A numerical simulation method for laser surface remelting microstructure of particulate reinforced magnesium matrix composite

Abstract

The application discloses a numerical simulation method for laser surface remelting microstructure of particle reinforced magnesium matrix composite, and belongs to the technical field of numerical simulation of composite microstructure.The application solves the problem that the existing numerical simulation method does not fully consider the interaction between dendrite growth and particle movement.Based on the electron probe experimental characterization result, the application takes the real solid phase composition field of the as-cast state as the initial condition of calculation, more truly reproduces the actual solidification process, simultaneously carries out coupling calculation on the microstructure evolution and particle movement, adopts the cellular automaton technology to simulate the magnesium alloy existing the reinforcing particles, considers the influence of the dendrite growth on the particle movement, can realize the numerical prediction of the microstructure of the laser surface remelting particle reinforced magnesium matrix composite, and can more accurately predict the microstructure formation and particle migration in the molten pool in the laser melting metal process.The method can be applied to the numerical simulation of the microstructure of the particle reinforced magnesium matrix composite.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of composite material microstructure, specifically relating to a numerical simulation method for particle dispersion in the molten pool of laser-remelted particle-reinforced magnesium matrix composite material. Background Technology

[0002] Magnesium alloys possess advantages such as low density, high specific strength and stiffness, good electromagnetic shielding, and machinability, making them the lightest engineering materials currently available. However, their relatively low strength and hardness, as well as poor wear resistance and corrosion resistance, limit their development to some extent. Introducing ceramic particles into magnesium alloys can achieve exceptional physical, chemical, and mechanical properties. Particle-reinforced magnesium matrix composites not only inherit the advantages of magnesium alloys but also significantly enhance absolute strength, high-temperature mechanical properties, and frictional properties, making them one of the most advantageous approaches to improving the mechanical properties of magnesium alloys and enabling industrial applications. However, a significant factor limiting the rapid development of as-cast particle-reinforced magnesium matrix composites is the relatively large grain size resulting from the low cooling rate during casting. These large grains form triangular grain boundaries, reducing the continuity of the eutectic phase distribution at the grain boundaries. When exposed to corrosive media, if the eutectic phase is continuously distributed at the grain boundaries, it can act as a passivating phase to protect the magnesium matrix and slow down the corrosion rate; however, if the eutectic phase is discontinuously distributed at the grain boundaries, it cannot act as a passivating phase to protect the magnesium matrix. Since corrosion begins on the surface of components, research on surface modification of particle-reinforced magnesium matrix composites is particularly important.

[0003] Laser surface remelting (LSR) utilizes a high-energy-density laser beam to irradiate a metal surface, instantly melting a surface layer of a certain thickness. The molten pool then rapidly solidifies through heat transfer and cooling within the substrate, thereby improving the material's surface microstructure, strength, toughness, and corrosion resistance. However, different LSR processes have varying effects on the surface microstructure, consequently affecting mechanical properties and ultimately the product's usability. Experimentally exploring the quantitative relationship between LSR processes and microstructure is inherently risky; extensive experimentation involves significant trial and error, consuming substantial human, material, and financial resources.

[0004] With the development of computer technology, numerical simulation has become an important and effective tool for studying metal solidification processes. Numerical simulation allows for quantitative or qualitative analysis of a series of physical phenomena during nonlinear, unsteady solidification processes, such as heat / mass / momentum transport, particle transport, and grain nucleation and growth. The simulation results provide crucial guidance for process development and optimization. Numerical simulation can establish quantitative relationships between process parameters and microstructure in a short time, thus shortening the R&D cycle. However, current numerical simulation research focuses primarily on the molten pool evolution during LSR (Laminated Solidification), with less emphasis on the microstructure evolution during solidification. There are two main reasons for this: First, LSR involves melting, and the melted material is not homogeneous, meaning the assumption of "uniform composition in the initial state" no longer applies. Second, the system contains two substances: magnesium dendrites and ceramic particles. During LSR solidification, magnesium dendrites grow while ceramic particles move. Collisions between dendrites and particles can trigger particle movement, and particles also undergo Brownian motion under high temperatures. However, the interaction between dendrite growth and particle movement has not yet been fully considered. Therefore, the numerical simulation method for the microstructure of laser surface remelting particle-reinforced magnesium matrix composites developed needs to be based on real component test results to establish a remelting model, map the real physical process to the numerical simulation process, so as to better reflect the real physical process and provide necessary theoretical guidance and technical support for the research and development and production of high-performance magnesium matrix composites. Summary of the Invention

[0005] The purpose of this invention is to address the problem that existing numerical simulation methods do not fully consider the interaction between dendrite growth and particle movement, and to propose a numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite materials, the method specifically including the following steps:

[0007] Step 1: Using the prepared cast sample as a substrate, the substrate surface is sandblasted, and then the treated substrate is laser-remelted, and the molten pool depth L is measured. molten-pool and primary dendrite spacing λ PDAS ;

[0008] Calculate the liquidus temperature T' during non-equilibrium solidification. l Then according to T' l Molten pool depth L molten-pool and primary dendrite spacing λ PDAS Calculate the eutectic reaction temperature T' during non-equilibrium solidification. e ;

[0009] Step 2: Determine the relationship between the melt viscosity and temperature of the particle-reinforced magnesium matrix composite material;

[0010] Step 3: Divide the molten pool region and air layer into cubic meshes. The size of each cubic mesh is Δx×Δx×Δx.

[0011] The substrate layer is divided into cubic meshes, and the size of each cubic mesh is Δx. o ×Δx o ×Δx o Δx < Δx o ;

[0012] Mesh generation allows for the calculation of heat and momentum transfer within the molten pool during the LSR process, thereby describing the changes in temperature and flow fields during molten pool formation.

[0013] Step 4: Based on the liquidus temperature T' during the non-equilibrium solidification process l Eutectic reaction temperature T' e The flow field in the air layer and molten pool region is calculated by analyzing the relationship between melt viscosity and temperature, and the average density and the flow velocity of the molten metal are obtained.

[0014] Step 5: For the air layer, molten pool region, and substrate region, calculate the temperature field based on the average density and molten metal flow velocity obtained in Step 4.

[0015] Step 6: For the molten pool region, calculate the net force on the particles based on the molten metal flow velocity obtained in Step 4. Solve the particle motion equations based on the net force on the particles and the molten metal flow velocity obtained in Step 4 to obtain the particle motion velocity field.

[0016] Step 7: Determine whether the laser scanning process is complete;

[0017] If the laser scanning process is completed, stop the calculation and output the temperature field, liquid flow velocity field and particle motion velocity field of the local area of ​​the molten pool at different times, and then continue to execute step eight.

[0018] If the laser scanning process is not finished, increment the time step by 1, and return to step four using the net force on the particle calculated in step six.

[0019] Step 8: Select a sub-region from the molten pool region as the computational domain for the tissue simulation. Mesh the selected computational domain, with each mesh having a size of Δx. sub-cell ·Δx sub-cell And Δx>Δx sub-cell The number of grid rows obtained is N X-cell The number of grid columns is NY-cell ;

[0020] Based on the temperature field of the local region of the molten pool output in step seven, the cooling curve of the computational domain for microstructure simulation is obtained, and the maximum temperature on the cooling curve is denoted as T. max-cell The total number of particles N in the tissue simulation computational domain is obtained based on the particle motion velocity field. par ;

[0021] Step 9: According to T max-cell The specific process of microstructure formation is as follows:

[0022] Step 91: Read the experimental result data file obtained from electron probe characterization; the experimental result data file is an N... X-cell Line N Y-cell A matrix of columns;

[0023] Step 92: Assign the temperature T at different times to the grid in the i-th row and j-th column of the computational domain based on the cooling curve. cell,k (i,j), the cooling curve includes NK time points and a time step of Δt. cell =Time cell,2 -Time cell,1 =Time cell,3 -Time cell,2 =…=Time cell,NK -Time cell,NK-1 , where Time cell,1 This is the time corresponding to the first moment; and at the same moment, the temperature of each grid in the computational domain is the same;

[0024] Based on the experimental data file obtained from electron probe characterization, the solid phase composition Cs at the initial time is assigned to each grid in the computational domain. cell,1 (i,j), where i takes values ​​in the range [1,N]. X-cell The value of j is [1, N]. Y-cell ];

[0025] Step 93: At the initial moment, initialize the initial value of the liquid phase composition of the mesh (i,j) to C. l,1 (i,j)=Cs cell,1 (i,j) / k v k v This represents the non-equilibrium solute partition coefficient, with the initial solid fraction of grid (i,j) being f. s-r,1 (i,j)=1, the initial value of the composition at the solid-liquid interface is The initial value of the solid fraction in the resolidification stage is f. s-s,k (i,j)=0;

[0026] Initialization time k = 1;

[0027] Step 94, according to f s-r,k The melting factor q of the computational mesh (i,j) is calculated. m :

[0028]

[0029] Where, q m Let f be the melting factor of grid (i,j), m be the first nearest neighbor of grid (i,j), m' be the second nearest neighbor of grid (i,j), and d2 be a constant; if at time k, the solid fraction f of the m-th grid in the first nearest neighbor of grid (i,j) is... s-r,k (m)>0, then otherwise, If at time k, the solid fraction f of the m'th grid in the second nearest neighbor of grid (i,j) is... s-r,k (m')>0, then otherwise,

[0030] The composition at the solid-liquid interface Change in solid fraction Δf s-r and the solid fraction f in the remelting stage s-r for:

[0031]

[0032] Among them, T m For melting point, Δf s-r,k (i,j) represents the change in solid fraction at time k, f s-r,k+1 (i,j) represents the solid fraction of the grid (i,j) at time k+1. This represents the composition at the solid-liquid interface of the mesh (i,j) at time k+1;

[0033] The partial differential equation for solute diffusion during remelting is solved using an explicit difference algorithm:

[0034]

[0035] Among them, C l,k+1 (i,j) represents the liquid phase composition of the grid (i,j) at time k+1;

[0036] Step 95: Let k = k + 1, and determine whether all grids satisfy f. s-r,k (i,j)=0;

[0037] If all grids satisfy f s-r,k If (i,j) = 0, it indicates complete melting, and Cs cell,k If (i,j) = 0, continue with step 96;

[0038] If not all grids satisfy f s-r,k If (i,j) = 0, then return to step nine four;

[0039] Step 96, according to f s-s,k (i,j) computes the solidification factor q of the grid (i,j). s :

[0040]

[0041] The composition at the solid-liquid interface Change in solid fraction Δf s-s and solid fraction f during the resolidification stage s-s for:

[0042]

[0043] Where Γ is the Gibbs coefficient, wmc is the curvature of the solid-liquid interface, and Δf s-s,k (i,j) represents the change in solid fraction at time k, f s-s,k+1 This represents the solid fraction during the resolidification stage at time k+1;

[0044] The formula for calculating the curvature of the solid-liquid interface is:

[0045]

[0046] in, For anisotropic functions, Represents the divergence of a vector;

[0047]

[0048] Where, n z =0 represents a two-dimensional tissue simulation, and ε1, ε2, and ε3 are coefficients;

[0049]

[0050] The partial differential equations are solved using an explicit difference algorithm. The solute diffusion equation during resolidation is as follows:

[0051]

[0052] in,

[0053] Step 97: Let k = k + 1, and determine whether all grids within the computational domain satisfy f. s-s,k (i,j)=1;

[0054] If all grids satisfy f s-s,k If (i,j) = 1, it indicates complete solidification, C l,k(i,j)=0;

[0055] If not all grids satisfy f s-s,k If (i,j) = 1, then return to step nine six;

[0056] Cellular automata technology is used to simulate the process represented by the calculation results of steps 94 and 96, that is, to simulate the remelting of the solid phase and the formation of dendrites in the liquid phase, and output the microstructure at different times.

[0057] The beneficial effects of this invention are:

[0058] This invention obtains the temperature gradient and primary dendrite spacing within the molten pool based on experimental characterization, thereby calculating the liquidus line and eutectic reaction temperature during non-equilibrium solidification. Based on electron probe microanalysis results, the actual solid phase composition field in the as-cast state is used as the initial condition for calculation, more realistically reproducing the actual solidification process. Simultaneously, the microstructure evolution and particle movement are coupled in the calculation, solving the current problem of inaccurately predicting the microstructure formation of particle-reinforced magnesium matrix composites. This provides theoretical guidance and data support for a deeper understanding of the microstructure formation within the molten pool and the optimization of process parameters during laser forming of composite materials.

[0059] This invention employs cellular automata technology to simulate magnesium alloys with reinforcing particles, using experimental data as the initial conditions for simulation calculations to simulate remelting. Considering the influence of dendrite growth on particle movement, numerical prediction of the microstructure of particle-reinforced magnesium matrix composites remelted by laser surface melting can be achieved. This invention can more accurately predict the formation of microstructure and particle migration within the molten pool during laser melting of metals, providing theoretical support for optimizing laser forming processes for composite materials. Attached Figure Description

[0060] Figure 1 This is a flowchart of a numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites according to the present invention;

[0061] Figure 2(a) shows the metallographic image of the microstructure of the SiC / Mg-9wt.%Al composite material at a scanning speed of 150 mm / s during the laser surface remelting process;

[0062] Figure 2(b) shows the metallographic image of the microstructure of the SiC / Mg-9wt.%Al composite material at a scanning speed of 350 mm / s during the laser surface remelting process.

[0063] Figure 2(c) shows the metallographic image of the microstructure of the SiC / Mg-9wt.%Al composite material at a scanning speed of 450 mm / s during the laser surface remelting process.

[0064] Figure 3(a) shows the curves of temperature gradient versus scanning speed;

[0065] Figure 3(b) shows the average λ PDAS A graph showing the change in scanning speed;

[0066] Figure 3(c) shows the curve of dendrite tip radius versus scanning speed;

[0067] Figure 3(d) shows the curves of liquidus temperature versus scanning speed during non-equilibrium solidification.

[0068] Figure 3(e) shows the curves of the eutectic reaction temperature versus the scanning rate during the non-equilibrium solidification process;

[0069] Figure 4(a) shows the dimensions of the sprue, glide runner, and thin-walled casting during the filling experiment of the SiC / Mg-9wt.%Al composite thin-walled part;

[0070] Figure 4(b) shows the casting process of the thin-walled casting;

[0071] Figure 5(a) shows the length of the magnesium-based composite material after being filled with liquid metal at different particle addition amounts (0 wt.%, 1 wt.%, and 3 wt.%).

[0072] Figure 5(b) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 0 wt.%.

[0073] The minimum temperature zone in the eighth second of filling refers to the minimum temperature range during the 8th second of filling; Casting temperature refers to the casting temperature; Mold temperature refers to the mold temperature; Filling Time refers to the filling time.

[0074] Figure 5(c) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 1 wt.%.

[0075] Particle indicates the amount of particles added;

[0076] Figure 5(d) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 3 wt.%.

[0077] Figure 5(e) shows the liquid phase viscosity versus time curve obtained by the reverse calculation method;

[0078] Viscosity indicates the viscosity of the liquid phase;

[0079] Figure 6 For setting the calculation area;

[0080] Figure 7(a) shows the non-equilibrium solidification liquidus temperature (T') at a scanning speed of 150 mm / s. l ) and eutectic reaction temperature (T' e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0081] Moltenpool means molten pool;

[0082] Figure 7(b) shows the non-equilibrium solidification liquidus temperature (T') at a scanning speed of 350 mm / s. l ) and eutectic reaction temperature (T' e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0083] Figure 7(c) shows the non-equilibrium solidification liquidus temperature (T') at a scanning speed of 450 mm / s. l ) and eutectic reaction temperature (T' e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0084] Figure 7(d) shows the equilibrium solidification liquidus temperature (T) at a scanning speed of 150 mm / s. l ) and eutectic reaction temperature (T e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0085] Figure 7(e) shows the equilibrium solidification liquidus temperature (T0) at a scanning speed of 350 mm / s. l ) and eutectic reaction temperature (T e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0086] Figure 7(f) shows the equilibrium solidification liquidus temperature (T) at a scanning speed of 450 mm / s. l ) and eutectic reaction temperature (T e A comparison of the temperature field obtained from numerical calculation (left) and the molten pool depth obtained from experimental measurement (right);

[0087] Figure 8 The flow field inside the molten pool obtained by numerical calculation at different scanning speeds;

[0088] (a) is the non-equilibrium phase diagram data T' at a scan speed of 150 mm / s. l and T' e The flow field inside the molten pool obtained through numerical calculation;

[0089] (b) is the non-equilibrium phase diagram data T' at a scan speed of 350 mm / s. l and T' e The flow field inside the molten pool obtained through numerical calculation;

[0090] (c) is the non-equilibrium phase diagram data T' when the scan speed is 450 mm / s. l and T' e The flow field inside the molten pool obtained through numerical calculation;

[0091] (d) is the equilibrium phase diagram data T when the scan speed is 150 mm / s. l and T e The flow field inside the molten pool obtained through numerical calculation;

[0092] (e) is the result of using the equilibrium phase diagram data T at a scan speed of 350 mm / s. l and T e The flow field inside the molten pool obtained through numerical calculation;

[0093] (f) is the result of using the equilibrium phase diagram data T at a scan speed of 450 mm / s. l and T e The flow field inside the molten pool obtained through numerical calculation;

[0094] Figure 9 The particle dispersion in the molten pool obtained by numerical calculation at different scanning speeds;

[0095] (a) is the non-equilibrium phase diagram data T' at a scan speed of 150 mm / s. l and T' e The particle dispersion within the molten pool obtained through numerical calculation;

[0096] NPs velocity represents the velocity of particle movement;

[0097] (b) is the non-equilibrium phase diagram data T' at a scan speed of 350 mm / s. l and T' e The particle dispersion within the molten pool obtained through numerical calculation;

[0098] (c) is the non-equilibrium phase diagram data T' when the scan speed is 450 mm / s. l and T' e The particle dispersion within the molten pool obtained through numerical calculation;

[0099] (d) is the equilibrium phase diagram data T when the scan speed is 150 mm / s. l and T e The particle dispersion within the molten pool obtained through numerical calculation;

[0100] (e) is the result of using the equilibrium phase diagram data T at a scan speed of 350 mm / s. l and T e The particle dispersion within the molten pool obtained through numerical calculation;

[0101] (f) is the result of using the equilibrium phase diagram data T at a scan speed of 450 mm / s. l and T e The particle dispersion within the molten pool obtained through numerical calculation;

[0102] Figure 10 This is a curve showing the temperature change over time at a local location in the molten pool, obtained from numerical calculations.

[0103] The scanning speeds were 150 mm / s, 350 mm / s and 450 mm / s, respectively;

[0104] Figure 11 The distribution of aluminum elemental composition (wt.%) obtained by electron probe microanalysis (EPMA) for cast samples (substrate);

[0105] Figure 12 The aluminum element composition distribution in the computational domain after the remelting process is calculated by using the experimental electron probe test results as input data.

[0106] (a) indicates a scanning speed of 150 mm / s; (b) indicates a scanning speed of 350 mm / s; (c) indicates a scanning speed of 450 mm / s.

[0107] Figure 13 To calculate the grain structure and particle distribution at different scanning speeds;

[0108] (a1) and (a2) show the grain structure and particle distribution at a scanning speed of 150 mm / s, respectively; (b1) and (b2) show the grain structure and particle distribution at a scanning speed of 350 mm / s, respectively; (c1) and (c2) show the grain structure and particle distribution at a scanning speed of 450 mm / s, respectively.

[0109] Figure 14 Grain structure diagrams and grain size distribution statistics at different scanning speeds were obtained from backscattered electron diffraction (EBSD) images of the grain structure in the molten pool and substrate.

[0110] (a) Grain structure at a scanning speed of 150 mm / s, (b) Grain structure at a scanning speed of 350 mm / s, (c) Grain structure at a scanning speed of 450 mm / s, (d) Grain size distribution at a scanning speed of 150 mm / s, (e) Grain size distribution at a scanning speed of 350 mm / s, (f) Grain size distribution at a scanning speed of 450 mm / s; Average grain size in molten pool represents the average grain size in the molten pool, Equivalent diameter of grain represents the equivalent diameter of the grain, and Relative frequency represents the relative frequency. Detailed Implementation

[0111] Specific implementation method one: Combining Figure 1 This embodiment describes a numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites. The method specifically includes the following steps:

[0112] Step 1: Using the prepared cast sample as a substrate, the substrate surface is sandblasted, and then the treated substrate is laser-remelted, and the molten pool depth L is measured. molten-pool and primary dendrite spacing λ PDAS ;

[0113] Calculate the liquidus temperature T' during non-equilibrium solidification. l Then according to T' l Molten pool depth L molten-pool and primary dendrite spacing λ PDAS Calculate the eutectic reaction temperature T' during non-equilibrium solidification. e ;

[0114] Step 2: Determine the relationship between the melt viscosity and temperature of the particle-reinforced magnesium matrix composite material;

[0115] Step 3: Divide the molten pool region and air layer into cubic meshes. The size of each cubic mesh is Δx×Δx×Δx.

[0116] The substrate layer is divided into cubic meshes, and the size of each cubic mesh is Δx. o ×Δx o ×Δx o Δx < Δx o ;

[0117] Mesh generation allows for the calculation of heat and momentum transfer within the molten pool during the LSR process, thereby describing the changes in temperature and flow fields during molten pool formation.

[0118] Step 4: Based on the liquidus temperature T' during the non-equilibrium solidification process l Eutectic reaction temperature T' e The flow field in the air layer and molten pool region is calculated by analyzing the relationship between melt viscosity and temperature, and the average density and the flow velocity of the molten metal are obtained.

[0119] Step 5: For the air layer, molten pool region, and substrate region, calculate the temperature field based on the average density and molten metal flow velocity obtained in Step 4.

[0120] Step 6: For the molten pool region, calculate the net force on the particles based on the molten metal flow velocity obtained in Step 4. Solve the particle motion equations based on the net force on the particles and the molten metal flow velocity obtained in Step 4 to obtain the particle motion velocity field.

[0121] Step 7: Determine whether the laser scanning process is complete;

[0122] If the laser scanning process is completed, stop the calculation and output the temperature field, liquid flow velocity field and particle motion velocity field of the local area of ​​the molten pool at different times, and then continue to execute step eight.

[0123] If the laser scanning process is not finished, increment the time step by 1, and return to step four using the net force on the particle calculated in step six.

[0124] Step 8: Select a sub-region from the molten pool region as the computational domain for tissue simulation (it should be noted that the selected region should not contain agglomerates, and the selected region should be a local area on a two-dimensional cross-section). Mesh the selected computational domain, with each mesh having a size of Δx. sub-cell ·Δx sub-cell And Δx>Δx sub-cell The number of grid rows obtained is N. X-cell The number of grid columns is N Y-cell ;

[0125] Based on the temperature field of the local region of the molten pool output in step seven, the cooling curve (i.e., the temperature-time curve) of the microstructure simulation calculation domain is obtained, and the maximum temperature on the cooling curve is denoted as T. max-cell The total number of particles N in the tissue simulation computational domain is obtained based on the particle motion velocity field. par It outputs a data file (tem-time.dat) containing cooling curve information and a data file (particle-num.dat) containing particle count information;

[0126] Step 9, according to T max-cell The specific process of microstructure formation is as follows:

[0127] Step 91: Read the experimental data file obtained from electron probe microanalysis (EPMA) characterization, which will be used to assign initial values ​​to the solid phase composition later. s The value of (EPMA) comes from reading the experimental results data file; the experimental results data file is an N... X-cell Line N Y-cell A matrix of columns;

[0128] Therefore, the computational domain for the microstructure simulation is the same size as the experimental test region contained in the experimental results data file. Thus, in the experimental results data file, the size of each grid in the computational domain is Δx. sub-cell ·Δx sub-cell The area of ​​the computational domain is N. X-cell ·Δx sub-cell ·N Y-cell· Δx sub-cell Therefore, the X direction of the computational domain contains N. X-cell There are N grids, with N grids in the Y direction. Y-cell The number of grids means that the experimental results data file is an N-cell grid. X-cell Line N Y-cell A matrix of columns;

[0129] Step 92: Read the cooling curve file (tem-time.dat) output in Step 8, and assign the temperature T at different times to the grid in the i-th row and j-th column of the computational domain according to the cooling curve. cell,k (i,j), the cooling curve includes NK time points and a time step of Δt. cell =Time cell,2 -Time cell,1 =Time cell,3 -Time cell,2 =…=Time cell,NK -Time cell,NK-1 , where Time cell,1 This refers to the time corresponding to the first moment;

[0130] Furthermore, at the same time, the temperature of each grid in the computational domain is the same; that is, no heat transfer calculations are performed between grids at the same time, and each grid in the computational domain simultaneously obtains the maximum temperature T on the cooling curve. max-cell ;

[0131] Based on the experimental data file obtained from electron probe characterization, the solid phase composition Cs at the initial time is assigned to each grid in the computational domain. cell,1 (i,j), at each time point during the remelting stage, the solid composition of each grid remains unchanged, where i takes values ​​in [1,N]. X-cell The value of j is [1, N]. Y-cell ];

[0132] Step 93: At the initial moment, initialize the initial value of the liquid phase composition of the mesh (i,j) to C. l,1 (i,j)=Cs cell,1 (i,j) / k v k v This represents the non-equilibrium solute partition coefficient, with the initial solid fraction of grid (i,j) being f. s-r,1 (i,j)=1, the initial value of the composition at the solid-liquid interface is The initial value of the solid fraction in the resolidification stage is f. s-s,k (i,j)=0, only parameter f s-s,k In (i,j), k represents the first moment of the resolidification stage;

[0133] Initialization time k = 1;

[0134] Step 94, according to f s-r,k The melting factor q of the computational mesh (i,j) is calculated. m :

[0135]

[0136] Where, q m Let f be the melting factor of grid (i,j), m be the first nearest neighbor of grid (i,j), m' be the second nearest neighbor of grid (i,j), and d2 be a constant; if at time k, the solid fraction f of the m-th grid in the first nearest neighbor of grid (i,j) is... s-r,k (m)>0, then otherwise, If at time k, the solid fraction f of the m'th grid in the second nearest neighbor of grid (i,j) is... s-r,k (m')>0, then otherwise,

[0137] The first nearest neighbor of grid (i,j) contains 4 grids, meaning the value of 1st is 4, namely (i-1,j), (i+1,j), (i,j-1), and (i,j+1); the second nearest neighbor of grid (i,j) also contains 4 grids, meaning the value of 2nd is 4, namely (i-1,j+1), (i+1,j+1), (i-1,j-1), and (i+1,j+1). At the boundaries of the computational domain, i.e., i = 0, i = N X-cell j=0 or j=N Y-cell Each grid has 4 first nearest neighbors and 4 second nearest neighbors; non-existent grids are replaced by their own grid.

[0138] The composition at the solid-liquid interface Change in solid fraction Δf s-rand the solid fraction f in the remelting stage s-r for:

[0139]

[0140] Among them, T m For melting point, Δf s-r,k (i,j) represents the change in solid fraction at time k, f s-r,k+1 (i,j) represents the solid fraction of the grid (i,j) at time k+1. This represents the composition at the solid-liquid interface of the mesh (i,j) at time k+1;

[0141] The partial differential equation for solute diffusion during remelting is solved using an explicit difference algorithm:

[0142]

[0143] Among them, C l,k+1 (i,j) represents the liquid phase composition of the grid (i,j) at time k+1. In the partial differential equation, C l,k (i,j) is abbreviated as C l (i,j), f s-r,k (i,j) is abbreviated as f s-r (i,j);

[0144] Step 95: Let k = k + 1, and determine whether all grids satisfy f. s-r,k (i,j)=0;

[0145] If all grids satisfy f s-r,k If (i,j) = 0, it indicates complete melting (the next moment enters the resolidification stage), and Cs is at this time. cell,k If (i,j) = 0, continue with step 96;

[0146] If not all grids satisfy f s-r,k If (i,j) = 0, then return to step nine four;

[0147] Step 96, according to f s-s,k (i,j) computes the solidification factor q of the grid (i,j). s :

[0148]

[0149] The composition at the solid-liquid interface Change in solid fraction Δf s-s and solid fraction f during the resolidification stage s-s for:

[0150]

[0151] Where Γ is the Gibbs coefficient, wmc is the curvature of the solid-liquid interface, and Δf s-s,k (i,j) represents the change in solid fraction at time k, f s-s,k+1 This represents the solid fraction during the resolidification stage at time k+1. Formulas (2) and (3) in step one relate to k. v and m lv Calculations were performed;

[0152] The solid-liquid interface curvature (wmc) is calculated only for the mesh during the remelting and resolidification stage. The formula for calculating the solid-liquid interface curvature is as follows:

[0153]

[0154] in, For anisotropic functions, Represents the divergence of a vector;

[0155]

[0156] Where, n z =0 represents a two-dimensional tissue simulation, and ε1, ε2, and ε3 are coefficients;

[0157]

[0158] The partial differential equations are solved using an explicit difference algorithm. The solute diffusion equation during resolidation is as follows:

[0159]

[0160] in,

[0161] Step 97: Let k = k + 1, and determine whether all grids within the computational domain satisfy f. s-s,k (i,j)=1;

[0162] If all grids satisfy f s-s,k If (i,j) = 1, it indicates complete solidification, C l,k (i,j)=0;

[0163] If not all grids satisfy f s-s,k If (i,j) = 1, then return to step nine six;

[0164] Cellular automata technology (a graphical display technology) is used to simulate the process represented by the calculation results of steps 94 and 96, that is, to simulate the remelting of the solid phase and the formation of dendrites in the liquid phase, and output the microstructure at different times.

[0165] In this invention, when the mesh is in the heating stage (i.e., the remelting stage), the temperature T of mesh (i,j) is...cell (i,j) satisfy: T' e <T cell (i,j) <T' l And T cell (i,j) has not yet reached T max-cell When the mesh is in the cooling stage (remelting and resolidification stage), the temperature T of mesh (i,j) is... cell (i,j) satisfy: T' e <T cell (i,j) <T' l And T cell (i,j) has reached T max-cell .

[0166] Specific Implementation Method Two: This implementation method further defines Specific Implementation Method One, wherein the calculation of the liquidus temperature T' during the non-equilibrium solidification process... l Then according to T' l Molten pool depth L molten-pool and primary dendrite spacing λ PDAS Calculate the eutectic reaction temperature T' during non-equilibrium solidification. e Specifically:

[0167]

[0168] T′ l =(T l -ΔT R (6)

[0169] ΔT ls =(T l -ΔT R )-T′ e (7)

[0170] Among them, R tip V is the radius of the dendrite tip. scan For laser scanning speed, D L Let m be the diffusion coefficient of the solute in the liquid phase. lv k is the slope of the liquidus line during non-equilibrium solidification. v C is the liquid solute partition coefficient in a non-equilibrium solidification process. o Γ represents the initial composition of the alloy, Γ is the Gibbs coefficient, and m le To balance the slope of the liquidus line during solidification, k e To balance the solute partition coefficient during solidification, ΔT R For curvature supercooling, ΔT ls The crystallization temperature range (i.e., ΔT) during non-equilibrium solidification. ls =T' l -T' e ), GT T represents the temperature gradient between the molten pool surface and the substrate. l T' is the liquidus temperature corresponding to the equilibrium phase diagram. e T' is the eutectic reaction temperature during non-equilibrium solidification. l ν is the liquidus temperature during non-equilibrium solidification, and l is the interatomic distance at the solid-liquid interface.

[0171] The other steps and parameters are the same as in Specific Implementation Method 1.

[0172] The variables in formulas (2) and (3) can be determined through experimental characterization and literature review. The dendrite tip radius R is calculated by first solving formula (1). tip Obtain the dendrite tip radius R. tip Then, solving formula (4) will yield ΔT. R Value; λ PDAS The value has been obtained through experimental characterization, therefore, solving formula (5) will yield ΔT. ls The value can be obtained by solving formula (6); then T' can be obtained. l Value; based on the already obtained ΔT ls Value and T' l The value of T' can be obtained by solving formula (7). e value.

[0173] Specific Implementation Method 3: This implementation method further defines Specific Implementation Method 2, wherein the temperature gradient G between the molten pool surface and the substrate is... T for:

[0174] G T =(T surface -T substrate ) / (0.827·L molten-pool (8)

[0175] Among them, T substrate T represents the initial temperature of the substrate (room temperature). surface L represents the highest surface temperature of the molten pool (this highest surface temperature is the initial value obtained without considering particles and under the equilibrium phase diagram). molten-pool Indicates the depth of the molten pool.

[0176] The other steps and parameters are the same as in Specific Implementation Method Two.

[0177] Specific Implementation Method Four: This implementation method is a further limitation of Specific Implementation Method Three. The specific process of step two is as follows:

[0178] Step 21: Under the known particle content, a sand-casting gravity casting process is used to conduct a filling experiment of thin-walled composite material melt. After the casting is completely solidified, a stepped thin-walled casting is obtained, and the melt filling length is measured.

[0179] The stepped thin-walled castings have wall thicknesses of 6mm, 5mm, 4mm, and 3mm respectively, and the design pouring temperature (T) is... p ) and mold preheating temperature (T mold Design the sprue and runner, and finally complete the pouring experiment;

[0180] Step 22: Under the experimental parameters of the sand casting process in Step 21, based on the viscosity curve of magnesium alloy melt as a function of temperature. ProCAST numerical simulation was performed to obtain the melt filling length obtained from the simulation.

[0181] Where μ represents the melt viscosity of the magnesium alloy, T represents the temperature, and a o and b o The coefficient of the curve;

[0182] Step 23: Subtract the melt filling length measured in Step 21 from the melt filling length obtained from the simulation to obtain the difference result;

[0183] If the absolute value of the difference does not exceed 1 mm, a viscosity-temperature curve is obtained, which is denoted as μ = aT. -b , where a and b are the coefficients of the curve;

[0184] It should be noted that if the melt viscosity does not need to be adjusted throughout the process, then a = a o b = b o When it is necessary to adjust the melt viscosity value, the values ​​of a and b are finally obtained based on the adjustment result;

[0185] If the absolute value of the difference result exceeds 1 mm, then increase the melt viscosity value by 0.1 Pa·s and continue to step two and four.

[0186] Step 24: Use the adjusted melt viscosity value to perform ProCAST numerical simulation calculations to obtain the simulated melt filling length;

[0187] Then return to steps two and three.

[0188] The other steps and parameters are the same as in Specific Implementation Method 3.

[0189] When the particle content is 0 wt.%, the viscosity-temperature curve of a certain grade of magnesium alloy melt from the existing database is used. Simulation calculations were performed. When the particle content was greater than 0 wt.%, the viscosity-temperature curve of a certain grade of magnesium alloy melt from the existing database was first used. Simulation calculations are performed, and the calculated filling length is compared with the experimental measurement. If the calculated result does not match the measured result, the melt viscosity value is increased by 0.1 Pa·s, and the simulation calculation is repeated. This process is repeated until the simulated filling length matches the experimental measurement well, that is, the absolute value of the difference between the two does not exceed 1 mm. At this point, the viscosity-temperature curve obtained is μ=aT -b Use this curve as the input parameter required for the calculation in step four.

[0190] Specific Implementation Method Five: This implementation method is a further limitation of Specific Implementation Method Four. The specific process of step four is as follows:

[0191] For the temperature T in the air layer and molten pool region, T is less than T' e The grid, i.e., for T' e For grids with a value greater than T, the flow field does not need to be calculated.

[0192] For the temperature T in the air layer and molten pool region, T is greater than or equal to T' e The grid, i.e., for T' e For grids with a value ≤ T, the flow field needs to be calculated using the following equations:

[0193]

[0194]

[0195] in, For average density, Let t be the velocity of the molten metal flow and t be time. This indicates the calculation of the gradient, where p is the pressure and η is the dynamic viscosity calculated based on the relationship between viscosity and temperature (η = μ = aT). -b (The output results in step two) It is the acceleration due to gravity. The volume forces caused by solid particles. For buoyancy, For recoil pressure, For surface tension, For the Mariganni shear force, α1 is the volume fraction of the metallic phase (α1=1 indicates that it is entirely metallic), 1-α1 is the volume fraction of the gas phase, and ρ Mg-9Al ρ is the density of the metal. gas For gas density, β T Where P is the coefficient of thermal expansion, P0 is the standard atmospheric pressure, and L is the pressure. v T is the latent heat of vaporization of the metal, M is the molar mass, and T is the latent heat of vaporization ofv Let R be the metal evaporation temperature, R be the gas constant, and T be the temperature of the molten metal in the molten pool. The gradient of α1, equal Let σ0 be the normal vector of the molten pool surface, k1 be the curvature of the molten pool surface, and σ0 be the liquidus temperature T'. l The corresponding surface tension coefficient, dσ / dT, is the slope of the curve of the surface tension coefficient as a function of temperature T (which is a constant). V is the net force acting on the particle's motion. c The volume of the mesh (valued as Δx×Δx×Δx), |·| represents the absolute value, and the temperature gradient. Gradient of the normal vector on the surface of the molten pool

[0196] The other steps and parameters are the same as in Specific Implementation Method Four.

[0197] The mass conservation equation of formula (9) is a partial differential equation. Solving formula (9) yields the density. Therefore, the central scheme finite difference method is used to discretize and numerically calculate it. The momentum conservation equation of formula (10) is also a partial differential equation. Solving formula (10) yields the liquid flow velocity. Therefore, the central scheme finite difference method coupled with the staggered grid method is used to discretize and numerically calculate it.

[0198] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Method Five. The specific process of step five is as follows:

[0199]

[0200] H = c pMg-9Al T+(1-f s-mico )L latent (20)

[0201]

[0202]

[0203] Where H is the enthalpy change, λ is the thermal conductivity of the magnesium-based composite material, and q laser For the heat input from the laser, q v q represents the heat loss due to evaporation. rad c is the heat loss due to radiation. pMg-9Al For the specific heat of magnesium alloys, f s-mico L represents the solid fraction. latent For magnesium alloy latent heat, Q0 is the coefficient required for laser thermal input calculation, χ is the energy density ratio, and z eis the position of the upper surface of the conical laser heat source along the Z-axis, z i is the position of the lower surface of the conical laser heat source along the Z-axis, r0(z) is the radius of the conical laser heat source at the Z-axis position where the device is located, c pgas is the specific heat of the gas, η l is the laser absorption rate, Q l is the laser power, r e is the radius of the upper surface of the conical laser heat source, r i is the radius of the lower surface of the conical laser heat source, γ is the Stefan-Boltzmann constant, τ is the radiation heat transfer grayness, T0 is the room temperature, (x, y, z) are the coordinate values of the grid center in three-dimensional space (by substituting different coordinates, the temperature of each grid in each region can be obtained), is the specific heat of the mixture of magnesium alloy and gas, e is the base of the natural logarithm.

[0204] Other steps and parameters are the same as those in the fifth specific implementation manner.

[0205] Formula (19) is a partial differential equation. The temperature can be obtained by solving Formulas (19) to (26). In the process of solving Formula (19), the central format finite difference method is used for discretization, and the iterative algorithm is used for numerical calculation.

[0206] Specific implementation manner seven: This implementation manner is a further limitation on the sixth specific implementation manner. The specific process of step six is as follows:

[0207] Step six one: For the grids in the molten pool region where T' e ≥T, there is no need to calculate the force on the particles;

[0208] For the grids in the molten pool region where T' e <T, the forces acting on the particles include gravity, buoyancy, pressure, drag force, and mass force. Then, the classical discrete particle model is used to calculate the resultant force on the particles is:

[0209]

[0210] Among them, is the buoyancy, is the pressure, is the drag force, is the mass force, d is the particle diameter, ρ SiC is the particle density, R e is the Reynolds number, is the movement speed of the particle in the molten metal, m add is the mass coefficient;

[0211] Step 6.2: Based on the resultant force on the particles and the instantaneous flow field of the particles obtained in Step 4, predict the particle motion. If at least A particles move to the same position within the current time step, the particles that move to the same position form an agglomerate.

[0212] The other steps and parameters are the same as in Specific Implementation Method Six.

[0213] The Lagrange method is used to solve the equations of motion for the particles. The instantaneous flow field obtained in step four... Used to predict particle motion. The velocity of the particles at the end of the time step is calculated using implicit discretization of the motion equations. The size of the time step is automatically determined by the particle velocity. At any given moment within the current time step, if A or more particles move to the same position, these particles are considered to have formed an agglomeration, and they will no longer participate in subsequent flow motion calculations (calculated using formulas (27) to (31)). These A or more particles will remain fixed within this grid. At any given moment within the current time step, if fewer than A particles move to the same position, these particles are considered not to have formed an agglomeration, and they will continue to participate in subsequent flow motion calculations.

[0214] Specific Implementation Method Eight: This implementation method is a further limitation of Specific Implementation Method Seven. The prediction of particle motion based on the resultant force on the particle and the instantaneous flow field of the particle obtained in step four is based on the Lagrange method.

[0215] The other steps and parameters are the same as in Specific Implementation Method Seven.

[0216] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Method Eight, wherein the value of A is 5.

[0217] The other steps and parameters are the same as in Specific Implementation Method 8.

[0218] Specific Implementation Method Ten: This implementation method further defines Specific Implementation Method One. The method also includes particle motion coupling simulation, performing particle Brownie motion calculations at each time step; due to N par <(N X-cell ·N Y-cell At the initial moment, N par Each particle is randomly assigned to a grid within the computational domain, and each grid can be assigned at most one particle. If a particle is assigned to the grid in the i-th row and j-th column of the computational domain, then Pii... cell,1 (i,j) is 1, otherwise Pii cell,1 The value of (i,j) is 0;

[0219] For time cell,kFor any given mesh containing particles, taking that mesh as the object of study, if there are 0 particles in the first and second nearest neighbor meshes of that mesh... <f s-s,k For meshes (i,j)≤1 (i,j) (meshes in the resolidation stage), the effect of the solid-liquid interface on particle displacement or capture needs to be considered, i.e., step 1 is executed; otherwise, step 2 is executed directly.

[0220] Step 1: Calculate the critical velocity V for particle capture at the solid-liquid interface. pcr :

[0221]

[0222] Where A is the Hamaker constant, h cr η is the critical distance between the particle and the solid-liquid interface, η is the viscosity of the melt, d is the diameter of the particle, and a0 is the interatomic distance of magnesium.

[0223] Calculate the migration velocity V of the solid-liquid interface during solidification. sl :

[0224] V sl =(Δf s-s,k (i,j)·Δx sub-cell ) / (6·Δt cell )

[0225] Where, Δf s-s,k (i,j) represents the change in solid fraction corresponding to the remelting and resolidification stage;

[0226] If V sl >V pcr If the growth rate of the solid-liquid interface is greater than the critical capture rate, the particles will be captured by the solid-liquid interface, and there is no need to perform further calculations to move the particles within the grid.

[0227] If V sl ≤V pcr This indicates that the solid-liquid interface growth rate has not exceeded the capture critical rate at time Time. cell,k The particles will not be captured by the solid-liquid interface, so proceed to step 2.

[0228] Step 2: Determine whether there exists a grid (i,j) that satisfies condition (1) or (2) among all the first and second nearest neighbor grids of the grid.

[0229] Condition (1): T' l <T cell,k (i,j);

[0230] Condition (2): T' e <T cell,k (i,j) <T'l And T cell,k (i,j) has reached T max-cell ;

[0231] If there exists a grid (i,j) that satisfies condition (1) or (2), then the particles in the grid of the object under study can move to any one of the grids that satisfies condition (1) or (2). It should be noted that if there are multiple grids that satisfy condition (1) or condition (2), then the particles can move to any one of these grids.

[0232] The velocity v of the particle pr and the migration distance l within a time step pr They are respectively:

[0233]

[0234] l pr =v pr ·β·Δt cell

[0235] Among them, T cell,k Let be the time corresponding to the k-th moment, γ be the Stefan-Boltzmann constant, and m be the time. pr Let β be the mass of the particle, and β be the number of calculations.

[0236] Since the particle's migration distance may not change in the simulation software after a certain time interval, the particle's migration distance is calculated by summing the migration distances over β time intervals, thus completing a Δt time interval. cell The calculation, β = 1, completed five Δt calculations. cell The calculation is as follows: β = 5, and so on.

[0237] like The particle then moves from the current grid (i.e., the grid of the object under study) to its first nearest neighbor grid. The particle then moves from the current grid to its second nearest neighbor grid; after the particle in the current grid has completed its migration, the value of the current grid at time k+1 is Pii. cell,k+1 A value of 0 indicates the value of Pii at time k+1 for the mesh to which particles will migrate. cell,k+1 It is denoted as 1.

[0238] The other steps and parameters are the same as in Specific Implementation Method 1. Specific Implementation

[0240] SiC ceramic particles and Mg-9wt.%Al alloy were selected as the research objects. A thin-walled casting with dimensions of 49cm×6cm×4cm was prepared by sand gravity casting. The pouring temperature was T. p The preheating temperature of the mold is 700℃. moldThe temperature was 50℃. Through calculations in step two, the melt viscosity as a function of temperature was obtained: when the particle addition was 0 wt.%, μ = 1.36281 * 10⁻⁶. 4 T -2.492 When the particle addition amount is 1 wt.%, μ = 2.32463 * 10 4 T -2.492 When the particle addition amount is 3 wt.%, μ = 3.40827 * 10 4 T -2.492 .

[0241] SiC ceramic particles and Mg-9wt.%Al alloy were selected as the research objects. A 10cm×20cm×5cm as-cast sample was prepared using sand gravity casting, and this as-cast sample served as the substrate. The substrate surface was sandblasted, and then laser surface remelting experiments were performed. The process parameters used in the laser surface remelting experiment were: laser power 180W, laser spot diameter 100μm, and scanning speeds of 150mm / s, 350mm / s, and 450mm / s. During the laser processing, the surface temperature of the molten pool (T0) was calculated. surface The results are listed in Table 1. After laser surface remelting, metal samples were cut out and subjected to OM (Optical Oxidation Mechanism) tests to observe the grain structure and measure the average primary dendrite spacing (λ). PDAS (Specific values ​​are listed in Table 1). The temperature gradient (G) can be calculated from the surface temperature of the molten pool. T Dendrite tip radius (R) tip ) and non-equilibrium liquidus temperature (T' l ) and non-equilibrium eutectic reaction temperature (T' e ).

[0242] Secondary development was carried out based on the FLUENT fluid dynamics calculation platform to perform numerical calculations on the formation of the molten pool during laser remelting. The thermophysical parameters and calculation parameters of the SiC / Mg-9wt.%Al composite material are listed in Table 2.

[0243] Table 1

[0244]

[0245] Table 2

[0246]

[0247]

[0248]

[0249] Figures 2(a), 2(b), and 2(c) show metallographic images of the dendritic microstructure of SiC / Mg-9wt.%Al magnesium-based composite material at three different scanning speeds (150 mm / s, 350 mm / s, and 450 mm / s) during laser surface remelting. The locations marked with dashed circles indicate defect positions. The primary dendrite spacing (λ) was measured using the line segment intercept method. PDAS When performing this operation, the locations of these defects must be avoided. In each metallographic photograph, three lines (line 1, line 2, and line 3) are selected. Using these three line segments, the intercept method is employed to obtain λ. PDAS Take the average value.

[0250] Figure 3(a) shows the temperature gradient obtained through experimental measurement, where the temperature of the molten pool substrate (T) obtained in the experiment is... substrate ), molten pool surface temperature (T) surface ) and molten pool depth (L molten-pool The temperature gradient can be obtained from these three values, as shown in Table 1. Figure 3(b) shows the average λ obtained from the experimental measurements. PDAS Figure 3(c) shows the calculated dendrite tip radius (R). tip Figure 3(d) shows the liquidus temperature (T') of the non-equilibrium solidification process. l The temperatures were 594.3℃, 584.18℃, and 579.31℃, respectively. Figure 3(e) shows the eutectic reaction temperatures (T') of the obtained non-equilibrium solidification process. e The temperatures at which the phases of the equilibrium phase diagram are calculated are 339.3℃, 316.18℃, and 291.31℃, respectively. Therefore, the solidification intervals are 255℃, 268℃, and 288℃. The liquidus line (T) on the equilibrium phase diagram... l ) and eutectic reaction temperature (T e The temperature range is divided into 605℃ and 437℃, with a solidification interval of 168℃. It can be seen that as the scanning speed increases, the solidification interval corresponding to non-equilibrium solidification (ΔT) increases. ls =T l -T e ) and the solidification interval (ΔT) corresponding to equilibrium solidification ls =T' l -T' e The differences are significant. Therefore, in the calculation process, it is necessary to use the temperature corresponding to the non-equilibrium solidification process to ensure the accuracy and reliability of the numerical simulation results.

[0251] A sand-cast gravity stepped-shape casting filling experiment was designed for thin-walled parts with wall thicknesses of 6 mm, 5 mm, 4 mm, and 3 mm. The sprue height was 66 mm and the runner length was 80 mm. Figure 4(a) shows the casting dimensions, and Figure 4(b) shows the casting pouring result. The stepped-shape casting design aims to ensure complete filling, thereby facilitating a better comparison between simulation and experiment, and determining the viscosity-temperature curve.

[0252] Figure 5(a) shows the filling length of the magnesium-based composite material obtained experimentally for different particle contents. When the particle content was 0 wt.%, 1 wt.%, and 3 wt.%, the measured filling lengths were 37.7 cm, 30.8 cm, and 26.8 cm, respectively. Iterative numerical simulations were performed using ProCAST software, adjusting the parameter to liquid phase viscosity until the simulated filling length closely matched the measured values. Figures 5(b), 5(c), and 5(d) show the liquid metal filling lengths obtained from ProCAST simulations for different particle addition amounts. Finally, a suitable liquid phase viscosity versus temperature curve was obtained, as shown in Figure 5(e). When the particle addition amount was 0 wt.%, μ = 1.36281 * 10⁻⁶. 4 T -2.492 When the particle addition amount is 1 wt.%, μ = 2.32463 * 10 4 T -2.492 When the particle addition amount is 3 wt.%, μ = 3.40827 * 10 4 T -2.492 .

[0253] Figure 6 In this design, the computational domain is divided into the molten pool region, the air layer, and the substrate region. The molten pool region and the air layer are the main areas where physical phenomena occur during the laser remelting process; therefore, the mesh size is relatively small (Δx×Δx×Δx=50×50×50μm). 3 This improves computational accuracy; the substrate region only experiences heat transfer and is a non-primary region, therefore the mesh size is relatively large (Δx). o ×Δx o ×Δx o =500×500×500μm 3 ).

[0254] exist Figures 7(a) to 7(c) In this context, the non-equilibrium solidification liquidus temperature (T') is used. l ) and eutectic reaction temperature (T' e The simulated temperature field (left) is shown, along with the experimentally determined melt pool depth (right). The simulation and experiment show good agreement, demonstrating the rationality of using the non-equilibrium liquidus temperature and the eutectic reaction temperature. Figures 7(d) to 7(f) In this process, the equilibrium solidification liquidus temperature (T) is used. l ) and eutectic reaction temperature (T e The simulated temperature field (left) is shown, and the experimentally determined melt pool depth (right) is also presented. It can be seen that the simulation and experiment do not match well, which indicates that the accuracy of using equilibrium liquidus temperature and eutectic reaction temperature in predicting melt pool depth is not as high as that of using non-equilibrium phase diagram data.

[0255] Figure 8 This is the flow field distribution obtained from numerical calculations. From... Figure 8 (a)~ Figure 8 (f) It can be seen that at all three scanning speeds, Mariganni flow and recoil pressure-induced flow exist within the molten pool. As the scanning speed decreases, the Mariganni flow and recoil pressure-induced flow become more intense and turbulent, mainly due to the high energy of the laser input. The keyhole phenomenon is more pronounced in the flow field obtained using non-equilibrium phase diagram data, while it is not obvious in the flow field obtained using equilibrium phase diagram data.

[0256] Figure 9 This represents the numerical calculation results of the particle dispersion state within the molten pool. From... Figure 9 (a)~ Figure 9 (f) It can be seen that as the scanning speed increases, the uniformity of particle dispersion weakens. This is because the flow intensity of the Magnus flow and the convection intensity caused by the back pressure in the molten pool both decrease, reducing the drag on the particles and preventing long-range migration, thus reducing the degree of uniform dispersion. Particles calculated using non-equilibrium phase diagram data are more dispersed; while particle dispersion calculated using equilibrium phase diagram data is less uniform, such as... Figure 9 (b) and (d) in the text, which is consistent with... Figure 10 The measurement results are inconsistent because Figure 10 When the scanning speed is 150 mm / s and 350 mm / s, the microhardness is 101.6 HV. 0.3 and 96.1HV 0.3 Higher microhardness corresponds to a more uniform particle dispersion. Figure 9 (a) and Figure 9 The particle dispersion predicted in (c) is more uniform and therefore more reasonable.

[0257] Figure 10 This is the temperature change curve calculated for a point in the molten pool. When the scan speed is 150 mm / s, the average heating rate at this point is 1.07 × 10⁻⁶. 5 K / s, with an average cooling rate of 1.44 × 10⁻⁶ K / s. 5 K / s; when the scanning speed is 350 mm / s, the average heating rate at this point is 1.23 × 10 K / s; 5 K / s, with an average cooling rate of 1.87 × 10⁻⁶ K / s. 5 K / s; when the scanning speed is 450 mm / s, the average heating rate at this point is 1.41 × 10 K / s; 5 K / s, with an average cooling rate of 1.73 × 10⁻⁶ K / s. 5K / s. As the scanning speed decreases, the heating rate also decreases because the laser moves slowly and requires a longer time to reach the maximum temperature. The cooling rate also decreases as the scanning speed decreases, but the pattern is not obvious. This is mainly because the laser input energy increases with decreasing scanning speed, which slows down the cooling rate. Simultaneously, as the laser input energy increases, the flow within the molten pool becomes more intense and complex. Therefore, under the combined effect of input energy and liquid flow, the cooling rate does not show a significant trend.

[0258] Figure 11 These are the results of electron probe microanalysis (EPMA) composition analysis. The EPMA test step size is 0.6 μm, which is submicron level, and the test area size is 240 μm × 180 μm. The EPMA test results of the as-cast Mg-9Al alloy show that the grain boundaries are rich in Al, approaching 20 wt.%, while the intragranular aluminum content is low, below 5 wt.%. Casting is a slow cooling process. According to the alloy equilibrium phase diagram, the composition of the first precipitated phase is low, while the grain boundaries are in the later solidification region, hence the high composition.

[0259] Figure 12 This represents the composition field distribution after remelting. When the scan speed is 150 mm / s, the liquid phase composition field after remelting is as follows: Figure 12 As shown in (a) above, compared to Figure 11 (Compositional distribution before remelting) shows a decrease in intergranular composition, but a uniform compositional distribution is not achieved, mainly because diffusion is the driving force for remelting. At a scan speed of 350 mm / s, the liquid phase compositional field after remelting is as follows: Figure 12 As shown in (b) above, compared to Figure 12 In (a), the intergranular composition is more uneven, mainly due to the increased cooling rate. When the scanning speed is 450 mm / s, the liquid phase composition field after remelting is as follows: Figure 12 As shown in (c) in the figure, compared to Figure 12 In (a) and (b), the intergranular composition is the most uneven because the cooling rate is faster. Figure 12 The obtained liquid phase composition field is used as the input parameter for subsequent tissue simulation calculations.

[0260] Figure 13 This simulation yields the grain structure and particle distribution at different scan rates. In (a1), (b1), and (c1), the calculated average grain sizes are 4 μm, 3.6 μm, and 4.56 μm, respectively. With increasing scan rate, the grain size first decreases and then increases. The simulated grain size variation trend and values ​​are consistent with... Figure 14The experimental trends are consistent with those in (a2), indicating that simulation can quantitatively reproduce experimental results to a certain extent. From (a2), (b2), and (c2), it can be seen that the particle distribution is relatively similar. Under rapid cooling conditions, the effect of microstructure formation on particle displacement is greatly reduced, and more particles are captured by rapidly growing grains and thus exist within the grains. This trend is consistent with previous theoretical studies.

[0261] Figure 14 This is a statistical diagram of grain structure and grain size distribution at different scan rates obtained from EBSD experimental characterization. Figure 14 In the figure, (a) and (d) are statistical diagrams of grain structure and grain size distribution at a scanning speed of 150 mm / s, respectively. Figure 14 Figures (b) and (e) show the grain structure and grain size distribution at a scanning speed of 350 mm / s, respectively. Figure 14 Figures (c) and (f) show the grain structure and grain size distribution at a scanning speed of 450 mm / s, respectively. The black dashed line represents the substrate, i.e., the as-cast structure. The as-cast structure within the substrate is coarse, while the structure within the molten pool is very fine. The grain size distribution chart shows that as the scanning speed increases, the grain size first decreases and then increases. The decrease is due to the increased cooling rate resulting from the increased scanning speed, thus refining the grain structure. The increase is due to the shallower molten pool depth and increased temperature gradient, which promotes the formation of some columnar crystals (approximately elongated). The formation of columnar crystals prevents the nucleation of some equiaxed crystals (approximately circular), thus ultimately resulting in a slight increase in grain size.

Claims

1. A numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites, characterized in that, The method specifically includes the following steps: Step 1: Using the prepared cast sample as a substrate, the substrate surface is sandblasted, and then the treated substrate is laser-remelted, and the molten pool depth L is measured. molten-pool and primary dendrite spacing λ PDAS ; Calculate the liquidus temperature T' during non-equilibrium solidification. l Then according to T' l Molten pool depth L molten-pool and primary dendrite spacing λ PDAS Calculate the eutectic reaction temperature T' during non-equilibrium solidification. e ; Step 2: Determine the relationship between the melt viscosity and temperature of the particle-reinforced magnesium matrix composite material; Step 3: Divide the molten pool region and air layer into cubic meshes. The size of each cubic mesh is Δx×Δx×Δx. The substrate layer is divided into cubic meshes, and the size of each cubic mesh is Δx. o ×Δx o ×Δx o Δx < Δx o ; Mesh generation allows for the calculation of heat and momentum transfer within the molten pool during the LSR process, thereby describing the changes in temperature and flow fields during molten pool formation. Step 4: Based on the liquidus temperature T' during the non-equilibrium solidification process l Eutectic reaction temperature T' e The flow field in the air layer and molten pool region is calculated by analyzing the relationship between melt viscosity and temperature, and the average density and the flow velocity of the molten metal are obtained. Step 5: For the air layer, molten pool region, and substrate region, calculate the temperature field based on the average density and molten metal flow velocity obtained in Step 4. Step 6: For the molten pool region, calculate the net force on the particles based on the molten metal flow velocity obtained in Step 4. Solve the particle motion equations based on the net force on the particles and the molten metal flow velocity obtained in Step 4 to obtain the particle motion velocity field. Step 7: Determine whether the laser scanning process is complete; If the laser scanning process is completed, stop the calculation and output the temperature field, liquid flow velocity field and particle motion velocity field of the local area of ​​the molten pool at different times, and then continue to execute step eight. If the laser scanning process is not finished, increment the time step by 1, and return to step four using the net force on the particle calculated in step six. Step 8: Select a sub-region from the molten pool region as the computational domain for the tissue simulation. Mesh the selected computational domain, with each mesh having a size of Δx. sub-cell ·Δx sub-cell And Δx>Δx sub-cell The number of grid rows obtained is N X-cell The number of grid columns is N Y-cell ; Based on the temperature field of the local region of the molten pool output in step seven, the cooling curve of the computational domain for microstructure simulation is obtained, and the maximum temperature on the cooling curve is denoted as T. max-cell The total number of particles N in the tissue simulation computational domain is obtained based on the particle motion velocity field. par ; Step 9, according to T max-cell The specific process of microstructure formation is as follows: Step 91: Read the experimental result data file obtained from electron probe characterization; the experimental result data file is an N... X-cell Line N Y-cell A matrix of columns; Step 92: Assign the temperature T at different times to the grid in the i-th row and j-th column of the computational domain based on the cooling curve. cell,k (i,j), the cooling curve includes NK time points and a time step of Δt. cell =Time cell,2 -Time cell,1 =Time cell,3 -Time cell,2 =…=Time cell,NK -Time cell,NK-1 , where Time cell,1 This refers to the time corresponding to the first moment; Furthermore, at the same time, the temperature of each grid in the computational domain is the same; Based on the experimental data file obtained from electron probe characterization, the solid phase composition Cs at the initial time is assigned to each grid in the computational domain. cell,1 (i,j), where i takes values ​​in the range [1,N]. X-cell The value of j is [1, N]. Y-cell ]; Step 93: At the initial moment, initialize the initial value of the liquid phase composition of the mesh (i,j) to C. l,1 (i,j)=Cs cell,1 (i,j) / k v k v This represents the non-equilibrium solute partition coefficient, with the initial solid fraction of grid (i,j) being f. s-r,1 (i,j)=1, the initial value of the composition at the solid-liquid interface is The initial value of the solid fraction in the resolidification stage is f. s-s,k (i,j)=0; Initialization time k = 1; Step 94, according to f s-r,k The melting factor q of the computational mesh (i,j) is calculated. m : Where, q m Let f be the melting factor of grid (i,j), m be the first nearest neighbor of grid (i,j), m' be the second nearest neighbor of grid (i,j), and d2 be a constant; if at time k, the solid fraction f of the m-th grid in the first nearest neighbor of grid (i,j) is... s-r,k (m)>0, then otherwise, If at time k, the solid fraction f of the m'th grid in the second nearest neighbor of grid (i,j) is... s-r,k (m')>0, then otherwise, The composition at the solid-liquid interface Change in solid fraction Δf s-r and the solid fraction f in the remelting stage s-r for: Among them, T m For melting point, Δf s-r,k (i,j) represents the change in solid fraction at time k, f s-r,k+1 (i,j) represents the solid fraction of the grid (i,j) at time k+1. This represents the composition at the solid-liquid interface of the mesh (i,j) at time k+1; The partial differential equation for solute diffusion during remelting is solved using an explicit difference algorithm: Among them, C l,k+1 (i,j) represents the liquid phase composition of the grid (i,j) at time k+1; Step 95: Let k = k + 1, and determine whether all grids satisfy f. s-r,k (i,j)=0; If all grids satisfy f s-r,k If (i,j) = 0, it indicates complete melting, and Cs cell,k If (i,j) = 0, continue with step 96; If not all grids satisfy f s-r,k If (i,j) = 0, then return to step nine four; Step 96, according to f s-s,k (i,j) computes the solidification factor q of the grid (i,j). s : The composition at the solid-liquid interface Change in solid fraction Δf s-s and solid fraction f during the resolidification stage s-s for: Where Γ is the Gibbs coefficient, wmc is the curvature of the solid-liquid interface, and Δf s-s,k (i,j) represents the change in solid fraction at time k, f s-s,k+1 This represents the solid fraction during the resolidification stage at time k+1; The formula for calculating the curvature of the solid-liquid interface is: in, For anisotropic functions, Represents the divergence of a vector; Where, n z =0 represents a two-dimensional tissue simulation, and ε1, ε2, and ε3 are coefficients; The partial differential equations are solved using an explicit difference algorithm. The solute diffusion equation during resolidation is as follows: in, Step 97: Let k = k + 1, and determine whether all grids within the computational domain satisfy f. s-s,k (i,j)=1; If all grids satisfy f s-s,k If (i,j) = 1, it indicates complete solidification, C l,k (i,j)=0; If not all grids satisfy f s-s,k If (i,j) = 1, then return to step nine six; Cellular automata technology is used to simulate the process represented by the calculation results of steps 94 and 96, that is, to simulate the remelting of the solid phase and the formation of dendrites in the liquid phase, and output the microstructure at different times.

2. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites according to claim 1, characterized in that, The calculation of the liquidus temperature T' during non-equilibrium solidification process l Then according to T' l Molten pool depth L molten-pool and primary dendrite spacing λ PDAS Calculate the eutectic reaction temperature T' during non-equilibrium solidification. e Specifically: T′ l =(T l -ΔT R ) (6) ΔT ls =(T l -ΔT R )-T′ e (7) Among them, R tip V is the radius of the dendrite tip. scan D represents the laser scanning speed. L m is the diffusion coefficient of the solute in the liquid phase. lv k is the slope of the liquidus line during non-equilibrium solidification. v C is the liquid solute partition coefficient in a non-equilibrium solidification process. o Γ is the initial composition of the alloy, m is the Gibbs coefficient, and Γ is the initial composition of the alloy. le To balance the slope of the liquidus line during solidification, k e To balance the solute partition coefficient during solidification, ΔT R For curvature supercooling, ΔT ls G represents the crystallization temperature range during non-equilibrium solidification. T T represents the temperature gradient between the molten pool surface and the substrate. l T' is the liquidus temperature corresponding to the equilibrium phase diagram. e T' is the eutectic reaction temperature during non-equilibrium solidification. l ν is the liquidus temperature during non-equilibrium solidification, and l is the interatomic distance at the solid-liquid interface.

3. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites according to claim 2, characterized in that, The temperature gradient G between the surface of the molten pool and the substrate T for: G T =(T surface -T substrate ) / (0.827·L molten-pool ) (8) Among them, T substrate T represents the initial temperature of the substrate (room temperature). surface L represents the highest temperature on the surface of the molten pool. molten-pool Indicates the depth of the molten pool.

4. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 3, characterized in that, The specific process of step two is as follows: Step 21: Under the known particle content, a sand-casting gravity casting process is used to conduct a filling experiment of thin-walled composite material melt. After the casting is completely solidified, a stepped thin-walled casting is obtained, and the melt filling length is measured. Step 22: Under the experimental parameters of the sand casting process in Step 21, based on the viscosity variation curve of magnesium alloy melt with temperature. ProCAST numerical simulation was performed to obtain the melt filling length obtained from the simulation. Where μ represents the melt viscosity of the magnesium alloy, T represents the temperature, and a o and b o The coefficient of the curve; Step 23: Subtract the melt filling length measured in Step 21 from the melt filling length obtained from the simulation to obtain the difference result; If the absolute value of the difference does not exceed 1 mm, a viscosity-temperature curve is obtained, which is denoted as μ = aT. -b , where a and b are the coefficients of the curve; If the absolute value of the difference result exceeds 1 mm, then increase the melt viscosity value by 0.1 Pa·s and continue to step two and four. Step 24: Use the adjusted melt viscosity value to perform ProCAST numerical simulation calculations to obtain the simulated melt filling length; Then return to steps two and three.

5. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composites according to claim 4, characterized in that, The specific process of step four is as follows: For the temperature T in the air layer and molten pool region, T is less than T0. ' e The grid, i.e., for T ' e For grids with a value greater than T, the flow field does not need to be calculated. For the temperature T in the air layer and molten pool region, T is greater than or equal to T ' e The grid, i.e., for T ' e For grids with a value ≤ T, the flow field needs to be calculated using the following equations: in, For average density, Let t be the velocity of the molten metal flow and t be time. This indicates the calculation of the gradient, where p is the pressure and η is the dynamic viscosity calculated based on the relationship between viscosity and temperature. It is the acceleration due to gravity. The volume forces caused by solid particles. For buoyancy, For recoil pressure, For surface tension, The value is the Mariganni shear force, α1 is the volume fraction of the metallic phase, 1-α1 is the volume fraction of the gas phase, and ρ is the volume fraction of the gas phase. Mg-9Al ρ is the density of the metal. gas For gas density, β T Where P is the coefficient of thermal expansion, P0 is the standard atmospheric pressure, and L is the pressure. v T is the latent heat of vaporization of the metal, M is the molar mass, and T is the latent heat of vaporization of the metal. v Let R be the metal evaporation temperature, R be the gas constant, and T be the temperature of the molten metal in the molten pool. Let α1 be the gradient. equal Let σ0 be the normal vector of the molten pool surface, k1 be the curvature of the molten pool surface, and σ0 be the liquidus temperature T'. l The corresponding surface tension coefficient, dσ / dT, is the slope of the curve of the surface tension coefficient as a function of temperature T. V is the net force acting on the particle's motion. c The volume of the mesh is represented by |·|, where |·| denotes the absolute value, and the temperature gradient is... Gradient of the normal vector on the surface of the molten pool 6. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 5, characterized in that, The specific process of step five is as follows: H=c pMg-9Al T+(1-f s-mico )L latent (20) Where H is the enthalpy change, λ is the thermal conductivity of the magnesium-based composite material, and q laser For the heat input from the laser, q v q represents the heat loss due to evaporation. rad c is the heat loss due to radiation. pMg-9Al For the specific heat of magnesium alloys, f s-mico L represents the solid fraction. latent For magnesium alloy latent heat, Q0 is the coefficient required for laser thermal input calculation, x is the energy density ratio, and z is the latent heat of magnesium alloy. e Let z be the position of the upper surface of the conical laser heat source along the Z-axis. i Let r0(z) be the position of the lower surface of the conical laser heat source along the Z-axis, and let c be the radius of the conical laser heat source at the Z-axis position of the device. pgas η is the specific heat of the gas. l Q represents the laser absorption rate. l Let r be the laser power, and r be the radius of the upper surface of the conical laser heat source. i is the radius of the lower surface of the conical laser heat source, γ is the Stefan-Boltzmann constant, τ is the radiative heat dissipation grayscale, T0 is the room temperature, and (x,y,z) are the coordinates of the grid center in three-dimensional space. Let be the specific heat of the mixture of magnesium alloy and gas, and e be the base of the natural logarithm.

7. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 6, characterized in that, The specific process of step six is ​​as follows: Step 61: For T' within the molten pool region e For meshes ≥T, it is not necessary to calculate particle forces; For T' within the molten pool region e <For the mesh of T, the forces acting on the particles include gravity, buoyancy, pressure, drag force, and mass force. Then, the classical discrete particle model is used to calculate the resultant force on the particles It is: in, For buoyancy, For pressure, For drag force, Let ρ be the mass force, d be the particle diameter, and ρ be the particle diameter. SiC R is the particle density. e Let Reynolds number be 1. Let m be the velocity of the particle in the molten metal. add This is the quality coefficient; Step 6.2: Based on the resultant force on the particles and the instantaneous flow field of the particles obtained in Step 4, predict the particle motion. If at least A particles move to the same position within the current time step, the particles that move to the same position form an agglomerate.

8. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 7, characterized in that, The prediction of particle motion based on the resultant force acting on the particle and the instantaneous flow field obtained in step four uses the Lagrange method.

9. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 8, characterized in that, The value of A is 5.

10. The numerical simulation method for the microstructure of laser-remelted particle-reinforced magnesium matrix composite material according to claim 1, characterized in that, The method also includes particle motion coupling simulation, performing particle Brownie motion calculations at each time step; at the initial time step, N... par Each particle is randomly assigned to a grid within the computational domain, and each grid can be assigned at most one particle. If a particle is assigned to the grid in the i-th row and j-th column of the computational domain, then Pii... cell,1 (i,j) is 1, otherwise Pii cell,1 The value of (i,j) is 0; For time cell,k For any given mesh containing particles, taking that mesh as the object of study, if there are 0 particles in the first and second nearest neighbor meshes of that mesh... <f s-s,k For grids (i,j)≤1, the effect of the solid-liquid interface on particle displacement or capture needs to be considered, i.e., step 1 is executed; otherwise, step 2 is executed directly. Step 1: Calculate the critical velocity V for particle capture at the solid-liquid interface. pcr : Where A is the Hamaker constant, h cr η is the critical distance between the particle and the solid-liquid interface, η is the viscosity of the melt, d is the diameter of the particle, and a0 is the interatomic distance of magnesium. Calculate the migration velocity V of the solid-liquid interface during solidification. sl : V sl =(Δf s-s,k (i,j)·Δx sub-cell ) / (6·Δt cell ) Where, Δf s-s,k (i,j) represents the change in solid fraction corresponding to the remelting and resolidification stage; If V sl >V pcr If the growth rate of the solid-liquid interface is greater than the critical capture rate, the particles will be captured by the solid-liquid interface, and there is no need to perform further calculations to move the particles within the grid. If V sl ≤V pcr This indicates that the solid-liquid interface growth rate has not exceeded the capture critical rate at time Time. cell,k The particles will not be captured by the solid-liquid interface, so proceed to step 2. Step 2: Determine whether there exists a grid (i,j) that satisfies condition (1) or (2) among all the first and second nearest neighbor grids of the grid. Condition (1): T' l <T cell,k (i,j); Condition (2): T' e <T cell,k (i,j) <T' l And T cell,k (i,j) has reached T max-cell ; If there exists a grid (i,j) that satisfies condition (1) or (2), then the particles in the grid of the research object move to any grid that satisfies condition (1) or (2); The velocity v of the particle pr and the migration distance l within a time step pr They are respectively: l pr =v pr ·β·Δt cell Among them, T cell,k Let be the time corresponding to the k-th moment, γ be the Stefan-Boltzmann constant, and m be the time. pr Let β be the mass of the particle, and β be the number of calculations. like The particle then moves from the current grid to its first nearest neighbor grid. The particle then moves from the current grid to its second nearest neighbor grid; after the particle in the current grid has completed its migration, the value of the current grid at time k+1 is Pii. cell,k+1 A value of 0 indicates the value of Pii at time k+1 for the mesh to which particles will migrate. cell,k+1 It is denoted as 1.

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