influence result graph of the external tensile / compressive stress on the microstructure morphology of the gamma prime phase of the nickel-based single crystal superalloy at t=10 4 time step and at a temperature of 927 DEG C; wherein (a) is the simulation initial configuration; (b) and (c) are respectively the microstructure morphology graphs of the gamma prime phase under the external compressive stress and tensile stress.

[0066] Figure 4 The distribution graph of the plastic strain epsilon 33 of the directional coarsening microstructure of the gamma prime phase of the nickel-based single crystal superalloy under the external compressive stress (a) and tensile stress (b) at t=10 4 time step.

[0067] Figure 5A flowchart of a phase field dynamics method for simulating the precipitation and evolution process of the γ' phase in nickel-based single-crystal superalloys. Detailed Implementation

[0068] like Figure 1 As shown, the specific process of establishing the numerical model program is as follows: Initial conditions include the initial composition X of Al elements. n (Al), Initial configuration φ n The Gibbs free energy f(X(r),φ) containing the γ and γ' phases at the target temperature was obtained by thermodynamic calculation. q (r)), considering the strain energy E of mismatch strain and plastic strain. el Fit the total free energy F; on the one hand, through the chemical free energy to the composition variation Solving the composition governing equations, the Cahn-Hilliard equations, using the semi-implicit Fourier spectral method, with the initial composition X... n Updated to component field variable X n+1 On the other hand, variational analysis of the structural field variables using free energy is performed. Solving the structural governing equations, the Allen-Cahn equations, using the semi-implicit Fourier spectral method, yields the initial configuration φ. n Updated to structural field variable φ n+1 Thus, the evolution process of directional coarsening tissue can be simulated.

[0069] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below through specific embodiments.

[0070] Example

[0071] Taking Ni-0.2Al (at.%) alloy as an example, the steps include:

[0072] (1) Thermodynamics and Equilibrium Composition

[0073] First, based on the phase transformation temperature of the Ni-0.2Al alloy, the Gibbs free energy data of the γ and γ' phases at the target temperature were obtained by thermodynamic calculation, and the free energy curve at the equilibrium of the two phases was simplified. Figure 2 ).

[0074] The free energy f of the γ and γ' phases in equilibrium in nickel-based single-crystal superalloys γ (X γ (r)), =f γ′ (X γ′ (r))(Unit: J / m 3 The curve expression simplifies to:

[0075]

[0076] where f0corresponds to the second derivative of the chemical free energy near the equilibrium composition, with unit J / mol. V m is the molar volume, with unit m 3 / mol. X γ (r) is the "virtual" composition corresponding to γ and γ', with unit at.%. Y γ′ (r) is the "virtual" composition corresponding to γ and γ', with unit at.%. Y is the equilibrium composition of Al in γ phase at the simulation temperature, with unit at.%. Y is the equilibrium composition of Al in γ' phase at the simulation temperature, with unit at.%. Based on the "virtual" composition, the composition (unit at.%) at each spatial position is expressed as:

[0077] X(r) = [1 - h(φ q (r))] X γ (r) + h(φ q (r)) X γ′ (r)

[0078] where h(φ q (r)) is the difference function:

[0079]

[0080] φ q (r) is the q-th structural field variable, q = 1,..., 4, with no unit. φ q (r) = 0 indicates γ phase, and φ q (r) = 1 indicates the q-th ordered γ' phase.

[0081] In this work, the local chemical free energy of the system f(X(r), φ q (r)) (unit J / m 3 ) is expressed as:

[0082] f(X(r), φ q (r)) = [1 - h(φ q (r))] f γ (X γ (r)) + h(φ q (r)) f γ′ (X γ′ (r)) + ω·g(φ q (r))

[0083] where ω·g(φ q (r)) represents the energy barrier between the two phases, and ω is the barrier height, with unit J / m 3 . And g(φ q (r)) is expressed as:

[0084]

[0085] where p is a subscript different from q, p, q = 1,..., 4. The parameter θ is related to the antiphase boundary energy, without unit.

[0086] The equilibrium composition of Al in γ and γ' phases at the target heat treatment temperature T = 927°C was obtained and used as the input of the initial configuration of the phase field, as shown in Table 1.

[0087] Table 1 Equilibrium composition of alloying elements in two phases at the target heat treatment temperature

[0088]

[0089] In terms of the kinetic data, the chemical mobility M c (unit: mol·m 2 / sJ) is expressed as M c = X Al X Ni (X Al M Ni + X Ni M Al , where M Al and M Ni are the atomic mobilities of Al and Ni atoms, with the unit of mol·m 2 / sJ; X Al and X Ni are the atomic percentages of Al and Ni, with the unit of at. %.

[0090] (2) Construction of strain energy term containing plastic strain

[0091] According to the phase field micropolar theory of Khachaturyan, under the stress-controlled boundary condition, the total elastic strain energy E el (unit: J / m 3 ) of the system can be written as:

[0092]

[0093] Here p and q represent different types of γ' variants, V is the total volume of the system, with the unit of m 3 . d is the differential operation, without unit. k is the reciprocal lattice vector, with the unit of m -1 . θ p (k) is the shape function, without unit. is the conjugate of the shape function, without unit. n is the unit vector along the k vector direction. is the applied stress, with the unit of MPa. is the stress-free strain of variant p, without unit. represents the Fourier transform form of the shape function θ p (k). B pq (n) is defined as:

[0094]

[0095] Here C ijkl is the elastic constant tensor with unit GPa. is the stress-free strain or eigenstrain of the pth variant, and n k is the kth component of the unit vector n with unit m -1 ; n l is the lth component of the unit vector n with unit m -1 ; is the stress-free strain or eigenstrain of the pth variant, unitless. is the stress-free strain or eigenstrain of the qth variant, unitless. n i is the ith component of the unit vector n with unit m -1 . is the phase transformation stress corresponding to the pth variant, unit GPa. Ω jk (n) is the Green function with unit m 2 / GPa. is the phase transformation stress corresponding to the qth variant, unit GPa.

[0096] In addition, the stress-free strain (unitless) between γ and γ' due to lattice mismatch is defined as:

[0097]

[0098] where a γ′ and a γ are the equilibrium lattice constants of γ' and γ, respectively, δ ij is the Kronecker symbol. is the degree of misfit between γ and γ', unitless. The stress-free strain (unitless) associated with dislocations is characterized by:

[0099]

[0100] Here b is the Burgers vector, n is the slip plane normal vector, η α (r) is the plastic strain field, is the eigen plastic strain of the αth slip system, b α is the Burgers vector of the αth slip system, n α is the slip plane normal vector of the αth slip system.

[0101] The strain energy term considering the variants, dislocations, and applied stress is:

[0102] ​​

[0103] Here is the Fourier transform of the function h(φ q (r)), is the Fourier transform of the plastic strain, η α (r), and:

[0104]

[0105] is the stress-free strain due to lattice mismatch, dimensionless. is also the stress-free strain due to lattice mismatch, dimensionless. n i is the i-th component of the unit vector n, dimension m -1 . is the stress due to lattice mismatch, unit GPa. Ω jk (n) is the Green function, dimension m 2 / GPa. is the stress due to lattice mismatch, unit GPa. n l is the i-th component of the unit vector n, dimension m -1 . is the stress corresponding to the a-th slip system, unit GPa. <B hh (n) > and are the average values of B hh (n) and along different orientations, respectively. In addition,

[0106]

[0107] is the two-body interaction potential, unit GPa. is the plastic strain corresponding to the a-th slip system, dimensionless. is the plastic strain corresponding to the β-th slip system, dimensionless. is the plastic stress corresponding to the a-th slip system, unit GPa. is the plastic stress corresponding to the β-th slip system, unit GPa.

[0108] It is noted that the integration of the strain energy excludes the k = 0 point, the energy term represents the plastic deformation work under external force loading. Then, the macroscopic plastic strain of the system can be expressed as:

[0109]

[0110] η α(r) is the plastic strain of the alpha slip system, unitless.

[0111] In fact, from the perspective of phase field simulation, the evolution of γ' phase morphology is the result of the competition between strain energy and interface energy between γ' phase and γ phase. The phase field dynamics method has obvious advantages in the study of microstructure evolution.

[0112] (3) Establishment of phase field control equation

[0113] The total free energy of the system is expressed as a functional of the field variables, including local chemical free energy, gradient energy and strain energy, that is:

[0114]

[0115] Wherein, The meanings and units of various symbols are: F represents the total free energy, unit: J / m 3 . dV is the volume element, unit m 3 . f(X(r), φ q (r)) is the local chemical free energy density, unit J / m 3 . κ φ and κ η are the coefficients of the gradient energy terms of the structure field variable and the plastic strain field, respectively, unit J / m. and represent the gradients of the structure field variable and the plastic strain field variable, unit m -1 . φ q is the qth structure field variable, unitless; η α is the plastic strain field corresponding to the alpha slip system, unitless; n α is the unit normal vector of the slip plane of the alpha slip system, unit 1.

[0116] Based on the Kim-Kim-Suzuki model, the interface satisfies:

[0117] df γ (X γ (r)) / dX γ (r) = df γ′ (X γ′ (r)) / dX γ′ (r)

[0118] The evolution of the concentration field with time is controlled by the diffusion equation, usually referred to as the Cahn-Hilliard equation:

[0119]

[0120] M c is the chemical mobility, which represents the diffusion rate of the solute, unit: mol·m2 The larger the value is, the faster the diffusion is. is a variation operation on the total free energy F, and is a variation operation on the total composition c(r).

[0121] The evolution of the structure and plastic strain order parameter field with time is described by a relaxation equation, usually referred to as a time-dependent Ginzburg-Landau (TDGL) equation or an Allen-Cahn equation:

[0122]

[0123] L φ L η is a kinetic coefficient representing the dynamics of the structure and plastic strain relaxation, with a unit of m 3 The larger the value is, the faster the structure relaxation is.

[0124] (4) Result output

[0125] The structure field and the concentration field control equation are solved based on a semi-implicit Fourier spectral method mainly according to the phase field model and the calculation parameters. The program describing the interface energy, strain energy, applied stress and plastic strain and the like influencing the evolution of the gamma' phase precipitation of the nickel-based single crystal high-temperature alloy at a certain temperature is written by using the Fortran language in the embodiment of the present application. Then, the order parameter evolution result output by the program is converted into a more intuitive image form by using a visual software, so that the purpose of visualizing the solid state phase transformation process in the nickel-based high-temperature alloy is achieved.

[0126] As Figure 5The phase field dynamics method for simulating the γ' phase precipitation evolution process in the nickel-based superalloy is shown in the following: first, according to the target composition of the nickel-based superalloy, the CALPHAD method is used to obtain the thermal and kinetic information of the γ phase and the γ' phase, calculate the equilibrium composition of the alloying elements, the simplified free energy curve of the γ phase and the γ' phase, the atomic mobility of each component in the γ phase and the γ' phase, summarize the slip system activation under the external stress, collect the Gibbs free energy data of the titanium alloy system and the equilibrium composition of each alloying element; then, define the stress-free strain generated by the lattice mismatch during the γ→γ' phase transition, construct the strain energy term containing the plastic strain, and the gradient energy term considering different slip system information; then, the phase field dynamics model is established, various physical parameters, boundary conditions and other conditions are input into the model, and the semi-implicit Fourier spectrum method is used to solve the phase field control equation, that is, the Cahn-Hilliard and Allen-Cahn equations; and the Kim-Kim-Suzuki interface model is used to solve the phase field control equation at the two-phase interface to obtain the order parameter result value, and the influence of different forms of external stress load and different plastic strain on the γ' phase precipitation growth is investigated; finally, the output results and composition field variables are visualized, the γ' phase precipitation evolution organization in the nickel-based superalloy is visualized, and the directional coarsening microstructure formation process is analyzed, and the influence of external stress and plastic strain on the γ' phase precipitation evolution is clarified. Thus, a visual simulation method for the γ' phase precipitation evolution organization formation in the nickel-based superalloy under the external stress load is provided.

[0127] A specific implementation example is provided below for the Ni-0.2Al (at.%) alloy, which undergoes γ→γ' solid state transition at the target heat treatment temperature T = 927℃, and the main physical parameters are as follows (see Table 2):

[0128] Table 2 Physical parameter values and units

[0129]

[0130] The specific implementation process of this embodiment is as follows:

[0131] (1) According to the target composition of the nickel-based superalloy, the CALPHAD method is used to obtain the thermal and kinetic information of the γ phase and the γ' phase, including the free energy curve of the two phases, the equilibrium composition and the atomic mobility of each component in the two phases;

[0132] (2) Construct the strain energy term containing the plastic strain, define the stress-free strain generated by the lattice mismatch during the γ→γ' phase transition, and the gradient energy term considering different slip system information;

[0133] (3) Establishes the phase field model, and solves the phase field control equation to obtain the sequence parameter result value at two-phase interface by using the Kim-Kim-Suzuki interface model, and investigates the influence of different forms of external stress load and different plastic strain on the growth of γ' phase precipitation;

[0134] (4) The model and equation established above are programmed by using Fortran language, initial values and periodic boundary conditions are brought in, the program is run, corresponding results are obtained and visual processing is carried out.

[0135] As shown in the drawings, the influence of the external stress on the γ' phase precipitation evolution behavior of the nickel-based single crystal superalloy at the target heat treatment temperature is investigated. Figure 3 Figure 3 (a) is the initial organizational configuration of simulation, and Figure 3 (b) and (c) can be seen that at T=927℃, the influence of the external stress on the γ' phase precipitation evolution organizational type is very obvious. When the lattice mismatch degree between γ / γ' is +0.003, N-type microstructure is generated under the external compression stress of 150MPa, and P-type microstructure is formed under the external tensile stress of 150MPa. Figure 4 (a) and (b) correspond to the plastic strain ε 33 distribution in the system under the external tensile / compression stress, respectively. It can be seen that the larger value of the plastic strain component is mainly distributed in the γ phase channel. It is found through simulation that the plastic strain generated under the external normal stress load makes the γ' phase grow preferentially along a certain direction, which is the main reason for the γ' phase morphology evolution, and the lattice mismatch degree directly determines the evolution type (i.e. N-type and P-type) of the γ' phase.

[0136] As a key structural material, the γ' phase precipitation evolution of the nickel-based superalloy and the creep deformation of the single crystal superalloy will determine the performance and service life of the engine turbine blade. The experimental cost of in-depth understanding of the directional coarsening formation reason and the regulation of the microstructure of the nickel-based single crystal superalloy is high, and when the solid phase transformation is transformed, the interface energy between phases, the strain energy of the system and the plastic deformation in the γ channel are difficult to be characterized by experiments, which has great limitations for investigating the microstructure evolution law of the γ' phase precipitation evolution process of the nickel-based single crystal superalloy. The present application uses the numerical simulation method to study the influence law of the external stress on the microstructure evolution of the γ' phase precipitation evolution process of the nickel-based single crystal superalloy at a certain temperature, which can effectively avoid the limitations of experimental research.

[0137] ​The application can introduce key influencing factors such as interphase interface energy, system strain energy, plastic strain, temperature, stress and equilibrium composition of two phases at target temperature into numerical simulation, can truly reproduce the microstructure morphology of γ' phase evolution during creep deformation, can more accurately simulate the evolution process of microstructure, and can provide reliable information for improving and optimizing the organization regulation of nickel-based superalloy. The method will determine the specific active slip system according to the applied stress state, introduce a group of dislocation density field variables according to the number of slip systems, and facilitate the characterization of dislocation activity originating from a specific slip system when plastic deformation occurs in the γ channel. Thus, the influence of different plastic strains on the γ' phase precipitation and growth process and the influence of different forms of applied stress load on the γ' evolution process can be investigated.

[0138] It should be understood that the above description of specific embodiments of the application is only for the purpose of illustrating the technical route and characteristics of the application, and the purpose is to enable those skilled in the art to understand the content of the application and to implement it, but the application is not limited to the above specific embodiments. Any changes or modifications made within the scope of the claims of the present application should be covered within the protection scope of the present application.

Claims

1. A phase field kinetic method to simulate the evolution of γ' phase precipitation in nickel-based superalloys under applied stress, characterized in that, The method comprises the following steps: S1. According to the target composition of the nickel-based superalloy, the thermal and kinetic information of the γ phase and the γ' phase is obtained by using the CALPHAD method, including the free energy curve, the equilibrium composition and the atomic mobility of each component in the two phases; S2. A strain energy term containing plastic strain is constructed, a stress-free strain caused by lattice mismatch during γ→γ' phase transition is defined, and a gradient energy term considering different slip system information is defined; S3. A phase field model is established, and the Kim-Kim-Suzuki interface model is used to solve the phase field control equation to obtain the order parameter result value at the two-phase interface, and the influence of different forms of external stress load and different plastic strain on the growth of the γ' phase is investigated; Step S3 includes the following contents: The total free energy of the system is expressed as a functional of the field variables, including the local chemical free energy, the gradient energy and the strain energy, that is: wherein, The meaning and units of each symbol are: F represents the total free energy, unit: J / m 3 ; dV is the volume element, unit m 3 ; f(X(r),φ q (r)) is the local chemical free energy density, unit J / m 3 ; κ φ and κ η are the structural field variable and the plastic strain field gradient energy term coefficient, unit J / m; and represent the structural field variable and the plastic strain field variable gradient, unit m -1 ; Based on the Kim-Kim-Suzuki model, the interface satisfies: df γ (X γ (r)) / dX γ (r) = df γ′ (X γ′ (r)) / dX γ′ (r) The evolution of the concentration field with time is controlled by the diffusion equation, usually referred to as the Cahn-Hilliard equation: wherein M c is the chemical mobility, representing the rate of solute diffusion, with units of mol·m 2 / s, and the greater the value, the faster the diffusion. The evolution of the structure and plastic strain order parameter field with time is described by the relaxation equation, usually referred to as the time-dependent Ginzburg-Landau (TDGL) equation or the Allen-Cahn equation: wherein L φ with L η is a kinetic coefficient characterizing the dynamics of the structure and plastic strain relaxation, in m 3 / J / s, the greater of which represents the faster structure relaxation; Chemical mobility is expressed as M c = X Al X Ni (X Al M Ni + X Ni M Al , where: M c is the chemical mobility, in mol·m 2 / sJ; M Al and M Ni are the atomic mobilities of Al and Ni atoms, in mol·m 2 / sJ; X Al and X Ni are the percentages of Al and Ni atoms, in at.%. S4. Visualize the γ' phase precipitation evolution in the nickel-based superalloy, and clarify the influence of external stress and plastic strain on the γ' phase precipitation evolution.

2. The phase field dynamics method of simulating the evolution of the gamma prime phase precipitation in a monocrystalline high temperature alloy under applied stress as recited in claim 1, wherein, Step S1 includes the following contents: The free energy curve expression of the γ and γ' phases in the nickel-based single crystal superalloy at two-phase equilibrium is simplified as: where f γ (X γ (r)) is the Gibbs free energy of the gamma phase, in J / m 3 ; f γ′ (X γ′ (r)) is the Gibbs free energy of the gamma prime phase, in J / m 3 ; f0corresponds to the second derivative of the chemical free energy near the equilibrium composition, in J / mol; V m is the molar volume, in m 3 / mol; X γ (r) and X γ′ (r) are the "virtual" compositions corresponding to the gamma and gamma prime phases, in at.%; the composition (in at.%) at each spatial location is expressed in terms of the "virtual" compositions as follows: X(r) = [1 - h(φ q (r))] X γ (r) + h(φ q (r)) X γ′ (r) where h(φ q (r)) is a difference function: where φ q (r) is the qth structural field variable, q = 1,..., 4, dimensionless; φ q (r) = 0 indicates the γ phase, φ q (r) = 1 indicates the qth ordered γ' phase; System local chemical free energy (in J / m 3 ) is expressed as: f(X(r), φ q (r)) = [1 - h(φ q (r))]f γ (X γ (r)) + h(φ q (r))f γ′ (X γ′ (r)) + ω · g(φ q (r)) Wherein, ω·g(φ q (r) represents the energy barrier between the two phases, and ω is the energy barrier height, in J / m. 3 And g(φ) q (r)) is expressed as: Wherein, p is a subscript different from q; the parameter θ is related to the anti-phase domain boundary energy and has no unit.

3. The phase field dynamics method of simulating the evolution of the γ' phase precipitation in a nickel-base superalloy under applied stress as recited in claim 1, wherein, Step S2 includes the following contents: According to the phase field micro-elastic theory of Khachaturyan, under the stress control boundary condition, the total elastic strain energy of the system is written as: where E el is the elastic strain energy, in J / m 3 ; p and q represent different kinds of γ' variants, V is the total volume of the system, in m 3 ; n is the unit vector along the k vector direction; is the applied stress, in MPa; denotes the shape function, whose Fourier transform is given by p (k); B pq (n) is defined as: where C ijkl is the elastic constant tensor, in GPa; is the stress-free strain or eigenstrain of the pth variant, and Further, the unstressed strain between γ / γ' due to lattice mismatch is defined as: is: where a γ′ with a γ is the equilibrium lattice constant of γ' and γ phases, δ ij is the Kronecker symbol; the dislocation related stress-free strain is characterized by: where b is the Burgers vector, n is the slip plane normal, and η α (r) is the plastic strain field, is the eigen plastic strain of the a-th slip system. Considering the variant, dislocation and external stress, the strain energy term is: wherein is the Fourier transform of the function h(φ q (r)), and is the Fourier transform of the plastic strain η α (r), and where <B hh (n) is the average value of the numerical values along different orientations; in addition, B hh (n) is the average value of the numerical values along different orientations; in addition, where <B hh (n) is the average value of the numerical values along different orientations; in addition, B hh (n) is the Energy term The macroscopic plastic strain of the system is expressed as the work of the external force load under plastic deformation:

4. The phase field dynamics method of simulating the evolution of the γ' phase precipitation in a nickel-base superalloy under applied stress of claim 3, wherein, The integral of the strain energy excludes the k = 0 point,

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