Selective laser melting simulation method simultaneously considering molten pool and microstructure evolution

Abstract

The invention discloses a selective laser melting simulation method simultaneously considering molten pool and microstructure evolution, which mainly comprises establishment and calculation methods of powder laying and a powder melting and solidification process model, and comprises the following specific steps: setting the geometric dimension and the number of internal crystal grains of a substrate to generate a polycrystalline substrate; establishing a discrete element model, simulating a roll shaft powder spreading process, and obtaining particle information; introducing a sequence parameter, constructing a free energy density functional, and establishing a heat-flow-microstructure strong coupling phase field model; constructing a powder bed geometric model, distributing grain orientation, and dividing grids for the powder bed geometric structure; setting material attributes and boundary conditions, and solving the phase field model by a finite element method; and carrying out visualization processing on a calculation result to obtain a molten pool and a microstructure morphology. Evolution behaviors of the molten pool and the microstructure in the selective laser melting process can be simulated at the same time, alternate simulation and data transmission of the powder laying process and the laser scanning process are achieved, and therefore actual machining production is guided, and technological parameters are optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of metal additive manufacturing, and in particular to a laser selective melting simulation method that simultaneously considers the evolution of a molten pool and a microstructure. Background Art

[0002] Selective laser melting is a typical representative of metal additive manufacturing technology. It has the advantages of high processing precision and is widely used in the aerospace field. The manufacturing process of selective laser melting materials mainly includes two steps: powder laying and laser scanning. In the selective laser melting process, the interaction between the high-energy laser beam and the powder and molten pool has an important influence on the microstructure after solidification, which determines the quality of the printed part. Therefore, in order to regulate the mechanical properties of selective laser melting parts, it is necessary to explore the interaction mechanism of laser-molten pool-microstructure, so as to optimize the process parameters to obtain a good microstructure.

[0003] Since the trial and error method is inefficient and costly, it is very effective to use numerical simulation to study the laser-molten pool-microstructure coupling mechanism in the laser selective melting process. By simulating the powder spreading and laser scanning process, the microstructure morphology after printing can be predicted at low cost for process optimization. In recent years, with the development of computer technology, the multi-field coupling model of laser selective melting has made great progress, and numerical models of different methods have been developed. Among them, the most widely used is the heat-fluid coupling model. This model combines the heat conduction equation and the molten pool dynamics equation to simulate laser heat absorption and the flow of the molten pool, and can study the formation of printing defects. Furthermore, the temperature field information calculated by the heat-fluid coupling model is input into the microstructure model, which can simulate the evolution of grains and predict the grain morphology after solidification. However, this algorithm does not consider the influence of defects such as pores and bubbles on grain nucleation and growth in microstructure simulation, the prediction accuracy is limited, and the information loss during model transmission is serious, and the prediction effect is quite different from the experimental results. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a laser selective melting simulation method that simultaneously considers the evolution of the molten pool and the microstructure, comprehensively considering the interaction between the laser, powder bed, molten pool and microstructure, so as to achieve a higher prediction accuracy for the microstructure of the molten pool after solidification.

[0005] Technical solution: The present invention provides a laser selective melting simulation method that simultaneously considers the evolution of the molten pool and microstructure, comprising the following steps:

[0006] Step 1: Set the geometric dimensions of the polycrystalline substrate and the number of grains inside the polycrystalline substrate to generate the polycrystalline substrate;

[0007] Step 2: Establish a discrete element model of powder particle collision, simulate the powder spreading process of the roller, and output the position and particle size information of the powder particles deposited in the powder falling area;

[0008] Step 3: Introduce order parameters representing gas phase, liquid phase, solid phase and grain orientation, construct free energy density functional, establish a heat-flow-microstructure strong coupling phase field model including energy conservation equation, molten pool flow equation and microstructure evolution equation, and realize dynamic process modeling of laser scanning powder bed;

[0009] Step 4: Construct a powder bed geometry model including a polycrystalline substrate and powder particles in a powder drop zone, assign a grain orientation to each powder particle and substrate grain, and mesh the powder bed geometry model;

[0010] Step 5: Set material properties, initial values ​​and boundary conditions, combine the powder bed geometry model and the divided mesh data, and use the finite element method to solve the thermal-fluid-microstructure strong coupling phase field model to obtain a numerical solution;

[0011] Step 6: Visualize the numerical solution of the heat-fluid-microstructure strong coupling phase field model and output the simulation results of the molten pool and microstructure morphology;

[0012] Step 7: Use ray tracing method to extract the gas-solid interface of the solidified layer after the molten pool solidifies, lay a new particle layer on the solidified layer, and repeat steps 2-6 to realize the multi-layer numerical simulation of laser selective melting.

[0013] Furthermore, in step 1, a random two-dimensional Voronoi diagram is generated using a python function to represent the geometric structure of the grains inside the polycrystalline substrate.

[0014] Furthermore, in step 2, the geometric shape of the powder particles is considered to be spherical, and the diameter distribution conforms to the Gaussian random distribution law; the discrete element method is used to generate a powder pile and simulate the roller spreading process. The discrete element method is used to simulate the roller spreading process, including simulating the interaction between powder particles and powder particles, and between powder particles and roller / substrate. In the constructed discrete element model, the Johnson-Kendall-Roberts contact constitutive model considering adhesion is used.

[0015] Furthermore, in step 3, multiple order parameters are introduced to distinguish gas, solid, liquid phases and grain orientation, where ρ = 1 is solid / liquid phase and ρ = 0 is gas phase; when ρ = 1, φ = 1 and ρ-φ = 1 represent solid phase and liquid phase respectively; when φ = 1, the grain orientation field {η i}(i=1,2,…,,N), there is only one time η i =1, and the rest are equal to 0. The total free energy of the system is expressed as

[0016] F=∫(f loc+f grad +f ht )dV,

[0017] Where f loc is the local free energy density, which is related to the energy of the phase itself; f grad is the gradient free energy density, which is related to the interface; f ht is the free energy density term related to heat. The polynomial local free energy density expression describing the gas-liquid-solid-grain orientation multiphase system constructed based on Landau phase transition theory is as follows:

[0018]

[0019] Among them, W c , W h , W d is the temperature-dependent energy barrier height;

[0020] The gradient free energy density term expression is:

[0021]

[0022] Among them, κ ρ , κ φs , κ φl and κ η is the temperature-dependent gradient coefficient.

[0023] By constructing a non-isothermal free energy functional, a multi-phase and multi-field coupled phase-field model coupling the Navier-Stokes equation, the energy conservation equation, the Cahn-Hillard equation and the Allen-Cahn equation is established to achieve strong simulation of the heat-fluid-microstructure coupling of selective laser melting.

[0024] Furthermore, in step 4, the geometric model of the powder bed composed of the base polycrystal and the powder particles is meshed at the solid-gas surface and the grain boundary using an adaptive meshing technique; each powder particle is regarded as a grain, and a greedy algorithm is used to assign grain orientation order parameters to all the grains in the powder bed.

[0025] Furthermore, the finite element method is used to solve the multiphase and multifield coupled phase field model to obtain its numerical solution, output the simulation results, and use Paraview software for visualization to obtain the real-time molten pool and microstructure morphology.

[0026] Beneficial effects: The present invention provides a laser selective melting simulation method that considers both the molten pool and microstructure evolution, and strongly couples the phase field equation with the fluid Navier-Stokes equation and the energy conservation equation to model the mixed state of multiphase composition and the solid-liquid phase transition accurately without the need for additional interface tracking. The model considers more comprehensive physical phenomena, and the model parameters are more in line with physical meanings, and can be extended to calculate the microstructure morphology of different metal materials after laser selective melting.

[0027] The present invention can reproduce the grain nucleation, growth and coarsening process during the melting, molten pool flow and solidification of powder particles. The present invention adopts the finite element method to solve the phase field model and other multi-physics field equations with strong coupling, and adopts adaptive grid to mesh the simulation domain, thereby improving the calculation efficiency while ensuring the simulation accuracy. Through the pre- and post-processing of Python script, the parameter transfer of the powder spreading and scanning process can be realized, and the multi-layer scanning simulation results can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the simulation process of laser selective melting of the present invention;

[0029] Figure 2 It is the polycrystalline base map generated by Python programming in the present invention;

[0030] Figure 3 This is a schematic diagram of the discrete element simulation powder spreading process in the present invention;

[0031] Figure 4 It is a schematic diagram of the distribution of grain orientation order parameters and the meshing of the powder bed geometric model in the present invention;

[0032] Figure 5 It is a schematic diagram of the initial powder bed, molten pool and solidified microstructure in the laser scanning powder bed process of the present invention.

[0033] Figure 6 It is a schematic diagram of multi-layer simulation of laser selective melting in the present invention. DETAILED DESCRIPTION

[0034] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Example 1

[0036] This embodiment provides a laser selective melting simulation method that takes into account both the molten pool and microstructure evolution. In this embodiment, SS316L stainless steel powder is used as an example to simulate the molten pool and microstructure evolution morphology of a single layer and single channel during laser selective melting. Please refer to Figure 1 As shown, the following steps are included:

[0037] Step 1: Set the polycrystalline substrate shape to 300×60μm 2 The number of grains inside is 90. A random two-dimensional Voronoi diagram is generated by a script based on Python language to represent the polycrystalline structure of the substrate. The generated polycrystalline substrate is as follows Figure 1 shown.

[0038] Step 2: Use the discrete element method to simulate the roller's powder spreading process. First, a powder pile is generated, and then the roller is used to push the powder to move. The roller rotates and translates at the same time, and finally the powder particles are deposited in the powder falling area. The geometric shape of the powder particles is spherical, with a diameter range of 15-45μm, and the distribution law conforms to the Gaussian random distribution. In constructing a discrete element model that simulates the interaction between particles and particles, and between particles and rollers / substrates, the Johnson-Kendall-Roberts contact constitutive model considering adhesion is used, and the normal contact force F cn It is expressed as:

[0039]

[0040] Among them, E * is the equivalent Young's modulus, R * is the equivalent radius, a is the contact radius, and γ is the surface energy density between particles.

[0041] The discrete element model parameters are shown in Table 1, and the schematic diagram of the powder spreading process is shown in Figure 3 .

[0042] Table 1 Discrete element simulation material parameters

[0043]

[0044]

[0045] Step 3: By introducing multiple order parameters that distinguish gas, solid, liquid phases and grain orientation, the phase field free energy functional is constructed, the evolution equation of the order parameter is derived, and a multi-phase and multi-field coupled phase field model that includes the Navier-Stokes equation, the energy conservation equation, the Cahn-Hillard equation and the Allen-Cahn equation is established to achieve strong coupling modeling and simulation of heat-flow-microstructure of laser selective melting.

[0046] The order parameters include: φ, {η i} and ρ, where ρ = 1 represents the solid phase or liquid phase, and ρ = 0 represents the gas phase; when ρ = 1, φ = 1 and ρ-φ = 1 represent the solid phase and liquid phase respectively; when φ = 1, the solid is further characterized by a series of grain orientation order parameters {η i}, i=1,2,…,N distinguish different grains, and there is only one η in each grain. i=1, and the rest are equal to 0; the total free energy of the system can be expressed as:

[0047] F=∫(f loc +f grad +f ht )dV,

[0048] Among them, f loc is the local free energy density, which is related to the energy of the phase itself; f grad is the gradient free energy density associated with the interface; f ht is a free energy density term related to heat, representing the background energy at different temperatures; based on the Landau phase transition theory, a local free energy density describing the gas-liquid-solid-grain orientation multiphase system is constructed, and the expression is as follows:

[0049]

[0050] Among them, W c , W h , W d is the temperature-dependent energy barrier height;

[0051] The gradient free energy density expression is:

[0052]

[0053] Among them, κ ρ , κ φs , κ φl and κ η is the temperature-dependent gradient coefficient, ▽ is the gradient operator;

[0054] Order parameters φ, η i The evolution of and ρ is described by the Cahn-Hilliard equation and the Allen-Cahn equation, respectively:

[0055]

[0056] Among them, L φ is the parameter that controls the solid interface movement rate, L η is the parameter that controls the grain boundary movement rate, and M is the interface mobility.

[0057] The flow behavior of the molten metal pool is described by the incompressible Navier-Stokes equation:

[0058]

[0059] Where u is the velocity vector, ρ l is the density, p is the pressure, μ is the dynamic viscosity coefficient; f sf 、f vpare the physical expressions of surface tension and steam recoil pressure respectively; the physical expression of surface tension is δ ∑ is the Dirac function, which is expressed as is the curvature, is the tangential component of the surface tension, σ is the temperature-dependent surface tension coefficient, and its expression is

[0060]

[0061] Where σ0 is the surface tension coefficient at reference temperature, T0 is the reference temperature, represents the surface tension temperature gradient coefficient;

[0062] The Clausius-Clapeyron equation is introduced to express the saturated vapor pressure p s ,Right now

[0063]

[0064] Where p0 is standard atmospheric pressure, ΔH v is the latent heat of evaporation, k B is the Boltzmann constant, T v is the evaporation temperature, T s is the surface temperature; steam recoil pressure p r With saturated vapor pressure p s There is the following linear relationship:

[0065]

[0066] Where β is the recoil coefficient, which ranges from 0.18 to 1. The final physical form of the recoil pressure is f vp =-nδ ∑ p s .

[0067] The energy conservation equation includes molten pool convection, solid-liquid phase change energy, Gaussian laser moving heat source, evaporation heat dissipation, heat conduction, thermal radiation and thermal convection. The Gaussian laser moving heat source parameters include scanning speed, beam power, laser radius, penetration depth and laser absorptivity. The laser parameters are shown in Table 2.

[0068] Table 2 Laser parameters

[0069]

[0070] Step 4: Geometric modeling of the powder bed structure composed of polycrystalline substrate and powder drop zone particles, gas is filled in the gaps between particles, the entire simulation domain is meshed, and the mesh at the grain-grain and gas-solid transition interfaces is refined using adaptive meshes. A greedy algorithm is used to assign a grain orientation variable to each grain, that is, an order parameter with a value of 1, to ensure that the grain orientation order parameters of adjacent grains are different. See the schematic diagram of grain orientation order parameter assignment and mesh division for details. Figure 4 .

[0071] Step 5: Use the phase field model to simulate the laser scanning powder bed process, read the geometric model and mesh data of the powder bed, set the boundary conditions of material properties and variables, and solve the model using a finite element program.

[0072] Step 6: Output the calculation results and visualize them using Paraview software to obtain the morphology of the molten pool and microstructure evolution at different times, as shown in the attached figure. Figure 5 shown.

[0073] Step 7: After the laser stops working for a period of time, the ray tracing method is used to extract the gas-solid interface of the solidified layer after the molten pool solidifies, and steps 2-6 are repeated to lay a new particle layer on the solidified layer for laser scanning, thereby completing the alternating simulation and data transmission of the powder laying and laser scanning process to obtain the multi-layer microstructure morphology. See the schematic diagram of the multi-layer simulation for details. Figure 6 .

Claims

1. A laser selective melting simulation method that simultaneously considers the evolution of the molten pool and microstructure, characterized in that: The following steps are involved: Step 1: Set the geometric dimensions of the polycrystalline substrate and the number of grains inside the polycrystalline substrate to generate the polycrystalline substrate; Step 2: Establish a discrete element model of powder particle collision, simulate the powder spreading process of the roller, and output the position and particle size information of the powder particles deposited in the powder falling area; Step 3: Introduce order parameters representing gas phase, liquid phase, solid phase and grain orientation, construct free energy density functional, establish a heat-flow-microstructure strong coupling phase field model including energy conservation equation, molten pool flow equation and microstructure evolution equation, and realize dynamic process modeling of laser scanning powder bed; Step 4: Based on the generated polycrystalline substrate and the position and particle size information of the powder particles, a powder bed geometry model including the polycrystalline substrate and the powder falling area is constructed, a grain orientation is assigned to each powder particle and substrate grain, and the powder bed geometry model is meshed; Step 5: Set material properties, initial values ​​and boundary conditions, combine the powder bed geometry model and the divided mesh data, and use the finite element method to solve the thermal-fluid-microstructure strong coupling phase field model to obtain a numerical solution; Step 6: Visualize the numerical solution of the heat-fluid-microstructure strong coupling phase field model and output the simulation results of the molten pool and microstructure morphology; Step 7: Use ray tracing method to extract the gas-solid interface of the solidified layer after the molten pool solidifies, lay a new particle layer on the solidified layer, and repeat steps 2-6 to realize the multi-layer numerical simulation of laser selective melting.

2. The method for simulating selective laser melting considering both the molten pool and microstructure evolution according to claim 1, characterized in that: In step 1, the specific steps of generating the polycrystalline substrate are: according to the geometric parameters and the number of grains of the polycrystalline substrate, a random two-dimensional Voronoi diagram is generated using a python function, and the two-dimensional Voronoi diagram is used to represent the grain geometry of the polycrystalline substrate.

3. The method for simulating selective laser melting considering both the molten pool and microstructure evolution according to claim 1, characterized in that: In step 2, the geometric shape of the powder particles is spherical, and the diameter distribution conforms to the Gaussian random distribution; the discrete element method is used to generate the powder pile and simulate the powder spreading process of the roller.

4. The method for simulating selective laser melting considering both the molten pool and microstructure evolution according to claim 3, characterized in that: In step 2, the discrete element method is used to simulate the powder spreading process of the roller, including simulating the interaction between powder particles and powder particles, and between powder particles and the roller / substrate. In the constructed discrete element model, the Johnson-Kendall-Roberts constitutive model considering the adhesion force is adopted, and the normal contact force F cn It is expressed as: Among them, E * is the equivalent Young's modulus, R * is the equivalent radius, a is the contact radius, and γ is the surface energy density between particles.

5. The method for simulating selective laser melting considering both the evolution of the molten pool and the microstructure according to claim 1, characterized in that: In step 3, the order parameters introduced include φ, {η i } and ρ, where ρ = 1 represents the solid phase or liquid phase, and ρ = 0 represents the gas phase; when ρ = 1, φ = 1 and ρ-φ = 1 represent the solid phase and liquid phase respectively; when φ = 1, the solid is further characterized by the grain orientation field {η i }, i=1,2,…,N distinguish different grains, and there is only one η in each grain. i =1, and the rest are equal to 0; the total free energy of the system is expressed as: F=∫(f loc +f grad +f ht )dV, Among them, f loc is the local free energy density, which is related to the energy of the phase itself; f grad is the gradient free energy density associated with the interface; f ht is a free energy density term related to heat, representing the background energy at different temperatures; based on the Landau phase transition theory, a local free energy density describing the gas-liquid-solid-grain orientation multiphase system is constructed, and the expression is as follows: Among them, W c , W h , W d is the temperature-dependent energy barrier height; The gradient free energy density expression is: Among them, κ ρ , κ φs , κ φl and κ η is the temperature-dependent gradient coefficient, is the gradient operator; Order parameters φ, η i The evolution of and ρ is described by the Cahn-Hilliard equation and the Allen-Cahn equation, respectively: Among them, L φ is the parameter that controls the solid interface movement rate, L η is the parameter that controls the grain boundary movement rate, and M is the interface mobility that controls interface diffusion.

6. A method for simulating selective laser melting taking into account both the evolution of the molten pool and the microstructure according to claim 5, characterized in that: In step 3, the molten pool flow equation is described by the incompressible flow Navier-Stokes equation: Where u is the velocity vector, ρ l is the density, p is the pressure, μ is the dynamic viscosity coefficient; f sf 、f vp are the physical expressions of surface tension and steam recoil pressure respectively; the physical expression of surface tension is δ Σ is the Dirac function, which is expressed as is the curvature, is the tangential component of the surface tension, σ is the temperature-dependent surface tension coefficient, and its expression is Where σ0 is the surface tension coefficient at reference temperature, T0 is the reference temperature, represents the surface tension temperature gradient coefficient; The Clausius-Clapeyron equation is introduced to express the saturated vapor pressure p s ,Right now Where p0 is standard atmospheric pressure, ΔH v is the latent heat of evaporation, k B is the Boltzmann constant, T v is the evaporation temperature, T s is the surface temperature; steam recoil pressure p r With saturated vapor pressure p s There is the following linear relationship: Where β is the recoil coefficient, which ranges from 0.18 to 1. The final physical form of the recoil pressure is f vp =-nδ Σ p s .

7. The method for simulating selective laser melting considering both the evolution of the molten pool and the microstructure according to claim 1, characterized in that: In step 3, the energy conservation equation includes molten pool convection, solid-liquid phase change energy, Gaussian laser moving heat source, evaporative heat dissipation, heat conduction, thermal radiation and thermal convection, and the Gaussian laser moving heat source parameters include scanning speed, beam power, laser radius, penetration depth, and laser absorptivity.

8. The method for simulating selective laser melting considering both the evolution of the molten pool and the microstructure according to claim 1, characterized in that: In step 4, the polycrystalline substrate serves as the bottom geometry of the powder dropping zone, and together with the powder particles in the powder dropping zone, constitutes the geometric model of the powder bed, and the gaps between the powder particles are gas; each powder particle is regarded as a grain, and a greedy algorithm is used to assign order parameters representing the grain orientation to all grains, and an adaptive meshing technique is used to refine the mesh of the powder particle-gas transition surface and the grain-grain interface.

9. The method for simulating selective laser melting considering both the evolution of the molten pool and the microstructure according to claim 1, characterized in that: In step 5, the finite element method is used to solve the thermal-fluid-microstructure strong coupling phase field model, including deriving the residual and stiffness matrices of the thermal-fluid-microstructure strong coupling phase field model, and using the Streamline Upwind Petrov / Galerkin strategy to suppress the numerical oscillation problem in the process of solving the Navier-Stokes equations.

10. The method for simulating selective laser melting considering both the evolution of the molten pool and the microstructure according to claim 1, characterized in that: In step 6, the numerical solution of the heat-fluid-microstructure strong coupling phase field model is visualized using Paraview software to obtain the morphology of the molten pool and microstructure.

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