Multi-field coupling simulation method for microstructure evolution of electric arc additive pool solidification

Abstract

The application discloses a kind of electric arc additive-pool solidification microstructure evolution multi-field coupling simulation method, solve the problem that present stage additive phase field simulation ignores various physical phenomena in the solidification process of deposited metal and makes the low precision of solidification microstructure prediction.The method proposes the substrate material grain structure generation method, progressive arc process simulation method, equiaxed crystal heterogeneous nucleation method, dendritic solid phase movement speed calculation method and the coupling simulation method of electric arc additive-pool solidification temperature field, flow field, solute field and phase field.The simulation method proposed in the application is used to simulate the solidification process of certain aluminum-copper alloy electric arc additive-pool, and the results show that the method can accurately reproduce the phenomena of dendritic remelting, pool expansion, synnthetic crystallization, polycrystalline growth, pool flow, solute convection and diffusion, heterogeneous nucleation, columnar crystal-equiaxed crystal transformation and equiaxed crystal solid phase movement in the electric arc additive manufacturing process.

Description

Technical Field

[0001] The present invention proposes a multi-field coupled simulation method for the evolution of microstructure in the solidification of arc additive manufacturing molten pool, which belongs to the field of alloy solidification microstructure simulation and is applicable to the simulation of the liquid-solid transformation process in the solidification process of the entire layer molten pool in the arc additive manufacturing of binary rare alloys. Background Technology

[0002] The arc-fuse additive manufacturing technology for high-strength aluminum alloy components in aerospace vehicles has repeatedly revealed numerous technical bottlenecks in experimental research, including inhomogeneous microstructure and severe anisotropy in mechanical properties, which seriously hinder the widespread application of this technology. Understanding the solidification behavior and microstructure evolution mechanism of metal additive manufacturing is fundamental to solving the core scientific problems behind these technical bottlenecks and achieving scientific control over the microstructure and mechanical properties of arc-fuse components.

[0003] Domestic and international scholars have conducted extensive experimental research on the process, microstructure, defects, and properties of high-strength aluminum alloy arc-fused wire additive manufacturing. This research covers the influence of arc mode, deposition strategy, interlayer cold working, heat treatment, multi-wire additive manufacturing, matrix materials, thermal process control, and heterogeneous nucleation on microstructure and mechanical properties. However, most experimental studies rely on "post-hoc analysis" to infer solidification mechanisms, making qualitative speculations difficult to verify empirically. This fails to provide a fundamental understanding of the solidification behavior and microstructure evolution mechanisms during metal additive manufacturing. Even in-situ detection suffers from insufficient resolution, limited detectable phenomena, and restricted areas. Furthermore, the process window for experimental studies is narrow and fragmented, and parametric experiments are subject to uncontrollable randomness caused by environmental and human factors, making scientific rigor difficult to guarantee. Additive manufacturing is a complex solidification process involving multiple scales and physical fields, including heat transfer, mass transfer, phase transformation, flow, dendritic nucleation / growth / solid phase movement, heterogeneous nucleation, and columnar crystal to equiaxed crystal transformation (CET). At present, real-time quantitative research on the solidification behavior and microstructure evolution of arc-added metals still relies on numerical simulation technology of solidification microstructure.

[0004] Numerous scholars both domestically and internationally have developed various microstructure simulation techniques. Among them, the phase-field method has become the mainstream approach due to its clear physical mechanisms, avoidance of complex phase interface tracking, and ability to quantitatively study the curvature and kinetic effects of the solid-liquid interface. Based on microstructure simulation techniques combined with experimental verification, it is theoretically possible to efficiently, economically, and accurately reproduce the solidification microstructure evolution process of additive manufacturing. Furthermore, it allows for rigorous exploration of the influence mechanisms of additive microstructure and properties through high-throughput integrated computation, in-situ data extraction and mechanism analysis of the kinetic behavior of transient solidification of deposited metals, and studies the reachability to any time and location within the solidification model. However, constructing and solving multiphysics models of solidification microstructure evolution in additive manufacturing processes based on the phase-field method is extremely difficult and inefficient. At present, most additive phase-field simulations only realize solute diffusion in local solidification regions and a small number of single-orientation grain morphology evolutions. Most existing additive phase-field models ignore fluid flow, heterogeneous nucleation, and CET transformation within the welded metal, and consequently ignore solute convection, solid-phase movement and collision merging of free dendrites. This makes it impossible to explore the influence of solute transport on dendrite morphology and CET transformation under flow conditions, as well as the interaction mechanism between dendrites. It is difficult to realistically reproduce the solute distribution and grain structure within the welded metal, becoming a bottleneck restricting the application of microstructure simulation in additive manufacturing technology. Summary of the Invention

[0005] To address the problems described in the background section, this invention proposes a multi-field coupled simulation method for the evolution of microstructure during the solidification of molten pools in arc additive manufacturing. This method can comprehensively reproduce various physical phenomena during the arc additive manufacturing process of binary rare alloys, including matrix melting, molten pool flow, polycrystalline growth, solute diffusion and convection, heterogeneous nucleation, CET transformation, equiaxed crystal motion and collisions, etc. The basic simulation process is as follows:

[0006] Step 1: Matrix material grain structure generation: A specific number of initial crystal nuclei with random radii, larger than the critical growth size, are randomly arranged in the entire computational domain. The growth of the crystal nuclei is simulated by the simplified phase field discretization equation (Formula (1)) with a constant driving force to obtain the initial grain structure in the matrix metal.

[0007]

[0008] in f i To characterize the first i The order parameter of each grain, where λ is the coupling constant. is the interaction coefficient between grains, and the constant term β is the simplified driving force coefficient, with values ​​[-1, -0.1].

[0009] Step 2, Temperature field calculation: The temperature field T of the aluminum alloy arc additive deposition process is calculated based on the two-dimensional simplified double ellipse model (formula (2)). The temperature field only needs to be solved once in the two or more phase field calculation domain at the beginning of the calculation. Then, the temperature field isotherm is moved forward in real time with the deposition rate to reproduce the movement of the heat source without iterative calculation.

[0010]

[0011] in T m and T p The distribution represents the melting point temperature and peak temperature of the molten pool. d Indicates the depth of the molten pool. A unified representation of the front and rear axis lengths in a simplified two-dimensional biellipse model. and , and , respectively, are the x and y coordinates of the center of the molten pool and any node in the computational domain.

[0012] Step 3: Simulation of the gradual arc initiation process: First, given the initial morphology and size of the molten pool formed by the droplet transition and the depth of the molten pool, the isotherm of the temperature field is moved from top to bottom at a specific rate to reproduce the process of the heat source gradually melting the solid substrate during the arc initiation stage. This simulates the continuous expansion of the molten pool during the arc initiation stage until a stable maximum molten pool is formed. The region where the temperature exceeds the melting point is defined as the liquid phase region, and the phase field value of this region is... Set to -1. After arc initiation, set the initial solute concentration in the liquid phase and the initial flow conditions on the surface of the molten pool, including the magnitude and direction of the tangential flow velocity.

[0013] Step 4: Calculation of undercooling in the molten pool: Based on the real-time moving temperature field isotherms and the melting point of the alloy, the undercooling of all nodes inside the molten pool is calculated in real time.

[0014] Step 5, Real-time calculation and setting of equiaxed crystal nucleation probability: Based on the Gaussian distribution random nucleation model (formulas (3)-(4)), set a reasonable mean value of nucleation undercooling. Standard deviation of supercooling and maximum density N m Calculate the probability of generating an equiaxed crystal nucleus at each node, and set an equiaxed crystal nucleus of random size at the determined nucleation location. Calculate the phase field values ​​of all nodes in the nucleation region. Set it to 1.

[0015]

[0016] in N represents the degree of supercooling and its mean and standard deviation. mThis represents the maximum number of nuclei formed per unit volume of melt.

[0017] Step 6: Iterative calculation of molten pool flow velocity: Based on the initial or previous time step phase field value, fluid flow velocity, and dendritic solid phase motion velocity, solve for the density distribution function in the lattice Boltzmann model (Equation (5)) of the current time step. g ,according to g Calculate the velocity vector in the liquid phase of the molten pool at the current time step (Formula (6)). The distribution function and velocity vector at the boundary of the calculation domain are solved using non-equilibrium extrapolation conditions.

[0018]

[0019] Where ρ, The density and flow rate of the melt. Here, c is the weighting coefficient, c is the lattice velocity, and h is the Beckman constant. f s The solid fraction represents the solid phase fraction at the solid-liquid interface. W 0 represents the width of the solid-liquid interface. n To distinguish it from the kinematic viscosity, which is the fluid dynamic viscosity coefficient, For lattice space coordinate vectors, Let τ be the migration rate of a single particle in the lattice space, and τ be the relaxation time.

[0020] Step 7: Iterative calculation of dendritic solid phase motion velocity: Based on the initial or previous time step phase field value, melt flow velocity, solid particle motion velocity, solve for the translational velocity of solid particles in the current time step. (Equation (7)) and the rotational speed about the center of mass (Formula (8)), and then the velocity vector is obtained according to Euler's law of motion (Formula (9)). The solid-liquid interface of each equiaxed dendrite of the solid phase particle satisfies the no-slip boundary condition.

[0021]

[0022] in and The vector difference represents the distance from any point on the solid-liquid interface of all dendrites within the solid particle to the centroid of the solid particle. Let g be the area of ​​the two-dimensional grid, and g be the acceleration due to gravity. and These represent the densities of the simulated alloy in its solid and liquid phases, respectively. For the entire solid phase particles, This represents the volume of the entire solid particle.

[0023] Step 8, Iterative calculation of solute field: Solve the supersaturated field based on the initial or previous time step phase field value and melt flow rate (Formula (10)). The solution of the phase field and supersaturated field at the boundary of the calculation domain adopts the zero flux Newman boundary condition.

[0024]

[0025] in k The solute partition coefficient during liquid-solid transition. f 0 represents the sum of the multiphase fields, D represents the solute diffusion coefficient, and U represents the supersaturated field. The relationship between these fields and the solute concentration is as follows: .

[0026] Step 9: Iterative calculations for the growth of columnar and equiaxed polycrystalline crystals: For the co-crystallization process of semi-molten initial grains in the parent material, the multiphase field equation of the co-crystallized columnar crystals is solved based on the supersaturated field of the initial or previous time step (Equation 11), and the phase field variables of the columnar crystals at the current time are calculated. F ic and phase field increment Δ F ic .

[0027]

[0028] For equiaxed crystal nuclei that have reached the nucleation conditions in the molten pool, the multiphase field equations of the equiaxed crystals are solved based on the supersaturated field of the initial or previous time step (Equation 12), and the phase field variables of all equiaxed crystal nuclei at a certain time are calculated. F ie and phase field increment Δ F ie .

[0029]

[0030] Advection term in the equiaxed crystal phase field equation The solution is obtained using the WENO 5th order finite difference method, and the phase field values ​​of the equiaxed crystal after motion are updated. The discretization scheme for the advection term is then:

[0031] Among them, when hour At that time, the left and right state values ​​in the x-direction are taken respectively, that is and Similarly, when and At that time, the left and right state values ​​in the y direction are taken respectively, that is and .

[0032] Step 10: Free Dendrite Collision Detection and Merging Calculation: The presence of two or more grains whose phase field values ​​simultaneously exceed the solid-phase boundary order parameter threshold at a given node at a specific moment determines whether a collision has occurred. If a collision occurs, the colliding particles are merged, including recalculating the centroid, translational velocity, and rotational velocity of the new solid-phase particle. Momentum and angular momentum conservation are satisfied between the solid-phase particles before and after the collision. The translational and rotational velocities of the new solid-phase particle formed by the merging of two or more solid-phase particles satisfy the following equations:

[0033] In the formula n The number of all solid particles involved in a given collision. α i M is the numbering of all solid particles involved in a collision, γ is the numbering of the new solid particles generated in the collision, and M is the numbering of the new solid particles generated in the collision. αi Before the collision α i The total mass of each solid particle V T , , I and These are the conditions before the collision (subscript 1) α i The translational velocity, angular velocity, moment of inertia, and center of mass of each solid particle after merging (subscript γ).

[0034] Step 11: Repeat the calculations in steps (5) to (10) during the iterative solution process. Attached Figure Description

[0035] Figure 1 A basic flowchart for multi-field coupled simulation of the evolution of microstructure in the solidification of an arc additive manufacturing molten pool; Figure 2 This is a schematic diagram of the initial grain structure of the parent material; Figure 3 This is a schematic diagram of a test piece-level component model; Figure 4 This is a schematic diagram of the material parameters for a fully coupled simulation. Figure 5 This is a schematic diagram comparing the results of rapid simulation and fully coupled simulation. Detailed Implementation

[0036] Based on the multi-field coupled simulation method for the solidification microstructure evolution of an arc additive manufacturing molten pool provided by this invention, a high-precision simulation of the solidification process of an aluminum-copper alloy molten pool manufactured by arc additive manufacturing is performed, as follows: Step 1: Matrix material grain structure generation: The entire computational domain is 0.776 mm (height). 1.551 mm (length), computational domain mesh size 3584 7168, with 247 initial crystal nuclei randomly arranged, the critical growth size of the initial crystal nuclei is 0.65 μm, and the radius varies randomly within the range of 0.65 μm to 1.95 μm. The simplified driving force coefficient β is taken as -0.14, and the coupling constant λ is taken as 71.6. Based on the simplified phase-field equation, the initial grain structure of the matrix metal is simulated as follows. Figure 2 As shown.

[0037] Step 2, Temperature field calculation: The temperature field T of the aluminum alloy arc additive deposition process is calculated based on the two-dimensional simplified double ellipse model (formula (2)). The temperature field only needs to be solved once in the two or more times phase field calculation domain at the beginning of the calculation. Then, the temperature field isotherm is moved forward in real time with the deposition rate to reproduce the movement of the heat source without iterative calculation.

[0038] Step 3: Simulation of the gradual arc initiation process: First, given the initial morphology and size of the molten pool formed by the droplet transition and the depth of the molten pool, the isotherm of the temperature field is moved from top to bottom at a specific rate to reproduce the process of the heat source gradually melting the solid substrate during the arc initiation stage. This simulates the continuous expansion of the molten pool during the arc initiation stage until a stable maximum molten pool is formed. The region where the temperature exceeds the melting point is defined as the liquid phase region, and the phase field value of this region is... Set to -1. After arc initiation, set the initial solute concentration in the liquid phase and the initial flow conditions on the surface of the molten pool, including the magnitude and direction of the tangential flow velocity.

[0039] Step 4: Calculation of undercooling in the molten pool: Based on the real-time moving temperature field isotherms and the melting point of the alloy, the undercooling of all nodes inside the molten pool is calculated in real time.

[0040] Step 5, Real-time calculation and setting of equiaxed crystal nucleation probability: Based on the Gaussian distribution random nucleation model (formulas (3)-(4)), set a reasonable mean value of nucleation undercooling ΔT. av Standard deviation of supercooling ΔT sd and maximum density N m Calculate the probability of generating an equiaxed crystal nucleus at each node, and set an equiaxed crystal nucleus of random size at the determined nucleation location. Calculate the phase field values ​​of all nodes in the nucleation region. Set it to 1.

[0041] Step 6: Iterative calculation of molten pool flow velocity: Based on the initial or previous time step phase field value, fluid flow velocity, and dendritic solid phase motion velocity, solve for the density distribution function in the lattice Boltzmann model (Equation (5)) of the current time step. f ,according to f Calculate the velocity vector in the liquid phase of the molten pool at the current time step (Formula (6)). The distribution function and velocity vector at the boundary of the calculation domain are solved using non-equilibrium extrapolation conditions.

[0042] Step 7: Iterative calculation of dendritic solid phase motion velocity: Based on the initial or previous time step phase field value, melt flow velocity, solid particle motion velocity, solve for the translational velocity of solid particles in the current time step. (Equation (7)) and the rotational speed about the center of mass (Formula (8)), and then the velocity vector is obtained according to Euler's law of motion (Formula (9)). The solid-liquid interface of each equiaxed dendrite of the solid phase particle satisfies the no-slip boundary condition.

[0043] Step 8, Iterative calculation of solute field: Solve the supersaturated field based on the initial or previous time step phase field value and melt flow rate (Formula (10)). The solution of the phase field and supersaturated field at the boundary of the calculation domain adopts the zero flux Newman boundary condition.

[0044] Step 9: Iterative calculations for the growth of columnar and equiaxed polycrystalline crystals: For the co-crystallization process of semi-molten initial grains in the parent material, the multiphase field equation of the co-crystallized columnar crystals is solved based on the supersaturated field of the initial or previous time step (Equation 11), and the phase field variables of the columnar crystals at the current time are calculated. F ic and phase field increment Δ F ic .

[0045] For equiaxed crystal nuclei that have reached the nucleation conditions in the molten pool, the multiphase field equations of the equiaxed crystals are solved based on the supersaturated field of the initial or previous time step (Equation 12), and the phase field variables of all equiaxed crystal nuclei at a certain time are calculated. F ie and phase field increment Δ F ie .

[0046] Advection term in the equiaxed crystal phase field equation The solution is obtained using the WENO5-order finite difference method, and the phase field values ​​of the equiaxed crystal after motion are updated.

[0047] Step 10: Free Dendrite Collision Detection and Merging Calculation: The system determines whether a collision has occurred by checking if two or more grains at a given node simultaneously exceed the solid phase boundary order parameter threshold. If a collision occurs, the colliding particles are merged, including recalculating the centroid, translational velocity, and rotational velocity of the new solid phase particle. Momentum and angular momentum conservation are maintained between the solid phase particles before and after the collision. The merged solid phase particle is composed of two or more particles.

[0048] Step 11: Repeat the calculations in steps (5) to (10) during the iterative solution process.

Claims

1. A multi-field coupled simulation method for the evolution of microstructure in the solidification of an arc additive manufacturing molten pool, characterized in that, A coupled simulation method for the solidification temperature field, flow field, solute field, and phase field of an arc additive manufacturing molten pool is proposed. The method utilizes a simplified two-dimensional double-ellipse model to calculate the temperature field during the arc additive deposition process of aluminum alloys, a lattice Boltzmann model to calculate the flow field in the molten pool, an oversaturated field equation to solve for the evolution of the solute field during solidification, and a multiphase field equation to solve for the phase field distribution during the growth of columnar and equiaxed crystals. The phase field is coupled with the solute and temperature fields, and the solute field is coupled with the flow and phase fields. Furthermore, a full-process simulation method for the solidification of an arc additive manufacturing molten pool is proposed. A simplified phase field equation with a constant driving force is used to simulate the initial grain growth process of the matrix material. A constant-rate downward movement of the temperature field isotherms simulates the gradual arc initiation process. A real-time forward movement of the temperature field isotherms at the deposition rate reproduces the heat source movement process. Euler's laws of motion are used to simulate the solid-phase motion process of equiaxed dendrites. Momentum and angular momentum conservation is used to simulate the collision and merging processes of dendrites.

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