A selective laser melting temperature field simulation and phase field coupling simulation method

Abstract

This invention provides a method for simulating the temperature field and phase-field coupling of selective laser melting (SLM), comprising the following steps: constructing a geometric model of a randomly stacked powder bed based on the discrete element method (DEM); establishing a heat transfer-fluid flow model to simulate the macroscopic temperature distribution of the molten pool; extracting the temperature gradient and cooling rate at the molten pool boundary, and using these as inputs to a finite interface dissipative phase-field model to simulate the non-equilibrium solidification microstructure evolution of the molten pool microregion during SLM. This method constructs a refined SLM powder bed geometric model based on the discrete element method, establishes an accurate heat transfer-fluid flow model to simulate the macroscopic temperature distribution of the molten pool, extracts the temperature gradient and cooling rate at the molten pool boundary and inputs them into the finite interface dissipative phase-field model to simulate the non-equilibrium solidification microstructure evolution of the molten pool microregion during SLM, and establishes a quantitative relationship between process parameters and microstructure.

Description

Technical Field

[0001] This invention relates to the field of SLM temperature field and phase field simulation, and specifically to a method for fine-selective laser melting temperature field simulation and phase field coupling simulation. Background Technology

[0002] SLM (Solid Molding Laminate) is an advanced manufacturing method that uses lasers to melt and solidify powder layer by layer to print parts, aided by computer. However, SLM technology still faces many challenges, including uncertain process parameters, excessive defects in printed parts, and microstructural and chemical inhomogeneities. Establishing the relationship between composition, process parameters, microstructure, and properties is crucial for manufacturing parts with excellent overall performance. However, SLM involves numerous process parameters, leading to long experimental research cycles and high costs. With the development of computational materials science in recent years, researchers can use computer numerical simulations to study the relationship between process parameters and microstructure, thereby narrowing down the range of process parameters and guiding experiments.

[0003] The temperature field distribution within the molten pool has a crucial impact on the microstructure of solidification. Currently, in simulating the microstructure of the SLM process, researchers simplify geometric or temperature field models to simulate the temperature field, obtaining insufficiently accurate temperature data which is then input into phase-field simulations to study microstructure evolution, thus yielding inaccurate molten pool microstructure results. This invention aims to accurately predict the microstructure within the molten pool by constructing a refined powder bed geometric model and establishing an accurate heat transfer-fluid flow model to simulate the macroscopic temperature field distribution of the molten pool. Accurate temperature gradients and cooling rates are extracted and input into a finite-interface dissipative phase-field model to predict the microstructure evolution of microregions within the molten pool. A multi-scale quantitative relationship between process parameters and microstructure is established to predict the range of SLM process parameters for specific material systems.

[0004] Weak coupling of the temperature field solved by the finite element method with a finite interface dissipation phase field model (Karayagiz K, Johnson L, Seede R, et al. Finite interface dissipation phase field modeling of Ni-Nb under additive manufacturing conditions[J]. Acta Materialia, 2020, 185:320-339.) quantitatively simulated the microstructure evolution of NiNb alloy during laser powder bed melting and solidification. This work obtained solidification microstructure diagrams with temperature gradient and cooling rate as variables through extensive simulations. However, the temperature field simulation was very simplified. First, the powder bed geometry model was a cuboid, without considering randomly stacked powder bed geometry; second, only the heat transfer equation was solved, without considering the influence of melt flow on the temperature field. Therefore, the simulated temperature field data was not accurate enough, affecting the accuracy of subsequent phase field simulation results. Summary of the Invention

[0005] The purpose of this invention is to construct a fine powder bed geometric model and an accurate heat transfer-fluid flow model, establish an accurate heat transfer-fluid flow model to simulate the macroscopic temperature field distribution of the molten pool, and extract accurate temperature field data (temperature gradient and cooling rate) and input them into the finite interface dissipative phase field model to predict the microstructure evolution of the molten pool microregion.

[0006] The temperature distribution within the molten pool was studied, and the temperature gradient and cooling rate were extracted and input into FIDPFM to investigate the evolution of the microstructure in the micro-regions of the molten pool and establish a quantitative relationship between process parameters and microstructure.

[0007] The present invention is achieved by at least one of the following technical solutions.

[0008] A method for simulating the temperature field and phase-field coupling of laser melting in a finely selected area includes the following steps:

[0009] (1) Construct a geometric model of randomly stacked powder bed for selected laser melting based on the discrete element method;

[0010] (2) Establish a heat transfer-fluid flow model to simulate the macroscopic temperature distribution of the molten pool;

[0011] (3) Extract the temperature gradient and cooling rate of the molten pool boundary, and use the temperature gradient and cooling rate as inputs to the finite interface dissipative phase field model to simulate the evolution of non-equilibrium solidification structure in the micro-region of the molten pool during the selected area laser melting process.

[0012] Furthermore, the heat transfer model considers laser heating, convection, radiation, and thermal evaporation heat transfer mechanisms, and the fluid flow model adopts the Navier-Stokes equations, using the fluid volume method to track the free surface.

[0013] Furthermore, in the geometric model of the randomly stacked powder bed, the powder quantity and particle size distribution are set according to the actual working conditions.

[0014] Furthermore, the particle size of the powder follows a normal distribution and ranges from 20 to 50 μm.

[0015] Furthermore, the heat transfer-fluid flow model is as follows:

[0016]

[0017]

[0018]

[0019] Where ρ is density and t is time. For divergence operators, Indicates mass flow rate. Here, U is the gradient operator, and U is the velocity vector. The velocity of a fluid is expressed as a function of the convection of space, where μ is the viscosity. This represents the effect of viscous force on the velocity field, where P is the pressure vector. The force C represents the effect of pressure on the velocity field, f represents the external force, and C represents the force applied by the external force. P Here, T is the specific heat, k is the temperature, and k is the thermal conductivity. This represents the rate of change of temperature through conduction in space, where Q is the heat source term.

[0020] Furthermore, the heat source term includes the laser heat source q. beam Thermal radiation q rad Heat convection q conv and heat evaporation q vap The expression is as follows:

[0021] Q = q beam -q rad -q conv -q vap

[0022]

[0023] q rad =ε r σ B (T 4 -T amb 4 )

[0024] qconv =h(TT) amb )

[0025]

[0026] Where a is the absorption rate, P l r is the laser power. l Let r be the laser radius, r be the spatial position, r0 be the laser center point, and ε be the laser radius. r For emissivity, σ B T is the Stenfan-Blotzmann constant. am Where L is the ambient temperature, h is the convective heat transfer coefficient, and L is the tidal temperature. v For latent heat of vaporization, X i P represents the atomic percentage of element i. i (T) represents the voltage divider of element i, MW i Let n be the molar mass of element i, and n be the total number of elements.

[0027] Furthermore, the free surface is tracked using the fluid volume method, as shown in the following formula:

[0028]

[0029] Where F is the volume fraction of the material in the calculation unit. Indicates mass flow rate. Here, is the divergence operator, and U is the velocity vector.

[0030] Furthermore, FIDPFM describes the non-equilibrium solidification process in SLM, and its phase field evolution equation and concentration field evolution equation are as follows:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] in, For phase field value, It is a liquid phase. It is a solid phase, while at the interface... It varies continuously between 0 and 1; K is the kinetic coefficient; σ is the interfacial energy coefficient; η is the interfacial width; Δg phi Indicates the driving force of phase transition; c s It is the solid phase concentration, c l It is the concentration in the liquid phase; D sIt is the solid-phase diffusion coefficient, D l is the liquid-phase diffusion coefficient; P is the interfacial permeability, which describes the transport rate of solute at the phase interface. When P approaches infinity, the phase-field model reverts to the traditional equilibrium phase-field model where the chemical potentials of the two phases are equal. When P approaches 0, the solute exchange process between the two phases is suppressed, and the kinetic coefficient K approaches 0, thus stopping the phase transition; M is the interfacial mobility, f l It is the Gibbs free energy of the liquid phase, f s It is the solid-phase Gibbs free energy; Represents the liquid phase chemical potential. Represents the chemical potential of a solid phase;

[0037] f l and f s The formula is as follows:

[0038]

[0039]

[0040] Where R is the gas constant, T is the temperature, and V is the gas constant. m For molar volume, and These are the molar Gibbs free energies of element i in the liquid and solid phases, respectively. and These are the molar Gibbs free energies of another element j in the liquid and solid phases, respectively, which are temperature-dependent and obtained from thermodynamic data. l and I s These are the interaction coefficients in the liquid and solid phases, respectively.

[0041] Furthermore, the heat transfer-fluid flow model is solved using the finite difference method, and the calculation results are output and visualized to obtain macroscopic temperature field distribution data of the molten pool. Based on the temperature field data, the temperature gradient and cooling rate are extracted.

[0042] Furthermore, the coupling between the temperature field and the phase field is achieved through the following formula:

[0043] T PF =T0+Gx PF -R c t PF

[0044] Among them, T PF Let T0 be the initial temperature of the phase field simulation domain, G be the temperature gradient, and R be the initial temperature of the phase field simulation domain. c x is the cooling rate. PF Let t be the distance along the x-axis of the phase field simulation domain. PF Phase field simulation time

[0045] Compared with existing technologies, the beneficial effects of the present invention are as follows:

[0046] (1) This method obtains the precise temperature distribution in the molten pool by constructing a fine powder bed geometric model and an accurate heat transfer-fluid flow model, extracts the temperature gradient and cooling rate and inputs them into FIDPFM, simulates the evolution of solidification microstructure, and establishes a quantitative relationship between process parameters and microstructure across scales.

[0047] (2) The fine-selective laser melting temperature field simulation and phase-field coupling simulation method proposed in this invention has universality and can be applied to the heat transfer-fluid flow simulation of rapid solidification of various alloy SLMs based on the corresponding material physical parameters. At the same time, it can couple the thermodynamic and kinetic data of the corresponding materials to the microstructure evolution simulation of rapid solidification of various alloy SLMs. Attached Figure Description

[0048] Figure 1 This is a detailed geometric model diagram of the powder bed according to an embodiment of the present invention;

[0049] Figure 2 The diagram shows the differences in molten pool morphology, size, and temperature distribution between the powder bed model and the powder bed model in this embodiment of the invention.

[0050] Figure 3 The diagram shows the temperature distribution along the x-axis and the temperature evolution over time for the powder bed model and the powder bed model without a powder bed in this embodiment of the invention.

[0051] Figure 4 This is a graph showing the temperature distribution along the x-axis at different heights of the molten pool boundary in an embodiment of the present invention, and the temperature evolution at the center point of the line over time.

[0052] Figure 5 This is a solidification microstructure diagram of a micro-region within the molten pool according to an embodiment of the present invention. Detailed Implementation

[0053] To more clearly describe the technical solution of the present invention, the specific implementation of the present invention will be further explained below with reference to examples and accompanying drawings, but the implementation of the present invention is not limited thereto.

[0054] This invention provides a method for finely simulating the temperature field and phase-field coupling during selective laser melting (SLM), which is then applied to the Ti-Nb binary alloy system. This method is used to finely simulate the temperature distribution of the molten pool during SLM, extracting the temperature gradient and cooling rate, and inputting them into a finite interface dissipative phase-field model (FIDPFM) to study the evolution of the microstructure in the molten pool microregions.

[0055] The specific steps of the fine-selective laser melting temperature field simulation and phase-field coupling simulation method implemented in this embodiment are as follows:

[0056] (1) A fine geometric model of the selected laser melting (SLM) powder bed is constructed based on the discrete element method (DEM).

[0057] Prepare the geometric model: Build a cuboid cavity with dimensions of 1mm × 0.4mm × 0.06mm.

[0058] Powder filling: The powder quantity is set to 700 pieces, and the shape is round. To ensure good flowability, the particle size of the powder is assumed to follow a normal distribution and the particle size range is 20 to 50 μm.

[0059] Interparticle forces: gravity and elastic force.

[0060] Simulation calculation: Under the action of gravity and elastic force, powder particles randomly stack up in the rectangular cavity of a cuboid until the powder particles stabilize.

[0061] Output results: After the calculation is completed, the position, radius and other parameters of each discrete powder will be output.

[0062] In a preferred embodiment, a cuboid substrate with dimensions of 1 mm × 0.4 mm × 0.1 mm is constructed beneath the powder layer. The computational domain is set to have dimensions of 1 mm × 0.4 mm × 0.2 mm, including the substrate, the powder layer, and the gas region. Finally, the powder bed geometry model is as follows: Figure 1 As shown. On the other hand, to demonstrate the necessity of a fine powder bed geometry model, a cuboid model of the same size without a powder bed was constructed, and the temperature distribution differences between the powder bed model and the model without a powder bed were compared.

[0063] (2) The research system is a Ti-Nb binary alloy system. The thermophysical property parameters of Ti-25Nb (at.%) are collected and shown in Table 1. Due to the high uncertainty of some thermophysical property parameters of Ti-Nb alloy, some parameters of Ti-6Al-4V alloy were used. The SLM heat transfer-fluid flow model and the free surface tracking equation are as follows:

[0064]

[0065]

[0066]

[0067]

[0068] Q = q beam -q rad -q conv -q vap

[0069]

[0070] q rad =ε r σ B (T 4 -T amb 4 )

[0071] q conv =h(TT) amb )

[0072]

[0073] Where ρ is density, t is time, and U is the velocity vector. Indicates mass flow rate. The velocity represents the rate of change of fluid velocity with respect to convection in space; μ is the viscosity. This represents the effect of viscous force on the velocity field, where P is the pressure vector. The force C represents the effect of pressure on the velocity field, where f represents the external force. P Here, T is the specific heat, k is the temperature, and k is the thermal conductivity. This represents the rate of temperature change through spatial conduction, and F is the volume fraction of material in the calculation unit. Q is the heat source term, comprehensively considering the laser heat source q. beam Thermal radiation q rad Heat convection q conv and heat evaporation q vap Heat transfer mechanism. a is the absorptivity, P l r is the laser power. l Let r be the laser radius, r be the spatial position, r0 be the laser center point, and ε be the laser radius. r For emissivity, σ B T is the Stenfan-Blotzmann constant. amb Where is the ambient temperature, h is the convective heat transfer coefficient, and L is the tidal temperature. v It is the latent heat of vaporization, X Nb and X Ti These are the atomic percentages of elements Nb and Ti, respectively, and P. Nb (T) and P Ti (T) represent the partial voltages of elements Nb and Ti, respectively, in MW. Nb and MW Ti These are the molar masses of elements Nb and Ti, respectively.

[0074] As a preferred embodiment, the laser power is set to 150W and the scanning speed is 0.5m / s. The heat transfer-fluid flow model and the free surface equation are solved based on the finite difference method, and the data is visualized. Figure 2 The morphology, size, and temperature distribution of the molten pool are shown in both powder bed and powder bed models. Figure 2 (a) is a powder bed-free model. Figure 2(b) is a powder bed model.

[0075] Table 1. Thermophysical property parameters of Ti-Nb alloy

[0076]

[0077]

[0078] The temperature distribution and evolution along the x-axis were compared between the powder bed-free model and the powder bed model, as follows: Figure 3 As shown, where, Figure 3 (a) The temperature distribution along the x-axis at the center and bottom of the molten pool in the powder bed model and the powder bed model were compared. Figure 3 (b) The temperature evolution at the center and bottom of the molten pool was compared between the powder bed model and the powder bed model. Linear fitting was performed on the temperature distribution curves from 2030K to 2100K and from 2030K to the temperature peak. The slope of the fitting function represents the minimum temperature gradient (G). min ) and maximum temperature gradient (G max Minimum cooling rate and maximum cooling rate The results were obtained from the temperature-cooling curves between 2030K and 2100K and between 2030K and the peak temperature, respectively. The maximum temperature gradient and maximum cooling rate simulated by the two models are shown in Table 2.

[0079] Table 2 shows the maximum temperature gradient and maximum cooling rate simulated by the two models.

[0080] Middle of the molten pool without powder bed model <![CDATA[1.42×10 7 ]]> <![CDATA[6.77×10 6 ]]> The middle of the molten pool in the powder bed model <![CDATA[1.54×10 7 ]]> <![CDATA[8.01×10 6 ]]> Bottom of the molten pool without powder bed model <![CDATA[3.01×10 6 ]]> <![CDATA[1.41×10 6 ]]> Bottom of the molten pool in the powder bed model <![CDATA[3.56×10 6 ]]> <![CDATA[1.23×10 6 ]]>

[0081] Under process parameters of 150W laser power and 0.5m / s scanning speed, the temperature distribution along the x-axis through the molten pool at different heights of the molten pool boundary and the temperature evolution at the center point of this line over time are shown below. Figure 4 As shown, where, Figure 4 (b) and (c) show the work of Figure 4 The temperature distributions obtained from the dashed lines T1, T2, and T3 in (a) and the temperature evolution at the center point of these lines are shown in Table 3. The temperature gradients and cooling rates at different heights of the molten pool boundary are calculated.

[0082] Table 3 Temperature gradient and cooling rate at different heights of the molten pool boundary.

[0083] Top of the molten pool <![CDATA[1.66×10 6 ]]> <![CDATA[2.07×10 6 ]]> Middle of the molten pool <![CDATA[2.26×10 6 ]]> <![CDATA[1.78×10 6 ]]> Bottom of the molten pool <![CDATA[3.17×10 6 ]]> <![CDATA[1.23×10 6 ]]>

[0084] (3) Thermodynamic and kinetic data of Ti-25Nb (at.%) were collected and are shown in Table 4. Gibbs free energy f of the liquid phase and β phase were also included. l and f sThe expression can be represented by a regular solution model:

[0085]

[0086]

[0087] Among them, V m Let c be the molar volume, R be the gas constant, and c be the volume. l c is the Nb concentration in the liquid phase. s The concentration of Nb in the β phase; and These are the molar Gibbs free energies of element Nb in the liquid phase and β phase, respectively; and These are the molar Gibbs free energies of element Ti in the liquid phase and β phase, respectively; I l and I β These are the interaction coefficients in the liquid phase and the β phase, respectively. The expression is as follows:

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Furthermore, the chemical formula of Nb in the liquid phase can be calculated using the above formula. Chemical formula of Nb in the β phase Thus, the phase transition driving force Δg can be calculated. phi :

[0095]

[0096] Among them, f l and f s These are the Gibbs free energy of the liquid phase and the Gibbs free energy of the β phase, respectively.

[0097] Table 4. Thermodynamic, kinetic data and simulation parameters of Ti-25Nb (at.%)

[0098] Grid size Δx <![CDATA[1.0×10 -8 m]]> Interface width η <![CDATA[1.0×10 -7 m]]> Interfacial energy coefficient <![CDATA[σ0]]> <![CDATA[0.2Jm -2 ]]> Interface mobility coefficient <![CDATA[M0]]> <![CDATA[2.0×10 -8 m 4 J -1 s -1 ]]> Interface penetration <![CDATA[P0]]> <![CDATA[1.0×10 -4 m 3 J -1 s -1 ]]> Liquid phase diffusion coefficient <![CDATA[D l ]]> <![CDATA[6.5×10 -9 m 2 s -1 ]]> solid diffusion coefficient <![CDATA[D s ]]> <![CDATA[6.5×10 -13 m 2 s -1 ]]> molar volume <![CDATA[V m ]]> <![CDATA[1.2×10 -5 m 3 mol -1 <!-- 7 -->]]> Anisotropy coefficient ε 0.1 gas constant R <![CDATA[8.314472Jmol -1 K -1 ]]> Liquid phase interaction coefficient <![CDATA[I l ]]> <![CDATA[7406.1Jmol -1 ]]> Solid-phase interaction coefficient <![CDATA[I β ]]> <![CDATA[13045.3Jmol -1 ]]>

[0099] Establish the phase-field evolution equation and concentration-field evolution equation for the Ti-Nb binary alloy system:

[0100]

[0101]

[0102]

[0103]

[0104] in, For phase field value, It is a liquid phase. It is a solid phase, while at the interface... It varies continuously between 0 and 1. The kinetic coefficient K represents the effect of finite diffusion and redistribution at the interface on the phase transition kinetics. σ is the interfacial energy coefficient, and η is the interfacial width. D s It is the solid-phase diffusion coefficient, D l is the liquid-phase diffusion coefficient. P is the interfacial permeability, which describes the rate of solute transport at the phase interface. When P approaches infinity, the traditional equilibrium phase-field model with equal chemical potentials in both phases is restored. When P approaches 0, the solute exchange process between the two phases is suppressed. Simultaneously, the kinetic coefficient K approaches 0, and the phase transition ceases. M is the interfacial mobility.

[0105] To simulate cellular or dendritic growth, the interfacial energy and interfacial mobility are modified to have anisotropic properties. Anisotropic interface. and anisotropic interface mobility The expression is as follows:

[0106]

[0107]

[0108]

[0109] Where σ0 is the interfacial energy coefficient, M0 is the interfacial mobility coefficient, ε is the anisotropy coefficient, and n i Interface normal vector The components in the i-th direction, i = x, y, z.

[0110] The simulated temperature gradient and cooling rate in Table 3 are coupled into FIDPFM using the following formula:

[0111] T PF =T0+Gx PF -R c t PF

[0112] Among them, T PFLet T0 be the initial temperature of the phase field simulation domain, G be the temperature gradient, and R be the initial temperature of the phase field simulation domain. c x is the cooling rate. PF Let t be the distance along the x-axis of the phase field simulation domain. PF For phase field simulation time.

[0113] The phase-field simulation uses a two-dimensional simulation domain of 500Δx × 500Δy (actual size 5μm × 5μm). A thin β-phase layer (thickness 10Δx) is placed on the left side of the simulation domain, and a thick liquid layer is placed on the right side. The initial Nb concentration in the entire simulation domain is set to 25 at.%. By solving the heat transfer-fluid flow model using the finite difference method, the temperature at each grid point in the computational domain at any given time can be obtained, i.e., the temperature field. A program is written to perform discrete iterative solutions to the phase field and concentration field evolution equations, output the data, and visualize it to obtain the evolution process of the micro-region solidification structure of the Ti-Nb alloy SLM melt pool, as shown below. Figure 5 As shown, where, Figure 5 (a) shows the macroscopic temperature field, while Figure 5 (b), (c), and (d) show the solidification microstructure of different locations in the molten pool simulated based on the temperature gradient and cooling rate within the white boxes. These results demonstrate the coupling between the temperature field and phase field simulations.

[0114] Figure 1 A detailed powder bed geometry model was constructed. The computational domain size was 1 mm × 0.4 mm × 0.2 mm, comprising a substrate (100 μm), a powder layer (60 μm), and a gas region (40 μm). A total of 700 powder particles were used, with particle sizes following a normal distribution from 20 μm to 50 μm. The mesh size was set to 3 μm to ensure simulation accuracy, resulting in a total of 3,120,527 mesh elements.

[0115] Figure 2 The differences in molten pool morphology, size, and temperature distribution between the powder bed and non-powder bed models were investigated. Results show differences in melt channel morphology, molten pool shape, and size between the two models. The molten pool size in the non-powder bed model is 234 μm × 156 μm × 45 μm, while the molten pool size in the powder bed model is 249 μm × 138 μm × 54 μm. The molten pool in the powder bed model is longer, narrower, and deeper. The peak temperatures of the non-powder bed model and the powder bed model are 3710.4 K and 4034.0 K, respectively, with a peak temperature deviation of 8.72%.

[0116] Figure 3The temperature distribution along the x-axis at the center and bottom of the molten pool in both the powder bed and powder bed models, as well as the temperature evolution at the center point along this line, were statistically analyzed. Based on the temperature distribution and evolution curves, the temperature gradient and cooling rate were calculated, as shown in Table 2. The results show that in the middle of the molten pool, the deviations in temperature gradient and cooling rate for the powder bed and powder bed models are 8.45% and 18.32%, respectively. At the bottom of the molten pool, the deviations in temperature gradient and cooling rate for the two models are 26.29% and -12.77%, respectively. This demonstrates the necessity of a detailed powder bed geometry model in SLM temperature field simulation.

[0117] Figure 4 This table shows the temperature distribution along the x-axis at different heights of the molten pool boundary and the temperature evolution at the center point of this line over time. The dashed lines T1, T2, and T3 correspond to the bottom, middle, and top of the molten pool, respectively. The temperature gradient and cooling rate differ at different locations within the molten pool. With a laser power of 150W and a scanning speed of 0.5m / s, the temperature gradient and cooling rate at different heights near the molten pool boundary were calculated. The results show that the temperature gradient is larger at the bottom of the molten pool boundary, while the cooling rate is larger at the top, as shown in Table 3.

[0118] The simulated temperature gradient and cooling rate from Table 3 were input into FIDPFM to obtain the microstructure of the molten pool microregions, such as... Figure 4 As shown in the figure. The results indicate that Nb atoms are enriched in the β phase, while the interface and liquid phase are Nb-depleted regions. From top to bottom, the microstructure is observed to change from planar growth to cellular growth, and the degree of Nb solute segregation increases.

[0119] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for simulating the temperature field and phase-field coupling of laser melting in a finely selected area, characterized in that, Includes the following steps: (1) Construct a geometric model of randomly stacked powder bed for selective laser melting based on the discrete element method; in the geometric model of randomly stacked powder bed, the powder quantity and particle size distribution are set according to the actual working conditions, and the particle size of the powder follows a normal distribution and ranges from 20 to 50 μm; (2) Establish a heat transfer-fluid flow model to simulate the macroscopic temperature distribution of the molten pool; the heat transfer model considers the heat transfer mechanisms of laser heating, convection, radiation and thermal evaporation, and the fluid flow model adopts the Navier-Stokes equations and uses the fluid volume method to track the free surface. The heat transfer-fluid flow model is as follows: in, For density, For time, For divergence operators, Indicates mass flow rate. For gradient operators, It is a velocity vector. It represents the rate of change of fluid velocity with respect to convection in space. Viscosity, This represents the effect of viscous force on the velocity field. It is a pressure vector. This indicates the effect of pressure on the velocity field. Indicates external force. For specific heat, For temperature, Thermal conductivity, It represents the rate of change of temperature through conduction in space. For heat source items; (3) Extract the temperature gradient and cooling rate of the molten pool boundary, and use the temperature gradient and cooling rate as inputs to the finite interface dissipative phase field model to simulate the evolution of non-equilibrium solidification structure in the micro-region of the molten pool during the selected area laser melting process.

2. The method for simulating the temperature field and phase-field coupling of laser melting in a precise selected area according to claim 1, characterized in that, The heat source item includes laser heat source. thermal radiation Heat convection Evaporation The expression is as follows: in, For absorption rate, For laser power, For the laser radius, For spatial location, Center point of the laser For emission rate, It is the Stenfan-Blotzmann constant. For ambient temperature, The convective heat transfer coefficient, Latent heat of vaporization For elements atomic percentage, For elements The partial voltage, For elements molar mass, n The total number of elements.

3. The method for simulating the temperature field and phase-field coupling of laser melting in a precise selected area according to claim 1, characterized in that, The free surface is tracked using the fluid volume method, as shown in the following formula: in, F To calculate the volume fraction of material in the unit cell, Indicates mass flow rate. For divergence operators, This is the velocity vector.

4. The method for simulating the temperature field and phase-field coupling of laser melting in a precise selected area according to claim 1, characterized in that, FIDPFM describes the non-equilibrium solidification process in SLM, and its phase field evolution equation and concentration field evolution equation are as follows: in, For phase field value, It is a liquid phase. It is a solid phase, while at the interface... It changes continuously between 0 and 1; For kinetic coefficients; It is the interfacial energy coefficient. It is the interface width; Indicates the driving force of phase transition; It is the solid phase concentration. It refers to the liquid phase concentration; It is the solid-phase diffusion coefficient. It is the liquid phase diffusion coefficient; It is the interfacial permeability, which describes the rate of solute transport at the phase interface. As the potential approaches infinity, the phase-field model reverts to the traditional equilibrium phase-field model where the chemical potentials of the two phases are equal. When the kinetic coefficient approaches 0, the solute exchange process between the two phases is suppressed, and the kinetic coefficient also decreases. When the phase approaches zero, the phase transition stops; It's the interface migration rate. It is the Gibbs free energy in the liquid phase. It is the solid-phase Gibbs free energy; Represents the liquid phase chemical potential. Represents the chemical potential of a solid phase; and The formula is as follows: in, The gas constant is... For temperature, For molar volume, and They are elements Molar Gibbs free energy in liquid and solid phases and They are another element The molar Gibbs free energy in liquid and solid phases, which is temperature-dependent, is obtained from thermodynamic data. and These are the interaction coefficients in the liquid and solid phases, respectively.

5. The method for simulating the temperature field and phase-field coupling of laser melting in a precise selected area as described in claim 1, characterized in that, The heat transfer-fluid flow model is solved using the finite difference method, and the calculation results are output and visualized to obtain macroscopic temperature field distribution data of the molten pool. Based on the temperature field data, the temperature gradient and cooling rate are extracted.

6. A method for simulating the temperature field and phase-field coupling of laser melting in a precise selected area according to any one of claims 1 to 5, characterized in that, The coupling between the temperature field and the phase field is achieved through the following formula: in, For the phase field simulation domain temperature, The initial temperature of the phase field simulation domain. For temperature gradient, For cooling rate, For the phase field simulation domain along Distance between axes For phase field simulation time.

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