Simulation method for temperature field and phase field coupling of SLM formed nickel-based superalloy

Abstract

The invention relates to the technical field of numerical simulation of additive manufacturing nickel-based superalloy, and discloses a temperature field and phase field coupling simulation method of SLM forming nickel-based superalloy, which comprises the following steps: establishing a three-dimensional model of a forming part and a substrate for processing to obtain a temperature field basic model; simulating an SLM forming process on the temperature field basic model according to preset parameters to obtain temperature field data, and importing the temperature field data into a phase field simulation module to serve as predefined temperature field data; coupling the gamma ' / gamma mismatch degree and temperature correlation data to the basic phase field model to obtain a gamma' phase change model, correcting the gamma 'phase change model in combination with predefined temperature field data, and adding a nucleation model based on a Poisson seed method; and based on the gamma'phase change model and the nucleation model, growth and coarsening behaviors of the gamma 'phase in the SLM material increasing process are obtained, and a simulation report is formed. According to the method, the vacancy of gamma'phase structure evolution of the existing nickel-based superalloy with high (Al + Ti) content under the SLM complex thermal history condition is solved, and important help is provided for regulating and controlling the structure to obtain the required mechanical property.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for additive manufacturing of nickel-based superalloys, and particularly to a simulation method for the coupling of temperature field and phase field in SLM-formed nickel-based superalloys. Background Technology

[0002] Nickel-based superalloys are widely used in the manufacture of hot-end components for advanced aerospace propulsion systems, such as turbine blades, turbine disks, and casings for aero-engines. As the aerospace industry demands increasingly higher thrust and thrust-to-weight ratios from turbine engines, superalloy components are evolving towards higher performance, lighter weight, and more integrated designs. The shapes and structures of these parts are also becoming increasingly complex, such as turbine blades with intricate internal cavity structures. Therefore, there is an urgent need to develop new manufacturing processes that meet the requirements of precision forming and high flexibility. The rapidly developing additive manufacturing technology in recent years has provided a new technological approach for forming complex components. Applying additive manufacturing technology to the manufacture of complex superalloy structural parts will greatly promote the development of aerospace technology.

[0003] Slow-melting liquid chromatography (SLM) technology is widely used to prepare nickel-based superalloys. High (Al+Ti) content nickel-based superalloys (>4.5 wt.%) contain a high volume fraction of γ′ reinforcing phases coherent with the γ matrix, making them suitable for higher-temperature service environments. This has led to increasing attention being paid to the preparation of high (Al+Ti) content nickel-based superalloys using SLM. Currently, by adjusting SLM process parameters or increasing the induction preheating temperature, it is possible to prepare crack-free high (Al+Ti) content nickel-based superalloy deposited samples. Controlling the microstructure of the deposited samples to achieve the desired properties has become a key focus of future research. During the preparation process, rapid molten pool solidification and subsequent repeated heating-cooling thermal cycles (i.e., thermal history) jointly determine the final microstructure of the sample. Among these, the evolution and formation of the γ′ phase, the main reinforcing phase, under complex thermal history conditions has a crucial impact on the mechanical properties of the sample. Therefore, explaining the microstructure evolution process, laws, and mechanisms of high (Al+Ti) content nickel-based superalloys under the complex thermal history conditions of SLM is of great significance for controlling the microstructure to obtain the desired mechanical properties. Summary of the Invention

[0004] To address the shortcomings of existing technologies, such as the tendency for high (Al+Ti) content nickel-based superalloys to develop cracks during additive manufacturing, this invention provides a simulation method for the coupling of temperature field and phase field in SLM-formed nickel-based superalloys. This method fills the gap in current research on the evolution of the γ′ phase microstructure of high (Al+Ti) content nickel-based superalloys under the complex thermal history conditions of SLM, and provides important assistance in controlling the microstructure to obtain the desired mechanical properties.

[0005] This invention provides a simulation method for the coupling of temperature field and phase field in SLM-formed nickel-based superalloys, comprising:

[0006] S1. Establish a three-dimensional model of the molded part and the substrate, and process the three-dimensional model using a preset method to obtain a basic model of the temperature field.

[0007] S2. Simulate the SLM forming process on the temperature field basic model according to the preset parameters to obtain temperature field data that includes temperature changes throughout the process.

[0008] S3. Import the temperature field data into the phase field simulation module as the predefined temperature field data called by the phase field simulation module;

[0009] S4. Couple the γ′ / γ mismatch degree and temperature correlation data to the basic phase field model of the phase field simulation module to obtain the γ′ phase transition model. Combine the predefined temperature field data to correct the γ′ phase transition model, and add a nucleation model based on the Poisson seed method to the corrected γ′ phase transition model.

[0010] S5. Based on the γ′ phase transformation model, nucleation model and associated temperature field data, the growth and coarsening behavior of the γ′ phase during SLM additive manufacturing is obtained, and a simulation report is generated.

[0011] Furthermore, S1 specifically includes:

[0012] S101. Establish a three-dimensional model of the molded part and the substrate using meter as the unified unit of measurement, and input the material properties, absolute zero and Stefan-Boltzmann constant; wherein, the material properties include density, specific heat capacity, thermal conductivity and coefficient of thermal expansion;

[0013] S102. Discretize the three-dimensional model of the molded part and the substrate into regular hexahedral units in the X, Y and Z directions, wherein the dimension in the Z direction is consistent with the single-channel width and the diameter of the heat source laser spot.

[0014] S103. The analysis steps in the additive manufacturing process are set by the birth and death element method and the boundary conditions are set to obtain the basic model of the temperature field; wherein, the boundary conditions include initial temperature, thermal radiation, thermal convection and free surface boundary conditions.

[0015] Furthermore, in S103, setting boundary conditions includes:

[0016] Initial temperature:

[0017] T(x,y,z,t)| t＝0 =T0=298K

[0018] Where T(x,y,z,t) is the temperature at the initial time t=0 and the spatial location (x,y,z);

[0019] Free surface boundary conditions:

[0020]

[0021] Where k is the thermal conductivity of the material; q represents the spatial temperature gradient along the normal direction of the free surface; q represents the heat flux applied by the laser heat source; q c q represents the heat flux corresponding to thermal convection. r This represents the heat flux corresponding to thermal radiation.

[0022] Thermal convection:

[0023] q c =h(T-T0)

[0024] Where h is the convective heat transfer coefficient; T is the real-time temperature of the model surface; and T0 is the ambient temperature.

[0025] Thermal radiation:

[0026] q r =σε(T 4 -T0 4 )

[0027] Where σ is the Stefan-Boltzmann constant; ε is the thermal emissivity of the material.

[0028] Furthermore, S2 specifically includes:

[0029] S201. Set the laser power and scanning speed range for the formed part and the substrate, determine the time step based on the scanning speed and perform pre-simulation, and determine the lower limit of the process parameters according to the forming state of the corresponding position of the first layer by laser scanning, so as to determine the final process parameter range.

[0030] S202. Based on the final process parameter range, revise the key parameters of the double ellipsoidal moving heat source equation. The double ellipsoidal moving heat source equation discretizes the spatial domain into the time domain by establishing the relationship between the position function and time. The key parameters include shape parameters a, b, and c. f c b Effective heat input power q0;

[0031] S203. Combining the dimensions of the hexahedral unit of the temperature field basic model, as well as the material properties of the formed part, the material properties of the substrate, and the thermal properties of the powder material, determine the maximum allowable calculation time step through relevant thermal calculation criteria.

[0032] S204. Combine the revised double ellipsoidal moving heat source equation with the preset scanning strategy, and start the SLM forming process simulation on the temperature field basic model to obtain temperature field data; wherein, the temperature field data includes the full-process temperature change data of each node unit of the model throughout the forming process.

[0033] Furthermore, the equation for the moving heat source on the double ellipsoid is:

[0034] The volumetric heat flux density distribution of the first half of the ellipsoid is as follows:

[0035]

[0036] The volumetric heat flux density distribution of the latter half of the ellipsoid is as follows:

[0037]

[0038] Where, q f (x,y,z) represents the volumetric heat flux density of the first half of the ellipsoid; q b (x, y, z) represents the volumetric heat flux density of the latter half of the ellipsoid; x, y, z are spatial rectangular coordinates; a, b, cf, cb are shape parameters; q0 is the effective heat input power; a is the semi-axis length of the ellipsoid in the x-axis direction; b is the semi-axis length of the ellipsoid in the y-axis direction; c f c is the semi-axis length of the first half of the ellipsoid in the z-axis direction; b This represents the length of the semi-axis of the latter half of the ellipsoid along the z-axis.

[0039] Furthermore, S4 specifically includes:

[0040] S401. Couple the γ′ / γ mismatch degree and temperature correlation data into the basic phase field model of the phase field simulation module to construct a γ′ phase transition model for SLM forming.

[0041] S402. Call the predefined temperature field data and modify the γ′ phase transition model based on the continuous temperature variation characteristics of rapid molten pool solidification and repeated thermal cycling during the SLM process.

[0042] S403. Add a nucleation model based on the Poisson seed method to the modified γ′ phase transition model, set the expected nucleation probability, and use the nucleation rate formula to determine the influence of supercooling and element diffusion on nucleation; wherein, the formula for the expected nucleation probability is:

[0043] P n = 1 - exp(-JΔt(Δx) 3 )

[0044] Among them, P nΔt is the expected nucleation probability; J is the nucleation rate; Δt is the time step; Δx is the mesh size, i.e., the spatial discrete element in the nucleation model calculation;

[0045] The formula for the nucleation rate is:

[0046]

[0047] f(θ)=0.25×(2+cosθ)×(1-cosθ) 2

[0048]

[0049] Δg v =L m ×ΔT / T i

[0050] Where A is the atomic transition frequency factor; The free energy barrier for uniform nucleation; f(θ) is the contact angle correction factor; k is the Boltzmann constant; T is the temperature; N atom The number of atoms at the liquid / solid interface; h is Planck's constant; Q D σ is the activation energy for atomic diffusion; R is the gas constant; θ is the contact angle, representing the wetting properties between the γ′ phase nucleus and the γ matrix; p Δg is the surface energy of the γ′ phase. v The difference in Gibbs free energy per unit volume between the solid and liquid phases; L m ΔT represents the latent heat of fusion of a material, indicating the heat required for the material to melt; ΔT represents the degree of supercooling; T i The value is the melting point of the material.

[0051] Furthermore, in S402, the core governing equation of the modified γ′ phase transition model is the Cahn-Hilliard equation, which describes the concentration field evolution, specifically:

[0052]

[0053] Where c(r,t) is the concentration field sequence parameter used to describe the evolution state of the γ′ phase during the second-order aging process, r is the spatial location, and t is the time; The concentration field sequence parameter is the rate of change over time; M is the mobility coefficient. Here, F is the Laplace operator; F is the total free energy. ξ is the functional derivative of the total free energy with respect to the concentration field order parameter c(r,t); c (r,t) represents the concentration field-related fluctuation term.

[0054] Furthermore, the thermodynamic and kinetic parameters of the modified γ′ phase transition model specifically include:

[0055] Total free energy F:

[0056]

[0057] Where V is the integral volume, i.e., the computational domain volume of the phase-field simulation; f local (r) represents the local free energy density; The spatial gradient of the concentration field sequence parameter; F el For elastic properties;

[0058] The local free energy density is fitted using a double-well polynomial, specifically as follows:

[0059] f local (r)=μ(c(r,t)-c m (T)) 2 (c(r,t)-c p (T)) 2

[0060] Where μ is the free energy fitting parameter; c m c represents the equilibrium concentration of Al atoms in the γ matrix. p The equilibrium concentration of Al atoms in the γ′ phase; T is the temperature;

[0061] Establish the relationship between the gradient term coefficient α and the γ′ / γ interfacial energy;

[0062]

[0063] Where, σ inter γ′ / γ is the γ′ / γ interface energy, which characterizes the energy properties of the interface between the γ′ phase and the γ matrix; α is the gradient term coefficient.

[0064] Furthermore, in the core governing equation, the mobility coefficient M is related to the diffusion coefficient D of Al atoms in the γ matrix, that is:

[0065]

[0066] Where D0 is the diffusion frequency factor; ΔU is the activation energy of atomic diffusion; and k is the Boltzmann constant.

[0067] Furthermore, S5 specifically includes:

[0068] S501. Start the phase field simulation module, call the integrated phase field model formed by the γ′ phase transition model and the nucleation model, and load the predefined temperature field data to ensure that the simulation environment is completely matched with the actual SLM thermal history.

[0069] S502. Solve the Cahn-Hilliard equation and nucleation rate formula through the phase field simulation module, and combine the thermodynamic and kinetic parameters to completely simulate the full-cycle micro-evolution process of the γ′ phase from nucleation initiation, continuous growth to later coarsening during SLM additive manufacturing; wherein, the thermodynamic parameters include free energy and interface energy, and the kinetic parameters include mobility coefficient and diffusion activation energy.

[0070] S503. Extract the core evolutionary features of the γ′ phase from the simulation results, including the nucleation location distribution, morphological changes, size growth curve, volume fraction changes, and coarsening rate of the γ′ phase;

[0071] S504. Based on the predefined temperature field data, analyze the regulation of the thermal environment factors such as temperature gradient, thermal cycle intensity, and cooling rate on the nucleation efficiency, growth rate, and coarsening trend of the γ′ phase, and determine the growth and coarsening dynamics mechanism of the γ′ phase based on the evolution data.

[0072] S505. Organize the evolution law, dynamic characteristics and temperature influence mechanism of the γ′ phase obtained from the simulation analysis to form a complete simulation report.

[0073] The beneficial effects of this invention are as follows:

[0074] This invention establishes a temperature field model for SLM-formed nickel-based superalloys; it also establishes a γ′ phase transformation model for SLM-formed nickel-based superalloys. Combined with finite element analysis (FEM) calculations, this γ′ phase transformation model can simulate the evolution of the γ′ phase microstructure during the SLM process, simulate the influence of temperature gradients during SLM, reveal the precipitation and growth process of the γ′ phase, and explain the growth and coarsening kinetics of the γ′ phase. By determining the molten pool morphology and size corresponding to different process parameters through SLM single-layer forming, and based on single-pass data from actual SLM experiments, the "process parameter-molten pool size" temperature field model is modified. The molten pool temperature field is calculated using finite element software. The correlation between γ′ / γ mismatch and temperature is coupled into the phase field model, modifying the continuously temperature-varying phase field model. To simultaneously simulate grain nucleation and growth, a nucleation model is introduced into the PF model, thus allowing the growth and coarsening of the γ′ phase to be intuitively obtained from the γ′ phase evolution phase field model. Attached Figure Description

[0075] Figure 1 This is a schematic flowchart of the simulation method for temperature field and phase field coupling of SLM-formed nickel-based superalloys according to the present invention.

[0076] Figure 2 This is a schematic diagram of the additive manufacturing model of the nickel-based high-temperature alloy substrate and the formed part in this invention.

[0077] Figure 3 This is a schematic diagram of the additive model mesh generation for the nickel-based high-temperature alloy substrate and the formed part in this invention.

[0078] Figure 4 This is a schematic diagram of the double ellipsoidal laser heat source in this invention.

[0079] Figure 5 The figure shows the simulation results of the additive temperature field of the nickel-based high-temperature alloy substrate and the formed part in this invention.

[0080] Figure 6 The figure shows the simulation calculation results of the γ′ phase in the additive manufacturing process of the nickel-based superalloy in this invention.

[0081] Figure 7 The figure shows the simulation results of the γ′ phase in the additive manufacturing process of nickel-based superalloys under thermal history conditions in this invention.

[0082] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0083] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0084] Nickel-based superalloys with high (Al+Ti) content (>4.5 wt.%) contain a high volume fraction of γ′ reinforcing phases that are coherent with the γ matrix, making them suitable for use in higher temperature service environments. As a result, the preparation of high (Al+Ti) content nickel-based superalloys using SLM is receiving increasing attention.

[0085] The formation and evolution of the γ′ phase during solidification melting (SLM) are extremely complex, influenced by the solidification microstructure, post-solidification cooling rate, and thermal cycling. Currently, studies on the formation and morphology of the γ′ phase in high (Al+Ti) content nickel-based superalloys during SLM solidification, cooling, and thermal cycling are all based on experimental observations, with few reports on the evolution of the γ→γ′ phase. How these factors affect the formation and evolution of the γ′ phase remains unclear and requires further systematic and in-depth research and elucidation. Therefore, this invention establishes a temperature field model for an SLM-formed nickel-based superalloy (composition by mass percentage: 15.79% chromium, 8.25% cobalt, 3.4% aluminum, 3.4% titanium, 2.54% tungsten, 1.77% molybdenum, 1.74% tantalum, 0.11% niobium, 0.11% carbon, with the remainder being nickel); and establishes a γ′ phase transformation model for the SLM-formed nickel-based superalloy. Combined with finite element analysis, this γ′ phase transformation model can simulate the evolution of the γ′ phase microstructure during the SLM process, simulate the influence of the temperature gradient during SLM, reveal the precipitation and growth process of the γ′ phase, and elucidate the growth and coarsening kinetics of the γ′ phase. This invention simulates the precipitation and growth process of the γ′ phase during SLM, providing simulation support for actual printing.

[0086] Calculating the temperature field of nickel-based superalloys requires obtaining the material's thermophysical parameters. Therefore, Jmatpro software is used to calculate these parameters by inputting the material's composition. The table below shows the composition of nickel-based superalloys:

[0087] C Cr Al Ti Mo W Co Nb Ta Si Fe B Ni 0.11 15.79 3.4 3.4 1.77 2.54 8.25 0.11 1.74 0.049 0.078 0.008 Bal.

[0088] like Figure 1 As shown, this invention provides a simulation method for the coupling of temperature field and phase field in SLM-formed nickel-based superalloys, comprising:

[0089] S1. Establish a three-dimensional model of the molded part and the substrate, and process the three-dimensional model using a preset method to obtain a basic temperature field model. Specifically, this includes:

[0090] S101, such as Figure 2 As shown, a three-dimensional model of the molded part and the substrate is established in the finite element software using meter as the uniform unit of measurement. Material property parameters, absolute zero, and Stefan-Boltzmann constant are input. The material property parameters include density, specific heat capacity, thermal conductivity, and coefficient of thermal expansion.

[0091] S102, such as Figure 3 As shown, the three-dimensional model of the molded part and the substrate is discretized into regular hexahedral units in the X, Y and Z directions, wherein the dimension in the Z direction is consistent with the single-channel width and the diameter of the heat source laser spot;

[0092] S103. The analysis steps in the additive manufacturing process are set using the element-birth method, and boundary conditions are defined to obtain a basic temperature field model; wherein, the boundary conditions include initial temperature, thermal radiation, thermal convection, and free surface boundary conditions; specifically,

[0093] Initial temperature:

[0094] T(x,y,z,t)| t＝0 =T0=298K

[0095] Where T(x,y,z,t) is the temperature at the initial time t=0 and the spatial location (x,y,z);

[0096] Free surface boundary conditions:

[0097]

[0098] Where k is the thermal conductivity of the material; q represents the spatial temperature gradient along the normal direction of the free surface; q represents the heat flux applied by the laser heat source; q c q represents the heat flux corresponding to thermal convection. r This represents the heat flux corresponding to thermal radiation.

[0099] Thermal convection:

[0100] q c =h(T-T0)

[0101] Where h is the convective heat transfer coefficient; T is the real-time temperature of the model surface; and T0 is the ambient temperature.

[0102] Thermal radiation:

[0103] q r =σε(T 4 -T0 4 )

[0104] Where σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁶). -8 W / (m 2 ·K 4 ε is the thermal radiation coefficient of the material.

[0105] S2. Simulate the SLM forming process on the temperature field basic model according to preset parameters to obtain temperature field data that includes temperature changes throughout the process. Specifically, this includes:

[0106] S201. Set the laser power and scanning speed range for the formed part and the substrate. Determine the time step based on the scanning speed and perform a pre-simulation. Determine the lower limit of the process parameters according to the forming state of the corresponding position of the first layer of laser scanning (when the surface temperature at this position does not reach the melting point of the material, the corresponding parameter is the selected lower limit of the process parameters) to determine the final process parameter range.

[0107] S202. Based on the final process parameter range, revise the key parameters of the double ellipsoidal moving heat source equation. The double ellipsoidal moving heat source equation discretizes the spatial domain into the time domain by establishing the relationship between the position function and time, and loads the laser heat source to different positions at different times through cyclic loading. The key parameters include shape parameters a, b, and c. f c b Effective heat input power q0; such as Figure 4 As shown, the equation for the moving heat source in a double ellipsoid is:

[0108] The volumetric heat flux density distribution of the first half of the ellipsoid is as follows:

[0109]

[0110] The volumetric heat flux density distribution of the latter half of the ellipsoid is as follows:

[0111]

[0112] Where, q f (x,y,z) represents the volumetric heat flux density of the first half of the ellipsoid; qb (x, y, z) represents the volumetric heat flux density of the latter half of the ellipsoid; x, y, z are spatial rectangular coordinates; a, b, cf, cb are shape parameters; q0 is the effective heat input power; a is the semi-axis length of the ellipsoid in the x-axis direction; b is the semi-axis length of the ellipsoid in the y-axis direction; c f c is the semi-axis length of the first half of the ellipsoid in the z-axis direction; b This represents the length of the semi-axis of the latter half of the ellipsoid along the z-axis.

[0113] S203. Combining the dimensions of the hexahedral units of the aforementioned temperature field basic model, as well as the material properties of the formed part, the material properties of the substrate, and the thermophysical parameters of the powder material, the maximum allowable calculation time step is determined through relevant thermal calculation criteria.

[0114] S204. Combine the revised double-ellipsoidal moving heat source equation with the preset scanning strategy, and start the SLM forming process simulation on the temperature field basic model to obtain temperature field data, such as... Figure 5 As shown; wherein, the temperature field data includes the temperature change data of each node unit of the model throughout the entire forming process.

[0115] S3. Import the temperature field data into the phase field simulation module as the predefined temperature field data called by the phase field simulation module.

[0116] S4. Couple the γ′ / γ mismatch degree and temperature correlation data to the basic phase field model of the phase field simulation module to obtain the γ′ phase transition model. Correct the γ′ phase transition model by combining it with the predefined temperature field data, and add a nucleation model based on the Poisson seed method to the corrected γ′ phase transition model. Specifically, this includes:

[0117] S401. Couple the γ′ / γ mismatch degree and temperature correlation data into the basic phase field model of the phase field simulation module to construct a γ′ phase transition model for SLM forming.

[0118] S402. Using the predefined temperature field data, and based on the continuous temperature variation characteristics of rapid molten pool solidification and repeated thermal cycling during the SLM process, modify the γ′ phase transition model; wherein, the core governing equation of the modified γ′ phase transition model is the Cahn-Hilliard equation, which describes the evolution of the concentration field, specifically:

[0119]

[0120] Where c(r,t) is the concentration field sequence parameter used to describe the evolution state of the γ′ phase during the second-order aging process, r is the spatial location, and t is the time; The concentration field sequence parameter is the rate of change over time; M is the mobility coefficient. Here, F is the Laplace operator; F is the total free energy. ξ is the functional derivative of the total free energy with respect to the concentration field order parameter c(r,t); c (r,t) represents the concentration field-related fluctuation term.

[0121] Phase-field models can simulate the microstructure during temperature variations. This requires correlating parameters with temperature. The mobility coefficient M is related to the diffusion coefficient D of Al atoms in the γ matrix, i.e.:

[0122]

[0123] Where D0 is the diffusion frequency factor; ΔU is the activation energy of atomic diffusion; and k is the Boltzmann constant.

[0124] The thermodynamic and kinetic parameters of the modified γ′ phase transition model specifically include:

[0125] Total free energy F:

[0126]

[0127] Where V is the integral volume, i.e., the computational domain volume of the phase-field simulation; f local (r) represents the local free energy density; The spatial gradient of the concentration field sequence parameter; F el For elastic properties;

[0128] The local free energy density is fitted using a double-well polynomial, specifically as follows:

[0129] f local (r)=μ(c(r,t)-c m (T)) 2 (c(r,t)-c p (T)) 2

[0130] Where μ is the free energy fitting parameter; c m c represents the equilibrium concentration of Al atoms in the γ matrix. p The equilibrium concentration of Al atoms in the γ′ phase; T is the Kelvin temperature;

[0131] Establish the relationship between the gradient term coefficient α and the γ′ / γ interfacial energy;

[0132]

[0133] Where, σ inter γ′ / γ is the γ′ / γ interface energy, which characterizes the energy properties of the interface between the γ′ phase and the γ matrix; α is the gradient term coefficient.

[0134] S403. To simultaneously simulate grain nucleation and growth, a nucleation model based on the Poisson seed method is added to the modified γ′ phase transition model (the Poisson seed method is suitable for simulating stochastic nucleation processes when the time step is much larger than the nucleation timescale, and the probability of nucleus introduction is related to the local nucleation rate J). An expected nucleation probability is set, and the influence of undercooling and element diffusion on nucleation is determined using the nucleation rate formula; the formula for the expected nucleation probability is:

[0135] P n = 1 - exp(-JΔt(Δx) 3 )

[0136] Among them, P n Δt is the expected nucleation probability; J is the nucleation rate; Δt is the time step; Δx is the mesh size, i.e., the spatial discrete element in the nucleation model calculation; only when P n A cell nucleus will only be added to the unit if the number is greater than the random number.

[0137] The formula for the nucleation rate is:

[0138]

[0139] f(θ)=0.25×(2+cosθ)×(1-cosθ) 2

[0140]

[0141] Δg v =L m ×ΔT / T i

[0142] Where A is the atomic transition frequency factor; The free energy barrier for uniform nucleation; f(θ) is the contact angle correction factor; k is the Boltzmann constant; T is the temperature; N atom The number of atoms at the liquid / solid interface; h is Planck's constant; Q D σ is the activation energy for atomic diffusion; R is the gas constant; θ is the contact angle, representing the wetting properties between the γ′ phase nucleus and the γ matrix; p Δg is the surface energy of the γ′ phase. v The difference in Gibbs free energy per unit volume between the solid and liquid phases; L m ΔT represents the latent heat of fusion of a material, indicating the heat required for the material to melt; ΔT represents the degree of supercooling; T i The value is the melting point of the material.

[0143] S5. Based on the γ′ phase transformation model, nucleation model, and associated temperature field data, the growth and coarsening behavior of the γ′ phase during SLM additive manufacturing is obtained, and a simulation report is generated. For example... Figure 6 , 7As shown, it specifically includes:

[0144] S501. Start the phase field simulation module, call the integrated phase field model formed by the γ′ phase transition model and the nucleation model, and load the predefined temperature field data to ensure that the simulation environment is completely matched with the actual SLM thermal history.

[0145] S502. Solve the Cahn-Hilliard equation and nucleation rate formula through the phase field simulation module, and combine the thermodynamic and kinetic parameters to completely simulate the full-cycle micro-evolution process of the γ′ phase from nucleation initiation, continuous growth to later coarsening during SLM additive manufacturing; wherein, the thermodynamic parameters include free energy and interface energy, and the kinetic parameters include mobility coefficient and diffusion activation energy.

[0146] S503. Extract the core evolutionary features of the γ′ phase from the simulation results, including the nucleation location distribution, morphological changes, size growth curve, volume fraction changes, and coarsening rate of the γ′ phase;

[0147] S504. Based on the predefined temperature field data, analyze the regulation of the thermal environment factors such as temperature gradient, thermal cycle intensity, and cooling rate on the nucleation efficiency, growth rate, and coarsening trend of the γ′ phase, and determine the growth and coarsening dynamics mechanism of the γ′ phase based on the evolution data.

[0148] S505. Organize the evolution law, dynamic characteristics and temperature influence mechanism of the γ′ phase obtained from the simulation analysis to form a complete simulation report.

[0149] In summary, the simulation method for temperature field and phase field coupling of SLM-formed nickel-based superalloys provided by this invention is mainly used to address the current gap in the evolution of γ′ phase microstructure in high (Al+Ti) content nickel-based superalloys under complex SLM thermal history conditions, and provides assistance in controlling the microstructure to obtain the desired mechanical properties.

[0150] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0151] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A simulation method of temperature field and phase field coupling of SLM formed nickel-based superalloy, characterized in that, The method comprises the following steps: S1, a three-dimensional model of a shaped part and a substrate is established, and a preset method is used to process the three-dimensional model to obtain a temperature field basic model; S2, the SLM forming process is simulated on the temperature field basic model according to preset parameters to obtain temperature field data containing temperature changes throughout the process; S3, the temperature field data is imported into a phase field simulation module as predefined temperature field data called by the phase field simulation module; S4, the γ' / γ mismatch degree and the temperature correlation data are coupled to the basic phase field model of the phase field simulation module to obtain a γ' phase phase transition model, the γ' phase phase transition model is corrected in combination with the predefined temperature field data, and a nucleation model based on the Poisson seed method is added to the corrected γ' phase phase transition model; S5, based on the γ' phase phase transition model, the nucleation model and the associated temperature field data, the growth and coarsening behavior of the γ' phase in the SLM additive process is obtained, and a simulation report is formed.

2. The method of claim 1, wherein the temperature field and phase field coupling of the SLM formed nickel-based superalloy is simulated by using a finite element method. The S1 specifically comprises: S101, a three-dimensional model of a shaped part and a substrate is established in meter as a unified unit of measurement, material physical property parameters, absolute zero and the Stefan-Boltzmann constant are input; wherein the material physical property parameters include density, specific heat capacity, thermal conductivity and thermal expansion coefficient; S102, the three-dimensional model of the shaped part and the substrate is discretized into hexahedron units according to X, Y and Z directions, wherein the size of Z direction is consistent with the single pass width and the laser spot diameter of the heat source; S103, the analysis step in the additive manufacturing process is set by the live and dead unit method, and the boundary conditions are set to obtain the temperature field basic model; wherein the boundary conditions include initial temperature, heat radiation, heat convection and free surface boundary condition.

3. The simulation method for temperature field and phase field coupling of SLM-formed nickel-based superalloys according to claim 2, characterized in that, In the S103, the boundary conditions include: Initial temperature: T(x, y, z, t) t＝0 = To = 298 K Wherein, T(x, y, z, t) is the temperature at the space position (x, y, z) at the initial time t = 0 of the model; Free surface boundary condition: where k is the thermal conductivity of the material; is the spatial gradient of the temperature in the normal direction of the free surface; q is the heat flux applied by the laser heat source; q c is the heat flux corresponding to the heat conduction; q r is the heat flux corresponding to the heat radiation; Heat convection: q c = h(T - T0) Wherein, h is the heat transfer coefficient; T is the real-time temperature of the model surface; T0 is the environmental temperature; Heat radiation: q r = σ (T 4 - T0 4 ) Wherein, σ is the Stefan-Boltzmann constant; ε is the thermal radiation coefficient of the material.

4. The simulation method for temperature field and phase field coupling of SLM-formed nickel-based superalloys according to claim 3, characterized in that, The S2 specifically comprises: S201, the laser power and scanning speed interval of the shaped part and the substrate are set, the time step is determined based on the scanning speed and pre-simulation is performed, the lower limit of the process parameter is determined according to the forming state of the shaped part at the corresponding position of the first layer of laser scanning, so as to determine the final process parameter range; S202、based on the final process parameter range, revising the key parameters of the double-ellipsoid moving heat source equation, the double-ellipsoid moving heat source equation is used to establish the relationship between the position function and the time, and to disperse the spatial domain to the time domain; wherein, the key parameters include shape parameters a, b, c f 、c b , effective heat input power q0; S203, the maximum allowable calculation time step is determined by relevant thermal calculation criteria in combination with the hexahedron unit size of the temperature field basic model, and the thermal physical property parameters of the shaped part material, the substrate material and the powder material; S204, the revised double-ellipsoid moving heat source equation is combined with the preset scanning strategy to start the SLM forming process simulation on the temperature field basic model to obtain temperature field data; wherein the temperature field data contains the whole process temperature change data of each node unit of the model throughout the forming process.

5. The simulation method for temperature field and phase field coupling of SLM-formed nickel-based superalloys according to claim 4, characterized in that, The double-ellipsoid moving heat source equation is: The body heat flux density distribution of the front half part of the ellipsoid is: The body heat flux density distribution of the rear half part of the ellipsoid is: wherein q f (x,y,z) is the volume heat flux density of the first half ellipsoid; q b (x,y,z) is the volume heat flux density of the second half ellipsoid; x, y, z are the spatial rectangular coordinates; a, b, cf, cb are shape parameters, q0 is the effective heat input power; a is the half-axis length of the ellipsoid in the x-axis direction; b is the half-axis length of the ellipsoid in the y-axis direction; c f is the half-axis length of the first half ellipsoid in the z-axis direction; c b is the half-axis length of the second half ellipsoid in the z-axis direction.

6. The method of claim 5, wherein the temperature field and phase field coupling of the SLM shaped nickel-based superalloy is simulated by, The S4 specifically comprises: S401, coupling the γ' / γ mismatch degree and temperature correlation data into the basic phase field model of the phase field simulation module, constructing a γ' phase phase transition model for SLM forming; S402, calling the pre-defined temperature field data, correcting the γ' phase phase transition model according to the continuous temperature variation characteristics of the rapid molten pool solidification and repeated thermal cycle in the SLM process; S403, adding a nucleation model based on the Poisson seed method to the corrected γ' phase phase transition model, setting an expected nucleation probability, and determining the influence of supercooling and element diffusion on nucleation by using a nucleation rate formula; wherein the expected nucleation probability formula is: P n = 1 - exp(-JΔt(Δx) 3 ) where P n is the expected nucleation probability; J is the nucleation rate; Δt is the time step; Δx is the grid size, i.e. the spatial discretization unit in the nucleation model calculation; The nucleation rate formula is: f(0) = 0.25 x (2 + cos 0) x (1 - cos 0) 2 Δg v = L m x ΔT / T i where A is the atomic jump frequency factor; is the homogeneous nucleation free energy barrier; f(θ) is the contact angle correction factor; k is the Boltzmann constant; T is the temperature; N atom is the number of atoms in the liquid / solid interface; h is the Planck constant; Q D is the activation energy for atomic diffusion; R is the gas constant; θ is the contact angle, which represents the wetting characteristics between the γ' phase nuclei and the γ matrix; σ p is the surface energy of the γ' phase; Δg v is the Gibbs free energy difference per unit volume of solid liquid; L m is the latent heat of fusion of the material, which represents the amount of heat required for the material to melt; ΔT is the undercooling; T i is the melting point of the material.

7. The method of claim 6, wherein the temperature field and phase field coupling of the SLM shaped nickel-based superalloy is simulated by using a finite element method. In the S402, the core control equation of the corrected γ' phase phase transition model is the Cahn-Hilliard equation, which describes the evolution of the concentration field, specifically: where c(r,t) is the concentration field order parameter, which is used to describe the evolution state of γ' phase in the secondary aging process, r is the spatial position, and t is the time; is the rate of change of the concentration field order parameter with time; M is the mobility coefficient; is the Laplace operator; F is the total free energy; is the functional derivative of the total free energy with respect to the concentration field order parameter c(r,t); ξ c (r,t) is the concentration field related fluctuation term.

8. The method of claim 7, wherein the temperature field and phase field coupling of the SLM shaped nickel-based superalloy is simulated by using a finite element method. In the S402, the thermodynamic parameters and kinetic parameters of the corrected γ' phase phase transition model specifically include: Total free energy F: where V is the integral volume, i.e. the volume of the calculation domain of the phase field simulation; f local (r) is the local free energy density; is the spatial gradient of the concentration field order parameter; F el is the elastic energy; The local free energy density is fitted by a double-well polynomial, specifically: f local (r) = μ(c(r, t) - c m (T)) 2 (c(r, t) - c p (T)) 2 wherein μ is a free energy fitting parameter; c m is the equilibrium concentration of Al atoms in the γ matrix; c p is the equilibrium concentration of Al atoms in the γ' phase; T is the temperature; Establish the correlation between the gradient term coefficient α and the γ' / γ interface energy; where σ inter is the γ' / γ interface energy, representing the energy characteristic of the interface between the γ' phase and the γ matrix; and α is the gradient term coefficient.

9. The method of claim 8, wherein the temperature field and phase field coupling of the SLM shaped nickel-based superalloy is simulated by using a finite element method. In the core control equation, the mobility coefficient M is related to the diffusion coefficient D of Al atoms in the γ matrix, that is: Where D0 is the diffusion frequency factor; ΔU is the activation energy of atomic diffusion; k is the Boltzmann constant.

10. The method of claim 8, wherein the temperature field and phase field coupling of the SLM shaped nickel-based superalloy is simulated by, The S5 specifically includes: S501, starting the phase field simulation module, calling the integrated phase field model formed by the γ' phase phase transition model and the nucleation model, and loading the pre-defined temperature field data to ensure that the simulation environment is completely matched with the actual SLM thermal history; S502, solving the Cahn-Hilliard equation and the nucleation rate formula by the phase field simulation module, combining the thermodynamic parameters and kinetic parameters, and completely simulating the whole cycle micro-evolution process of the γ' phase from nucleation initiation, continuous growth to late coarsening in the SLM additive process; wherein the thermodynamic parameters include free energy and interface energy, and the kinetic parameters include mobility coefficient and diffusion activation energy; S503, extracting the core evolution characteristics of the γ' phase from the simulation results, including the nucleation position distribution, morphology change, size growth curve, volume fraction change and coarsening rate of the γ' phase; S504, combining the pre-defined temperature field data, analyzing the regulation of the thermal environmental factors such as temperature gradient, thermal cycle strength and cooling rate on the nucleation efficiency, growth rate and coarsening trend of the γ' phase, and determining the growth and coarsening kinetics mechanism of the γ' phase based on the evolution data; S505, organizing the γ' phase evolution law, kinetic characteristics and temperature influence mechanism obtained from the simulation analysis to form a complete simulation report.

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