Multi-field coupling simulation method for microstructure evolution in additive manufacturing process

Abstract

The invention relates to the technical field of additive manufacturing process modeling and material microstructure evolution simulation, and discloses a multi-field coupling simulation method for microstructure evolution in an additive manufacturing process, which comprises the following steps: acquiring temperature field distribution and corresponding thermal cycle curves under different additive manufacturing process parameters; constructing a coupling model of a phase field used for describing solid-liquid interface migration and an orientation field used for describing grain orientation; setting a geometric configuration, an initial condition and a boundary condition based on a physical scene of the additive manufacturing process; coupling the thermal cycle curve with the phase field-orientation field coupling model, and driving and simulating grain nucleation, growth, competition and preferred orientation evolution in the whole solidification and cooling process of the molten pool to obtain a simulation result; and quantitative characterization information of the microstructure is extracted based on a simulation result, and a predictable mapping relation between the process parameters and microstructure evolution defined based on the quantitative characterization information is established. The invention provides an effective technical means for improving the consistency of additive manufacturing components.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of modeling and microstructure evolution simulation of additive manufacturing process, and particularly relates to a multi-field coupling simulation method for microstructure evolution in an additive manufacturing process. BACKGROUND

[0002] As a typical metal additive manufacturing technology, selective laser powder bed fusion (SLM / LPBF) has the characteristics of high heating and cooling rate, complex thermal cycle and layer-by-layer stacking forming. Due to the strong space-time non-uniform heat input of the laser on the powder bed and the substrate, the molten pool undergoes an extreme rapid heating, melting and cooling process, and the solidification rate is much higher than that of traditional casting or welding process. This unique thermodynamic and kinetic condition directly leads to the complex evolution of microstructure, including the preferred epitaxial growth of columnar crystals along the substrate or the formed layer, the regeneration of equiaxed crystals under high supercooling or impurity induction, and the morphological transformation between dendrites / cellular crystals. At the same time, due to the inevitable introduction of remelting phenomenon by multi-layer and multi-pass scanning, the interlayer structure often shows obvious redistribution and transition characteristics, resulting in uneven structure and anisotropic performance in the formed component.

[0003] However, the existing microstructure simulation methods have obvious deficiencies in analyzing the above complex phenomena. On the one hand, many phase field studies are still limited to two-dimensional small-scale models, which can only capture the nucleation and expansion of local dendrites, and cannot effectively describe the grain competition and texture evolution rules in the large-scale, multi-pass and multi-layer construction process. On the other hand, the traditional model often ignores the strong coupling effect between the temperature field and the latent heat release, making it difficult to truly reflect the influence of process parameters such as laser power, scanning speed, path distance and layer thickness on the thermal cycle curve, thereby limiting the prediction accuracy of the dynamic evolution of microstructure in the whole process of solidification and cooling. In addition, although some studies have introduced a heat source model, they are still simplified in terms of boundary condition processing, interlayer remelting effect and multi-physical field interaction, which limits their engineering application value.

[0004] In actual engineering applications, the service reliability of additive manufacturing components in the field of energy power is extremely high, and the controllability of microstructure is directly related to the stability and consistency of mechanical properties. Therefore, it is urgent to develop a simulation method that can predict across scales and process conditions. This method should have the following characteristics: first, it can truly couple the non-isothermal energy conservation equation with the phase field and orientation field, reflecting the latent heat effect and grain orientation evolution under rapid solidification conditions; second, it can adapt to multi-pass and multi-layer scanning strategies, capturing the interlayer remelting and structure transition characteristics; third, it can be combined with thermodynamic and kinetic databases to realize the mapping of material parameters and process parameters, and then output quantifiable grain orientation, size and distribution information. SUMMARY

[0005] This invention provides a multi-field coupled simulation method for microstructure evolution during additive manufacturing. This method obtains the temperature field distribution under different process parameters through finite element analysis and extracts typical thermal cycling curves during the solidification process and subsequent air cooling to room temperature. Then, combined with a thermodynamic and kinetic database of the material, the extracted thermal cycling curves are coupled with a phase-field model to simulate grain nucleation, growth, and competitive evolution behavior during molten pool solidification and cooling, thereby obtaining quantitative characterization information such as grain orientation, grain size, and distribution. Based on this, this invention can establish a predictable relationship between process parameters and microstructure, providing an effective approach for process optimization and microstructure control. Simultaneously, this method overcomes the limitations of traditional two-dimensional models and simplified thermal field treatment, forming a systematic framework in parameter mapping, boundary condition setting, and microstructure statistical output, possessing engineering application value and providing solid technical support for achieving microstructure control and performance improvement.

[0006] This invention is achieved through the following technical solution:

[0007] A multi-field coupled simulation method for microstructure evolution during additive manufacturing includes:

[0008] S1. Obtain the temperature field distribution and corresponding thermal cycling curves under different additive manufacturing process parameters;

[0009] S2. Construct a coupled model of the phase field used to describe solid-liquid interface migration and the orientation field used to describe grain orientation.

[0010] S3. Based on the physical scene of the additive manufacturing process, set the geometric configuration, initial conditions and boundary conditions;

[0011] S4. Based on the geometric configuration, initial conditions and boundary conditions, the thermal cycle curve is coupled with the phase field-orientation field coupling model to drive and simulate the evolution of grain nucleation, growth, competition and preferred orientation during the entire solidification and cooling process of the molten pool, so as to obtain simulation results;

[0012] S5. Based on the simulation results, extract the quantitative characterization information of the microstructure and establish a predictable mapping relationship between the process parameters and the tissue evolution defined based on the quantitative characterization information.

[0013] As an optimization, the temperature field distribution and thermal cycle curve are obtained by solving the non-isothermal energy conservation equation that explicitly introduces the moving heat source and the latent heat of phase change.

[0014] As an optimization, the specific formula for the non-isothermal energy conservation equation is as follows:

[0015] ;

[0016] Where: T is temperature, t is time. For material density, Let ρ be the specific heat capacity, k be the thermal conductivity, Q(x,y,z,t) be the moving heat source, and L be the latent heat of phase change. This is the phase field sequence parameter.

[0017] As an optimization, the moving heat source adopts either the Gaussian heat source model or the Rosenthal analytical thermal field model.

[0018] As an optimization, the evolution equation of the phase field adopts the Allen-Cahn equation, whose free energy density function is in double-well form and includes a temperature-driven term, and its expression is:

[0019] ;

[0020] in, λ is the thermal drive coefficient. Let W be the equilibrium melting point of the alloy, W be the potential well height constant, and m(T) be the thermal driving force term.

[0021] As an optimization, the evolution equation of the phase field is:

[0022] ;

[0023] in, For the phase relaxation time, Let be the interfacial diffusion tensor that varies with grain orientation. Let be the free energy density function. Let t be the phase field order parameter, and t be time; the interface diffusion tensor is... To characterize the anisotropy of the interface, the expression is: ; Here, c is the interface width parameter, c is the anisotropy intensity, and N is the crystal symmetry number. The angle between the interface normal and the crystal orientation.

[0024] As an optimization, the orientation field The dynamic equation is:

[0025] ;

[0026] in: To determine the field relaxation time; The orientation diffusion coefficient is... This is the driving force related to grain boundary energy.

[0027] As an optimization, the initial conditions are set as follows: an epitaxial growth orientation is set in the substrate region, and random nucleation points are arranged in the powder bed region and different initial grain orientations are assigned.

[0028] The boundary conditions include: the temperature field adopts a combination of bottom plate convection and radiation, side wall convection and top radiation boundary; the phase field and orientation field adopt zero flux boundary or weak orientation constraint boundary.

[0029] As an optimization, the simulation process in step S4 uses the finite element method or finite volume method for spatial discretization and employs implicit or semi-implicit schemes for time advancement.

[0030] As an optimization, at least one of the following numerical stability control strategies is also implemented during the simulation process:

[0031] a) Perform term splitting on the latent heat term in the non-isothermal energy conservation equation;

[0032] b) Introduce regularization to the orientation field gradient term in the orientation field dynamic equation.

[0033] As an optimization, in step S5, establishing a predictable mapping relationship specifically involves using the response surface methodology to establish a mapping model between process parameters and microstructure quantitative information, and optimizing the combination of process parameters based on a multi-objective optimization algorithm; wherein, the process parameters include laser power, scanning speed, channel spacing, layer thickness, and preheating temperature.

[0034] As an optimization, an equivalent bias induced by the Marangoni effect is introduced when simulating solid-liquid phase boundary migration to correct the migration direction of the interface.

[0035] As an optimization, the thermal cycle curve is extracted from one or more of the following locations: the molten pool boundary, the interlayer interface, and representative locations. The thermal cycle curve contains thermal history information of the solidification stage and the air-cooling to room temperature stage.

[0036] As an optimization, in step S5, the quantitative characterization information includes one or more of the following: grain orientation distribution function texture, equivalent grain size, columnar to equiaxed crystal transformation index, dendritic or cellular principal axis tilt angle, and interlayer remelting depth.

[0037] As an optimization, the parameters in the phase-field-orientation-field coupling model are calibrated by combining material thermodynamics or kinetic databases with experimental observation data; the experimental observation data includes electron backscatter diffraction data or microstructure images; the parameters include at least one of the following: potential well height constant, interface width parameter, thermal driving coefficient, anisotropy intensity, orientation diffusion coefficient, or driving force term related to grain boundary energy.

[0038] As an optimization, the specific process for establishing a predictable mapping relationship in step S5 is as follows:

[0039] S5.1. Using the response surface methodology, establish a mapping model between the process parameters and the quantitative characterization information of the microstructure, and perform sensitivity analysis on the process parameters.

[0040] S5.2 Based on the mapping model, a multi-objective optimization algorithm is used to optimize the combination of process parameters.

[0041] As an optimization, the method is applied to the laser powder bed fusion additive manufacturing process; the process parameters include laser power, scanning speed, scanning channel spacing, powder layer thickness and substrate preheating temperature, and can simulate single-channel, multi-channel or multi-layer scanning processes; the scanning strategy used in the scanning process includes at least one of linear scanning, serpentine scanning or interlayer rotational scanning.

[0042] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0043] By coupling the non-isothermal energy conservation equation with the phase-orientation field multiphysics model, the complex thermodynamic laws of rapid heating, solidification, and cooling during laser powder bed melting can be accurately reflected, enabling precise simulation of the molten pool temperature field distribution and microstructure evolution. The method incorporates key mechanisms such as latent heat effect, interfacial anisotropy, and the Marangoni effect, allowing for reasonable prediction of grain morphology, columnar-equiaxed grain transformation, and interlayer remelting effects, thus avoiding the biases caused by traditional models and simplified thermal field treatments. This invention couples the thermal cycling curves obtained from finite element analysis with the phase-field model, establishing a predictable mapping relationship between process parameters and microstructure, quantifying the influence of process variables such as laser power, scanning speed, channel spacing, and layer thickness on grain orientation, size, and distribution. This method not only enables the prediction of microstructure characterization information (grain size, orientation texture, remelting depth, etc.) but also allows for optimization of process parameters during the design phase, achieving controllable microstructure and improved performance. This invention provides an effective technical means to improve the consistency, reliability and mechanical properties of additively manufactured components, and has good prospects for engineering applications. Attached Figure Description

[0044] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0045] Figure 1 A flowchart of a multi-field coupled simulation method for microstructure evolution in additive manufacturing;

[0046] Figure 2 The results are simulations of the temperature field, orientation field, and phase field of selective laser melting of 316H stainless steel along the thickness z-direction.

[0047] Figure 3This is an EBSD observation of selective laser melting of 316H stainless steel along the thickness z-direction.

[0048] Figure 4 The results are simulations of the temperature field, orientation field, and phase field of the phase field of selective laser melting of 316H stainless steel along the xy horizontal plane.

[0049] Figure 5 It is an EBSD observation of selective laser melting of 316H stainless steel along the xy horizontal plane.

[0050] Figure 6 It is the Pareto frontier for multi-objective optimization of additive manufacturing processes and microstructure. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0052] This embodiment 1 provides a multi-field coupled simulation method for the microstructure evolution during additive manufacturing, such as... Figure 1 As shown, it includes:

[0053] S1. Obtain the temperature field distribution and corresponding thermal cycling curves under different additive manufacturing process parameters.

[0054] More specifically, the thermal cycle curve is extracted from one or more of the following locations: the molten pool boundary, the interlayer interface, and representative locations. The thermal cycle curve contains thermal history information of the solidification stage and the air-cooling to room temperature stage.

[0055] In some embodiments, the temperature field distribution and thermal cycle curve are obtained by solving the non-isothermal energy conservation equation that explicitly incorporates the moving heat source and the latent heat term of phase change.

[0056] In some embodiments, under known material thermophysical properties (density, specific heat capacity, thermal conductivity k, latent heat, laser absorptivity) and process parameters (laser power, scanning speed, channel spacing, layer thickness, preheating temperature), a non-isothermal energy conservation equation is established:

[0057] ;

[0058] Where: T is temperature (K), and t is time (s). The density of the material is (kg / m³). denoted as , where is the specific heat capacity (J / (kg·K)), k is the thermal conductivity (W / (m·K)), Q(x,y,z,t) is the moving heat source (W / m³), and L is the latent heat of phase change (J / m³). This is the phase field sequence parameter.

[0059] In some embodiments, the mobile heat source employs a Gaussian heat source model or a Rosenthal analytical thermal field model.

[0060] (1) Based on the additive manufacturing process parameters (laser power, scanning speed, track spacing, layer thickness, preheating temperature), the moving heat source adopts the Gaussian heat source model:

[0061] ;

[0062] in: Let P be the laser absorptivity, P be the laser power (W), a and b be the spot radii (m), and H be the layer thickness (m). The coordinates (m) of the heat source center that moves with the scanning speed. This is the attenuation function in the thickness direction.

[0063] (2) The moving heat source can be selected using the Rosenthal analytical thermal field model, and the effect of latent heat release on the temperature field is explicitly considered.

[0064] S2. Construct a coupled model of the phase field used to describe solid-liquid interface migration and the orientation field used to describe grain orientation.

[0065] In some embodiments, the evolution equation of the phase field adopts the Allen-Cahn equation, the free energy density function of which is in the form of a double potential well and includes a temperature-driven term.

[0066] The Allen-Cahn form of phase-field equations is used to describe the solid-liquid interface migration and phase transition dynamics, where the phase field... Describes solid-liquid interface migration and orientation field. Describe grain orientation.

[0067] In some embodiments, the evolution equation of the phase field is:

[0068] ;

[0069] in, For the phase relaxation time, Let be the interfacial diffusion tensor that varies with grain orientation. Let be the free energy density function. This is the phase field sequence parameter.

[0070] Let be the free energy density function, and its double-well form is expressed as:

[0071] ;

[0072] Where W is the potential well height constant, and m(T) is the thermal driving force term. λ is the thermal drive coefficient. This is the equilibrium melting point of the alloy.

[0073] Interface anisotropy is mediated by the diffusion tensor (i.e., the field of grain orientation). The changing interface diffusion tensor represents:

[0074] ;

[0075] in, Here, c is the interface width parameter, c is the anisotropy intensity, and N is the crystal symmetry number. The angle between the interface normal and the crystal orientation.

[0076] S3. Based on the physical scene of the additive manufacturing process, set the geometric configuration, initial conditions and boundary conditions.

[0077] This step involves constructing the physical computational domain, starting point, and environmental constraints for the numerical simulation, as detailed below:

[0078] S3.1 Set the geometry:

[0079] The geometry is a three-dimensional cuboid computational domain used to simulate the powder bed and substrate during laser powder bed melting. The dimensions of this computational domain in the horizontal plane (xy plane) are determined based on the number of scanning channels and channel pitch in the simulation, for example, it can be set to 2 mm × 1 mm. In the vertical direction (z-axis), the geometry comprises two parts: the upper part is the powder bed region to be melted, with a thickness... The thickness of the powder layer is consistent with that of additive manufacturing, typically 20-80 μm; the lower part is the solid substrate area, whose thickness is... Much larger than the powder layer, for example 200 μm, to simulate the thick substrate in actual manufacturing and provide a reliable heat sink effect.

[0080] S3.2 Set initial conditions:

[0081] Initial conditions are set separately for different physical fields and spatial regions:

[0082] Initial temperature conditions: The initial temperature T (t=0) of the entire computational domain is set to the substrate preheating temperature. For operating conditions without preheating, Set to room temperature (e.g., 25 degrees Celsius); for operating conditions requiring preheating, It can be set to 80-200 degrees Celsius.

[0083] Phase field initial conditions: In the substrate region, the phase field order parameter Initialized to 1, indicating that the initial state of this region is completely solid. In the powder bed region, Initializing to 0 indicates that the initial state of this region is unmelted solid powder (which can be equivalent to a solid with corresponding thermal properties in the macroscopic thermal model), and it will then undergo melting and solidification phase transition driven by a moving heat source.

[0084] Orientation field initial conditions:

[0085] In the substrate region, the alignment field It is configured to have grains with a single or a small number of specific epitaxial orientations to simulate the crystallographic template provided by an actual substrate. For example, it can be configured as follows: <001> The orientation is parallel to the construction direction (z-axis).

[0086] In the powder bed region, to simulate the random nucleation behavior during solidification, several randomly distributed nucleation points are arranged, and each nucleation point is assigned a specific nucleation point. Initial grain orientation randomly generated within the range .

[0087] S3.3 Set boundary conditions:

[0088] Boundary conditions are set based on the properties of the physical field and the actual environment of additive manufacturing:

[0089] Temperature field boundary conditions:

[0090] Top boundary (in contact with air / protective gas): Apply a radiative heat dissipation boundary condition, following the Stefan-Boltzmann law, i.e. ,in The emissivity of the material surface. It is the Stefan-Boltzmann constant. Let n be the ambient temperature and n be the boundary normal vector.

[0091] Bottom boundary (substrate bottom): Apply a combined convection and radiation heat dissipation boundary condition, i.e. ,in The convective heat transfer coefficient is... The emissivity of the material surface. It is the Stefan-Boltzmann constant. Let n be the ambient temperature, n be the boundary normal vector, and k be the thermal conductivity of the material.

[0092] Sidewall boundary: Apply convective heat dissipation boundary conditions, i.e. .

[0093] Phase field and orientation field boundary conditions: To simulate the natural evolution of the internal structure of materials and avoid artificial interference at the boundaries, the phase field is... and orientation field Zero flux (Neumann) boundary conditions are applied on all external boundaries, i.e. and , where n is the boundary normal. This indicates that there is no net inflow or outflow of phase transformation and grain orientation at the boundary. In some embodiments, for specific simulation needs, a weak orientation constraint boundary may be used for the orientation field at the bottom of the substrate to fix the initial orientation of the substrate.

[0094] S3.4 Thermal-Phase Field Coupling Settings:

[0095] The core of this invention lies in the dynamic coupling of the thermal field and the tissue field. The specific implementation method is as follows:

[0096] The thermal cycle curve T(x, y, z, t) obtained by solving the non-isothermal energy conservation equation in step S1 is used as the driving function and is input into the phase field equation and orientation field equation constructed in step S2 in real time.

[0097] Specifically, the thermal cycle curve T(t) is directly substituted into the free energy density function of the phase field equation. In the thermal driving force term m(T), the spatiotemporally changing temperature field is transformed into the driving force for the evolution of the phase field.

[0098] The evolution of the phase field (the movement of the solid / liquid interface) in turn is transmitted through the latent heat term. Feedback to the energy conservation equation enables bidirectional coupling between the thermal field and the phase field. The temperature field, through thermal driving force, influences the competition and selection of grain orientation.

[0099] This coupling mechanism ensures that the simulation can realistically reflect the complete physical picture of temperature-driven phase transitions in additive manufacturing, where the phase transitions react on the temperature field, and together determine the evolution of the microstructure.

[0100] S4. Based on the geometric configuration, initial conditions and boundary conditions, the thermal cycle curve is coupled with the phase field-orientation field coupling model to drive and simulate the grain nucleation, growth, competition and preferred orientation evolution during the entire solidification and cooling process of the molten pool, so as to obtain simulation results.

[0101] In some embodiments, the orientation field The evolution adopts the orientation field dynamic equation:

[0102] ;

[0103] Let be the field relaxation time (s); This is the orientation diffusion coefficient, ensuring that orientation diffusion in the liquid phase is suppressed; The driving force related to grain boundary energy is taken at its maximum value in the interface region, where t is time.

[0104] In some embodiments, the simulation process in step S4 uses the finite element method or the finite volume method for spatial discretization and employs an implicit or semi-implicit scheme for time progression.

[0105] During the simulation, at least one of the following numerical stability control strategies is also implemented:

[0106] a) Perform term splitting on the latent heat term in the non-isothermal energy conservation equation;

[0107] b) Introduce regularization to the orientation field gradient term in the orientation field dynamic equation.

[0108] Numerical calculations were performed using finite volume discretization and implicit / semi-implicit time progression. The stability settings are as follows: the latent heat term was split to improve numerical stability; Item introduction Regularization avoids gradient singularities; parallel computing can be accelerated using GPUs to support multi-layer simulations.

[0109] In simulating solid-liquid phase boundary migration, an equivalent bias induced by the Marangoni effect is introduced to correct the migration direction of the interface.

[0110] In some embodiments, the parameters in the phase-field-orientation-field coupling model are calibrated by combining a materials thermodynamic or kinetic database with experimental observation data; the experimental observation data includes electron backscatter diffraction data or microstructure images; the parameters include at least one of the following: potential well height constant, interface width parameter, thermal driving coefficient, anisotropy intensity, orientation diffusion coefficient, or driving force term related to grain boundary energy.

[0111] S5. Based on the simulation results, extract the quantitative characterization information of the microstructure and establish a predictable mapping relationship between the process parameters and the tissue evolution defined based on the quantitative characterization information.

[0112] Visualize the output phase-field sequence parameters Orientation field Based on the temperature field T and these field variable data, quantitative characterization information such as grain morphology, orientation, distribution and size, and interlayer remelting depth is obtained through post-processing calculations.

[0113] In some embodiments, the quantitative characterization information includes one or more of the following: grain orientation distribution function texture, equivalent grain size, columnar to equiaxed crystal transformation index, dendritic or cellular principal axis tilt angle, and interlayer remelting depth.

[0114] In some embodiments, in step S5, establishing a predictable mapping relationship specifically involves using the response surface methodology to establish a mapping model between process parameters and microstructure quantification information, and optimizing the combination of process parameters based on a multi-objective optimization algorithm; wherein, the process parameters include laser power, scanning speed, channel spacing, layer thickness, and preheating temperature.

[0115] The specific process of establishing a predictable mapping relationship is as follows:

[0116] S5.1. Using the response surface methodology, establish a mapping model between the process parameters and the quantitative characterization information of the microstructure, and perform sensitivity analysis on the process parameters.

[0117] S5.2 Based on the mapping model, a multi-objective optimization algorithm is used to optimize the combination of process parameters.

[0118] Establish the mapping relationship between process parameters and microstructure. Based on the response surface methodology, establish the mapping relationship between additive manufacturing process parameters (laser power, scanning speed, pass spacing, layer thickness, preheating temperature) and microstructure orientation / morphology and grain size, perform sensitivity analysis, and establish a response surface model.

[0119] Multi-objective optimization of additive manufacturing process based on response surface methodology. Using the NSGA3 multi-objective optimization algorithm, and combining the established additive manufacturing process parameters with the response surface model of the microstructure, the optimal combination of process parameters for the additive manufacturing process is obtained.

[0120] In some embodiments, the method is applied to a laser powder bed fusion additive manufacturing process; the process parameters include laser power, scanning speed, scanning channel spacing, powder layer thickness and substrate preheating temperature, and can simulate single-channel, multi-channel or multi-layer scanning processes; the scanning strategy used in the scanning process includes at least one of linear scanning, serpentine scanning or interlayer rotational scanning.

[0121] Next, specific numerical values ​​will be used to illustrate the invention.

[0122] Example: Simulation of microstructure evolution during additive manufacturing of 316H stainless steel

[0123] 316L stainless steel powder prepared by gas atomization was selected, with a particle size distribution of 15-45 μm and good sphericity. The substrate material was 316L steel plate of the same composition, with substrate dimensions of 20 mm × 20 mm × 5 mm. Laser powder bed melting was performed using a fiber laser with a wavelength of 1070 nm and a spot diameter of 80 μm. Typical process parameters were as follows: laser power P = 190 W; scanning speed v = 900 mm / s; scanning spacing h = 0.1 mm; layer thickness H = 40 μm; substrate preheating temperature T0 = 50 ℃.

[0124] Step 1: Given the material's known thermophysical properties (density 7900 kg / m³, specific heat 500 J / (kg·K), thermal conductivity 25 W / (m·K), latent heat 2.7 × 10⁻⁶), ... 5 Under the conditions of J / kg, laser absorptivity 0.35) and process parameters, a non-isothermal energy conservation equation is established:

[0125] ;

[0126] Where: T is temperature (K), t is time (s), ρ is material density (kg / m³), and C is temperature (K). p denoted as , where is the specific heat capacity (J / (kg·K)), k is the thermal conductivity (W / (m·K)), Q(x, y, z, t) is the moving heat source (W / m³), L is the latent heat (J / m³), and Φ is the phase field sequence parameter.

[0127] Step 2: Construct a phase-field-orientation-field coupled model. The Allen-Cahn form of the phase-field equation is used to describe the solid-liquid interface migration and phase transformation dynamics, where the phase field Φ describes the solid-liquid interface migration and the orientation field θ describes the grain orientation.

[0128] ;

[0129] Where: τ Φ Let be the phase field relaxation time (s), D(θ) be the interface diffusion tensor varying with grain orientation, and f(Φ, T) be the free energy density function. Its double-well form is expressed as:

[0130] ;

[0131] Where: W is the potential well height constant, and m(T) is the thermal driving force term, defined as:

[0132] ;

[0133] Wherein: T m The value is 1723, and the value of 𝜆 is 17.

[0134] Interface anisotropy is represented by a diffusion tensor:

[0135] ;

[0136] Where: α is the interface width parameter, c is the anisotropy intensity, N is the crystal symmetry number, and ψ is the angle between the interface normal and the crystal direction.

[0137] Step 3: Modeling Orientation Field Dynamics. The evolution of grain orientation φ is modeled using the orientation field dynamics equations:

[0138] ;

[0139] in: Let be the field relaxation time (s); This is the orientation diffusion coefficient, ensuring that orientation diffusion in the liquid phase is suppressed; The driving force related to grain boundary energy is taken at its maximum value in the interface region.

[0140] Model parameter calibration. Using the Thermo-Calc thermodynamic database and experimental EBSD data of 316L stainless steel, the model parameters W, α, λ, c, and φ were calibrated. , Calibration was performed to ensure that the simulated grain size distribution matched the actual microstructure.

[0141] Thermal-phase field coupling and initial / boundary conditions are set. Epitaxial crystal orientation is defined in the substrate region, and random equiaxed crystal nuclei are arranged in the powder bed region with different initial orientations. Boundary conditions are: bottom plate convection / radiation, sidewall convection, top radiation, and zero flux conditions for the phase field and orientation field boundaries.

[0142] Numerical computation and stability settings. Implicit time advancement and parallel computing are employed. Latent heat terms are treated with term splitting to avoid numerical divergence; orientation gradient is used. ε-regularization is introduced. The calculation is performed with a mesh size of dx = 0.2 μm and a time step of... s.

[0143] Results and microstructure characterization: The phase field order parameter Φ, orientation field θ, and temperature field T are visualized to obtain grain morphology, orientation, distribution, and size, as well as interlayer remelting depth, and good consistency is achieved with experimental observations. Figure 2 The simulation results of temperature field, orientation field and phase field of selective laser melting of 316H stainless steel along the thickness (z) direction are shown. Figure 3 EBSD observation of selective laser melting of 316H stainless steel along the thickness (z) direction. Figure 4 The simulation results of the temperature field, orientation field, and phase field for the selective laser melting of 316H stainless steel along the horizontal plane (xy plane) are presented. Figure 5 EBSD observations were performed on selected areas of 316H stainless steel melted by laser along a horizontal plane (xy plane). Good consistency was achieved between the simulated and experimental microstructures at different cross-sections.

[0144] Step 8: Establish the mapping relationship between process parameters and microstructure. The response surface methodology was used to establish the mapping relationship between laser power, scanning speed, channel pitch, and grain size / orientation. The results show that increasing laser power leads to increased grain size, while increasing scanning speed refines the grains and suppresses texture enhancement.

[0145] Step 9: Multi-objective optimization of additive manufacturing process based on response surface methodology. Using the NSGA-III multi-objective optimization algorithm, the three objectives of "minimum grain size + weak texture + moderate melt depth" are optimized, such as... Figure 6 As shown. The optimal combination of process parameters was obtained: P=180 W, v=900 mm / s, h=0.09 mm, H=40 μm.

[0146] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-field coupled simulation method for microstructure evolution during additive manufacturing, characterized in that, include: S1. Obtain the temperature field distribution and corresponding thermal cycling curves under different additive manufacturing process parameters; S2. Construct a coupled model of the phase field used to describe solid-liquid interface migration and the orientation field used to describe grain orientation. S3. Based on the physical scene of the additive manufacturing process, set the geometric configuration, initial conditions and boundary conditions; S4. Based on the geometric configuration, initial conditions and boundary conditions, the thermal cycle curve is coupled with the phase field-orientation field coupling model to drive and simulate the evolution of grain nucleation, growth, competition and preferred orientation during the entire solidification and cooling process of the molten pool, so as to obtain simulation results; S5. Based on the simulation results, extract the quantitative characterization information of the microstructure and establish a predictable mapping relationship between the process parameters and the tissue evolution defined based on the quantitative characterization information.

2. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The temperature field distribution and thermal cycle curves are obtained by solving the non-isothermal energy conservation equations that explicitly incorporate the moving heat source and the latent heat of phase change.

3. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 2, characterized in that, The specific formula for the non-isothermal energy conservation equation is as follows: ； Where: T is temperature, t is time. For material density, Let ρ be the specific heat capacity, k be the thermal conductivity, Q(x,y,z,t) be the moving heat source, and L be the latent heat of phase change. This is the phase field sequence parameter.

4. A multi-field coupled simulation method for microstructure evolution during additive manufacturing according to claim 2 or 3, characterized in that, The mobile heat source adopts either the Gaussian heat source model or the Rosenthal analytical thermal field model.

5. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The evolution equation of the phase field adopts the Allen-Cahn equation, whose free energy density function is in double-potential-well form and includes a temperature-driven term. Its expression is as follows: ； in, λ is the thermal drive coefficient. Let W be the equilibrium melting point of the alloy, W be the potential well height constant, and m(T) be the thermal driving force term.

6. The multi-field coupling simulation method for microstructure evolution in additive manufacturing according to claim 5, characterized in that, The evolution equation of the phase field is: ； in, For the phase relaxation time, Let be the interfacial diffusion tensor that varies with grain orientation. Let be the free energy density function. Let t be the phase field order parameter, and t be time; the interface diffusion tensor is... To characterize the anisotropy of the interface, the expression is: ; Here, c is the interface width parameter, c is the anisotropy intensity, and N is the crystal symmetry number. The angle between the interface normal and the crystal orientation.

7. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The orientation field The dynamic equation is: ； in: To determine the field relaxation time; The orientation diffusion coefficient is... This is the driving force related to grain boundary energy.

8. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The initial conditions are set as follows: an epitaxial growth orientation is set in the substrate region, and random nucleation points are arranged in the powder bed region and different initial grain orientations are assigned. The boundary conditions include: the temperature field adopts a combination of bottom plate convection and radiation, side wall convection and top radiation boundary; the phase field and orientation field adopt zero flux boundary or weak orientation constraint boundary.

9. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The simulation process in step S4 uses the finite element method or finite volume method for spatial discretization and employs implicit or semi-implicit schemes for time progression.

10. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, During the simulation, at least one of the following numerical stability control strategies is also implemented: a) Perform term splitting on the latent heat term in the non-isothermal energy conservation equation; b) Introduce regularization to the orientation field gradient term in the orientation field dynamic equation.

11. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, In step S5, establishing a predictable mapping relationship specifically involves using the response surface methodology to establish a mapping model between process parameters and microstructure quantitative information, and optimizing the combination of process parameters based on a multi-objective optimization algorithm; wherein the process parameters include laser power, scanning speed, pass spacing, layer thickness, and preheating temperature.

12. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, In simulating solid-liquid phase boundary migration, an equivalent bias induced by the Marangoni effect is introduced to correct the migration direction of the interface.

13. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The thermal cycle curve is extracted from one or more of the following locations: the molten pool boundary, the interlayer interface, and representative locations. The thermal cycle curve contains thermal history information of the solidification stage and the air-cooling to room temperature stage.

14. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, In step S5, the quantitative characterization information includes one or more of the following: grain orientation distribution function texture, equivalent grain size, columnar to equiaxed crystal transformation index, dendritic or cellular principal axis tilt angle, and interlayer remelting depth.

15. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The parameters in the phase-field-orientation-field coupling model are calibrated by combining material thermodynamic or kinetic databases with experimental observation data; the experimental observation data includes electron backscatter diffraction data or microstructure images; the parameters include at least one of the following: potential well height constant, interface width parameter, thermal driving coefficient, anisotropy intensity, orientation diffusion coefficient, or driving force term related to grain boundary energy.

16. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, In step S5, the specific process of establishing a predictable mapping relationship is as follows: S5.

1. Using the response surface methodology, establish a mapping model between the process parameters and the quantitative characterization information of the microstructure, and perform sensitivity analysis on the process parameters. S5.2 Based on the mapping model, a multi-objective optimization algorithm is used to optimize the combination of process parameters.

17. The multi-field coupled simulation method for microstructure evolution in additive manufacturing according to claim 1, characterized in that, The method is applied to laser powder bed fusion additive manufacturing process; the process parameters include laser power, scanning speed, scanning channel spacing, powder layer thickness and substrate preheating temperature, and can simulate single-channel, multi-channel or multi-layer scanning processes; the scanning strategy used in the scanning process includes at least one of linear scanning, serpentine scanning or interlayer rotational scanning.

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