Phase field dynamics method for simulating precipitation evolution of gamma'phase in nickel-based superalloy under external stress

Abstract

The invention relates to the field of metallurgical casting, in particular to a phase field dynamics method for simulating precipitation evolution of a gamma'phase in nickel-based superalloy under external stress. The method comprises the following steps: S1, acquiring thermal and dynamic information of a gamma phase and a gamma'phase by adopting a CALPHAD method according to target components of the nickel-based superalloy; s2, constructing a strain energy item containing plastic strain, and defining stress-free strain generated by lattice mismatch during gamma-to-gamma 'phase transformation and a gradient energy item capable of considering different slip system information; s3, establishing a phase field model, solving a phase field control equation at a two-phase interface by adopting a Kim-Kim-Suzuki interface model to obtain a sequence parameter result value, and investigating the influence of different forms of external stress loads and different plastic strains on gamma'phase precipitation growth; and S4, the gamma'phase precipitation evolution structure in the nickel-based high-temperature alloy is subjected to visualization treatment, and the influence rule of the external stress and the plastic strain on gamma 'phase precipitation evolution is clarified.

Description

Technical Field

[0001] The invention relates to the field of metallurgical casting, in particular to a phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high-temperature alloy under external stress. Background Art

[0002] Nickel-based superalloys are key structural materials widely used in aerospace, navigation, energy, and chemical industries. Among them, nickel-based superalloy blades are the core hot-end components of high-end equipment such as aircraft engines, and often face harsh service environments such as high temperature, oxidation, thermal corrosion, and complex stress. Generally, under the action of stress and high temperature for a long time, the cubic γ' phase in nickel-based superalloys usually grows preferentially in a certain direction, which is called directional coarsening. According to the relationship between the external stress and the directional coarsening of the γ' phase, <001> The directional coarsening of the γ' phase in oriented nickel-based superalloys can be divided into two types: N-type and P-type: N-type, the directional coarsening direction of the γ' phase is perpendicular to the direction of the applied stress; P-type, the directional coarsening direction of the γ' phase is parallel to the direction of the applied stress. The directional coarsening of the γ' phase and the creep deformation in nickel-based superalloys will determine the performance and service life of the engine turbine blades, which depends on the creep (temperature, stress) conditions and the microstructure of the alloy (γ' phase size, volume fraction, γ' / γ mismatch, etc.). However, in elastic anisotropy and inhomogeneous systems, the complexity of the closely coupled process of the γ / γ' microstructure evolution and the plastic deformation in the γ channel has brought great difficulties to the research. Therefore, it is of great significance to characterize the evolutionary kinetics of the γ' phase segregation and predict the evolution of the microstructure morphology by means of computational simulation. Summary of the invention

[0003] 1. Technical issues to be resolved

[0004] In order to improve and optimize the microstructure design of nickel-based superalloys, the purpose of the present invention is to provide a phase field dynamics method for simulating the evolution of γ' phase segregation in nickel-based superalloys under external stress. The method can reproduce the γ' phase precipitation growth process in nickel-based single crystal superalloys under external stress, and provide an effective prediction method for the microstructure evolution law of the γ' phase directional coarsening process in nickel-based superalloys.

[0005] (II) Technical solution

[0006] In order to achieve the above object, the main technical solution adopted by the present invention is:

[0007] A phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high temperature alloy under applied stress comprises the following steps:

[0008] S1. According to the target composition of nickel-based high-temperature alloy, the CALPHAD method is used to obtain the thermal and kinetic information of the γ phase and γ' phase, including the free energy curves, equilibrium composition and atomic mobility of each component in the two phases;

[0009] S2, construct the strain energy term including plastic strain, define the stress-free strain caused by lattice mismatch during γ→γ' phase transformation, and the gradient energy term that can consider the information of different slip systems;

[0010] S3. Establish a phase field model, and use the Kim-Kim-Suzuki interface model at the interface between the two phases to solve the phase field control equation to obtain the order parameter result value, and investigate the effects of different forms of applied stress loads and different plastic strains on the precipitation and growth of γ' phase;

[0011] S4. Visualize the microstructure evolution of γ' phase segregation in nickel-based high-temperature alloys to clarify the influence of external stress and plastic strain on the evolution of γ' phase segregation.

[0012] The phase field dynamics method for simulating the evolution of γ' phase segregation in a single crystal high temperature alloy under applied stress, step S1 comprises the following contents:

[0013] The free energy curve expression of the γ and γ' phases in the nickel-based single crystal high-temperature alloy when the two phases are in equilibrium is simplified to:

[0014]

[0015] Among them, f γ (X γ (r)) is the Gibbs free energy of the γ phase, in J / m 3 ;f γ′ (X γ′ (r)) is the Gibbs free energy of the γ' phase, in J / m 3 ; f0 corresponds to the second derivative of chemical free energy near the equilibrium composition, unit J / mol; V m is the molar volume, in m 3 / mol;X γ (r) and X γ′ (r) is the “virtual” component corresponding to γ ​​and γ', in at.%; based on the “virtual” component, the component (in 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] Among them, h(φ q (r)) is the difference function:

[0018]

[0019] Among them, φ q (r) is the qth structural field variable, q = 1,…,4, unitless; φ q (r) = 0 indicates the γ phase, φ q (r) = 1 indicates the qth ordered γ' phase;

[0020] The local chemical free energy of the system (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] Among them, ω·g(φ q (r)) represents the energy barrier between the two phases, ω is the energy barrier height, 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 antiphase domain boundary energy and has no unit.

[0025] The phase field dynamics method for simulating the evolution of γ' phase segregation in single crystal high temperature alloy under external stress, 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, in mol·m 2 / sJ;M Al With M Ni are the atomic mobilities of Al and Ni atoms, in mol·m 2 / sJ;X Al With X Ni They are the atomic percentages of Al and Ni respectively, in at.%.

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

[0027] According to Khachaturyan's phase field microelasticity theory, under stress-controlled boundary conditions, the total elastic strain energy of the system is written as:

[0028]

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

[0030]

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

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

[0033]

[0034] Among them, a γ′ with a γ is the equilibrium lattice constant of γ' and γ phases, δ ij is the Kronecker symbol; the stress-free strain associated with the dislocation is:

[0035]

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

[0037] Taking deformation, dislocation and applied stress into consideration, the strain energy term is:

[0038]

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

[0040]

[0041] Among them, <B hh (n)>with B hh (n) The average of the values ​​along different orientations; in addition,

[0042]

[0043] Energy term represents the plastic deformation work under external load, and the macroscopic plastic strain of the system is expressed as:

[0044]

[0045] The phase field dynamics method for simulating the evolution of γ' phase segregation in single crystal high temperature alloy under external stress, the integral of strain energy excludes the k=0 point,

[0046] The phase field dynamics method for simulating the evolution of γ' phase segregation in a single crystal high temperature alloy under applied stress, step S3 comprises the following contents:

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

[0048]

[0049] in, The meaning and unit of each symbol are: F represents total free energy, unit: J / m 3 ; dV is the volume element, unit is m 3 ; f(X(r),φ q (r)) is the local chemical free energy density, in J / m 3 κ φ With κ η are the coefficients of the structural field variables and the gradient energy term of the plastic strain field, in J / m; and Represents the gradient of structural field variables and plastic strain field variables, in units of 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 over time is governed by the diffusion equation, usually referred to as the Cahn-Hilliard equation:

[0053]

[0054] Among them, M c is the chemical mobility, which characterizes the diffusion rate of the solute, and the unit is mol·m 2 / sJ, the larger the value, the faster the diffusion;

[0055] The temporal evolution of the structural and plastic strain order parameter fields is described by relaxation equations, usually the time-dependent Ginzburg-Landau (TDGL) equations or the Allen-Cahn equations:

[0056]

[0057] Among them, L φ With L η is the dynamic coefficient that characterizes the relaxation of structure and plastic strain, and its unit is m 3 / J / s, the larger the value, the faster the structural relaxation.

[0058] The design idea of ​​the present invention is: considering the limitations of experimental research on characterization and testing, giving full play to the advantages of material computational simulation methods, using the phase field dynamics method on the mesoscopic scale to simulate the evolutionary structure formation process of γ' phase segregation in nickel-based high-temperature alloys under external stress, and clarifying the influence of different plastic strains on the precipitation and growth process of γ' phase and different forms of external stress loads on the directional coarsening process of γ' phase. This simulation method lays a theoretical and methodological foundation for a deep understanding of the formation causes of directional coarsening of γ' phase in nickel-based high-temperature alloys and the regulation of microstructure.

[0059] (III) Beneficial effects

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

[0061] 1. As a key structural material, the directional coarsening of the γ' phase and the creep deformation in the nickel-based high-temperature alloy will determine the performance and service life of the engine turbine blades. The experimental cost of deeply understanding the formation cause of the directional coarsening of the γ' phase of the nickel-based high-temperature alloy and regulating the microstructure is high. In addition, during the solid-state phase transformation, the interface energy between the phases, the system strain energy, and the plastic deformation in the γ channel are difficult to characterize experimentally, which has great limitations in investigating the microstructural evolution law of the γ' phase precipitation evolution process of the nickel-based high-temperature alloy. The present invention uses a numerical simulation method to study the influence of external stress on the microstructural evolution of the directional coarsening process of the γ' phase in the nickel-based high-temperature alloy at a certain temperature, which can effectively avoid the limitations of experimental research.

[0062] 2. The present invention can introduce key influencing factors such as interphase interface energy, system strain energy, plastic strain, temperature, stress and equilibrium composition of the two phases at the target temperature into the numerical simulation, which can truly reproduce the microstructural morphology of directional coarsening of the γ' phase during creep deformation, and more accurately simulate the evolution of the microstructure, providing reliable information for improving and optimizing the organizational regulation of nickel-based high-temperature alloys. This method will identify the specific activatable slip system based on the external stress state, and introduce a set of dislocation density field variables according to the number of slip systems. When plastic deformation occurs in the γ channel, it is convenient to characterize the dislocation activity originating from a specific slip system, and can focus on the influence of different plastic strains on the precipitation and growth process of the γ' phase and different forms of external stress loads on the directional coarsening process of γ'. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 A specific flow chart for establishing the numerical model program in the present invention.

[0064] Figure 2 It is the Gibbs free energy curve of γ and γ' phases in the nickel-based high-temperature alloy in the specific embodiment of the present invention.

[0065] Figure 3 In the specific embodiment of the present invention, at a temperature of 927°C, t=10 4 The result diagram of the effect of applied tensile / compressive stress on the microstructure morphology of γ' phase in nickel-based single crystal high-temperature alloy at time step ; where (a) is the simulated initial configuration; (b) and (c) are the microstructure morphologies of γ' phase under external compressive and tensile stresses, respectively.

[0066] Figure 4 For t = 10 4 Plastic strain ε in the microstructure of γ' phase directional coarsening of nickel-based single crystal superalloy under external compressive stress (a) and tensile stress (b) at time step 33 Distribution map of .

[0067] Figure 5Flowchart of the phase field dynamics method for simulating the evolution process of γ' phase precipitation in nickel-based single crystal high-temperature alloy. DETAILED DESCRIPTION

[0068] like Figure 1 As shown in the figure, the specific process of establishing the numerical model program is as follows: the initial conditions include the initial composition X of the Al element n (Al), initial configuration φ n The Gibbs free energy f(X(r),φ) of the two phases γ and γ' at the target temperature is obtained by thermodynamic calculation. q (r)), considering the strain energy E of mismatch strain and plastic strain el , fitting the total free energy F; on the one hand, through the chemical free energy variation of the components The semi-implicit Fourier spectral method is used to solve the component control equation: the Cahn-Hilliard equation. The initial component X n Update to the component field variable X n+1 On the other hand, the free energy is used to calculate the variation of the structural field variables The semi-implicit Fourier spectral method is used to solve the structural control equation: the Allen-Cahn equation. n Updated to the structural field variable φ n+1 . Thus, the evolution process of directional coarsening organization is simulated.

[0069] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation methods.

[0070] Example

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

[0072] (1) Thermodynamics and equilibrium components

[0073] Firstly, according to the phase transition temperature of Ni-0.2Al alloy, the Gibbs free energy data of γ and γ' phases at the target temperature are obtained by thermodynamic calculation, and the free energy curve of the two phases in equilibrium is simplified ( Figure 2 ).

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

[0075]

[0076] Where f0 corresponds to the second derivative of chemical free energy near the equilibrium composition, in J / mol. m is the molar volume, in m 3 / mol.X γ (r) and X γ′ (r) is the “virtual” component corresponding to γ ​​and γ', in at.%. is the equilibrium composition of Al in the γ phase at the simulation temperature, in at.%. is the equilibrium composition of Al in the γ' phase at the simulated temperature, in at.%. Based on the "virtual" composition, the composition (in at.%) at each position in space is expressed as:

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

[0078] Among them, h(φ q (r)) is the difference function:

[0079]

[0080] φ q (r) is the qth structural field variable, q = 1,…,4, unitless. φ q (r) = 0 indicates the γ phase, φ q (r) = 1 indicates the qth 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] Among them, ω·g(φ q (r)) represents the energy barrier between the two phases, ω is the energy barrier height, unit J / m 3 . And g(φ q (r)) is expressed as:

[0084]

[0085] Wherein, p is a subscript different from q, p,q = 1, ..., 4. The parameter θ is related to the antiphase domain boundary energy and has no unit.

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

[0087] Table 1 Balanced composition of alloy elements in two phases at target heat treatment temperature

[0088]

[0089] In terms of 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 With M Ni are the atomic mobility of Al and Ni atoms, in mol·m 2 / sJ;X Al With X Ni They are the atomic percentages of Al and Ni respectively, in at.%.

[0090] (2) Construction of strain energy terms including plastic strain

[0091] According to Khachaturyan's phase field microelasticity theory, under stress-controlled boundary conditions, the total elastic strain energy E of the system is el (Unit J / m 3 ) can be written as:

[0092]

[0093] Here p and q represent different types of γ' variants, and V is the total volume of the system in m 3 d is the differential operation, unitless. k is the reciprocal lattice vector, unit m -1 θ p (k) is the shape function and has no units. is the conjugate of the shape function and has no units. n is the unit vector along the direction of the k vector. is the applied stress, unit: MPa. is the stress-free strain of variant p and has no units. represents the shape function θ p (k) is the Fourier transform form. B pq (n) is defined as:

[0094]

[0095] Here C ijkl is the elastic constant tensor, unit is 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 units m -1 ;n l is the lth component of the unit vector n, with units m -1 ; is the stress-free strain or eigenstrain of the pth variant and has no units. is the stress-free strain or eigenstrain of the qth variant and has no units. i is the i-th component of the unit vector n, with units m -1 . is the phase transition stress corresponding to the pth variant, in GPa. Ω jk (n) is the Green's function, unit is m 2 / GPa. is the phase transition stress corresponding to the qth variant, in GPa.

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

[0097]

[0098] Among them, a γ′ with a γ is the equilibrium lattice constant of γ' and γ phases, δ ij is the Kronecker symbol. is the mismatch between γ / γ', unitless. Characterizes the stress-free strain associated with the dislocation (unitless) is:

[0099]

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

[0101] Taking deformation, dislocation and applied stress into consideration, the strain energy term is:

[0102]

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

[0104]

[0105] It is the stress-free strain due to lattice mismatch and has no units. Also the stress-free strain due to lattice mismatch, unitless. i is the i-th component of the unit vector n, with units m -1 . It is the stress caused by lattice mismatch, unit is GPa. Ω jk (n) is the Green's function, unit is m 2 / GPa. It is the stress caused by lattice mismatch, in GPa. l is the i-th component of the unit vector n, with units m -1 . is the stress corresponding to the αth slip system, in GPa. <B hh (n)>with B hh (n) The average of the values ​​along different orientations. In addition,

[0106]

[0107] is the two-body interaction potential, unit: GPa. is the plastic strain corresponding to the αth slip system and has no units. is the plastic strain corresponding to the βth slip system and has no units. is the plastic stress corresponding to the αth slip system, in GPa. is the plastic stress corresponding to the β slip system, in GPa.

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

[0109]

[0110] η α(r) is the plastic strain corresponding to the αth slip system and has no units.

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

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

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

[0114]

[0115] in, The meaning and unit of each symbol are: F represents total free energy, unit: J / m 3 dV is the volume element, unit is m 3 f(X(r),φ q (r)) is the local chemical free energy density, in J / m 3 κ φ With κ η They are the structural field variables and the plastic strain field gradient energy term coefficients, respectively, in J / m. and Represents the gradient of structural field variables and plastic strain field variables, in units of m -1 φ q is the qth structural field variable, unitless; η α is the plastic strain field corresponding to the αth slip system, unitless; n α is the unit normal vector of the slip plane of the αth slip system, with 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 over time is governed by the diffusion equation, usually referred to as the Cahn-Hilliard equation:

[0119]

[0120] M c is the chemical mobility, which characterizes the diffusion rate of the solute, and the unit is mol·m2 / sJ, the larger the value, the faster the diffusion. δF is the variational operation on the total free energy F, and δc(r) is the variational operation on the total component c(r).

[0121] The temporal evolution of the structural and plastic strain order parameter fields is described by relaxation equations, usually the time-dependent Ginzburg-Landau (TDGL) equations or the Allen-Cahn equations:

[0122]

[0123] L φ With L η is the dynamic coefficient that characterizes the relaxation of structure and plastic strain, and its unit is m 3 / J / s, the larger the value, the faster the structural relaxation.

[0124] (4) Result output

[0125] Mainly, the control equations of the structural field and the concentration field are solved based on the semi-implicit Fourier spectrum method according to the phase field model and its calculation parameters. The embodiment of the present invention uses Fortran language to write a program that describes the effects of interface energy, strain energy, external stress and plastic strain on the evolution of γ' phase separation in nickel-based single crystal high-temperature alloys at a certain temperature, and then converts the order parameter evolution results output by the program into a more intuitive image form using visualization software, thereby achieving the purpose of visualizing the solid-state phase change process in nickel-based high-temperature alloys.

[0126] like Figure 5As shown in Figure 1, the phase field dynamics method for simulating the evolution of γ' phase segregation in nickel-based high-temperature alloys is as follows: First, according to the target composition of the nickel-based high-temperature alloy, the CALPHAD method is used to obtain the thermal and kinetic information of the γ phase and γ' phase, calculate the equilibrium composition of the alloy elements, the simplified free energy curves of the γ phase and γ' phase, the atomic mobility of each component in the γ phase and γ' phase, summarize the slip system activation under external stress, etc., collect the single-phase Gibbs free energy data of the titanium alloy system and the equilibrium composition of each alloy element; then, define the stress-free strain caused by the lattice mismatch when the γ→γ' phase transformation occurs, construct the strain energy term containing the plastic strain, and the gradient energy term that can consider the information of different slip systems; then, establish the phase field dynamics method. Mechanical model, various physical parameters, boundary conditions and other conditions are input into the model, and the phase field control equations, namely Cahn-Hilliard and Allen-Cahn equations, are solved with the help of semi-implicit Fourier spectrum method; and the Kim-Kim-Suzuki interface model is used at the interface between the two phases to solve the phase field control equations to obtain the order parameter result value, and the influence of different forms of external stress loads and different plastic strains on the precipitation and growth of γ' phase is investigated; finally, the output results and composition field variables are visualized, the evolutionary structure of γ' phase segregation in nickel-based high-temperature alloys is visualized, and the formation process of directional coarsening microstructure is analyzed to clarify the influence of external stress and plastic strain on the evolution of γ' phase segregation. Thus, a visual simulation method is provided for the formation of γ' phase segregation evolutionary structure in nickel-based high-temperature alloys under external stress loads.

[0127] A specific implementation example is provided below. For Ni-0.2Al (at.%) alloy, a γ→γ' solid-state transformation occurs at the target heat treatment temperature T=927°C. The main physical property parameters are as follows (see Table 2):

[0128] Table 2 Physical property parameters and units

[0129]

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

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

[0132] (2) Construct the strain energy term including plastic strain, define the stress-free strain caused by lattice mismatch during γ→γ' phase transformation, and the gradient energy term that can consider the information of different slip systems;

[0133] (3) A phase field model is established, and the Kim-Kim-Suzuki interface model is used to solve the phase field control equation at the interface between the two phases to obtain the result value of the order parameter, and the effects of different forms of applied stress loads and different plastic strains on the precipitation and growth of the γ' phase are investigated;

[0134] (4) Use Fortran language to program the model and equations established above, input initial values ​​and periodic boundary conditions, run the program, obtain the corresponding results and perform visualization.

[0135] like Figure 3 As shown in Figure 2, at the target heat treatment temperature, the influence of applied stress on the evolution behavior of γ' phase separation in Ni-based single crystal high-temperature alloy was investigated. Figure 3 (a) is the initial organizational structure of the simulation, Figure 3 (b) and (c) show that at T = 927 ° C, the effect of applied stress on the evolution of the microstructure type of γ' phase separation is very obvious. When the lattice mismatch between γ / γ' is +0.003, an N-type microstructure is produced when the external compressive stress is 150 MPa, while a P-type microstructure is formed when the external tensile stress is 150 MPa. Figure 4 (a) and (b) correspond to the plastic strain ε in the system under external tensile / compressive stress, respectively. 33 Distribution, it can be seen that the larger value of the plastic strain component is mainly distributed in the γ phase channel. Through simulation, it is found that the plastic strain generated under the external positive stress load makes the γ' phase preferentially grow along a specific direction, which is the main reason for the evolution of the γ' phase morphology, and the lattice mismatch directly determines its precipitation evolution type (i.e., N-type and P-type).

[0136] Nickel-based high-temperature alloys are key structural materials. The precipitation evolution of the γ' phase and the creep deformation in single-crystal high-temperature alloys will determine the performance and service life of engine turbine blades. The experimental cost of deeply understanding the causes of directional coarsening of nickel-based single-crystal high-temperature alloys and regulating microstructures is high. In addition, during solid-state phase transformation, the interface energy between phases, system strain energy, and plastic deformation in the γ channel are difficult to characterize experimentally, which has great limitations in investigating the microstructural evolution law of the precipitation evolution process of nickel-based single-crystal high-temperature alloys. The present invention uses a numerical simulation method to study the influence of applied stress on the microstructural evolution of the γ' phase precipitation evolution process in nickel-based single-crystal high-temperature alloys at a certain temperature, which can effectively avoid the limitations of experimental research.

[0137] The present invention can introduce key influencing factors such as interphase interface energy, system strain energy, plastic strain, temperature, stress and equilibrium composition of the two phases at the target temperature into the numerical simulation, can truly reproduce the microstructural morphology of the γ' phase evolution during creep deformation, and more accurately simulate the evolution process of the microstructure, providing reliable information for improving and optimizing the organizational regulation of nickel-based high-temperature alloys. This method will identify the specific activatable slip system based on the external stress state, and introduce a set of dislocation density field variables according to the number of slip systems. When plastic deformation occurs in the γ channel, it is convenient to characterize the dislocation activity originating from a specific slip system. Therefore, it is possible to focus on the influence of different plastic strains on the precipitation and growth process of the γ' phase and the influence of different forms of external stress loads on the γ' evolution process.

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

Claims

1. A phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high temperature alloy under applied stress, characterized in that: The following steps are involved: S1. According to the target composition of nickel-based high-temperature alloy, the CALPHAD method is used to obtain the thermal and kinetic information of the γ phase and γ' phase, including the free energy curves, equilibrium composition and atomic mobility of each component in the two phases; S2, construct the strain energy term including plastic strain, define the stress-free strain caused by lattice mismatch during γ→γ' phase transformation, and the gradient energy term that can consider the information of different slip systems; S3. Establish a phase field model, and use the Kim-Kim-Suzuki interface model at the interface between the two phases to solve the phase field control equation to obtain the order parameter result value, and investigate the effects of different forms of applied stress loads and different plastic strains on the precipitation and growth of γ' phase; S4. Visualize the microstructure evolution of γ' phase segregation in nickel-based high-temperature alloys to clarify the influence of external stress and plastic strain on the evolution of γ' phase segregation.

2. The phase field dynamics method for simulating the evolution of γ' phase separation in a single crystal high temperature alloy under applied stress according to claim 1, characterized in that: Step S1 includes the following contents: The free energy curve expression of the γ and γ' phases in the nickel-based single crystal high-temperature alloy when the two phases are in equilibrium is simplified to: Among them, f γ (X γ (r)) is the Gibbs free energy of the γ phase, in J / m 3 ;f γ′ (X γ′ (r)) is the Gibbs free energy of the γ' phase, in J / m 3 ; f0 corresponds to the second derivative of chemical free energy near the equilibrium composition, unit J / mol; V m is the molar volume, in m 3 / mol;X γ (r) and X γ′ (r) is the "virtual" component corresponding to γ ​​and γ', unit at.%; based on the "virtual" component, the component (unit at.%) at each position in space is expressed as: X(r)=[1-h(φ q (r))]X γ (r)+h(φ q (r))X γ′ (r) Among them, h(φ q (r)) is the difference function: Among them, φ q (r) is the qth structural field variable, q = 1,…,4, unitless; φ q (r) = 0 indicates the γ phase, φ q (r) = 1 indicates the qth ordered γ' phase; The local chemical free energy of the system (unit: 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)) Among them, ω·g(φ q (r)) represents the energy barrier between the two phases, ω is the energy barrier height, unit J / m 3 ; and g(φ q (r)) is expressed as: Where p is a subscript different from q; the parameter θ is related to the antiphase domain boundary energy and has no unit.

3. The phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high temperature alloy under applied stress according to claim 2, characterized in that: Chemical mobility is expressed as M c =X Al X Ni (X Al M Ni +X Ni M Al ), where Mc is the chemical mobility, in mol·m 2 / sJ;M Al With M Ni are the atomic mobility of Al and Ni atoms, in mol·m 2 / sJ;X Al With X Ni They are the atomic percentages of Al and Ni respectively, in at.%.

4. The phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high temperature alloy under applied stress according to claim 1, characterized in that: Step S2 includes the following contents: According to Khachaturyan's phase field microelasticity theory, under stress-controlled boundary conditions, the total elastic strain energy of the system is written as: Among them, E el is the elastic strain energy, in J / m 3 ; p and q represent different types of γ' variants, V is the total volume of the system, unit is m 3 ; n is the unit vector along the direction of k vector; is the applied stress, unit: MPa; represents the shape function, whose Fourier transform is θ p (k); B pq (n) is defined as: Among them, C ijkl is the elastic constant tensor, unit GPa; is the stress-free strain or eigenstrain of the pth variant, and In addition, the stress-free strain due to lattice mismatch between γ / γ' is defined as for: Among them, a γ′ with a γ is the equilibrium lattice constant of γ' and γ phases, δ ij is the Kronecker symbol; the stress-free strain associated with the dislocation is: Where b is the Burgers vector, n is the normal vector of the sliding surface, and η α (r) is the plastic strain field, is the intrinsic plastic strain of the αth slip system; Taking deformation, dislocation and applied stress into consideration, the strain energy term is: in, is the function h(φ q (r)) in Fourier transform form, is the plastic strain η α (r) is the Fourier transform form, and: Among them, <B hh (n)>with B hh (n) The average of the values ​​along different orientations; in addition, Energy term represents the plastic deformation work under external load, and the macroscopic plastic strain of the system is expressed as:

5. The phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high-temperature alloy under applied stress according to claim 4, characterized in that: The integral of strain energy excludes the point k = 0, 6. The phase field dynamics method for simulating the evolution of γ' phase segregation in a nickel-based high temperature alloy under applied stress according to claim 1, characterized in that: Step S3 includes the following contents: The total free energy of the system is expressed as a functional of field variables, including local chemical free energy, gradient energy and strain energy, that is: in, The meaning and unit of each symbol are: F represents total free energy, unit: J / m 3 ; dV is the volume element, unit is m 3 ; f(X(r),φ q (r)) is the local chemical free energy density, in J / m 3 κ φ With κ η are the coefficients of the structural field variables and the gradient energy term of the plastic strain field, in J / m; and Represents the gradient of structural field variables and plastic strain field variables, in units of 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 over time is governed by the diffusion equation, usually referred to as the Cahn-Hilliard equation: Among them, M c is the chemical mobility, which characterizes the diffusion rate of the solute, and the unit is mol·m 2 / sJ, the larger the value, the faster the diffusion; The temporal evolution of the structural and plastic strain order parameter fields is described by relaxation equations, usually the time-dependent Ginzburg-Landau (TDGL) equations or the Allen-Cahn equations: Among them, L φ With L η is the dynamic coefficient that characterizes the relaxation of structure and plastic strain, and its unit is m 3 / J / s, the larger the value, the faster the structural relaxation.

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