Simulation Method of Equiaxed Crystals in Multiphysics Coupled Welding Pool of High-Entropy Alloys

Abstract

This invention discloses a simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling, comprising the following steps: Step 1, simplifying the conditions of the weld pool solidification process; Step 2, establishing a macroscopic temperature field model of the welding process using the finite element method; Step 3, converting the macroscopic temperature field into a microscopic temperature field model using interpolation; Step 4, establishing an electromagnetic field model based on electromagnetic field theory; Step 5, establishing nucleation and growth models of grains based on solidification theory; Step 6, coupling the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model, and growth model into simulation software, inputting material parameters and process parameters, and then calculating and outputting the simulation results. This invention solves the problem of the lack of numerical simulation methods for the welding process of high-entropy alloys in current research.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology for welding processes of metallic materials, specifically involving a simulation method for equiaxed crystals in the weld pool of high-entropy alloys through multi-physics coupling welding. Background Technology

[0002] High-entropy alloys, a new type of alloy composed of five or more metallic elements in approximately equal atomic ratios, break through the traditional design concept of single-element matrix alloys with their unique "high mixing entropy effect," "slow diffusion effect," "cocktail effect," and "lattice distortion effect," exhibiting excellent comprehensive performance. The diversity of their constituent elements and the adjustability of their proportions result in outstanding performance in mechanical properties (such as high strength, high toughness, good wear resistance, and fatigue resistance), physical properties (such as low thermal conductivity and moderate coefficient of thermal expansion), and chemical properties (such as excellent corrosion resistance and oxidation resistance). The primary welding method for high-entropy alloys is arc welding. During arc welding, the heat distribution input to the workpiece directly affects the performance of the weld joint. Furthermore, the presence of the electric arc during arc cladding generates electric and magnetic fields, which also influence the solidification process of the high-entropy alloy cladding pool. Moreover, electromagnetic fields are difficult to observe experimentally. Experimental methods are often used to study the welding process of high-entropy alloys. However, this method has the disadvantages of being time-consuming, labor-intensive, and economically inefficient. Moreover, the heat generated during the welding process is instantaneous, concentrated, and dynamic, making it difficult to observe the temperature and electromagnetic field changes of the weld pool in real time using traditional methods. Consequently, it is impossible to observe the evolution of the grain structure within the weld pool in real time.

[0003] With the development of computer technology, numerical simulation methods can be used to study the welding process of high-entropy alloys, representing a new research approach. Cellular automata, with its solid physical foundation and advanced probabilistic concepts, has achieved significant progress in numerous disciplines. Therefore, applying it to simulate the microstructure evolution during high-entropy welding is clearly feasible. This not only provides a new perspective and method for studying high-entropy welding processes but also highlights the importance and urgency of establishing a method for simulating the microstructure of high-entropy weld pools. Summary of the Invention

[0004] The purpose of this invention is to provide a simulation method for equiaxed crystals in the weld pool of high-entropy alloys through multiphysics coupling welding, which solves the problem of the lack of numerical simulation methods for the welding process of high-entropy alloys in current research.

[0005] The technical solution adopted in this invention is a simulation method for equiaxed crystals in the weld pool of high-entropy alloys through multiphysics coupling welding, comprising the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0006] The invention is further characterized by: The simplification of conditions in step 1 includes: the entire solidification process only has three cellular states: liquid phase, solid phase and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model.

[0007] Step 2 is as follows: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field.

[0008] In step 2.3, a double ellipsoidal heat source is selected as the welding heat source. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; bFor ellipsoidal depth parameters; v This refers to the welding speed.

[0009] Step 3 specifically involves: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation.

[0010] In step 4, the electromagnetic field model is constructed based on the electromagnetic force equation, the current continuity equation, the Joule heating equation, and the magnetic field calculation equation. The electromagnetic force equation is expressed by equation (3); (3); in, It is a current density vector; It is the magnetic field strength vector; The equations for current continuity are expressed by equations (4)-(6); (4); (5); (6); in, It is electric potential; It is electrical conductivity; J r and J z These are the radial and axial current densities, respectively. The Joule heating equation is expressed by equation (7); (7); The equation for calculating the magnetic field is expressed by equation (8); (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; It is the integral variable.

[0011] Step 5 specifically involves: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Construct the nucleation model of the grain according to equations (9) and (10); (9); (10); Where, Δ T Supercooling; N This refers to the grain nucleation density; N max The maximum nucleation density; Δ T θ Standard curvature undercooling; Δ T max For maximum nucleation undercooling; Step 5.3: Construct a grain growth model; Specifically: the grain growth model is the supercooling Δ at a certain moment. T ( t n The solid fraction increment Δf at a single time step s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s Determine the cell state; Supercooling Δ at a certain moment T ( t n The interface propulsion rate v function is represented by equation (11); (11); The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by (12); (12); in, t n For a certain moment; μ k ( θ ) represents the interfacial dynamics coefficient; Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; rand A random number between 0 and 1; Based on equations (11) and (12), and combined with the eight-cell Moore solute diffusion model, a grain growth model is obtained.

[0012] In step 6, the simulation software is MATLAB. The material parameters include the thermophysical and electromagnetic parameters of the high-entropy alloy, and the process parameters include welding current, welding voltage, and welding speed.

[0013] High-entropy alloy is FeCoNiCrAl 0.5 Welding current 140-160A, welding voltage 18.6-19V, welding speed 0.20-0.25m / min.

[0014] The beneficial effects of this invention are: The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling provided by this invention solves the shortcomings of current simulations of the microstructure of high-entropy alloys; it can simulate columnar crystals during the solidification process of the weld pool of high-entropy alloys under different welding processes; and it conforms to the concepts of safety, greenness, and environmental protection. Attached Figure Description

[0015] Figure 1 This is a diagram showing the change of the magnetic field on the grid during the growth process of equiaxed crystals in the high-entropy alloy multi-physics coupled welding molten pool in an embodiment of the present invention. Figure 2 This is a simulation result of the equiaxed crystal of the high-entropy alloy multiphysics coupled welding molten pool under a current of 140A in an embodiment of the present invention. Figure 3 This is a simulation result of the equiaxed crystal of the high-entropy alloy multiphysics coupled welding molten pool under a current of 150A in an embodiment of the present invention. Figure 4 This is a simulation result of the equiaxed crystal of the high-entropy alloy multiphysics coupled welding molten pool under a current of 160A in an embodiment of the present invention. Detailed Implementation

[0016] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0017] Example 1 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0018] Example 2 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0019] Example 3 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Specifically: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; A double ellipsoidal heat source was selected as the welding heat source for the heat source load. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v For welding speed; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0020] Example 4 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Specifically: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; A double ellipsoidal heat source was selected as the welding heat source for the heat source load. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v For welding speed; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Specifically: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0021] Example 5 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Specifically: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; A double ellipsoidal heat source was selected as the welding heat source for the heat source load. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v For welding speed; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Specifically: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; The electromagnetic field model is constructed based on the electromagnetic force equation, the current continuity equation, the Joule heating equation, and the magnetic field calculation equation; The electromagnetic force equation is expressed by equation (3); (3); in, It is a current density vector; It is the magnetic field strength vector; The equations for current continuity are expressed by equations (4)-(6); (4); (5); (6); in, It is electric potential; It is electrical conductivity; J r and J z These are the radial and axial current densities, respectively. The Joule heating equation is expressed by equation (7); (7); The equation for calculating the magnetic field is expressed by equation (8); (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; For integration variables; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0022] Example 6 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Specifically: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; A double ellipsoidal heat source was selected as the welding heat source for the heat source load. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v For welding speed; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Specifically: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; The electromagnetic field model is constructed based on the electromagnetic force equation, the current continuity equation, the Joule heating equation, and the magnetic field calculation equation; The electromagnetic force equation is expressed by equation (3); (3); in, It is a current density vector; It is the magnetic field strength vector; The equations for current continuity are expressed by equations (4)-(6); (4); (5); (6); in, It is electric potential; It is electrical conductivity; J r and J z These are the radial and axial current densities, respectively. The Joule heating equation is expressed by equation (7); (7); The equation for calculating the magnetic field is expressed by equation (8); (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; For integration variables; Step 5: Establish nucleation and growth models of grains based on solidification theory; Specifically: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Construct the nucleation model of the grain according to equations (9) and (10); (9); (10); Where, Δ T Supercooling; N This refers to the grain nucleation density; N max The maximum nucleation density; Δ T θ Standard curvature undercooling; Δ T max For maximum nucleation undercooling; Step 5.3: Construct a grain growth model; Specifically: the grain growth model is the supercooling Δ at a certain moment. T ( t n The solid fraction increment Δf at a single time step s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s Determine the cell state; Supercooling Δ at a certain moment T ( t n The interface propulsion rate v function is represented by equation (11); (11); The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by (12); (12); in, t n For a certain moment; μ k ( θ ) represents the interfacial dynamics coefficient; Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; rand A random number between 0 and 1; Based on equations (11) and (12), and combined with the eight-cell Moore solute diffusion model, a grain growth model is obtained; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

[0023] Example 7 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; The simplification of conditions includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square elements, each element being a cell; the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model. Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Specifically: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; A double ellipsoidal heat source was selected as the welding heat source for the heat source load. The heat flux density of the front ellipsoid of the welding heat source is represented by equation (1); (1); The heat flux density of the back ellipsoid of the welding heat source is represented by equation (2); (2); in q ( x, y, z, t (time) t exist( x, y, z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v For welding speed; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Specifically: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory, such as... Figure 1 As shown; The electromagnetic field model is constructed based on the electromagnetic force equation, the current continuity equation, the Joule heating equation, and the magnetic field calculation equation; The electromagnetic force equation is expressed by equation (3); (3); in, It is a current density vector; It is the magnetic field strength vector; The equations for current continuity are expressed by equations (4)-(6); (4); (5); (6); in, It is electric potential; It is electrical conductivity; J r and J z These are the radial and axial current densities, respectively. The Joule heating equation is expressed by equation (7); (7); The equation for calculating the magnetic field is expressed by equation (8); (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; For integration variables; Step 5: Establish nucleation and growth models of grains based on solidification theory; Specifically: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Construct the nucleation model of the grain according to equations (9) and (10); (9); (10); Where, Δ T Supercooling; N This refers to the grain nucleation density; N max The maximum nucleation density; Δ T θ Standard curvature undercooling; Δ Tmax For maximum nucleation undercooling; Step 5.3: Construct a grain growth model; Specifically: the grain growth model is the supercooling Δ at a certain moment. T ( t n The solid fraction increment Δf at a single time step s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s Determine the cell state; Supercooling Δ at a certain moment T ( t n The interface propulsion rate v function is represented by equation (11); (11); The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by (12); (12); in, t n For a certain moment; μ k ( θ ) represents the interfacial dynamics coefficient; Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; rand A random number between 0 and 1; Based on equations (11) and (12), and combined with the eight-cell Moore solute diffusion model, a grain growth model is obtained; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results. The simulation software is MATLAB. The material parameters include the thermal properties and electromagnetic field parameters of the high-entropy alloy, as shown in Table 1. The process parameters include welding current, welding voltage and welding speed. High-entropy alloy is FeCoNiCrAl 0.5Welding current 140-160A, welding voltage 18.6-19V, welding speed 0.20-0.25m / min.

[0024] Table 1 FeCoNiCrAl 0.5 Table of thermophysical and electromagnetic parameters of high-entropy alloys

[0025] Example 8 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Simplified condition 1: The entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface. Simplified condition 2: Simplify the weld pool into a regular semi-circular shape; Simplified condition 3: During the simulation, kinetic supercooling is ignored; only temperature supercooling and compositional supercooling are considered. and excessive curvature; Simplified condition 4: The simulation region is divided into square units, and each unit is a cell; Simplified condition 5: Cell neighborhood relationships adopt the Moore-type diffusion model, i.e., eight neighborhoods; Step 2 is implemented in the following steps: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; A double-ellipsoidal heat source is selected as the welding heat source, and its model is represented by the following equation: The heat flux density distribution on the anterior ellipsoid is as follows: (1); The heat flux density distribution on the posterior ellipsoid is as follows: (2); In the above formula: q ( x, y, z, t (time) t exist( x, y, z Heat flow at location k The heat source concentration factor, f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. fl + f 2=2, c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively. a For the ellipsoid width parameter, b For ellipsoidal depth parameters, v For welding speed; Step 3 is implemented in the following steps: Step 3.1: Select the thermal cycle curve of the finite element node in the temperature field calculated in Step 2, i.e., the time-temperature curve. The welding parameters are set as follows during the finite element analysis: welding current is 140A, welding voltage is 18.7V, and welding speed is 0.22m / min. Step 3.2: Use MATLAB to fit the thermal cycle curve obtained in Step 3.1 to obtain the macroscopic temperature field model; Step 3.3: Use linear interpolation to transform the macroscopic temperature field model into a microscopic temperature field model suitable for microstructure calculation; Step 4 is implemented in the following steps: The electromagnetic field model and its magnitude are established and calculated using the following formula: (3); The above formula is for calculating electromagnetic force, where It is a current density vector; It is the magnetic field strength vector; Governing equations (current continuity): (4); in, It is electric potential; It is electrical conductivity; Solve from the above formula Then, J is calculated using the difference method: (5); (6); in, J r and J z These are the radial and axial current densities, respectively. Calculation of Joule heat: (7); Magnetic field calculation: (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; rThe current coordinates; For integration variables; Step 5 is implemented in the following steps: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Calculate the probability of crystal nucleation using the following formula: (9); In the above formula, Δ T For supercooling, N This represents the grain nucleation density.

[0026] in, dN / d (Δ T ) is represented as: (10); In the above formula, N max For the maximum nucleation density, Δ T θ For standard curvature undercooling, Δ T max For maximum nucleation undercooling, formulas (9) and (10) together construct the nucleation model of the grain; Step 5.3: Construct a grain growth model: Grain growth models include the octagonal Moore solute diffusion model. Essentially, the grain growth model represents the supercooling Δ at a given moment. T ( t n The solid fraction increment Δ at a single time step f s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s The specific process for determining the cell state is as follows: Supercooling Δ at a certain moment T ( t n Regarding the interface advancement rate v The function is as follows: (11); In the above formula: t n At a certain moment, μ k (θ ) represents the interfacial dynamics coefficient; The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by the following formula: (12); In the above formula: Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; rand The random number is 0-1; (11) and (12) combined with the eight-cell Moore solute diffusion model are the grain growth model; Step 6 is implemented in the following steps: Step 6.1: Import the macroscopic temperature field model, microscopic temperature field model, electromagnetic field model and grain nucleation and growth model obtained in Steps 2-4 into MATLAB simulation software. After coupling, it becomes the equiaxed crystal evolution model of the high-entropy alloy welding molten pool. Step 6.2: Input the thermal properties and electromagnetic field parameters of the high-entropy alloy and the welding process parameters into the microstructure evolution model of the high-entropy alloy welding pool, perform calculations, and obtain the simulation results, such as... Figure 2 As shown.

[0027] Example 9 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Simplified condition 1: The entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface. Simplified condition 2: Simplify the weld pool into a regular semi-circular shape; Simplified condition 3: In the simulation process, kinetic supercooling is ignored, and only temperature supercooling, composition supercooling and curvature supercooling are considered; Simplified condition 4: The simulation region is divided into square units, and each unit is a cell; Simplified condition 5: Cell neighborhood relationships adopt the Moore-type diffusion model, i.e., eight neighborhoods; Step 2 is implemented in the following steps: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; A double-ellipsoidal heat source is selected as the welding heat source, and its model is represented by the following equation: The heat flux density distribution on the anterior ellipsoid is as follows: (1); The heat flux density distribution on the posterior ellipsoid is as follows: (2); In the above formula: q ( x, y, z, t (time) t exist( x, y, z Heat flow at location k The heat source concentration factor, f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2, c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively. a For the ellipsoid width parameter, b For ellipsoidal depth parameters, v For welding speed; Step 3 is implemented in the following steps: Step 3.1: Select the thermal cycle curve of the finite element node in the temperature field calculated in step 2, i.e., the time-temperature curve. The welding parameters are set as follows during the finite element analysis: welding current is 150A, welding voltage is 18.7V, and welding speed is 0.22m / min. Step 3.2: Use MATLAB to fit the thermal cycle curve obtained in Step 3.1 to obtain the macroscopic temperature field model; Step 3.3: Use linear interpolation to transform the macroscopic temperature field model into a microscopic temperature field model suitable for microstructure calculation; Step 4 is implemented in the following steps: The electromagnetic field model and its magnitude are established and calculated using the following formula: (3); The above formula is for calculating electromagnetic force, where It is a current density vector; It is the magnetic induction intensity vector.

[0028] Governing equations (current continuity): (4); in, It is electric potential; It is electrical conductivity.

[0029] Solve from the above formula Then, J is calculated using the difference method: (5); (6); in, J r and J z These are the radial and axial current densities, respectively. Calculation of Joule heat: (7); Magnetic field calculation: (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 r is the current coordinate; For integration variables; Step 5 is implemented in the following steps: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Calculate the probability of crystal nucleation using the following formula: (9); In the above formula, Δ T For supercooling, N This refers to the grain nucleation density; in, dN / d (Δ T ) is represented as: (10); In the above formula, N max For the maximum nucleation density, Δ T θ For standard curvature undercooling, Δ T max For maximum nucleation undercooling, formulas (9) and (10) together construct the nucleation model of the grain; Step 5.3: Construct a grain growth model: Grain growth models include the octagonal Moore solute diffusion model. Essentially, the grain growth model represents the supercooling Δ at a given moment. T ( t n The solid fraction increment Δ at a single time step f s The function, using the supercooling Δ at a certain moment.T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s The specific process for determining the cell state is as follows: Supercooling Δ at a certain moment T ( t n Regarding the interface advancement rate v The function is as follows: (11); In the above formula: t n At a certain moment, μ k ( θ ) represents the interfacial dynamics coefficient; The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by the following formula: (12); In the above formula: Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; rand The random number is 0-1; (11) and (12) combined with the eight-cell Moore solute diffusion model are the grain growth model; Step 6 is implemented in the following steps: Step 6.1: Import the macroscopic temperature field model, microscopic temperature field model, electromagnetic field model and grain nucleation and growth model obtained in Steps 2-4 into MATLAB simulation software. After coupling, it becomes the equiaxed crystal evolution model of the high-entropy alloy welding molten pool. Step 6.2: Input the thermal properties and electromagnetic field parameters of the high-entropy alloy and the welding process parameters into the microstructure evolution model of the high-entropy alloy welding pool, perform calculations, and obtain the simulation results, such as... Figure 3 As shown.

[0030] Example 10 The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling proposed in this embodiment includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Simplified condition 1: The entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface. Simplified condition 2: Simplify the weld pool into a regular semi-circular shape; Simplified condition 3: In the simulation process, kinetic supercooling is ignored, and only temperature supercooling, composition supercooling and curvature supercooling are considered; Simplified condition 4: The simulation region is divided into square units, and each unit is a cell; Simplified condition 5: Cell neighborhood relationships adopt the Moore-type diffusion model, i.e., eight neighborhoods; Step 2 is implemented in the following steps: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field; A double-ellipsoidal heat source is selected as the welding heat source, and its model is represented by the following equation: The heat flux density distribution on the anterior ellipsoid is as follows: (1); The heat flux density distribution on the posterior ellipsoid is as follows: (2); In the above formula: q ( x, y, z, t (time) t exist( x, y, z Heat flow at location k The heat source concentration factor, f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2, c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively. a For the ellipsoid width parameter, b For ellipsoidal depth parameters, v For welding speed; Step 3 is implemented in the following steps: Step 3.1: Select the thermal cycle curve of the finite element node in the temperature field calculated in Step 2, i.e., the time-temperature curve. The welding parameters are set as follows during the finite element analysis: welding current is 160A, welding voltage is 18.7V, and welding speed is 0.22m / min. Step 3.2: Use MATLAB to fit the thermal cycle curve obtained in Step 3.1 to obtain the macroscopic temperature field model; Step 3.3: Use linear interpolation to transform the macroscopic temperature field model into a microscopic temperature field model suitable for microstructure calculation; Step 4 is implemented in the following steps: The electromagnetic field model and its magnitude are established and calculated using the following formula: (3); The above formula is for calculating electromagnetic force, where It is a current density vector; It is the magnetic induction intensity vector.

[0031] Governing equations (current continuity): (4); in, It is electric potential; It is electrical conductivity; Solve from the above formula Then, J is calculated using the difference method: (5); (6); in, J r and J z These are the radial and axial current densities, respectively. Calculation of Joule heat: (7); Magnetic field calculation: (8); in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; For integration variables; Step 5 is implemented in the following steps: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Calculate the probability of crystal nucleation using the following formula: (9); In the above formula, Δ T For supercooling, N This represents the grain nucleation density.

[0032] in, dN / d( Δ T)Represented as: (10); In the above formula, N max For the maximum nucleation density, Δ T θ For standard curvature undercooling, Δ T max For maximum nucleation undercooling, formulas (9) and (10) together construct the nucleation model of the grain; Step 5.3: Construct a grain growth model: Grain growth models include the octagonal Moore solute diffusion model. Essentially, the grain growth model represents the supercooling Δ at a given moment. T ( t n The solid fraction increment Δ at a single time step f s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s The specific process for determining the cell state is as follows: Supercooling Δ at a certain moment T ( t n Regarding the interface advancement rate v The function is as follows: (11); In the above formula: t n At a certain moment, μ k ( θ ) represents the interfacial dynamics coefficient; The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by the following formula: (12); In the above formula: Δ x The unit cell size; Δ t For a single computation time step; G For adjacent grid state parameters; A For disturbance factor; randThe random number is 0-1; (11) and (12) combined with the eight-cell Moore solute diffusion model are the grain growth model; Step 6 is implemented in the following steps: Step 6.1: Import the macroscopic temperature field model, microscopic temperature field model, electromagnetic field model and grain nucleation and growth model obtained in Steps 2-4 into MATLAB simulation software. After coupling, it becomes the equiaxed crystal evolution model of the high-entropy alloy welding molten pool. Step 6.2: Input the thermal properties and electromagnetic field parameters of the high-entropy alloy and the welding process parameters into the microstructure evolution model of the high-entropy alloy welding pool, perform calculations, and obtain the simulation results, such as... Figure 4 As shown.

[0033] The addition of an electromagnetic field in this invention increases the number of equiaxed grains. This is because the presence of the electromagnetic field has a scouring effect on the equiaxed grains, which is more consistent with the actual arc cladding process. As the current increases (140-160A), the number of secondary dendrites on the dendrite walls of the equiaxed grains increases, and the grains become smaller. This is because the increased current leads to a stronger electric field, generating a stronger impact force on the dendrite walls.

Claims

1. A simulation method for equiaxed crystals in the molten pool of high-entropy alloy multiphysics coupled welding, characterized in that, Includes the following steps: Step 1: Simplify the conditions for the solidification process of the weld pool; Step 2: Establish a macroscopic temperature field model of the welding process using the finite element method; Step 3: Transform the macroscopic temperature field into a microscopic temperature field model using interpolation. Step 4: Establish an electromagnetic field model based on electromagnetic field theory; Step 5: Establish nucleation and growth models of grains based on solidification theory; Step 6: Couple the above macroscopic temperature field model, microscopic temperature field model, electromagnetic field model, nucleation model and growth model into the simulation software, input the material parameters and process parameters, and then calculate and output the simulation results.

2. The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling according to claim 1, characterized in that, The simplification of conditions in step 1 includes: the entire solidification process consists of only three cellular states: liquid phase, solid phase, and interface; the weld pool is simplified to a regular semi-circular shape; kinetic supercooling is ignored, and only temperature supercooling, composition supercooling, and curvature supercooling are considered; the simulation region is divided into square units, each unit being a cell; and the cell neighborhood relationship adopts the Moore-type eight-neighbor diffusion model.

3. The simulation method for equiaxed crystals in the weld pool of high-entropy alloys using multiphysics coupling according to claim 1, characterized in that, Step 2 specifically involves: Step 2.1: Model the object in the finite element software according to its dimensions; Step 2.2: Assign material properties to the finite element geometric model according to the selected material; Step 2.3: Set boundary conditions, heat source load, initial temperature, and appropriate analysis steps; Step 2.4: After setting up, perform simulation calculations and export the macroscopic temperature field.

4. The simulation method for equiaxed crystals in the weld pool of high-entropy alloy multiphysics coupled welding according to claim 3, characterized in that, In step 2.3, a double ellipsoidal heat source is selected as the welding heat source for the heat source load. The front ellipsoidal heat flux density of the welding heat source is represented by equation (1); （1）； The back ellipsoidal heat flux density of the welding heat source is represented by equation (2); （2）； in q ( x,y,z,t (time) t exist( x,y,z Heat flow at location ) k The heat source concentration factor; f l , f 2 represents the energy distribution coefficients in the front and rear portions of the molten pool, respectively. f l + f 2=2; c 1, c 2 represents the length parameters of the front and rear hemispheres, respectively; a This refers to the ellipsoid width parameter; b For ellipsoidal depth parameters; v This refers to the welding speed.

5. The simulation method for equiaxed crystals in a multiphysics coupled welding pool of high-entropy alloys according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: Select the thermal cycling curve of the finite element node from the macroscopic temperature field calculated in Step 2; Step 3.2: Use MATLAB to fit the thermal cycle curve to obtain the macroscopic temperature field model; Step 3.3: Transform the macroscopic temperature field model into a microscopic temperature field model using linear interpolation.

6. The simulation method for equiaxed crystals in a multiphysics coupled welding pool of high-entropy alloys according to claim 1, characterized in that, The electromagnetic field model described in step 4 is constructed based on the electromagnetic force equation, the current continuity equation, the Joule heating equation, and the magnetic field calculation equation. The electromagnetic force equation is represented by equation (3); （3）； in, It is a current density vector; It is the magnetic flux density vector; The current continuity equation is represented by equations (4)-(6); （4）； （5）； （6）； in, It is electric potential; It is electrical conductivity; J r and J z These are the radial and axial current densities, respectively. The Joule heating equation is expressed by equation (7); （7）； The magnetic field calculation equation is expressed by equation (8); （8）； in, It is the free permeability, with a value of 1.2566 × 10⁻⁶. -6 ; r The current coordinates; It is the integral variable.

7. The simulation method for equiaxed crystals in a multiphysics coupled welding pool of high-entropy alloys according to claim 1, characterized in that, Step 5 specifically involves: Step 5.1: Simplify the nucleation and growth model of grains; Step 5.2: Construct the nucleation model of the grain according to equations (9) and (10); （9）； （10）； Where, Δ T Supercooling; N This refers to the grain nucleation density; N max The maximum nucleation density; Δ T θ Standard curvature undercooling; Δ T max For maximum nucleation undercooling; Step 5.3: Construct a grain growth model; Specifically: the grain growth model is the supercooling Δ at a certain moment. T ( t n The solid fraction increment Δf at a single time step s The function, using the supercooling Δ at a certain moment. T ( t n ) and interface advancement rate v Calculate the solid fraction increment Δ at a single time step f s The solid fraction increment Δ at a single time step f s Determine the cell state; Supercooling Δ at a certain moment T ( t n The interface propulsion rate v function is represented by equation (11); （11）； The solid fraction increment Δ at a single time step f s Regarding the interface progression rate v The function is represented by (12); （12）； in, t n For a certain moment; μ k ( θ ) represents the interfacial dynamics coefficient; Δ x Δ is the cell unit size; t For a single computation time step; G These are the state parameters of the adjacent grid. A For disturbance factors; rand A random number between 0 and 1; Based on equations (11) and (12), and combined with the eight-cell Moore solute diffusion model, a grain growth model is obtained.

8. The simulation method for equiaxed crystals in a high-entropy alloy multiphysics coupled welding molten pool according to claim 1, characterized in that, The simulation software mentioned in step 6 is MATLAB software, the material parameters include the thermophysical parameters and electromagnetic field parameters of the high-entropy alloy, and the process parameters include welding current, welding voltage and welding speed.

9. The simulation method for equiaxed crystals in a high-entropy alloy multiphysics coupled welding molten pool according to claim 8, characterized in that, The high-entropy alloy is FeCoNiCrAl 0.5 The welding current is 140-160A, the welding voltage is 18.6-19V, and the welding speed is 0.20-0.25m / min.

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