Multi-scale simulation method for high-fidelity selective laser melting forming and phase field-lattice Boltzmann coupling

Abstract

The invention provides a multi-scale simulation method for high-fidelity selective laser melting forming and phase field-lattice Boltzmann coupling, and belongs to the technical field of selective laser melting numerical simulation. The method comprises the specific steps that a selective laser melting powder laying process model is constructed based on a discrete element method, and a randomly stacked powder bed model is obtained; a high-fidelity selective laser melting forming thermal fluid dynamic model is established, and macroscopic temperature distribution and flow field distribution of a molten pool are simulated; establishing a phase field model-lattice Boltzmann coupling model; and extracting temperature gradient, solidification velocity and melt flow velocity data of local positions of the boundary of the steady-state molten pool, and simulating solidification structure evolution under flowing of molten metal in the molten pool by taking the data as initial conditions of the phase field-lattice Boltzmann coupling model. According to the method, through high-fidelity multi-scale simulation, the relation between the process parameters and the microstructure is established more comprehensively, and reliable numerical support is provided for selective laser melting process optimization and microstructure prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical simulation of selective laser melting, and particularly relates to a multi-scale simulation method for high-fidelity selective laser melting forming and phase field-lattice Boltzmann coupling. Background Art

[0002] Selective laser melting (SLM) technology is one of the most promising additive manufacturing technologies at present. By using the energy provided by a laser to melt metal powder, parts with arbitrarily complex geometric shapes can be directly produced from a three-dimensional model. However, during the SLM forming process, complex phenomena such as melt flow, radiation, and phase change often occur, resulting in many defects such as balling, porosity, and spatter in the formed parts, which in turn affect the microstructure and properties of the formed parts. The formation of these defects is closely related to the heat flow dynamics behavior of the molten pool.

[0003] Due to the ultra-transient characteristics of SLM, experimental means are difficult to characterize the dynamic evolution process of the molten pool and key microphysical behaviors. In addition, the experimental method requires a large amount of economic cost and time. With the development of computer simulation technology, numerical simulation, as an efficient and cost-effective quantitative analysis technology, provides an important method for understanding the SLM forming process.

[0004] Currently, for the simulation of the SLM forming process, most studies are carried out based on simplified continuum models, ignoring the discrete characteristics, melting, and interaction of powders, deviating from the actual processing conditions. Simplified continuum models usually do not consider important physical effects such as evaporation, melt flow, and solute mass transfer, which makes the simulation results of the temperature field and flow field obtained based on such models inaccurate, and thus an inaccurate microstructure of the molten pool is obtained. In addition, the influence of melt flow on the microstructure of the molten pool is also ignored. Therefore, in order to deeply study the dynamic behavior of the molten pool and the influence of melt flow on the micro-solidification structure, it is necessary to construct a high-fidelity numerical model to simulate the SLM forming process in order to obtain more realistic and reliable prediction results. Summary of the Invention

[0005] The purpose of the present invention is to construct a multi-scale simulation method for high-fidelity selective laser melting forming and phase field-lattice Boltzmann coupling. By establishing a high-fidelity SLM forming model, the thermal behavior, flow behavior, and microstructure evolution of the molten pool during the SLM forming process are accurately simulated, so as to obtain more accurate results. This method can provide reliable numerical support for process optimization and microstructure prediction during the SLM forming process.

[0006] In order to achieve the above-mentioned invention purpose, the present invention provides the following technical solutions:

[0007] A multi-scale simulation method based on high-fidelity selective laser melting forming and the coupling of phase field and lattice Boltzmann includes the following steps:

[0008] (1) Establish a powder bed model for selective laser melting powder laying process based on the discrete element method to obtain a randomly stacked powder bed model;

[0009] (2) Establish a high-fidelity selective laser melting forming thermo-fluid dynamics model to obtain the evolution laws of the temperature field and flow field of the macroscopic molten pool;

[0010] (3) Establish a phase field model to simulate the solidification microstructure evolution, establish a lattice Boltzmann model to simulate the flow of molten metal, and couple the phase field model and the lattice Boltzmann model to realize the solidification microstructure evolution under the flow of molten metal.

[0011] (4) Extract the temperature gradient, solidification velocity and melt flow velocity data at the local position of the steady-state molten pool boundary and use them as the initial conditions of the phase field-lattice Boltzmann coupling model to realize the solidification microstructure evolution of the molten metal in the molten pool.

[0012] Furthermore, in the randomly stacked powder bed model, the particle size range of the powder is 15-53 µm and it follows a normal distribution.

[0013] Furthermore, in the thermo-fluid dynamics model, the model is meshed so that the mesh size is 2-4 µm, the overall number of meshes is 3.6 million, and the volume of fluid method is used to track the free surface.

[0014] Furthermore, the control equations of the thermo-fluid dynamics model are:

[0015]

[0016]

[0017]

[0018] Among them, ρ is the material density, k is the thermal conductivity, μ is the kinematic viscosity, p is the pressure, represents the gravitational acceleration, represents the three-dimensional velocity vector, is the momentum source term, is the energy source term, H represents the thermal enthalpy of the material; the expression of the H is:

[0019]

[0020] Among them, is the reference thermal enthalpy, is the specific heat, T is the temperature, T ref is the reference temperature, is the latent heat of phase change, is the liquid phase fraction of the liquid melt during the calculation process; the expression is:

[0021]

[0022] where is the liquidus temperature of the material, is the solidus temperature of the material.

[0023] Furthermore, the volume of fluid method is used to track the free surface, and the expression is as follows:

[0024]

[0025] where is the volume fraction of the metal phase.

[0026] Furthermore, the momentum source term includes surface tension , Marangoni effect , mushy zone resistance , buoyancy and recoil pressure , and the expression is as follows:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] where is the surface tension coefficient, is the interface curvature, is the normal at the interface, is the magnitude of the gradient vector, is the surface tension temperature coefficient, is the mushy zone parameter, is the standard atmospheric pressure, is the latent heat of evaporation, is the molar mass of the material, is the evaporation temperature, represents the coefficient of thermal expansion of the material, is the two-phase mixture density, and are the two-phase densities respectively.

[0034] Furthermore, the energy source term includes a laser heat source , thermal radiation , heat convection and evaporation , and the expression is as follows:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] wherein, is the laser absorption rate, is the laser power, is the spatial position, coordinates of the laser heat source, is the effective area of the laser beam, is the convective heat transfer coefficient, is the ambient temperature, is the Stefan-Boltamann constant, is the emissivity.

[0041] Furthermore, in step (3), an order parameter is introduced into the phase field model, and its value usually ranges from -1 to 1. = 1 represents the solid phase region, = -1 represents the liquid phase region, and the phase field equation is:

[0042]

[0043] wherein, , is the anisotropy expression, is the local angle between the interface normal direction and the reference direction; is calculated using the cooling temperature approximation method, is the thermal length, is the liquidus slope, is the initial solute concentration, is the temperature gradient, is the solidification velocity;

[0044] The concentration field equation of the phase field model is:

[0045]

[0046] Among them, , is the dimensionless supersaturation concentration, is the reverse solute rejection term, is the melt flow rate, is the solute diffusion coefficient.

[0047] Furthermore, in step (3), the governing equation of the two-dimensional D2Q9 lattice Boltzmann model is:

[0048]

[0049] Among them, and are the time step and the relaxation time respectively, is the discrete external force, is the equilibrium distribution function; is expressed as:

[0050]

[0051] Among them, c is the lattice sound speed, is the discrete velocity, is the melt density, is the fluid velocity, is the weight coefficient.

[0052] The expression of

[0053]

[0054] Among them, is the dissipation resistance at the interface, is the forced convection term, is a constant, A is the amplitude intensity, and W0 is the interface width.

[0055] Furthermore, the steps of coupling the thermo-hydrodynamic model with the phase field-lattice Boltzmann model are as follows:

[0056] S1. Solve the thermo-hydrodynamic model by the finite volume method to obtain the data of the temperature field and the flow field of the macroscopic molten pool;

[0057] S2. Extract the temperature gradient G, the solidification rate V p and the flow velocity u, and input them into the phase field-lattice Boltzmann model;

[0058] S3. Initialize the model and give the initial conditions and boundary conditions;

[0059] S4. Calculate the solidification microstructure by the phase field model and update the flow field by the lattice Boltzmann model;

[0060] S5. Iterate according to the set loop steps. In each loop step, calculate the flow field simultaneously and transfer it into the concentration field equation.

[0061] The beneficial effects of the present invention are as follows:

[0062] The method of the present invention constructs a high-fidelity powder bed geometric model and a thermal fluid dynamics model, and simultaneously considers many physical phenomena such as the Marangoni effect, recoil pressure, convection, and radiation. Compared with the existing simplified models, it can truly reproduce the random stacking of metal powder particles and the interaction between the laser and the powder, simulate more realistic molten pool behaviors, and obtain accurate molten pool morphologies, temperature distributions, and flow field distributions.

[0063] The method of the present invention obtains accurate temperature distributions and flow field distributions inside the molten pool through the thermal fluid dynamics model, extracts the temperature gradient, solidification rate, and flow velocity and inputs them into the phase field-Lattice Boltzmann model, considers the influence of the flow field on the tissue evolution, and realizes the accurate prediction of the microstructure of the molten pool.

[0064] The method of the present invention couples the thermal fluid dynamics model with the phase field-Lattice Boltzmann model to establish a multi-scale model for the high-fidelity SLM forming process. Through this multi-scale model, the connection between process parameters and microstructures is established more comprehensively, and the quantitative prediction between process parameters and microstructures is realized, laying a theoretical foundation for the SLM process optimization and tissue regulation. Description of the Drawings

[0065] Figure 1 It is a geometric model diagram of the high-fidelity selective laser melting according to the embodiment of the present invention;

[0066] Figure 2 It is a molten pool morphology, temperature distribution, and flow field distribution diagram of the selective laser melting forming process according to the embodiment of the present invention;

[0067] Figure 3 It is a single-track morphology diagram obtained by actual printing forming and simulation according to the embodiment of the present invention;

[0068] Figure 4 It is a solidification microstructure diagram at different positions inside the molten pool obtained by experiment and simulation according to the embodiment of the present invention;

[0069] Figure 5 It is a dendrite and its flow field distribution diagram according to the embodiment of the present invention. Detailed Embodiments

[0070] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0071] The present invention provides a multi-scale simulation method combining high-fidelity selective laser melting forming and phase field-lattice Boltzmann coupling, and the specific steps are as follows:

[0072] Step 1: Establish a high-fidelity powder spreading process model for selective laser melting based on the discrete element method.

[0073] Particle model: The powder particles are set as spheres, and the density and Young's modulus of the particles are set. The powder particle size is set according to the actual powder particle size, follows a normal distribution, and the range is 15-53 µm. The forces between the powders are gravity, friction, and elastic force.

[0074] Establish a powder particle factory: Generate a sufficient number of powder particles in the powder supply bin. The powder particles stack in the powder supply bin under the action of gravity. Subsequently, the powder spreader starts to uniformly push the powder in the powder supply bin towards the forming bin. The size of the forming bin is 1 mm × 0.4 mm × 0.05 mm. Finally, after the powder spreader leaves the forming bin, the powder particles randomly stack in the forming bin.

[0075] Output results: After the calculation is completed, output parameters such as the position and radius of each discrete powder.

[0076] Step 2: Establish a high-fidelity macroscopic molten pool thermo-hydrodynamics model.

[0077] Set the size of the computational domain to 1 mm × 0.4 mm × 0.25 mm, including the substrate, powder layer, and gas region. The constructed geometric model is as Figure 1 shown. And perform mesh division on the model so that the mesh size is 2-4 µm, and the overall number of meshes is 3.6 million.

[0078] In the present invention, the control equations of the thermo-hydrodynamics model are as follows:

[0079]

[0080]

[0081]

[0082] where ρ is the material density, k is the thermal conductivity, μ is the kinematic viscosity, p is the pressure, represents the acceleration due to gravity, represents the three-dimensional velocity vector, is the momentum source term, is the energy source term, and H represents the thermal enthalpy of the material; the expression of the said H is:

[0083]

[0084] where, is the reference thermal enthalpy, is the specific heat, T is the temperature, T ref is the reference temperature, is the latent heat of phase change, is the liquid fraction of the liquid melt during the calculation process; the expression is:

[0085]

[0086] where, is the liquidus temperature of the material, is the solidus temperature of the material.

[0087] The volume-of-fluid method is used to track the free surface, and the expression is as follows:

[0088]

[0089] where, is the volume fraction of the metal phase.

[0090] The momentum source term includes surface tension 、Marangoni effect 、resistance in the mushy zone 、buoyancy and recoil pressure , and the expression is as follows:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] where, is the surface tension coefficient, is the interface curvature, is the normal at the interface, is the magnitude of the gradient vector, is the surface tension temperature coefficient, is the mushy zone parameter, is the standard atmospheric pressure, is the latent heat of evaporation, is the molar mass of the material, is the evaporation temperature, represents the coefficient of thermal expansion of the material, is the two-phase mixing density, and are the two-phase densities respectively.

[0098] Energy source term includes a laser heat source , thermal radiation , heat convection and evaporation , and the expression is as follows:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] Among them, is the laser absorption rate, is the laser power, is the spatial position, laser heat source coordinates, is the effective area of the laser beam, is the convective heat transfer coefficient, is the ambient temperature, is the Stefan-Boltzmann constant, is the emissivity.

[0105] Step 3: Based on the powder bed model established in Step 1 and the thermal fluid dynamics model established in Step 2. The material is selected as Inconel 738 alloy, and the thermal physical parameters and laser parameters are imported into the macroscopic molten pool thermal fluid dynamics model to calculate and monitor the transient characteristics and spatial distribution of the temperature field and flow field during the SLM forming process.

[0106] As a preferred embodiment, the laser power is set to 200 W and the scanning speed is 0.8 m / s. Based on the finite volume method, the thermal fluid dynamics model is solved, Figure 2 which is the molten pool morphology, temperature distribution and flow field distribution during the SLM forming process obtained by simulation.

[0107] Single-pass forming experiments are carried out using the same process parameters and compared with the simulation results. The melt channel morphology is as Figure 3 shown, Figure 3 where (a) in Figure 3 is the melt channel morphology obtained by experiment, and (b) in

[0108] Step 4: Construct a phase-field lattice Boltzmann coupling model.

[0109] Step 4.1: Construct a phase-field model to calculate the dendrite growth during the solidification process of the molten pool. Introduce an order parameter in the phase-field model, and its value usually ranges from -1 to 1. = 1 represents the solid phase region, = -1 represents the liquid phase region. The phase-field equation is:

[0110]

[0111] where , is the anisotropy expression, is the local angle between the interface normal direction and the reference direction, is calculated using the cooling temperature approximation method, is the thermal length, is the liquidus slope, is the initial solute concentration, is the temperature gradient, is the solidification velocity;

[0112] The concentration field equation of the phase-field model is:

[0113]

[0114] where , is the dimensionless supersaturation concentration, is the anti-solute trapping term, is the melt flow velocity, is the solute diffusion coefficient.

[0115] Step 4.2: Construct a two-dimensional D2Q9 lattice Boltzmann model to calculate the melt flow. The governing equation is:

[0116]

[0117] where and are the time step and relaxation time respectively, is the discrete external force, is the equilibrium distribution function; is expressed as:

[0118]

[0119] where c is the lattice sound speed, is the discrete velocity, is the melt density, is the fluid velocity. is the weight coefficient;

[0120] The expression of

[0121]

[0122] where is the dissipation resistance at the interface, is the forced convection term, is a constant, A is the amplitude intensity, and W0 is the interface width.

[0123] Step 5: Input the extracted macroscopic molten pool boundary parameters (temperature gradient, scanning speed, and flow velocity at the solid-liquid interface) and the physical property parameters of Inconel 738 alloy into the phase-field lattice Boltzmann coupling model. The solidification microstructure is calculated by the phase-field model, and the flow field is updated by the lattice Boltzmann model. Iteration is performed according to the set cycle steps to simulate the solidification microstructure of the Inconel 738 alloy SLM molten pool.

[0124] Figure 4 is the stable molten pool morphology and solidification microstructure diagram of the SLM-formed Inconel 738 alloy obtained at a laser power of 200 W and a scanning speed of 0.8 m / s, Figure 4 (a), (b), (c) are the solidification microstructure diagrams of different positions of the molten pool obtained by simulation, Figure 4 (d), (e), (f) are the actual microstructure diagrams of different positions of the molten pool obtained from the SLM experiment.

[0125] From Figure 4 (a), (b), (c) and Figure 4 (d), (e), (f), it can be seen that the number of dendrites gradually decreases from the top to the bottom of the molten pool, and the dendrite spacing increases. The simulation results are in good agreement with the experimental results.

[0126] Figure 5 is the microstructure and its flow field distribution diagram. From Figure 5 it can be seen that fluid flow will generate vortices between dendrites, and solutes near the dendrite tips will be redistributed, thus affecting the growth of dendrites.

[0127] The above is a specific description of the preferred embodiment of the present invention. However, the present invention is not limited to the above embodiments. For those skilled in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A multi-scale simulation method for high-fidelity selective laser melting forming and coupling of phase field-lattice Boltzmann, characterized in that, The method includes the following steps: (1) Establish a powder bed model for selective laser melting powder laying process based on the discrete element method to obtain a randomly stacked powder bed model; (2) Establish a high-fidelity selective laser melting forming thermo-fluid dynamics model to obtain the evolution laws of the temperature field and flow field of the macroscopic molten pool; (3) Establish a phase field model to simulate the solidification microstructure evolution, establish a lattice Boltzmann model to simulate the flow of molten metal, and couple the phase field model and the lattice Boltzmann model to realize the solidification microstructure evolution under the flow of molten metal; (4) Extract the temperature gradient, solidification velocity and melt flow velocity data at the local position of the steady-state molten pool boundary, and use them as the initial conditions of the phase field-lattice Boltzmann coupling model to realize the solidification microstructure evolution of the molten metal in the molten pool.

2. The method according to claim 1, wherein In the randomly stacked powder bed model, the particle size range of the powder is 15-53 μm and follows a normal distribution.

3. The method according to claim 1, characterized in that, In the thermo-fluid dynamics model, the model is meshed so that the mesh size is 2-4 μm, the total number of meshes is 3.6 million, and the volume of fluid method is used to track the free surface.

4. The method according to claim 1, characterized in that, The control equations of the thermo-fluid dynamics model are as follows: where ρ is the material density, k is the thermal conductivity, μ is the kinematic viscosity, p is the pressure, represents the acceleration due to gravity, represents the three-dimensional velocity vector, is the momentum source term, S L is the energy source term, H represents the specific enthalpy of the material; the expression for H is: where h r is the reference enthalpy, C p is the specific heat, T is the temperature, and T ref is the reference temperature, L m is the latent heat of phase change, and f is the liquid phase fraction of the liquid melt during the calculation process; the expression of the said f is: Among them, T l is the liquidus temperature of the material, and T s is the solidus temperature of the material.

5. The method according to claim 3, characterized in that The volume of fluid method is used to track the free surface, and the expression is as follows: where α is the volume fraction of the metal phase.

6. The method according to claim 4, characterized in that, The momentum source term includes surface tension Marangoni effect resistance in the mushy zone buoyancy and recoil pressure The expressions are as follows: where, σ is the surface tension coefficient, κ is the interface curvature, is the normal vector at the interface, is the magnitude of the gradient vector, is the surface tension temperature coefficient, A m is the mushy zone parameter, P0 is the standard atmospheric pressure, L v is the latent heat of evaporation, M is the molar mass of the material, T v is the evaporation temperature, β represents the coefficient of thermal expansion of the material, is the two-phase mixture density, ρ m and ρ g are the two-phase densities respectively.

7. The method according to claim 4, wherein The energy source term S L includes a laser heat source q laser , a thermal radiation q r , a heat convection q c and an evaporation q evap , and the expression is as follows: Among them, η is the laser absorption rate, P is the laser power, r1 is the spatial position, r0 is the laser heat source coordinate, r is the effective area of the laser beam, h is the convective heat transfer coefficient, T a is the ambient temperature, σ is the Stefan-Boltzmann constant, and ε is the emissivity.

8. The method according to claim 1, characterized in that In step (3), an order parameter φ is introduced into the phase field model, and its value is usually between -1 and 1. φ = 1 represents the solid phase region, and φ = -1 represents the liquid phase region. The phase field equation is: Among them, is the anisotropic expression, and α is the local angle between the interface normal direction and the reference direction; Calculated using the cooling temperature approximation method, is the thermal length, m is the liquidus slope, c ∞ is the initial solute concentration, G is the temperature gradient, is the solidification velocity; The concentration field equation of the phase field model is: wherein, is the dimensionless supersaturation concentration, is the reverse solute rejection term, u is the melt flow velocity, is the solute diffusion coefficient.

9. The method according to claim 1, characterized in that In step (3), the control equations of the two-dimensional D2Q9 lattice Boltzmann model are: where $\delta t$ and $\tau$ LBM are the time step and the relaxation time respectively, and G i is the discrete external force, and f i eq is the equilibrium distribution function; and f i eq is expressed as: Among them, c is the lattice sound velocity, c i is the discrete velocity, ρ is the melt density, u is the fluid velocity, w i is the weight coefficient; G i The expression of Among them, is the dissipation resistance at the interface, is the forced convection term, h is a constant, A is the amplitude intensity, and W0 is the interface width.

10. The method according to any one of claims 1 to 9, characterized in that, The steps of coupling the thermo-fluid dynamics model and the phase field-lattice Boltzmann model are as follows: S1, Solve the thermo-fluid dynamics model by the finite volume method to obtain the data of the temperature field and flow field of the macroscopic molten pool; S2. Extract the temperature gradient G, solidification rate V p and flow velocity u, and input them into the phase-field lattice Boltzmann model; S3, Initialize the model and give the initial conditions and boundary conditions; S4, Calculate the solidification microstructure morphology by the phase field model and update the flow field by the lattice Boltzmann model; S5, Iterate according to the set loop steps. In each loop step, the flow field is calculated simultaneously and transferred to the concentration field equation.

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