CN110619157B - Method for simulating microstructure evolution of titanium alloy welding pool - Google Patents
Method for simulating microstructure evolution of titanium alloy welding pool Download PDFInfo
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Abstract
The invention discloses a method for simulating microstructure evolution of a titanium alloy welding pool, which comprises the steps of firstly establishing a finite element calculation model of a welding transient macroscopic temperature field model by using finite element calculation software based on a finite element method, then converting the macroscopic temperature field model into a microscopic temperature field model suitable for microstructure calculation by using a linear interpolation principle, establishing a nucleation and growth model of a titanium alloy on the premise of simplifying partial physical conditions, and finally integrating the three models established in the prior art into a microstructure evolution model of the titanium alloy welding pool by programming on MATLAB simulation software. The model can calculate the change of the temperature field in the titanium alloy welding process under different process parameters and working conditions, and calculate the evolution process of the microstructure in the welding pool under the action of the welding temperature field with high dynamic change through macro-micro coupling, thereby providing a high-efficiency and reliable research means for related research.
Description
Technical Field
The invention belongs to the field of a numerical simulation method for microstructure evolution in a metal solidification process, and particularly relates to a simulation method for microstructure evolution of a titanium alloy welding pool.
Background
With the rapid development of the fields of aerospace, shipbuilding, chemical engineering, biomedical treatment and the like, the requirements of related materials are increasingly huge, the titanium alloy in various materials has unique advantages of low density, high specific strength, good heat resistance, good corrosion resistance and the like, the welding has the advantages of good flexibility, strong adaptability, simple and convenient operation and the like, and the method is the most main connecting method of the titanium alloy at present, so how to improve the welding quality has a very important meaning.
The weld microstructure has a great influence on the weld quality, and traditional experimental methods such as metallographic experiments and the like can only study the solidification structure of the final state after welding, but the solidification process of the weld pool microstructure is high in complexity, the complex microstructure evolution process cannot be comprehensively studied only from the final state structure, and the complex microstructure evolution process cannot be intuitively known, so that the problem that the cost is difficult to control even special experimental equipment is utilized is unavoidable, and a research method with controllable cost and definite physical background is urgently needed. In recent years, a numerical simulation method which is based on the rapid development of computer technology provides a new option for relevant scholars, the method achieves some achievements in the field of material research, particularly solidification, and a mathematical model is established based on a physical process to finally realize the visualization of the physical process.
Therefore, the establishment of a method for simulating the microstructure evolution of the titanium alloy welding pool is particularly important.
Disclosure of Invention
The invention aims to provide a method for simulating the microstructure evolution of a titanium alloy welding pool, which solves the problems of low efficiency of a microstructure evolution model and undefined physical background in the prior art.
The technical scheme adopted by the invention is that the method for simulating the microstructure evolution of the titanium alloy welding pool is implemented according to the following steps:
and 4, processing numerical calculation and calculation results.
The invention is also characterized in that:
the step 1 is implemented according to the following steps:
step 1.1, inputting the size of a model in finite element software, and establishing a finite element geometric model;
step 1.2, according to the selected materials, giving material attributes to the finite element geometric model to obtain a finite element geometric material model;
step 1.3, setting an analysis step according to the actual process of molten pool evolution to be simulated;
step 1.4, setting boundary conditions according to the actual conditions of a molten pool, wherein the boundary conditions specifically comprise setting of initial temperature and determination of heat exchange relation between the molten pool and the environment;
step 1.5, setting a load according to the actual condition of a molten pool, wherein the load specifically comprises the setting of boundary constraint and the setting of surface heat flux, namely the selection of a heat source model, and the heat source model selects a double-ellipsoid heat source model;
and step 1.6, combining the finite element geometric material model with boundary conditions and loads to form a finite element model, dividing the finite element model into finite element units with the same size to obtain a finite element calculation model, and calculating a welding transient macroscopic temperature field model by using the finite element calculation model.
The step 2 is implemented according to the following steps:
step 2.1, selecting a proper calculation domain, and extracting a thermal cycle curve, namely a time-temperature curve, of the finite element node;
step 2.2, fitting a thermal cycle curve by using simulation software MATLAB to obtain a temperature-time function of the finite element node, and obtaining a macroscopic temperature field model;
step 2.3, converting the macroscopic temperature field model into a microscopic temperature field model suitable for calculating the microstructure by adopting a linear interpolation method, wherein the specific mathematical expression is as follows:
T o temperature, T, of the micro-cells O i Is the macro-unit temperature around the O point, L i N is the number of macro-units around the micro-unit, which is the distance from the point O to the surrounding macro-units, and has a value of 8.
step 3.1, simplifying the conditions for constructing nucleation and growth models of the crystal grains;
step 3.2, establishing a crystal grain nucleation model, wherein the crystal grain nucleation model is substantially a function of the supercooling degree delta T relative to the crystal grain nucleation density N (delta T), and the probability of crystal grain nucleation is calculated by utilizing the supercooling degree delta T and the crystal grain nucleation density N (delta T), and the specific process is as follows:
the degree of supercooling Δ T is a function of the grain nucleation density N (Δ T) as shown in the following equation:
wherein dN/d (Δ T) is represented by:
in the formula: n is a radical of max Is the maximum nucleation density, Δ T θ Is a standard degree of curvature supercooling, Δ T max Supercooling for maximum nucleation; the combination of the formulas (1) and (2) is a grain nucleation model;
step 3.3, establishing a grain growth model, wherein the grain growth model comprises an eight-neighbor Moore type solute diffusion model, and the grain growth model is substantially the supercooling degree delta T (T) at a certain moment n ) Solid fraction increment Δ f for a single time step s Using the degree of supercooling Δ T (T) at a certain time n ) Calculating solid phase ratio increment delta f of single time step with interface advancing speed upsilon s Increase in solid phase fraction Δ f by a single time step s Judging the state of the cells, and the specific process is as follows:
supercooling degree DeltaT (T) at a certain time n ) The function on the interface advance rate v is shown as follows:
υ＝μ k (θ)·ΔT(t n ) (3)
in the formula: t is t n Is a certain time, mu k (θ) is the interfacial kinetic coefficient, determined by the following formula:
μ k (θ)＝μ av (1+ξ k cos(4(θ-θ 0 ))) (4)
in the formula: theta is the angle between the normal direction of the interface and the horizontal direction, theta 0 Is the preferred growth direction of the grains, mu av Is the average interface dynamics coefficient, ξ k Is the dynamic anisotropic strength;
solid fraction increment of single time step Δ f s The function upsilon about the interface advance rate is expressed by the following formula:
in the formula: Δ x is the cell unit size; Δ t is a single calculation time step; g is an adjacent position grid state parameter; a is a disturbance factor; rand is a random number of 0-1;
solid fraction increment Δ f by a single time step s The cellular state is judged by the following process:
in the formula: n is the iteration number; Δ t is the time step when f s (t) =1, the state of the cell is changed to a solid phase; (3) (4) (5) combining the grain growth model with an eight-neighbor Moore type solute diffusion model;
the simplified conditions for constructing the nucleation and growth model of the crystal grains comprise:
a. the liquid interface has no thickness, and the simulation area only has cells in three states of liquid, solid and interface;
b. only the formation of primary grains is considered, and the solid-state phase transition during cooling is not considered.
The specific process of step 4 is as follows:
step 4.1, introducing the welding transient macroscopic temperature field model, the microscopic temperature field model and the nucleation and growth model of the crystal grains constructed in the step 1-3 into simulation software Matlab to be combined to form a microstructure evolution model of the titanium alloy welding pool;
and 4.2, inputting thermophysical parameters and welding process parameters of the titanium alloy into the microstructure evolution model of the titanium alloy welding pool, and calculating to obtain a simulation result image.
The invention has the beneficial effects that:
(1) The method for simulating the microstructure evolution of the titanium alloy welding pool is provided, and a new method is provided for researching the solidification process of the welding pool;
(2) The characteristics of high calculation speed and high calculation precision of commercial finite element software are combined, so that the calculation efficiency is greatly improved;
(3) The method conforms to the safe, green and environment-friendly concept.
Drawings
FIG. 1 is a simulation flow chart of a method for simulating microstructure evolution of a titanium alloy welding pool according to the invention;
FIG. 2 is a finite element geometric model of a method for simulating microstructure evolution of a titanium alloy welding pool according to the invention;
FIG. 3 is a schematic diagram of a dual ellipsoid heat source model of a simulation method for microstructure evolution of a titanium alloy weld pool according to the present invention;
FIG. 4 is a geometric model meshing of a simulation method for the microstructure evolution of a titanium alloy welding pool;
FIG. 5 is a schematic diagram of linear interpolation of a method for simulating microstructure evolution of a titanium alloy weld pool according to the present invention;
FIG. 6 is a Moore neighborhood relationship diagram of a simulation method of microstructure evolution of a titanium alloy weld pool according to the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Example 1
The invention discloses a method for simulating microstructure evolution of a titanium alloy welding pool, which is implemented according to the following steps as shown in figure 1:
and 4, calculating numerical values and processing calculation results.
The step 1 is implemented according to the following steps:
step 1.1, inputting the size of a model in finite element software, and establishing a finite element geometric model as shown in figure 2;
step 1.2, according to the selected materials, giving material attributes to the finite element geometric model to obtain a finite element geometric material model;
step 1.3, setting an analysis step according to the actual process of molten pool evolution to be simulated;
step 1.4, setting boundary conditions according to the actual conditions of a molten pool, wherein the boundary conditions specifically comprise setting of initial temperature and determination of heat exchange relation between the molten pool and the environment;
step 1.5, setting a load according to the actual condition of a molten pool, wherein the load specifically comprises the setting of boundary constraint and the setting of surface heat flux, namely the selection of a heat source model, and the heat source model selects a double-ellipsoid heat source model, as shown in fig. 3, the mathematical expression of the model is as follows:
the front ellipsoid heat flow density distribution is:
the rear ellipsoid heat flux density distribution is:
in the formula: q (x, y, z, t) is the heat flow at the (x, y, z) position at time t, k is the heat source concentration coefficient, f 1 ，f 2 Energy distribution coefficients at the front and rear parts of the molten bath, respectively, f 1 +f 2 ＝2，c 1 ，c 2 Respectively the length parameters of front and rear semi-ellipsoids, a is the width parameter of the ellipsoid, b is the depth parameter of the ellipsoid, and v is the welding speed;
step 1.6, as shown in fig. 4, combining the finite element geometric material model with the boundary conditions and the loads to form a finite element model, dividing the finite element model into finite element units with the same size to obtain a finite element calculation model, and calculating a welding transient macroscopic temperature field model by using the finite element calculation model;
the step 2 is implemented according to the following steps:
step 2.1, selecting a proper calculation domain, and extracting a thermal cycle curve, namely a time-temperature curve, of the finite element node;
step 2.2, fitting a thermal cycle curve by using simulation software MATLAB to obtain a temperature-time function of the finite element node, and obtaining a macroscopic temperature field model;
step 2.3, converting the macroscopic temperature field model into a microscopic temperature field model suitable for calculating the microstructure by adopting a linear interpolation method, wherein the interpolation principle is shown in fig. 4, and the specific mathematical expression is as follows:
T o temperature, T, of the micro-cells O i Is the macro-unit temperature around the O point, L i Is the distance from point O to the surrounding macro-units, N is the number of macro-units surrounding the micro-units, and has a value of 8;
step 3.1, simplifying the construction conditions of the nucleation and growth model of the crystal grains: a. the liquid interface has no thickness, and the simulation area only has cells in three states of liquid, solid and interface;
b. only the formation of primary grains is considered, and the solid phase transformation in the cooling process is not considered;
step 3.2, establishing a crystal grain nucleation model, wherein the crystal grain nucleation model is substantially a function of the supercooling degree delta T related to the crystal grain nucleation density N (delta T), the supercooling degree delta T is in one-to-one correspondence with the crystal grain nucleation density N (delta T), and the probability of crystal grain nucleation represented by the crystal grain nucleation density N (delta T) is certain, so that the supercooling degree delta T corresponds to a certain probability of crystal grain nucleation through the crystal grain nucleation density N (delta T);
the degree of supercooling Δ T is a function of the grain nucleation density N (Δ T) as shown in the following equation:
wherein dN/d (Δ T) is represented by:
in the formula: n is a radical of max Is the maximum nucleation density, Δ T θ Is a standard degree of curvature supercooling, Δ T max Supercooling for maximum nucleation; the combination of the formulas (1) and (2) is a grain nucleation model;
step 3.3, establishing a grain growth model, as shown in fig. 6, wherein the grain growth model comprises an eight-neighbor Moore type solute diffusion model, and the grain growth model is substantially the supercooling degree delta T (T) at a certain moment n ) Solid fraction increment Δ f for a single time step s Using the degree of supercooling Δ T (T) at a certain time n ) Calculating solid phase ratio increment delta f of single time step with interface advancing speed upsilon s The two are connected together through the interface advancing speed, and the solid phase ratio delta f is changed along with the solid phase ratio in a period of time s The stacking fs (t) of fs (t) =1, the cellular state is changed into solid phase, when a plurality of cellular states are changed, the cellular state macroscopically appears as the growth of crystal grains, the diffusion process of solute is generated along with the growth of the crystal grains, and the diffusion process is obtained by solving a diffusion equation, and the specific process is as follows:
supercooling degree DeltaT (T) at a certain time n ) The function on the interface advance rate v is shown as follows:
υ＝μ k (θ)·ΔT(t n ) (3)
in the formula: t is t n Is a certain time, mu k (θ) is the interfacial kinetic coefficient, determined by the following formula:
μ k (θ)＝μ av (1+ξ k cos(4(θ-θ 0 ))) (4)
in the formula: theta is the sum of the interfacial normal directionsAngle of horizontal, theta 0 Is the preferred growth direction of the grains, mu av Is the average interface dynamics coefficient, ξ k Is the dynamic anisotropic strength;
the solid-liquid interface is advanced, and the solid phase ratio increment delta f of a single time step is accompanied with the change of the solid phase ratio of the cellular unit s Solid fraction increase Δ f at a single time step in proportion to the rate of interface advancement s The function upsilon about the interface advance rate is expressed by the following formula:
in the formula: Δ x is the cell unit size; Δ t is a single calculation time step; g is an adjacent position grid state parameter; a is a disturbance factor; rand is a random number of 0-1;
solid fraction increment Δ f by a single time step s Judging the state of the interface unit cell, the solid phase rate is increased continuously when the interface unit cell is changed into the solid phase unit cell, and the solid phase rate f of a certain interface unit cell is increased within the time t s (t) is:
in the formula: n is the iteration number; Δ t is the time step when f s (t) =1, the state of the cell is changed to a solid phase;
in the process of converting interface cells into solid-phase cells, redundant solutes are discharged to surrounding liquid-phase cells, and then a larger solute concentration gradient is generated between the liquid-phase cells, the process adopts an eight-adjacent-cell Moore type solute diffusion model, and the mathematical expression of the model is as follows:
in the formula:
and
respectively calculating the concentrations of liquid phase solute and solid phase solute in the liquid phase cells,
and
the concentrations of liquid phase solute and solid phase solute in the cells adjacent to the cell (i, j), respectively; Δ x is the cell size, Δ t is the time step, (3) (4) (5) is combined with an eight-neighbor Moore type solute diffusion model to form a grain growth model;
the specific process of step 4 is as follows:
step 4.1, introducing the welding transient macroscopic temperature field model, the microscopic temperature field model and the nucleation and growth model of the crystal grains constructed in the steps 1-3 into simulation software Matlab to be combined to form a microstructure evolution model of the titanium alloy welding pool;
and 4.2, inputting main thermophysical parameters and welding process parameters of the TC4 (Ti-6 Al-4V) alloy into the microstructure evolution model of the titanium alloy welding pool, and calculating to obtain a microstructure evolution simulation image of the TC4 (Ti-6 Al-4V) alloy welding pool as shown in the table 1.
TABLE 1
Table 1 shows the main thermophysical parameters of the TC4 (Ti-6 Al-4V) alloy.
Example 2
The invention discloses a method for simulating microstructure evolution of a titanium alloy welding pool, which is implemented according to the following steps as shown in figure 1:
the step 1 is implemented according to the following steps:
step 1.1, inputting the size of a model in finite element software, and establishing a finite element geometric model as shown in figure 2;
step 1.2, according to the selected materials, giving material attributes to the finite element geometric model to obtain a finite element geometric material model;
step 1.3, setting an analysis step according to the actual process of molten pool evolution to be simulated;
step 1.4, setting boundary conditions according to the actual conditions of a molten pool, wherein the boundary conditions specifically comprise setting of initial temperature and determination of heat exchange relation between the molten pool and the environment;
step 1.5, setting a load according to the actual condition of a molten pool, wherein the load specifically comprises the setting of boundary constraint and the setting of surface heat flux, namely the selection of a heat source model, and the heat source model selects a double-ellipsoid heat source model, as shown in fig. 3, the mathematical expression of the model is as follows:
the front ellipsoid heat flow density distribution is:
the rear ellipsoid heat flux density distribution is:
in the formula: q (x, y, z, t) is the heat flow at the (x, y, z) position at time t, k is the heat source concentration coefficient, f 1 ，f 2 Energy distribution coefficients at the front and rear parts of the molten bath, respectively, f 1 +f 2 ＝2，c 1 ，c 2 Respectively, the length parameters of front and back semi-ellipsoids, a is ellipseThe width parameter of the ball, b is an ellipsoid depth parameter, and v is a welding speed;
step 1.6, as shown in fig. 4, combining the finite element geometric material model with the boundary conditions and the loads to form a finite element model, dividing the finite element model into finite element units with the same size to obtain a finite element calculation model, and calculating a welding transient macroscopic temperature field model by using the finite element calculation model;
the step 2 is implemented according to the following steps:
step 2.1, selecting a proper calculation domain, and extracting a thermal cycle curve, namely a time-temperature curve, of the finite element node;
step 2.2, fitting a thermal cycle curve by using simulation software MATLAB to obtain a temperature-time function of the finite element node, and obtaining a macroscopic temperature field model;
step 2.3, converting the macroscopic temperature field model into a microscopic temperature field model suitable for calculating the microstructure by adopting a linear interpolation method, wherein the interpolation principle is shown in fig. 4, and the specific mathematical expression is as follows:
T o temperature, T, of the micro-cells O i Is the macro-unit temperature around the O point, L i Is the distance from point O to the surrounding macro-units, N is the number of macro-units surrounding the micro-units, and has a value of 8;
step 3.1, simplifying the construction conditions of the nucleation and growth model of the crystal grains: a. the liquid interface has no thickness, and the simulation area only has cells in three states of liquid, solid and interface;
b. only the formation of primary grains is considered, and the solid phase transformation in the cooling process is not considered;
step 3.2, establishing a crystal grain nucleation model, wherein the crystal grain nucleation model is substantially a function of the supercooling degree delta T related to the crystal grain nucleation density N (delta T), the supercooling degree delta T is in one-to-one correspondence with the crystal grain nucleation density N (delta T), and the probability of crystal grain nucleation represented by the crystal grain nucleation density N (delta T) is certain, so that the supercooling degree delta T corresponds to a certain probability of crystal grain nucleation through the crystal grain nucleation density N (delta T);
the degree of supercooling Δ T is a function of the grain nucleation density N (Δ T) as shown in the following equation:
wherein dN/d (Δ T) is represented by:
in the formula: n is a radical of max Is the maximum nucleation density, Δ T θ Is a standard degree of curvature supercooling, Δ T max Supercooling for maximum nucleation; the combination of the formulas (1) and (2) is a grain nucleation model;
step 3.3, establishing a grain growth model, as shown in fig. 6, wherein the grain growth model comprises an eight-neighbor Moore type solute diffusion model, and the grain growth model is substantially the supercooling degree delta T (T) at a certain moment n ) Solid fraction increment Δ f for a single time step s Using the degree of supercooling Δ T (T) at a certain time n ) Calculating solid phase ratio increment delta f of single time step with interface advancing speed upsilon s The two are connected together through an interface propulsion speed, fs (t) is continuously increased along with the superposition of the solid fraction delta fs within a period of time, when fs (t) =1, the cellular state is changed into a solid phase, and when a plurality of cellular states are changed, the cellular states macroscopically change into the growth of grains, the diffusion process of solute is generated along with the growth of the grains, and the solute is obtained by solving a diffusion equation, and the specific process is as follows:
supercooling degree DeltaT (T) at a certain time n ) The function on the interface advance rate v is shown as follows:
υ＝μ k (θ)·ΔT(t n ) (3)
in the formula: t is t n Is a certain time, mu k (θ) is the interfacial kinetic coefficient, determined by the following formula:
μ k (θ)＝μ av (1+ξ k cos(4(θ-θ 0 ))) (4)
in the formula: theta is the angle between the normal direction of the interface and the horizontal direction, theta 0 Is the preferred growth direction of the grains, mu av Is the average interface dynamics coefficient, ξ k Is the dynamic anisotropic strength;
the solid-liquid interface is advanced, along with the change of the solid phase ratio of the cellular unit, the solid phase ratio increment delta f of a single time step s Solid phase fraction increment Δ f at a single time step in direct proportion to interface advance rate s The function upsilon about the interface advance rate is expressed by the following formula:
in the formula: Δ x is the cell unit size; Δ t is a single calculation time step; g is an adjacent position grid state parameter; a is a disturbance factor; rand is a random number of 0-1;
solid fraction increment Δ f by a single time step s Judging the state of the interface unit cell, the solid phase rate is increased continuously when the interface unit cell is changed into the solid phase unit cell, and the solid phase rate f of a certain interface unit cell is increased within the time t s (t) is:
in the formula: n is the iteration number; Δ t is the time step when f s (t) =1, the state of the cell is changed to a solid phase;
in the process of converting interface cells into solid-phase cells, redundant solutes are discharged to surrounding liquid-phase cells, and then a larger solute concentration gradient is generated between the liquid-phase cells, the process adopts an eight-adjacent-cell Moore type solute diffusion model, and the mathematical expression of the model is as follows:
in the formula:
and
respectively calculating the concentrations of liquid phase solute and solid phase solute in the liquid phase cells,
and
the concentrations of liquid phase solute and solid phase solute in the cells adjacent to the cell (i, j), respectively; Δ x is the cell size, Δ t is the time step, (3) (4) (5) is combined with an eight-neighbor Moore type solute diffusion model to form a grain growth model;
the specific process of step 4 is as follows:
step 4.1, introducing the welding transient macroscopic temperature field model, the microscopic temperature field model and the nucleation and growth model of the crystal grains constructed in the step 1-3 into simulation software Matlab to be combined to form a microstructure evolution model of the titanium alloy welding pool;
and 4.2, inputting main thermophysical parameters and welding process parameters of the TA15 (Ti-6.5 Al-1Mo-1V-2 Zr) alloy into the microstructure evolution model of the titanium alloy welding pool, and calculating to obtain a TA15 (Ti-6.5 Al-1Mo-1V-2 Zr) alloy welding pool microstructure evolution simulation image as shown in the table 2.
TABLE 2
Table 2 shows the main thermophysical parameters of the TA15 (Ti-6.5 Al-1Mo-1V-2 Zr) alloy.
Example 3
The invention discloses a method for simulating microstructure evolution of a titanium alloy welding pool, which is implemented according to the following steps as shown in figure 1:
the step 1 is implemented according to the following steps:
step 1.1, inputting the size of a model in finite element software, and establishing a finite element geometric model as shown in figure 2;
step 1.2, according to the selected materials, giving material attributes to the finite element geometric model to obtain a finite element geometric material model;
step 1.3, setting an analysis step according to the actual process of molten pool evolution to be simulated;
step 1.4, setting boundary conditions according to the actual conditions of a molten pool, wherein the boundary conditions specifically comprise setting of initial temperature and determination of heat exchange relation between the molten pool and the environment;
step 1.5, setting a load according to the actual condition of a molten pool, wherein the load specifically comprises the setting of boundary constraint and the setting of surface heat flux, namely the selection of a heat source model, and the heat source model selects a double-ellipsoid heat source model, as shown in fig. 3, the mathematical expression of the model is as follows:
the front ellipsoid heat flow density distribution is:
the rear ellipsoid heat flux density distribution is:
in the formula: q (x, y, z, t) is the heat flow at the (x, y, z) position at time t, k is the heat source concentration coefficient, f 1 ，f 2 Are respectively in the meltEnergy distribution coefficient of front and rear parts of the tank, f 1 +f 2 ＝2，c 1 ，c 2 The length parameters of the front half ellipsoid and the rear half ellipsoid are respectively, a is an ellipsoid width parameter, b is an ellipsoid depth parameter, and v is a welding speed;
step 1.6, as shown in fig. 4, combining the finite element geometric material model with the boundary conditions and the loads to form a finite element model, dividing the finite element model into finite element units with the same size to obtain a finite element calculation model, and calculating a welding transient macroscopic temperature field model by using the finite element calculation model;
the step 2 is implemented according to the following steps:
step 2.1, selecting a proper calculation domain, and extracting a thermal cycle curve, namely a time-temperature curve, of the finite element node;
step 2.2, fitting a thermal cycle curve by using simulation software MATLAB to obtain a temperature-time function of the finite element node, and obtaining a macroscopic temperature field model;
step 2.3, converting the macroscopic temperature field model into a microscopic temperature field model suitable for calculating the microstructure by adopting a linear interpolation method, wherein the interpolation principle is shown in fig. 4, and the specific mathematical expression is as follows:
T o temperature, T, of the micro-cells O i The macro unit temperature, L, around the O point i Is the distance from point O to the surrounding macro-units, N is the number of macro-units surrounding the micro-units, and has a value of 8;
step 3.1, simplifying the construction conditions of the nucleation and growth model of the crystal grains:
the simplified conditions for constructing the nucleation and growth model of the crystal grains comprise:
a. the liquid interface has no thickness, and the simulation area only has cells in three states of liquid, solid and interface;
b. only the formation of primary grains is considered, and the solid-state phase change in the cooling process is not considered;
step 3.2, establishing a crystal grain nucleation model, wherein the crystal grain nucleation model is substantially a function of the supercooling degree delta T related to the crystal grain nucleation density N (delta T), the supercooling degree delta T is in one-to-one correspondence with the crystal grain nucleation density N (delta T), and the probability of crystal grain nucleation represented by the crystal grain nucleation density N (delta T) is certain, so that the supercooling degree delta T corresponds to a certain probability of crystal grain nucleation through the crystal grain nucleation density N (delta T);
the degree of supercooling Δ T is a function of the grain nucleation density N (Δ T) as shown in the following equation:
wherein dN/d (Δ T) is represented by:
in the formula: n is a radical of hydrogen max Is the maximum nucleation density, Δ T θ Is a standard degree of curvature supercooling, Δ T max Supercooling for maximum nucleation; the combination of the formulas (1) and (2) is a grain nucleation model;
step 3.3, establishing a grain growth model, as shown in fig. 6, wherein the grain growth model comprises an eight-neighbor Moore type solute diffusion model, and the grain growth model is substantially supercooling degree delta T (T) at a certain moment n ) Solid fraction increment Δ f for a single time step s Using the degree of supercooling Δ T (T) at a certain time n ) Calculating solid phase ratio increment delta f of single time step with interface advancing speed upsilon s The two are connected together through an interface propulsion speed, fs (t) is continuously increased along with the superposition of the solid fraction delta fs within a period of time, when fs (t) =1, the cellular state is changed into a solid phase, and when a plurality of cellular states are changed, the cellular states macroscopically change into the growth of grains, the diffusion process of solute is generated along with the growth of the grains, and the solute is obtained by solving a diffusion equation, and the specific process is as follows:
supercooling degree delta T (T) at a certain time n ) The function on the interface advance rate v is shown as follows:
υ＝μ k (θ)·ΔT(t n ) (3)
in the formula: t is t n Is a certain time, mu k (θ) is the interfacial kinetic coefficient, determined by the following formula:
μ k (θ)＝μ av (1+ξ k cos(4(θ-θ 0 ))) (4)
in the formula: theta is the angle between the normal direction of the interface and the horizontal direction, theta 0 Is the preferred growth direction of the grains, mu av Is the average interface dynamics coefficient, ξ k Is the dynamic anisotropic strength;
the solid-liquid interface is advanced, and the solid phase ratio increment delta f of a single time step is accompanied with the change of the solid phase ratio of the cellular unit s Solid fraction increase Δ f at a single time step in proportion to the rate of interface advancement s The function upsilon about the interface advance rate is expressed by the following formula:
in the formula: Δ x is the cell unit size; Δ t is a single calculation time step; g is an adjacent position grid state parameter; a is a disturbance factor; rand is a random number of 0-1;
solid fraction increment Δ f by a single time step s Judging the state of the interface unit cell, increasing the solid phase rate of the interface unit cell to the solid phase unit cell, and determining the solid phase rate f of the interface unit cell within the time t s (t) is:
in the formula: n is the iteration number; Δ t is the time step when f s (t) =1, the state of the cell is changed to a solid phase;
in the process of converting interface cells into solid-phase cells, redundant solutes are discharged to surrounding liquid-phase cells, and then a larger solute concentration gradient is generated between the liquid-phase cells, the process adopts an eight-adjacent-cell Moore type solute diffusion model, and the mathematical expression of the model is as follows:
in the formula:
and
respectively calculating the concentrations of liquid phase solute and solid phase solute in the liquid phase cells,
and
the concentrations of liquid phase solute and solid phase solute in the cells adjacent to the cell (i, j), respectively; Δ x is the cell size, Δ t is the time step, (3) (4) (5) is combined with an eight-neighbor Moore type solute diffusion model to form a grain growth model;
the specific process of step 4 is as follows:
step 4.1, introducing the welding transient macroscopic temperature field model, the microscopic temperature field model and the nucleation and growth model of the crystal grains constructed in the step 1-3 into simulation software Matlab to be combined to form a microstructure evolution model of the titanium alloy welding pool;
and 4.2, inputting main thermophysical parameters and welding process parameters of the TC18 (Ti-5 Al-4.75Mo-4.75V-1Cr-1 Fe) alloy into the microstructure evolution model of the titanium alloy welding pool, and calculating to obtain an evolution simulation image of the microstructure of the TC18 (Ti-5 Al-4.75Mo-4.75V-1Cr-1 Fe) alloy welding pool as shown in Table 3.
TABLE 3
Table 3 shows the main thermophysical parameters of the TC18 (Ti-5 Al-4.75Mo-4.75V-1Cr-1 Fe) alloy.
Claims (1)
1. A method for simulating microstructure evolution of a titanium alloy welding pool is characterized by comprising the following steps:
step 1, constructing a welding transient macroscopic temperature field model based on a finite element method, and specifically implementing the following steps:
step 1.1, inputting the size of a model in finite element software, and establishing a finite element geometric model;
step 1.2, according to the selected materials, giving material attributes to the finite element geometric model to obtain a finite element geometric material model;
step 1.3, setting an analysis step according to the actual process of molten pool evolution to be simulated;
step 1.4, setting boundary conditions according to the actual conditions of a molten pool, wherein the boundary conditions specifically comprise setting of initial temperature and determination of heat exchange relation between the molten pool and the environment;
step 1.5, setting a load according to the actual condition of a molten pool, wherein the load specifically comprises the setting of boundary constraint and the setting of surface heat flux, namely the selection of a heat source model, and the heat source model selects a double-ellipsoid heat source model;
step 1.6, combining the finite element geometric material model with boundary conditions and loads to form a finite element model, dividing the finite element model into finite element units with the same size to obtain a finite element calculation model, and calculating a welding transient macroscopic temperature field model by using the finite element calculation model;
step 2, constructing a microscopic temperature field model by utilizing an interpolation principle, and specifically implementing the following steps:
step 2.1, selecting a proper calculation domain, and extracting a thermal cycle curve, namely a time-temperature curve, of the finite element node;
step 2.2, fitting a thermal cycle curve by using simulation software MATLAB to obtain a temperature-time function of a finite element node, and obtaining a macroscopic temperature field model;
step 2.3, converting the macroscopic temperature field model into a microscopic temperature field model suitable for calculating the microstructure by adopting a linear interpolation method, wherein the specific mathematical expression is as follows:
T o temperature, T, of the micro-cells O i Is the macro-unit temperature around the O point, L i Is the distance from point O to the surrounding macro-units, N is the number of macro-units surrounding the micro-units, and has a value of 8;
and 3, constructing a nucleation and growth model of the crystal grains, and specifically implementing the following steps:
step 3.1, simplifying the construction conditions of the nucleation and growth model of the crystal grains: a. the liquid interface has no thickness, and the simulation area only has cells in three states of liquid, solid and interface;
b. only the formation of primary grains is considered, and the solid-state phase change in the cooling process is not considered;
step 3.2, establishing a crystal grain nucleation model, wherein the crystal grain nucleation model is substantially a function of the supercooling degree delta T relative to the crystal grain nucleation density N (delta T), and the probability of crystal grain nucleation is calculated by utilizing the supercooling degree delta T and the crystal grain nucleation density N (delta T), and the specific process is as follows:
the degree of supercooling Δ T is a function of the grain nucleation density N (Δ T) as shown in the following equation:
wherein dN/d (Δ T) is represented by:
in the formula: n is a radical of max Is the maximum nucleation density, Δ T θ Is a standard degree of curvature supercooling, Δ T max Supercooling for maximum nucleation; (1) The combination of the formula (2) and the formula (II)A grain nucleation model;
step 3.3, establishing a grain growth model, wherein the grain growth model comprises an eight-neighbor Moore type solute diffusion model, and the grain growth model is substantially the supercooling degree delta T (T) at a certain moment n ) Solid fraction increment Δ f for a single time step s Using the degree of supercooling Δ T (T) at a certain time n ) Calculating solid phase ratio increment delta f of single time step with interface advancing speed upsilon s Increase in solid phase fraction Δ f by a single time step s Judging the state of the cells, and the specific process is as follows:
supercooling degree DeltaT (T) at a certain time n ) The function on the interface advance rate v is shown as follows:
υ＝μ k (θ)·ΔT(t n ) (3)
in the formula: t is t n Is a certain time, mu k (θ) is the interfacial kinetic coefficient, determined by the following formula:
μ k (θ)＝μ av (1+ξ k cos(4(θ-θ 0 ))) (4)
in the formula: theta is the angle between the normal direction of the interface and the horizontal direction, theta 0 Is the preferred growth direction of the grains, mu av Is the average interface dynamics coefficient, ξ k Is the dynamic anisotropic strength;
solid fraction increment of single time step Δ f s The function as to the rate of interfacial advancement v is expressed by:
in the formula: Δ x is the cell unit size; Δ t is a single calculation time step; g is an adjacent position grid state parameter; a is a disturbance factor; rand is a random number of 0-1;
solid fraction increment Δ f by a single time step s The cellular state is judged by the following process:
in the formula: n is the iteration number; Δ t is the time step when f s (t) =1, the state of the cell is changed to a solid phase; (3) (4) (5) combining the grain growth model with an eight-neighbor Moore type solute diffusion model;
step 4, numerical calculation and calculation result processing, the specific process is as follows:
step 4.1, introducing the welding transient macroscopic temperature field model, the microscopic temperature field model and the nucleation and growth model of the crystal grains constructed in the step 1-3 into simulation software MATLAB to be combined to obtain a titanium alloy welding pool microstructure evolution model;
and 4.2, inputting thermophysical parameters and welding process parameters of the titanium alloy into the microstructure evolution model of the titanium alloy welding pool, and calculating to obtain a simulation result image.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105138772A (en) * | 2015-08-24 | 2015-12-09 | 北京星航机电装备有限公司 | Finite element modeling method for electron beam welding of variable-section component |
| WO2016173313A1 (en) * | 2015-04-27 | 2016-11-03 | 江苏金通灵流体机械科技股份有限公司 | Ansys-based duplex stainless steel and dissimilar steel welding deformation prediction method |
| CN106407623A (en) * | 2016-11-15 | 2017-02-15 | 南京航空航天大学 | Phase-field method-based microstructure evolution simulation method in welding process in transient state |
-
2019
- 2019-08-30 CN CN201910816501.XA patent/CN110619157B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2016173313A1 (en) * | 2015-04-27 | 2016-11-03 | 江苏金通灵流体机械科技股份有限公司 | Ansys-based duplex stainless steel and dissimilar steel welding deformation prediction method |
| CN105138772A (en) * | 2015-08-24 | 2015-12-09 | 北京星航机电装备有限公司 | Finite element modeling method for electron beam welding of variable-section component |
| CN106407623A (en) * | 2016-11-15 | 2017-02-15 | 南京航空航天大学 | Phase-field method-based microstructure evolution simulation method in welding process in transient state |
Non-Patent Citations (2)
| Title |
|---|
| Al-Cu合金近液相线铸造中组织演变的计算机模拟;张艳华等;《辽宁石油化工大学学报》;20101215(第04期);全文 * |
| 合金凝固组织微观模拟研究进展与应用;王同敏等;《金属学报》;20180211(第02期);全文 * |
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