A numerical simulation method for dispersion of particles in laser surface remelted particle reinforced magnesium matrix composite pool

Abstract

The application discloses a numerical simulation method for particle dispersion in a molten pool of a laser surface remelting particle reinforced magnesium matrix composite, and belongs to the technical field of numerical simulation of particle dispersion in a molten pool of a composite material.The application solves the problem that the particle dispersion in a laser surface remelting (LSR) process of a particle reinforced magnesium matrix composite cannot be accurately predicted at present.The temperature gradient and the primary dendrite arm spacing in the molten pool are obtained based on experimental characterization, so that the liquidus and eutectic reaction temperature of non-equilibrium solidification are calculated.The liquidus and eutectic reaction temperature of non-equilibrium solidification are used to calculate the molten pool evolution in the LSR process of the magnesium matrix composite, so that the molten pool formation characteristics and the migration behavior of the particles in the molten pool can be more accurately predicted, the particle dispersion in the molten pool formation process of the particle reinforced magnesium matrix composite can be accurately predicted, and theoretical guidance is provided for in-depth understanding of the molten pool evolution process in the laser forming process of the composite material and process parameter optimization.The application can be applied to the prediction of the particle dispersion in the molten pool of the composite material.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology of particle dispersion in the molten pool of composite materials, and specifically relates to a numerical simulation method for particle dispersion in the molten pool of laser-remelted particle-reinforced magnesium matrix composite materials. 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, friction properties, and hardness, 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 magnesium matrix composites is the agglomeration of added particle reinforcements at grain boundaries, which reduces the material's corrosion resistance, making the composite material more susceptible to corrosion than the matrix alloy. Since corrosion begins on the component surface, research on surface modification of magnesium matrix composites is particularly important.

[0003] Laser surface remelting (LSR) is a process that uses a laser beam with high energy density to irradiate a metal surface, causing a certain thickness of surface layer to melt instantly. Then, the molten pool is rapidly solidified by the heat transfer and cooling of the base component itself, thereby improving the surface structure of the material and enhancing its surface strength, toughness, and corrosion resistance.

[0004] However, different LSR processes have different effects on particle dispersion within the molten pool, which in turn affects mechanical properties and ultimately the use of the product. Trying to quantitatively explore the relationship between the LSR process and the physical phenomena that occur during LSR through experiments is inherently flawed. Extensive experimentation means a lot of trial and error, which consumes significant human, material, and financial resources, fails to achieve energy conservation and emission reduction, and is inconsistent with the concept of "green manufacturing."

[0005] With the development of computer technology, numerical simulation has become an important and effective means of studying metal solidification processes. Numerical simulation allows for quantitative or qualitative analysis of a series of physical phenomena, such as heat, mass, momentum, and particle transport, during nonlinear unsteady solidification processes. The simulation results provide crucial guidance for process development and optimization. Numerical simulation can establish a quantitative relationship between process parameters and molten pool formation in a short time, thus shortening the R&D cycle. Although a large number of numerical simulation studies have focused on the molten pool evolution process during LSR (Laser-Resistant Metal Reinforced Composite) processes, some problems still exist. The main reason is that the LSR process involves high temperature gradients and high cooling rates, making it a typical non-equilibrium solidification process. Equilibrium phase diagram data cannot be used to describe this process, and phase diagram data (liquidite line and eutectic reaction temperature) for non-equilibrium solidification processes are scarce. The viscosity of magnesium alloy molten metal with added particles changes significantly, but currently, there is a lack of viscosity-temperature curves for this composite material. Therefore, the numerical simulation method for particle dispersion within the molten pool of laser-remelted particle-reinforced magnesium matrix composites needs to be closely linked to experimental characterization data.

[0006] In summary, it is still impossible to accurately predict particle dispersion during the LSR process of particle-reinforced magnesium matrix composites. Therefore, research on particle dispersion prediction in laser surface remelting particle-reinforced magnesium matrix composites is of great significance and can provide necessary theoretical guidance and technical support for the research and development and production of high-performance magnesium matrix composites. Summary of the Invention

[0007] The purpose of this invention is to solve the problem of particle dispersion in the LSR process of particle-reinforced magnesium matrix composites, which cannot be accurately predicted at present, and proposes a numerical simulation method for particle dispersion in the molten pool of laser surface remelting particle-reinforced magnesium matrix composites.

[0008] The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a numerical simulation method for particle dispersion in the molten pool of laser-remelted particle-reinforced magnesium matrix composite material, the method specifically including the following steps:

[0009] 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 ;

[0010] 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 ;

[0011] Step 2: Determine the relationship between the melt viscosity and temperature of the particle-reinforced magnesium matrix composite material;

[0012] Step 3: Divide the molten pool region and air layer into cubic meshes. The size of each cubic mesh is Δx×Δx×Δx.

[0013] 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 ;

[0014] 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.

[0015] 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.

[0016] 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.

[0017] Step 7: Determine whether the laser scanning process is complete;

[0018] If the laser scanning process ends, the calculation stops and the temperature field, liquid flow velocity field, and particle motion velocity field of the local area of ​​the molten pool at different times are output.

[0019] If the laser scanning process is not finished, increment the time step by 1, and return to step four using the resultant force on the particle calculated in step six.

[0020] The beneficial effects of this invention are:

[0021] This invention first 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. By using the liquidus line and eutectic reaction temperature to calculate the molten pool evolution during the laser surface remelting process of magnesium-based composite materials, the characteristics of molten pool formation and the migration behavior of internal particles can be predicted more accurately. This solves the current problem of inaccurately predicting particle dispersion during the molten pool formation process of particle-reinforced magnesium-based composite materials, providing theoretical guidance and data support for a deeper understanding of the molten pool evolution process and optimization of process parameters during laser forming of composite materials.

[0022] This invention is applicable to the numerical prediction of molten pool formation in laser-remelted particle-reinforced magnesium matrix composites. Using this invention, the formation process of the molten pool during laser melting of metal can be predicted more accurately, providing theoretical support for the optimization of laser forming processes for composite materials, and showing great potential for market application. Attached Figure Description

[0023] Figure 1 This is a flowchart of a numerical simulation method for particle dispersion in a molten pool of a laser-remelted particle-reinforced magnesium matrix composite material according to the present invention.

[0024] 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;

[0025] 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.

[0026] 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.

[0027] Figure 3(a) shows the curves of temperature gradient versus scanning speed;

[0028] Figure 3(b) shows the average λ PDAS A graph showing the change in scanning speed;

[0029] Figure 3(c) shows the curve of dendrite tip radius versus scanning speed;

[0030] Figure 3(d) shows the curves of liquidus temperature versus scanning speed during non-equilibrium solidification.

[0031] Figure 3(e) shows the curves of the eutectic reaction temperature versus the scanning rate during the non-equilibrium solidification process;

[0032] 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;

[0033] Figure 4(b) shows the casting process of the thin-walled casting;

[0034] 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.%).

[0035] Figure 5(b) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 0 wt.%.

[0036] The minimum temperature zone in the eighth second of filling refers to the smallest 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.

[0037] Figure 5(c) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 1 wt.%.

[0038] Particle indicates the amount of particles added;

[0039] Figure 5(d) shows the metal liquid filling length obtained by ProCAST software simulation when the particle addition amount is 3 wt.%.

[0040] Figure 5(e) shows the liquid phase viscosity versus time curve obtained by the reverse calculation method;

[0041] Viscosity indicates the viscosity of the liquid phase;

[0042] Figure 6 For setting the calculation area;

[0043] 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);

[0044] Moltenpool means molten pool;

[0045] 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);

[0046] 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);

[0047] 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);

[0048] 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);

[0049] 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);

[0050] Figure 8 The flow field inside the molten pool obtained by numerical calculation at different scanning speeds;

[0051] (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;

[0052] (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;

[0053] (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;

[0054] (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;

[0055] (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;

[0056] (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;

[0057] Figure 9The particle dispersion in the molten pool obtained by numerical calculation at different scanning speeds;

[0058] (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;

[0059] NPs velocity represents the velocity of particle movement;

[0060] (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;

[0061] (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;

[0062] (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;

[0063] (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;

[0064] (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;

[0065] Figure 10 Microhardness testing of samples obtained at different scanning speeds in laser surface remelting experiments. Detailed Implementation

[0066] Specific implementation method one: Combining Figure 1 This embodiment describes a numerical simulation method for particle dispersion within the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material. The method specifically includes the following steps:

[0067] 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 ;

[0068] 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 ;

[0069] Step 2: Determine the relationship between the melt viscosity and temperature of the particle-reinforced magnesium matrix composite material;

[0070] Step 3: Divide the molten pool region and air layer into cubic meshes. The size of each cubic mesh is Δx×Δx×Δx.

[0071] 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 ;

[0072] 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.

[0073] 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.

[0074] 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.

[0075] 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.

[0076] Step 7: Determine whether the laser scanning process is complete;

[0077] If the laser scanning process ends, the calculation stops and the temperature field, liquid flow velocity field, and particle motion velocity field of the local area of ​​the molten pool at different times are output.

[0078] If the laser scanning process is not finished, increment the time step by 1, and return to step four using the resultant force on the particle calculated in step six.

[0079] 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:

[0080]

[0081]

[0082] T′ l =(T l -ΔT R (6)

[0083] ΔT ls =(T l -ΔT R )-T′ e (7)

[0084] 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 ), G 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.

[0085] The other steps and parameters are the same as in Specific Implementation Method 1.

[0086] 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.

[0087] 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:

[0088] G T =(T surface -T substrate ) / (0.827·L molten-pool (8)

[0089] 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.

[0090] The other steps and parameters are the same as in Specific Implementation Method Two.

[0091] 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:

[0092] 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.

[0093] 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;

[0094] 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.

[0095] 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;

[0096] 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;

[0097] 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;

[0098] 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;

[0099] 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.

[0100] Step 24: Use the adjusted melt viscosity value to perform ProCAST numerical simulation calculations to obtain the simulated melt filling length;

[0101] Then return to steps two and three.

[0102] The other steps and parameters are the same as in Specific Implementation Method 3.

[0103] 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.

[0104] 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:

[0105] 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.

[0106] 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:

[0107]

[0108] 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 of 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. The gradient of α1, equal Let κ1 be the normal vector of the molten pool surface, σ0 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

[0109] The other steps and parameters are the same as in Specific Implementation Method Four.

[0110] 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.

[0111] 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:

[0112]

[0113] H = c pMg-9Al T+(1-f s-mico )L latent (20)

[0114]

[0115] 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 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 r is the laser power. e It is the radius of the upper surface of the conical laser heat source, r i γ 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,e) are the coordinates of the grid center in three-dimensional space (by substituting different coordinates, the temperature of each grid in each region can be obtained). Let be the specific heat of the mixture of magnesium alloy and gas, and e be the base of the natural logarithm.

[0116] The other steps and parameters are the same as in Specific Implementation Method 5.

[0117] Equation (19) is a partial differential equation, and the temperature can be obtained by solving Equations (19) to (26). In the process of solving Equation (19), the finite difference method with a central format is used for discretization, and an iterative algorithm is used for numerical calculation.

[0118] Specific Embodiment Seven: This embodiment further limits Specific Embodiment Six. The specific process of Step Six is as follows:

[0119] Step Six One: For the grid where T' e ≥T in the molten pool region, there is no need to calculate the force on the particle;

[0120] For the grid where T' e <T in the molten pool region, the forces acting on the particle include gravity, buoyancy, pressure, drag force, and body force. Then, the classical discrete particle model is used to calculate the resultant force on the particle is:

[0121]

[0122] where, is the buoyancy, / / 这里原文似乎不完整,推测是公式里的某个部分,按照要求保留原文格式 is the pressure, / / 这里原文似乎不完整,推测是公式里的某个部分,按照要求保留原文格式 is the drag force, / / 这里原文似乎不完整,推测是公式里的某个部分,按照要求保留原文格式 is the body 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;

[0123] Step Six Two: Based on the resultant force on the particle and the instantaneous flow field of the particle obtained in Step Four, predict the movement of the particle. 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 aggregate.

[0124] Other steps and parameters are the same as those in Specific Embodiment Six.

[0125] The Lagrangian method is used to solve the particle motion equation. 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.

[0126] 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.

[0127] The other steps and parameters are the same as in Specific Implementation Method Seven.

[0128] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Method Eight, wherein the value of A is 5.

[0129] The other steps and parameters are the same as in Specific Implementation Method 8. Specific Implementation

[0131] 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℃. moid The 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 .

[0132] 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 ).

[0133] 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.

[0134] Table 1

[0135]

[0136] Table 2

[0137]

[0138]

[0139]

[0140]

[0141] 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.

[0142] 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.

[0143] 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.

[0144] 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 .

[0145] 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 ).

[0146] 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.

[0147] Figure 8The numerically calculated flow field distribution is shown. At all three scanning velocities, Marigny flow and recoil pressure-induced flow exist within the molten pool. As the scanning speed decreases, the Marigny flow and recoil pressure-induced flow become more intense and turbulent, primarily due to the higher laser input energy. The keyhole phenomenon is more pronounced in the flow field obtained using non-equilibrium phase diagram data, while it is less pronounced in the flow field obtained using equilibrium phase diagram data.

[0148] Figure 9 The results represent numerical calculations of particle dispersion within the molten pool. As the scan rate increases, the uniformity of particle dispersion decreases. This is because the flow intensity of the Marigny flow and the convection intensity caused by the backflow pressure both weaken, reducing the drag on the particles and hindering long-range migration, thus decreasing the degree of uniform dispersion. Particles calculated using non-equilibrium phase diagram data are more dispersed; while those calculated using equilibrium phase diagram data are less uniformly dispersed. 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.

[0149] Figure 10 The microhardness of samples obtained from laser surface remelting experiments at different scanning speeds is shown. The microhardness increases as the scanning speed decreases. The microhardness is 101.6 HV at scanning speeds of 150 mm / s and 350 mm / s. 0.3 and 96.1HV 0.3 All values ​​are at a relatively high level. The improvement in mechanical properties is due to the more uniform particle dispersion. Figure 9 (a) and Figure 9 (c)) thus also verifying Figure 9 (a) and Figure 9 (c) The rationality of the numerical calculation results.

[0150] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A numerical simulation method for particle dispersion within the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material, 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 ; 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 ends, the calculation stops and the temperature field, liquid flow velocity field, and particle motion velocity field of the local area of ​​the molten pool at different times are output. If the laser scanning process is not finished, increment the time step by 1, and return to step four using the resultant force on the particle calculated in step six.

2. The numerical simulation method for particle dispersion in the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material 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 particle dispersion in the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material 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. 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 particle dispersion in the molten pool of a 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 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. 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 particle dispersion in the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material 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 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. 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 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. The gradient of α1, 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 particle dispersion in the molten pool of a 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, χ is the energy density ratio, and z 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 r is the laser power. e It 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 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 particle dispersion in the molten pool of a 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 the T region within the molten pool ' e For meshes ≥T, it is not necessary to calculate particle forces; For T within the molten pool region ' e <For the grid of T, the forces acting on the particles include gravity, buoyancy, pressure, drag force, and mass force, and the resultant force on the particles is as follows: 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 particle dispersion in the molten pool of a 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 particle dispersion in the molten pool of a laser-remelted particle-reinforced magnesium matrix composite material according to claim 8, characterized in that, The value of A is 5.

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