Three-dimensional microstructure evolution simulation method for electric arc welding weld pool solidification process

Abstract

The invention discloses a three-dimensional microstructure evolution simulation method for an electric arc welding weld pool solidification process, and the method specifically comprises the following steps: carrying out macroscopic temperature field simulation in a welding process of a T-shaped joint of an aluminum alloy thin-wall part based on a finite element method, and obtaining local temperature field data; and on the basis of a linear interpolation method, carrying out time interpolation on the local temperature field data to obtain microscopic cellular temperature field data. A three-dimensional molten pool dendritic crystal growth model is established, and the position, the growth speed and the solid fraction of grain nucleation in a molten pool are calculated. And establishing a solute concentration field distribution model, and calculating solute distribution and diffusion in the interface cell growth process. Based on an eccentric regular octahedron algorithm, a space cellular capture model is established, and three-dimensional microstructure evolution simulation in the weld pool solidification process is completed. According to the three-dimensional microstructure evolution simulation method for the solidification process of the electric arc welding seam molten pool, simulation of three-dimensional microstructure morphology and solute concentration distribution in the solidification process of the welding seam molten pool can be achieved, and the method has great significance in more comprehensively describing the solidification process of the welding seam molten pool and improving the mechanical property of a welded joint.

Description

Technical Field

[0001] The invention belongs to the field of arc welding processing, and in particular relates to a three-dimensional microstructure evolution simulation method for a molten pool solidification process of an arc welding weld. Background Art

[0002] Welding is an important advanced manufacturing technology. It is widely used in the connection and assembly of aluminum alloy thin-walled parts due to its strong stability and fast forming speed. During the welding process, the temperature of the molten pool area changes rapidly, and complex physical processes such as melting, solidification, and heat conduction occur. These processes have an important impact on the microstructure and macroscopic properties of the welded joint. However, traditional sensors and detection equipment are difficult to achieve real-time control and detection of the welding process, so it is difficult to establish the correlation between the transient temperature field and the three-dimensional dendrite growth process, the microstructure morphology of the weld metal, and the performance of the welded joint.

[0003] The existing methods for simulating the microstructure of weld metal solidification process are mainly divided into deterministic methods, probabilistic methods and phase field methods. The deterministic model based on solidification dynamics cannot simulate the random nucleation and random crystal orientation in the dendrite growth process. Although the phase field method can describe the dendrite morphology, it is difficult to overcome the shortcomings of small calculation area and low calculation efficiency due to its large computational complexity. The cellular automaton method in the probabilistic method is simple and intuitive, and can well describe the randomness of nucleation position and crystal orientation, equiaxed crystal morphology in complex temperature fields, and larger simulation areas.

[0004] Patent 201911212284.X discloses a method for simulating the solidification process of BGA tin-lead solder balls based on cellular automata. The patent can simulate the growth of dendrites under different degrees of supercooling, but the patent cannot achieve arbitrary preferential orientation and cannot reveal the actual formation process of the microstructure morphology. Patent 202311368557.6 discloses a method for simulating the microstructure of arc welding welds based on cellular automata. The patent can simulate the two-dimensional structure morphology of the weld, but cannot fully describe the growth of dendrites in all dimensions. Its grain morphology and solute field are still far from the actual situation. Summary of the invention

[0005] The purpose of the present invention is to provide a method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool, so as to solve the problems that the models in the prior art cannot reflect the three-dimensional microstructure morphology and evolution process of arbitrary orientation, and the three-dimensional solute field is not conserved.

[0006] The technical solution of the present invention is: a method for simulating the evolution of three-dimensional microstructures in the solidification process of the arc welding weld pool. During the welding process, the aluminum alloy thin-walled part, under the influence of the heat source, melts in a part of the area above the liquidus temperature of the weld metal to form a molten pool. After the temperature is lowered, the liquid metal in the molten pool gradually solidifies with the growth of dendrites to form a new microstructure. The steps are as follows:

[0007] Step 1: Based on the finite element method, simulate the macroscopic temperature field of the T-joint welding process of aluminum alloy thin-walled parts, obtain the local temperature field data, and proceed to step 2.

[0008] Step 2: Based on the linear interpolation method, interpolate the local temperature field data with respect to time to obtain the microscopic cell temperature field data, define the cells with a temperature higher than the liquidus temperature of the material as liquid phase cells, and proceed to step 3.

[0009] Step 3: Based on the non-uniform continuous nucleation model, randomly determine the nucleation position in the calculation area and proceed to step 4.

[0010] Step 4: Based on the Gaussian distribution nucleation density model, determine whether the nucleation position cell is nucleated under the current total supercooling. When the total supercooling is greater than the critical supercooling, its state changes from liquid phase cell to nucleation cell, and proceed to step 5.

[0011] Step 5: Based on the solute flux balance, calculate the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell, and then calculate the length of the cell covered along the normal direction of the interface and solid fraction increment Δf s , to establish a three-dimensional melt pool dendrite growth model and proceed to step 6.

[0012] Step 6: Based on solute conservation and Fick's law, calculate the solute distribution and diffusion during the growth of the interface cell to establish a solute concentration field distribution model and proceed to step 7.

[0013] Step 7: Based on the eccentric octahedron algorithm, a spatial cell capture model is established, and the three-dimensional dendrite growth orientation is calculated according to the Euler angle. The neighboring cell state at the vertex of the octahedron is changed to a liquid phase cell. When the solid phase rate of the cell is f s When reaching 1, it grows into a solid phase cell and capture stops, and goes to step 8.

[0014] Step 8: Combine the non-uniform continuous nucleation model, the three-dimensional molten pool dendrite growth model, the solute concentration field distribution model, and the spatial cell capture model, and repeat steps 3 to 7 until the growth cells and liquid phase cells in the simulation area are transformed into solid phase cells, and the three-dimensional microstructure morphology of the weld metal is simulated.

[0015] Compared with the prior art, the present invention has the following significant advantages:

[0016] (1) The three-dimensional molten pool dendrite growth model established in the present invention can accurately calculate the length of the growth state cell covered along the normal direction of the interface, can reflect the true three-dimensional microstructure morphology, and can maintain the conservation of the solute field during the simulation of the three-dimensional microstructure evolution.

[0017] (2) The present invention adopts Euler angles to represent crystal orientation and an eccentric octahedron capture algorithm, which can accurately represent the direction vector of the crystal orientation in the local coordinate system, can realize the growth simulation of three-dimensional dendrites with arbitrary preferred orientation, can accurately calculate the distance through the cell along each crystal direction, and can accurately calculate the global coordinates of the vertices of the eccentric octahedron. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of a method for simulating the evolution of three-dimensional microstructure in the solidification process of a molten pool of an arc welding seam described in the present invention.

[0019] Figure 2 Schematic diagram of the growth of a regular hexahedron cell in an embodiment of the present invention.

[0020] Figure 3 It is the concentration field distribution evolution of a single equiaxed crystal in the embodiment of the present invention.

[0021] Figure 4 Schematic diagram of capturing cells using the eccentric octahedron algorithm in an embodiment of the present invention.

[0022] Figure 5 It is a schematic diagram of calculating the three-dimensional dendrite growth orientation based on the Euler angle in an embodiment of the present invention.

[0023] Figure 6 It is a single equiaxed crystal at different preferred orientation angles in the embodiment of the present invention.

[0024] Figure 7 It is a three-dimensional microstructure morphology diagram of the simulation of the weld molten pool solidification process in the embodiment of the present invention. DETAILED DESCRIPTION

[0025] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0027] The following will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention in combination with this design example.

[0028] When welding T-joints, aluminum alloy thin-walled parts are affected by high-temperature heat sources. Parts of the area above the liquidus temperature of the weld metal melt to form a molten pool. After the temperature drops, the liquid metal in the molten pool begins to nucleate, and gradually solidifies with the growth of dendrites to form the microstructure morphology of the weld area. The present invention uses a three-dimensional cellular automaton method to simulate the microstructure evolution of the molten pool solidification process, selects a local area of ​​the weld to be divided into microscopic cells, sets all cells at the initial stage to be in a liquid phase state, and the cells at the nucleation position gradually grow after nucleation and capture neighboring cells as liquid phase cells according to the spatial cell capture model. The liquid phase cells and the nucleation cells continue to grow and capture, and the state of the cells that have completed the growth becomes a solid phase, and the cycle continues until the states of all cells are transformed into a solid phase, and finally completes the three-dimensional microstructure simulation of weld solidification.

[0029] Combination Figure 1 The method for simulating the three-dimensional microstructure evolution of the arc welding weld pool solidification process of the present invention comprises the following steps:

[0030] Step 1: During the welding process, the metal is affected by the high-temperature heat source, and the area above the liquidus temperature of the weld metal melts to form a molten pool. After the temperature drops, the liquid metal solidifies to form a weld. Based on the finite element method, a welding process simulation model is established to complete the macroscopic temperature field simulation of the T-joint of aluminum alloy thin-walled parts, extract the data of the temperature field of the local area of ​​the molten pool over time, and proceed to step 2.

[0031] Step 2: Based on the linear interpolation method, the local temperature field data is interpolated with respect to time to obtain the temperature field data of the local area of ​​the macroscopic molten pool corresponding to the microscopic cell calculation area under the microscopic time step, that is, the microscopic cell temperature T loc , go to step 3.

[0032] Step 3: Based on the non-uniform continuous nucleation model, the nucleation position is randomly determined in the calculation area, as follows:

[0033] The nucleation probability P per unit time step in the local area of ​​the molten pool v , calculated by the following formula:

[0034]

[0035] In the formula, δNv is the total number of nucleation cells per unit time step in the simulation area, N CA is the number of cells in the local area of ​​the molten pool, δn v is the nucleation density increment of the local area of ​​the molten pool per unit time step, V CA is the volume of a single microscopic cell.

[0036] Step 4: Based on the Gaussian distribution nucleation density model, determine whether the nucleation position cell is nucleated under the current total supercooling. When the total supercooling is greater than the critical supercooling, its state changes from liquid phase cell to nucleation cell, as follows:

[0037] The nucleation density model based on Gaussian distribution is used to determine whether nucleation has occurred. The expression is as follows:

[0038]

[0039] Where n v is the nucleation density, δn v is the nucleation density increment of the local area of ​​the molten pool per unit time step, ΔT is the total undercooling, δ(ΔT) is the undercooling increment per unit time step, is the nucleation density distribution function, n max is the maximum nucleation density, ΔT N is the average nucleation undercooling, ΔT σ is the standard deviation of undercooling; ΔT′ is the nucleation undercooling.

[0040] The calculation of total subcooling includes thermal subcooling Composition supercooling and curvature undercooling ΔT r =ΓK, and its calculation formula is:

[0041]

[0042] In the formula, is the liquidus temperature at the initial liquid solute concentration, T loc is the microscopic cell temperature, m is the liquidus slope, C0 is the initial liquid solute concentration, is the equilibrium solute concentration in the liquid phase at the solid-liquid interface, Γ is the Gibbs-Thompson coefficient, and K is the interface curvature.

[0043] Step 5: Based on the solute flux balance, calculate the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell, and then calculate the length of the cell covered along the normal direction of the interface and solid fraction increment Δf s , in order to establish a three-dimensional melt pool dendrite growth model, as follows:

[0044] Step 5.1. Calculate the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell based on the solute flux balance:

[0045] During the dendrite growth process, the supercooling at the solid-liquid interface is balanced, based on which the equilibrium concentration of the liquid solute is calculated

[0046]

[0047] According to the local phase equilibrium of the solid-liquid interface, the solid phase solute equilibrium concentration can be obtained for:

[0048]

[0049] Where k0 is the solute equilibrium distribution coefficient.

[0050] The dendrite interface growth rate is calculated based on the solute flux balance, and its expression is:

[0051]

[0052] In the formula, is the normal velocity of the dendrite growth interface, D L is the diffusion coefficient of liquid solute, D S is the solid solute diffusion coefficient, C L is the liquid solute concentration, C S is the solid phase solute concentration, is the normal vector to the growth interface.

[0053] The dendrite interface growth rate is expressed as a finite difference form along the coordinate axes x, y, and z by the solid phase ratio:

[0054]

[0055]

[0056] Where i, j and k represent the element numbers.

[0057] The interface curvature of three-dimensional dendrite growth is calculated as follows:

[0058]

[0059] Where ε is the interface energy anisotropy parameter, (n x ,n y ,n z ) is the unit interface normal vector, is the partial derivative of the solid fraction in all directions.

[0060] Step 5.2: Calculate the length of the cell covered along the normal direction of the interface according to the velocity and normal direction of the growth interface. like Figure 2 As shown, with the solid phase rate increment Δf s :

[0061] The i-th vertex of the growth cell, i.e., the interface cell and the nucleation cell, is drawn as a plane parallel to the solid-liquid interface, and the distance from the cell center to the plane is d i , whose expression is:

[0062]

[0063] Among them, (x0, y0, z0) is the center coordinate of the cell in the local coordinate system, (x i ,y i ,z i ) is the coordinate of the i-th vertex of the cell in the local coordinate system.

[0064] The length of the coverage cell along the interface normal direction for:

[0065]

[0066] The solid fraction increment per unit time step is:

[0067]

[0068] Where GF is the shape factor, Δt is the time increment, V n is the dendrite interface growth rate.

[0069] The GF calculation rules are as follows:

[0070] (1) When there is a solid phase cell among the nearest neighbor cells of the growing cell, GF = 1;

[0071] (2) When there is a solid phase cell among the next neighboring cells of the growing cell,

[0072] (3) When there is a solid phase cell among the third neighbor cells of the growing cell,

[0073] Step 6: Based on solute conservation and Fick's law, calculate the solute distribution and diffusion during the growth of the interface cell to establish a solute concentration field distribution model, such as Figure 3 As shown, the details are as follows:

[0074] When the solid phase ratio of the growing cell increases, if there are liquid adjacent cells in its neighborhood, the solute ΔC will be discharged, and the calculation formula is:

[0075]

[0076] In the formula, is the liquid solute concentration before the cell state transition, Δf s is the solid phase rate increment, k0 is the solute equilibrium distribution coefficient, is the liquid solute concentration after growth, is the equilibrium solute concentration in the liquid phase at the solid-liquid interface, f s is the solid phase ratio.

[0077] If the solute concentration in the liquid phase of adjacent cell j is Less than the equilibrium solute concentration in the liquid phase at the solid-liquid interface that discharges the solute cell The excluded solute will be distributed to the cell, and its expression is:

[0078]

[0079] In the formula, is the liquid solute concentration of neighboring cell j at time t+1, is the liquid solute concentration of neighboring cell j at time t, is the liquid solute concentration of the nbth neighboring cell, and N is the total number of neighboring liquid cells.

[0080] Based on Fick's law, the solute diffusion in the three-dimensional microstructure evolution simulation satisfies the following equation:

[0081]

[0082]

[0083] In the formula, C L is the liquid solute concentration, C S is the solid solute concentration, D L is the diffusion coefficient of liquid solute, D S is the solid-phase solute diffusion coefficient.

[0084] Step 7: Based on the eccentric octahedron algorithm, establish a spatial cell capture model, such as Figure 4 As shown, the three-dimensional dendrite growth orientation is calculated based on the Euler angle, as Figure 5 As shown, the neighboring cell state at the vertex of the regular octahedron is changed to a liquid phase cell. When the solid phase rate of the cell is f s When it reaches 1, it grows into a solid phase cell and stops capturing, so as to establish a three-dimensional melt pool dendrite growth model with arbitrary orientation, such as Figure 6 As shown, the details are as follows:

[0085] Step 7.1, calculate the three-dimensional dendrite growth orientation based on the Euler angle:

[0086] For aluminum alloys with a face-centered cubic crystal structure, the vector representing the <100> crystal direction after rotation can be obtained by the rotation matrix R T Calculation: In the Cartesian coordinate system XYZ, rotate the XOY plane around the Z axis by angle w1, then rotate the YOZ plane around the X axis by angle w2, and finally rotate the XOY plane around the Z axis by angle w3 to obtain the new coordinate system X'Y'Z', where the coordinate system XYZ and the vector (x, y, z) in the coordinate system X'Y'Z' are T and vector (x',y',z') T The conversion relationship between them is expressed as:

[0087]

[0088] Step 7.2: Based on the eccentric octahedron algorithm, establish a spatial cell capture model:

[0089] An eccentric octahedron is set at the center of the nucleation cell. The three diagonals of the octahedron are parallel to the <100>, <010> and <001> directions of the face-centered cubic grains. The direction vector u of the crystal orientation in the local coordinate system is ＜100＞ 、v ＜010＞ and w ＜001＞ They are:

[0090] u ＜100＞ =[R 11 R 21 R 31 ]

[0091] v ＜010＞ =[R 12 R 22 R 32 ]

[0092] w ＜001＞ =[R 13 R 23 R 33 ]

[0093] Diagonal length L dia The solid fraction increment Δf s The accumulation of L dia The expression is:

[0094] L dia =∑Δf s L max

[0095] Maximum half diagonal length L max is the maximum distance through the cell along the crystal orientation, and its calculation formula is:

[0096] L max=max(L

[100] ,L

[010] ,L

[001] )

[0097] Where, L

[100] , L

[010] and L

[001] They represent the distances through the cell along the <100> crystal direction, <010> crystal direction, and <001> crystal direction, respectively, and their expressions are:

[0098]

[0099] The global coordinates (x0', y0', z0') of the kth vertex of an eccentric octahedron are k ,y k ,z k ) is calculated by the following formula:

[0100]

[0101] Where R1, R2 and R3 are the components of the crystal orientation vector on the X-axis, Y-axis and Z-axis, L R is the length of the crystal orientation direction vector.

[0102] As the diagonal grows, the vertex position of the eccentric octahedron will enter the neighboring cell. If it is a liquid phase cell, it will be captured as an interface cell, and a regular octahedron with the same deflection direction will be generated at the vertex position, thereby establishing a three-dimensional dendrite growth space cell capture model.

[0103] Step 8: Combine the non-uniform continuous nucleation model, the three-dimensional molten pool dendrite growth model, the solute concentration field distribution model, and the spatial cell capture model, and repeat steps 3 to 7 until the nucleation cells and liquid phase cells in the simulation area are transformed into solid phase cells to obtain the three-dimensional microstructure morphology of the weld molten pool solidification, such as Figure 7 As shown, the details are as follows:

[0104] After selecting the local area of ​​the macro weld as the microstructure simulation area, all cells are initialized to the liquid phase state. Based on the non-uniform continuous nucleation model, the nucleation position is randomly determined in the calculation area, and then based on the Gaussian distribution nucleation density model, it is judged whether the nucleation position cell is nucleated under the current total undercooling. Then, based on the solute flux balance, the velocity and normal direction of the growth interface in the nucleation cell or interface cell are calculated, and then the three-dimensional dendrite growth orientation is calculated according to the Euler angle, and then the length of the cell covered along the normal direction of the interface and the solid phase fraction increment are calculated. Then, based on the solute conservation and Fick's law, the solute distribution and diffusion in the cell growth process are calculated. Then, based on the spatial cell capture model of the eccentric octahedron algorithm, the distance through the cell along each crystal direction and the global coordinates of the eccentric octahedron vertices are calculated, and then the growth of the three-dimensional dendrite is calculated. The above process is repeated until the growth state cells and liquid phase cells in the simulation area are transformed into solid phase cells, and the three-dimensional microstructure morphology of the weld molten pool solidification is obtained.

Claims

1. A method for simulating the evolution of three-dimensional microstructures during the solidification process of arc welding weld pool. During the welding process, under the influence of a heat source, a portion of an aluminum alloy thin-walled part above the liquidus temperature of the weld metal melts to form a molten pool. After the temperature is lowered, the liquid metal in the molten pool gradually solidifies with the growth of dendrites to form a new microstructure. The method is characterized in that: Here are the steps: Step 1: Based on the finite element method, simulate the macroscopic temperature field of the T-joint welding process of aluminum alloy thin-walled parts, obtain the local temperature field data, and proceed to step 2; Step 2: Based on the linear interpolation method, the local temperature field data is interpolated with respect to time to obtain the microscopic cell temperature field data, and the cells with a temperature higher than the liquidus temperature of the material are defined as liquid phase cells, and then proceed to step 3; Step 3: Based on the non-uniform continuous nucleation model, randomly determine the nucleation position in the calculation area and proceed to step 4; Step 4: Based on the Gaussian distribution nucleation density model, determine whether the nucleation position cell is nucleated under the current total supercooling. When the total supercooling is greater than the critical supercooling, its state changes from liquid phase cell to nucleation cell, and proceed to step 5; Step 5: Based on the solute flux balance, calculate the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell, and then calculate the length of the cell covered along the normal direction of the interface and solid fraction increment Δf s , to establish a three-dimensional melt pool dendrite growth model, and proceed to step 6; Step 6: Based on solute conservation and Fick's law, calculate the solute distribution and diffusion during the growth of the interface cell to establish a solute concentration field distribution model, and then proceed to step 7; Step 7: Based on the eccentric octahedron algorithm, a spatial cell capture model is established, and the three-dimensional dendrite growth orientation is calculated according to the Euler angle. The neighboring cell state at the vertex of the octahedron is changed to a liquid phase cell. When the solid phase rate of the cell is f s When reaching 1, it grows into a solid phase cell and stops capturing, and goes to step 8; Step 8: Combine the non-uniform continuous nucleation model, the three-dimensional molten pool dendrite growth model, the solute concentration field distribution model, and the spatial cell capture model, and repeat steps 3 to 7 until the growth cells and liquid phase cells in the simulation area are transformed into solid phase cells, and the three-dimensional microstructure morphology of the weld metal is simulated.

2. A method for simulating the three-dimensional microstructure evolution of arc welding weld pool solidification process according to claim 1, characterized in that: In step 1, the macroscopic temperature field simulation of the T-joint welding process of aluminum alloy thin-walled parts is performed based on the finite element method to obtain the local temperature field data, as follows: Based on the finite element method, a simulation model of the welding process was established, the macroscopic temperature field simulation of the T-joint of aluminum alloy thin-walled parts was completed, and the data of the temperature field changing with time in the local area of ​​the molten pool were extracted.

3. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 2, characterized in that: In step 2, based on the linear interpolation method, the local temperature field data is interpolated over time to obtain the microscopic cell temperature field data, as follows: Linear interpolation is performed on the macroscopic time to obtain the temperature field data under the microscopic time step, and the temperature field data of the local area of ​​the macroscopic molten pool corresponding to the microscopic cell calculation area is obtained, that is, the microscopic cell temperature T loc .

4. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 3, characterized in that: In step 3, based on the non-uniform continuous nucleation model, the nucleation position is randomly determined in the calculation area, as follows: The nucleation probability P per unit time step in the local area of ​​the molten pool v , calculated by the following formula: In the formula, δN v is the total number of nucleation cells per unit time step in the simulation area, N CA is the number of cells in the local area of ​​the molten pool, δn v is the nucleation density increment of the local area of ​​the molten pool per unit time step, V CA is the volume of a single microscopic cell.

5. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 4, characterized in that: In step 4, based on the Gaussian distribution nucleation density model, it is determined whether the nucleation position cell is nucleated under the current total supercooling. When the total supercooling is greater than the critical supercooling, its state is transformed from a liquid phase cell to a nucleation cell, as follows: The nucleation density model based on Gaussian distribution is used to determine whether nucleation has occurred. The expression is as follows: Where n v is the nucleation density, δn v is the nucleation density increment of the local area of ​​the molten pool per unit time step, ΔT is the total undercooling, δ(ΔT) is the undercooling increment per unit time step, is the nucleation density distribution function, n max is the maximum nucleation density, ΔT N is the average nucleation undercooling, ΔT σ is the standard variance undercooling; ΔT′ is the nucleation undercooling; The calculation of total subcooling ΔT includes thermal subcooling Composition supercooling and curvature undercooling ΔT r =ΓK, ΔT is calculated as: In the formula, is the liquidus temperature at the initial liquid solute concentration, T loc is the microscopic cell temperature, m is the liquidus slope, C0 is the initial liquid solute concentration, is the equilibrium solute concentration in the liquid phase at the solid-liquid interface, Γ is the Gibbs-Thompson coefficient, and K is the interface curvature.

6. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 5, characterized in that: In step 5, based on the solute flux balance, the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell are calculated, and then the length of the cell covered along the normal direction of the interface is calculated. and solid fraction increment Δf s , in order to establish a three-dimensional melt pool dendrite growth model, as follows: Step 5.

1. Calculate the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell based on the solute flux balance: During the dendrite growth process, the supercooling at the solid-liquid interface is balanced, and the equilibrium solute concentration in the liquid phase at the solid-liquid interface is calculated based on this. According to the local phase equilibrium of the solid-liquid interface, the solid-phase solute equilibrium concentration can be obtained. for: Where k0 is the solute equilibrium distribution coefficient; The dendrite interface growth rate is calculated based on the solute flux balance, and the expression is: In the formula, is the normal velocity of the dendrite growth interface, D L is the diffusion coefficient of liquid solute, D S is the solid solute diffusion coefficient, C L is the liquid solute concentration, C S is the solid phase solute concentration, is the normal vector of the growth interface; The growth rate of the dendrite interface is expressed as a finite difference form along the coordinate axes X, Y, and Z through the solid phase ratio, that is, V x (i,j,k),V y (i,j,k),V z (i,j,k): Where i, j and k represent the element numbers; The interface curvature K of three-dimensional dendrite growth is calculated as follows: Where ε is the interface energy anisotropy parameter, (n x ,n y ,n z ) is the unit interface normal vector, is the first-order partial derivative of the solid phase ratio along the coordinate axis X, Y, and Z, and Q is an intermediate variable; Step 5.2: Calculate the length of the cell covered along the normal direction of the interface according to the velocity and normal direction of the growth interface. and solid fraction increment Δf s : The i-th vertex of the growth cell, i.e., the interface cell and the nucleation cell, is drawn as a plane parallel to the solid-liquid interface, and the distance from the cell center to the plane is d i , whose expression is: Among them, (x0, y0, z0) is the center coordinate of the cell in the local coordinate system, (x i ,y i ,z i ) is the coordinate of the i-th vertex of the cell in the local coordinate system; The length of the coverage cell along the interface normal direction for: Solid fraction increment Δf per unit time step s for: Where GF is the shape factor, Δt is the time increment, V n is the dendrite interface growth rate; The GF calculation rules are as follows: 1) When there is a solid phase cell among the nearest neighbor cells of the growing cell, GF = 1; 2) When there is a solid phase cell among the next neighboring cells of the growing cell, 3) When there is a solid phase cell in the third neighboring cell of the growing cell, 7. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 6, characterized in that: In step 6, based on solute conservation and Fick's law, the solute distribution and diffusion during the growth of the interface cell are calculated to establish a solute concentration field distribution model, as follows: When the solid phase ratio of the growing cell increases, if there are liquid adjacent cells in its neighborhood, the solute ΔC will be discharged, and the calculation formula is: In the formula, is the liquid solute concentration before the cell state transition, Δf s is the solid phase rate increment, k0 is the solute equilibrium distribution coefficient, is the liquid solute concentration after growth, is the equilibrium solute concentration in the liquid phase at the solid-liquid interface, f s is the solid phase ratio; If the solute concentration in the liquid phase of adjacent cell j is Less than the equilibrium solute concentration in the liquid phase at the solid-liquid interface that discharges the solute cell The excluded solute will be distributed to the cell, and its expression is: In the formula, is the liquid solute concentration of neighboring cell j at time t+1, is the liquid solute concentration of neighboring cell j at time t, is the liquid solute concentration of the nbth neighboring cell, and N is the total number of neighboring liquid cells; Based on Fick's law, the solute diffusion in the three-dimensional microstructure evolution simulation satisfies the following equation: In the formula, C L is the liquid solute concentration, C S is the solid solute concentration, D L is the diffusion coefficient of liquid solute, D S is the solid-phase solute diffusion coefficient.

8. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 7, characterized in that: In step 7, based on the eccentric octahedron algorithm, a spatial cell capture model is established, and the three-dimensional dendrite growth orientation is calculated according to the Euler angle. The neighboring cell state at the vertex of the octahedron is changed to a liquid phase cell. When the solid phase rate of the cell is f s When it reaches 1, it grows into a solid phase cell and stops capturing, as follows: Step 7.1, calculate the three-dimensional dendrite growth orientation based on the Euler angle: For aluminum alloys with a face-centered cubic crystal structure, the vector representing the <100> crystal direction after rotation can be obtained by the rotation matrix R T Calculation: In the Cartesian coordinate system XYZ, rotate the XOY plane around the Z axis by angle w1, then rotate the YOZ plane around the X axis by angle w2, and finally rotate the XOY plane around the Z axis by angle w3 to obtain the new coordinate system X'Y'Z', where the coordinate system XYZ and the vector (x, y, z) in the coordinate system X'Y'Z' are T with vector (x',y',z') T The conversion relationship between them is expressed as: Step 7.2: Based on the eccentric octahedron algorithm, establish a spatial cell capture model: An eccentric octahedron is set at the center of the nucleation cell. The three diagonals of the octahedron are parallel to the <100>, <010> and <001> directions of the face-centered cubic grains. The direction vector u of the crystal orientation in the local coordinate system is ＜100＞ 、v ＜010＞ and w ＜001＞ They are: u ＜100＞ =[R 11 R 21 R 31 ] v ＜010＞ =[R 12 R 22 R 32 ] w ＜001＞ =[R 13 R 23 R 33 ] Diagonal length L dia The solid fraction increment Δf s The accumulation of L dia The expression is: L dia =∑Δf s L max Maximum half diagonal length L max is the maximum distance through the cell along the crystal orientation, and its calculation formula is: L max =max(L [100] ,L [010] ,L [001] ) Where, L [100] , L [010] and L [001] They represent the distances through the cell along the <100> crystal direction, <010> crystal direction, and <001> crystal direction, respectively, and their expressions are: The center coordinates of the eccentric octahedron are (x0', y0', z0'), and the global coordinates of the kth vertex (x k ,y k ,z k ) is calculated by the following formula: Where R1, R2 and R3 are the components of the crystal orientation vector on the X-axis, Y-axis and Z-axis, L R is the length of the crystal orientation direction vector; As the diagonal grows, the vertex position of the eccentric regular octahedron will enter the neighboring cell. If it is a liquid phase cell, it will be captured as an interface cell, and a regular octahedron with the same deflection direction will be generated at the vertex position, thereby establishing a spatial cell capture model for three-dimensional molten pool dendrite growth.

9. A method for simulating the three-dimensional microstructure evolution during the solidification process of the arc welding weld pool as claimed in claim 8, characterized in that: In step 8, the non-uniform continuous nucleation model, the three-dimensional molten pool dendrite growth model, the solute concentration field distribution model, and the spatial cell capture model are combined to repeat steps 3 to 7 until the nucleation cells and liquid phase cells in the simulation area are transformed into solid phase cells, and the three-dimensional microstructure morphology of the weld pool is simulated, as follows: After selecting the local area of ​​the macro weld as the microstructure simulation area, all cells are initialized to the liquid phase state. Based on the non-uniform continuous nucleation model, the nucleation position is randomly determined in the calculation area, and then based on the Gaussian distribution nucleation density model, it is judged whether the nucleation position cell is nucleated under the current total supercooling degree. Then, based on the solute flux balance, the velocity magnitude and normal direction of the growth interface in the nucleation cell or interface cell are calculated, and then the three-dimensional dendrite growth orientation is calculated according to the Euler angle, and then the length of the cell covered along the normal direction of the interface and the solid phase fraction increment are calculated. Then, based on the solute conservation and Fick's law, the solute distribution and diffusion in the cell growth process are calculated, and then based on the spatial cell capture model of the eccentric octahedron algorithm, the growth of the three-dimensional dendrite is calculated. The above process is repeated until the growth cells and liquid phase cells in the simulation area are transformed into solid phase cells, and the three-dimensional microstructure morphology of the weld pool is obtained.

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