CN112185474B - Numerical simulation method for directional solidification process of Ti-45% Al alloy - Google Patents
Numerical simulation method for directional solidification process of Ti-45% Al alloy Download PDFInfo
- Publication number
- CN112185474B CN112185474B CN202010929261.7A CN202010929261A CN112185474B CN 112185474 B CN112185474 B CN 112185474B CN 202010929261 A CN202010929261 A CN 202010929261A CN 112185474 B CN112185474 B CN 112185474B
- Authority
- CN
- China
- Prior art keywords
- cells
- interface
- cell
- liquid phase
- solid phase
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000007711 solidification Methods 0.000 title claims abstract description 64
- 230000008023 solidification Effects 0.000 title claims abstract description 64
- 238000000034 method Methods 0.000 title claims abstract description 58
- 230000008569 process Effects 0.000 title claims abstract description 41
- 238000004088 simulation Methods 0.000 title claims abstract description 38
- 229910000838 Al alloy Inorganic materials 0.000 title claims abstract description 33
- 210000001787 dendrite Anatomy 0.000 claims abstract description 36
- 238000009792 diffusion process Methods 0.000 claims abstract description 16
- 238000004364 calculation method Methods 0.000 claims abstract description 9
- 230000006911 nucleation Effects 0.000 claims abstract description 8
- 238000010899 nucleation Methods 0.000 claims abstract description 8
- 210000004027 cell Anatomy 0.000 claims description 109
- 239000007791 liquid phase Substances 0.000 claims description 47
- 239000007790 solid phase Substances 0.000 claims description 42
- 238000004781 supercooling Methods 0.000 claims description 21
- 239000013078 crystal Substances 0.000 claims description 15
- 229910052751 metal Inorganic materials 0.000 claims description 5
- 239000002184 metal Substances 0.000 claims description 5
- 239000007788 liquid Substances 0.000 claims description 3
- 229910001338 liquidmetal Inorganic materials 0.000 claims description 3
- 150000002739 metals Chemical class 0.000 claims description 3
- 230000001131 transforming effect Effects 0.000 claims 1
- 229910045601 alloy Inorganic materials 0.000 abstract description 13
- 239000000956 alloy Substances 0.000 abstract description 13
- 230000007246 mechanism Effects 0.000 abstract description 4
- 238000011160 research Methods 0.000 abstract description 4
- 238000009826 distribution Methods 0.000 abstract description 2
- 230000001737 promoting effect Effects 0.000 abstract 1
- 238000001816 cooling Methods 0.000 description 6
- 238000002474 experimental method Methods 0.000 description 6
- 239000000463 material Substances 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 4
- 230000001413 cellular effect Effects 0.000 description 3
- 238000005266 casting Methods 0.000 description 2
- 238000009795 derivation Methods 0.000 description 2
- 239000007769 metal material Substances 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- 238000000465 moulding Methods 0.000 description 2
- 239000012071 phase Substances 0.000 description 2
- 238000003723 Smelting Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 229910002056 binary alloy Inorganic materials 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000004140 cleaning Methods 0.000 description 1
- 230000015271 coagulation Effects 0.000 description 1
- 238000005345 coagulation Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000155 melt Substances 0.000 description 1
- -1 molding Substances 0.000 description 1
- 239000004576 sand Substances 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
- G16C20/10—Analysis or design of chemical reactions, syntheses or processes
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
Abstract
The invention discloses a numerical simulation method for a directional solidification process of Ti-45% Al alloy, which comprises the following specific steps: step 1, simplifying model conditions; step 2, establishing a nucleation and growth model; step 3, solute redistribution and diffusion model establishment; step 4, defining a capturing rule; and 5, simulating calculation and result export. The model can simulate the nucleation and growth of dendrites and the distribution rule of solute concentration in the directional solidification process of Ti-45% Al alloy, and research the influence of parameters such as temperature gradient, disturbance amplitude, anisotropic strength and the like on the growth of dendrites, thereby playing a certain role in promoting the research of dendrite growth mechanism in the directional solidification process of alloy.
Description
Technical Field
The invention belongs to the technical field of numerical simulation of metal material casting processes, and particularly relates to a numerical simulation method of a directional solidification process of a Ti-45% Al alloy.
Background
Directional solidification is one of the important means for controlling the solidification structure of metallic materials. In the solidification process, a temperature gradient in a specific direction is established between the solidified metal and the non-solidified melt, so that the melt is solidified along the direction opposite to the heat flow, thereby obtaining grains with specific orientation, and the effects of effectively controlling the grain orientation, eliminating transverse grain boundaries and improving the longitudinal mechanical properties of the structure can be achieved. Since the directional solidification technology can be adopted to obtain the material with special orientation and excellent tissue and performance, many researchers are attracted to continuously explore the technological process from the birth of the material. There is a complex relationship between the directional solidification process parameters, solidification conditions and the formation process of the microstructure, and in the past, experimental methods and theoretical deductions are two important means for researching the evolution of the directional solidification structure. The experimental method is limited by experimental conditions, so that time and labor are wasted, and the obtained result is difficult to reflect the influence of a certain factor on the solidification structure independently; the theoretical derivation of the tissue evolution of the solidification process is difficult to obtain an analytical solution, and the established model is basically one-dimensional based, so that the one-dimensional model is difficult to reflect the actual situation.
With the rapid development of computer technology and the continuous improvement of solidification theory, it has become possible to study the alloy solidification process by adopting numerical simulation technology, and in the existing microstructure simulation method, the most well-known phase field method (PF) and Cellular Automaton (CA) are applied to the material field later than the phase field method, but the cellular automaton has been rapidly developed with high efficiency and strong engineering application capability, from the last eighties, a successive scholars have conducted simulation study on the metal solidification structure by using the cellular automaton, and then various more reasonable material structure evolution models, such as CA-PE models, CA-FE models and the like, are proposed, and the rationality and accuracy of the models are verified by comparing the simulation results with the experimental results. The numerical simulation technology can monitor the characteristics of grain morphology evolution, grain size evolution, grain distribution and the like in the alloy solidification process in real time, effectively analyze the influences of technological parameters and solidification conditions on the solidification process and the final solidification structure, and achieve the purposes of monitoring, predicting and controlling the final solidification structure, thereby providing a guarantee for obtaining the alloy with more excellent performance. Therefore, it is particularly important to establish a numerical simulation method of the alloy directional solidification process.
Disclosure of Invention
The invention aims to provide a numerical simulation method for a directional solidification process of Ti-45% Al alloy, which solves the problem of lack of a numerical model of a growth mechanism of dendrites in the directional solidification process in the prior art.
The technical scheme adopted by the invention is that the numerical simulation method of the directional solidification process of the Ti-45% Al alloy is implemented according to the following steps:
step 1, simplifying model conditions;
step 2, establishing a nucleation and growth model;
step 3, solute redistribution and diffusion model establishment;
step 4, defining a capturing rule;
and 5, simulating calculation and result export.
The invention is also characterized in that:
the step 1 of simplifying the model establishment condition comprises the following steps:
simplifying the condition 1, wherein the whole solidification process only has three cell states of liquid phase, solid phase and interface;
simplifying condition 2, adopting V.Neumann type neighborhood, namely four neighborhood, as cell neighborhood relation;
simplifying condition 3, neglecting dynamic supercooling, only considering temperature supercooling, component supercooling and curvature supercooling;
and 4, simplifying the condition 4, and dividing the simulation area into square grids, wherein each grid is a cell.
Step 2 is implemented according to the following specific steps:
the whole simulation area is defined as liquid phase cell, a plurality of solid phase cell are defined at the solidification starting position to be used as initial crystal nucleus cell for solidification, and the liquid phase cell around the initial crystal nucleus is defined as interface cell;
as known from the theory of solidification of metals, the liquid metal must have a supercooling degree to solidify, and the total supercooling degree can be calculated by formula (1):
wherein: t (T) l Is the liquidus temperature; t is the current cell temperature; m is m l Is the liquidus slope of the solute; c (C) 0 Is the initial concentration of solute; c (C) l * Balance the liquid phase fraction at the interface; ΓK is Gibbs-Thompson coefficient; epsilon is the strength of the surface energy anisotropy; theta is the included angle between the normal direction and the horizontal direction of the interface, and theta 0 An included angle between a preferred growth direction of the crystal and a horizontal direction;
given the degree of supercooling, the equilibrium liquid phase fraction at the interface can be calculated by equation (2):
when excess solute is discharged between the interface cell and the liquid-phase cell through the interface area Δx, the solute discharged during Δt time can be calculated by the formula (3):
wherein: d (D) l Is the liquid phase diffusion coefficient; Δx is the mesh size selected for simulation; Δt is unit time; nb is the liquid phase cell of the interface cell; c (C) nb Liquid adjacent cell concentration;
at this time, the solid phase fraction of interface cells increases by Δf s Can be calculated from equation (4):
wherein: a is a disturbance factor; k (k) 0 Distributing coefficients for balancing; rand () can be at [0,1]A random number is generated.
The step 3 is specifically implemented according to the following steps:
when there is Δf in the next time step of solidification s When the liquid phase of (a) is changed to the solid phase, the solute discharged during Δt can be determined by the formula (5):
wherein: f (f) s Is a solid phase fraction; c (C) l For the diffusion of the solutes in the liquid phase cells, which are discharged during the growth of interface cells, the concentration of the solutes in the liquid phase around dendrites is increased, the diffusion of the solutes in the liquid phase cells can be calculated by the formula (6):
wherein: d (D) l Is the liquid phase diffusion coefficient, n is the number of interface cells.
Step 4 is specifically implemented according to the following steps:
step 4: selecting an initial crystal nucleus cell, carrying out solid phase fraction solving and judging on interface cells around the initial crystal nucleus cell, if the solid phase fraction of the interface cells is greater than 1, converting the interface cells into solid phase cells, and capturing liquid phase cells around the newly converted cell into new interface cells;
and solving and judging the solid phase fraction of the interface cells around the newly transformed solid phase cells, wherein the solid phase fraction of the interface cells is larger than 1, the interface cells are transformed into solid phase cells, the liquid phase cells around the newly transformed solid phase cells are captured into new interface cells, and the like until all the liquid phase cells are transformed into solid phase cells.
The step 5 is implemented according to the following steps:
step 5.1: programming based on the Ti-45% Al alloy directional solidification process model constructed in the steps 1-4;
step 5.2: and (3) introducing the programmed program into a simulation software Matlab, and inputting the thermophysical parameters of the Ti-45% Al alloy to obtain a simulation result of the directional solidification process of the Ti-45% Al alloy.
The beneficial effects of the invention are as follows:
(1) The invention provides a numerical simulation method of a directional solidification process of Ti-45% Al alloy, which solves the problem of a dendrite growth mechanism numerical model in the lack of the directional solidification process in the prior art;
(2) The invention can simulate the dynamic change of the directional solidification process, and provides a new research method for further researching the directional solidification mechanism of the alloy;
(3) The traditional experimental method researches the casting and solidification process of the alloy, namely molding, sand mixing, molding and core making, smelting, pouring, solidification, cleaning and subsequent detection of tissue components, mechanical properties and the like, and has the advantages that the traditional experimental method is complicated in process, time-consuming and labor-consuming, real-time monitoring of the alloy temperature field and the tissue field evolution cannot be realized in the solidification process, compared with the traditional experimental method, the method simplifies the solidification condition of the alloy to a certain extent, simulates the solidification process and the tissue evolution of the alloy by programming and utilizing computer simulation software, saves a great amount of investment of manpower and material resources, is economical, efficient, energy-saving and environment-friendly.
Drawings
FIG. 1 is a flow chart of a numerical simulation method of a directional solidification process of a Ti-45% Al alloy according to the present invention;
FIG. 2 is a schematic diagram of a four-neighborhood cell relationship of a numerical simulation method of a directional solidification process of a Ti-45% Al alloy according to the present invention;
FIG. 3 is a plot of dendrite growth morphology at various times for the Ti-45% Al alloy of example 1;
FIG. 4 is a plot of dendrite growth morphology at different perturbation amplitudes for the Ti-45% Al alloy of example 2;
FIG. 5 is a plot of dendrite growth morphology at different anisotropy strengths for the Ti-45% Al alloy of example 3;
FIG. 6 is a plot of dendrite growth morphology at different cooling rates for the Ti-45% Al alloy of example 4.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
As shown in FIG. 1, the flow chart of the numerical simulation method of the directional solidification process of the Ti-45% Al alloy is implemented according to the following steps:
step 1, simplifying the model establishment conditions;
simplifying the condition 1, wherein the whole solidification process only has three cell states of liquid phase, solid phase and interface;
the simplified condition 2 and the cell neighborhood relation adopt V.Neumann type neighborhood, namely four neighborhood, as shown in figure 2;
simplifying condition 3, neglecting dynamic supercooling, only considering temperature supercooling, component supercooling and curvature supercooling;
and 4, simplifying the condition 4, and dividing the simulation area into square grids, wherein each grid is a cell.
Step 2, establishing a nucleation and growth model:
when partial areas in the simulation area reach nucleation conditions, the areas are regarded as solidification starting positions, a plurality of initial nucleation points are defined at the solidification starting positions, cells of the initial nucleation points are defined as solid-phase cells and serve as initial solidified crystal nucleus cells, and according to the characteristics of a V.Neumann type neighborhood model, four cells (shown in figure 2) on the upper, lower, left and right sides of the periphery of the initial crystal nucleus cells are defined as interface cells, and the other cells are defined as liquid-phase cells;
as known from the theory of solidification of metals, the liquid metal must have a supercooling degree for solidification, and the total supercooling degree Δt can be calculated by the formula (1):
wherein: t (T) l Is the liquidus temperature; t is the current cell temperature; m is m l Is the liquidus slope of the solute; c (C) 0 Is the initial concentration of solute; c (C) l * Balance the liquid phase fraction at the interface; ΓK is Gibbs-Thompson coefficient; epsilon is the strength of the surface energy anisotropy; theta is the included angle between the normal direction and the horizontal direction of the interface, and theta 0 An included angle between a preferred growth direction of the crystal and a horizontal direction;
given the degree of supercooling, the equilibrium liquid phase fraction at the interface can be calculated by equation (2):
when excess solute is discharged between the interface cell and the liquid-phase cell through the interface area Δx, the solute discharged during Δt time can be calculated by the formula (3):
wherein: d (D) l Is the liquid phase diffusion coefficient; Δx is the mesh size selected for simulation; Δt is unit time; nb is the liquid phase cell of the interface cell; c (C) nb Liquid adjacent cell concentration.
At this time, the solid phase fraction of interface cells increases by Δf s Can be calculated from equation (4):
wherein: a is a disturbance factor; k (k) 0 Distributing coefficients for balancing; rand () can be at [0,1]A random number is generated.
Step 3, establishing a solute redistribution and diffusion model;
when there is Δf in the next time step of solidification s When the liquid phase of (a) is changed to the solid phase, the solute discharged during Δt can be determined by the formula (5):
wherein: f (f) s Is a solid phase fraction; c (C) l For the diffusion of the solutes in the liquid phase cells, which are discharged during the growth of interface cells, the concentration of the solutes in the liquid phase around dendrites is increased, the diffusion of the solutes in the liquid phase cells can be calculated by the formula (6):
wherein: d (D) l Is the liquid phase diffusion coefficient, n is the number of interface cells.
Step 4, defining a capturing rule;
selecting an initial crystal nucleus cell, carrying out solid phase fraction solving and judging on interface cells around the initial crystal nucleus cell, if the solid phase fraction of the interface cells is greater than 1, converting the interface cells into solid phase cells, and capturing liquid phase cells around the newly converted cell into new interface cells;
and solving and judging the solid phase fraction of the interface cells around the newly transformed solid phase cells, wherein the solid phase fraction of the interface cells is larger than 1, the interface cells are transformed into solid phase cells, the liquid phase cells around the newly transformed solid phase cells are captured into new interface cells, and the like until all the liquid phase cells are transformed into solid phase cells.
Step 5, analog calculation and result derivation:
step 5.1: programming based on the model constructed in the steps 1-4, introducing the programmed program into a simulation software Matlab, inputting thermophysical parameters of the Ti-45% Al alloy, and calculating to obtain simulation results and conclusions of the directional solidification process of the Ti-45% Al binary alloy as shown in the table 1, which will be discussed later.
TABLE 1 calculation of thermophysical parameters for simulation of Ti-45% Al alloys
The simulation results were analyzed by examples, wherein example 1 analyzed the overall situation of the entire coagulation process; other parameters in the embodiment 2 are unchanged, and dendrite morphology under different disturbance amplitudes is analyzed; other parameters in the embodiment 3 are unchanged, and the dendrite morphology under different anisotropic strengths is analyzed; other parameters were unchanged in example 4, and dendrite morphology was analyzed at different cooling rates.
Example 1
The thermal physical parameters of the Ti-45% Al alloy in table 1 are input into the programmed model, the dendrite growth morphology of the Ti-45% Al alloy is obtained through calculation under different time, and the simulation results are shown in figures 3a and 3 b. It can be seen that upon onset of solidification, a cell form is formed. Over time, secondary dendrites will gradually germinate, grow on the primary dendrites and are approximately symmetrically distributed.
Example 2
Inputting various thermophysical parameters of the Ti-45% Al alloy in table 1 into a model programmed by the invention, and obtaining the Ti-45% Al alloy with a time step of 1500 and a temperature gradient of 1 x 10 by calculation 2 K/m, anisotropy intensity of 0.85, dendrite growth morphology with disturbance amplitude of 0 and 1 respectively, simulationThe results are shown in FIGS. 4a and 4 b. It can be found by comparison that when other conditions are unchanged, as the disturbance amplitude increases, the secondary dendrite ratio can be obviously coarsened, and the distance between the secondary dendrite arms can also be increased.
Example 3
Inputting various thermophysical parameters of the Ti-45% Al alloy in table 1 into a model programmed by the invention, and obtaining the Ti-45% Al alloy with a time step of 1500 and a temperature gradient of 1 x 10 by calculation 2 The dendrite growth morphology at a K/m, a disturbance amplitude of 0 and an anisotropy strength of 0.85 and 0.35, respectively, was simulated and the results are shown in FIGS. 5a and 5 b. It can be found by comparison that when other conditions are unchanged, as the anisotropic strength is reduced, primary dendrites are branched, the number of secondary dendrites is reduced, the distance between secondary dendrite arms is increased, and both primary dendrites and secondary dendrites are coarsened.
Example 4
The thermal physical parameters of the Ti-45% Al alloy in table 1 are input into the programmed model, the growth condition of dendrite of the Ti-45% Al alloy under the conditions of different cooling rates of 2k/s and 2.5k/s at the same time is obtained through calculation, and the simulation results are shown in figures 6a and 6 b. It can be seen that the increased cooling rate promotes dendrite growth, resulting in more secondary and tertiary dendrites that are generated, more vigorous inter-dendrite growth competition, and smaller primary and secondary dendrite arm spacing. Thus, the greater the cooling rate, the finer the dendrite spacing and the better the tissue properties.
From the four embodiments, the invention can successfully simulate the growth morphology of dendrites in the directional solidification process of Ti-45% Al alloy, and the influence of factors such as disturbance amplitude, anisotropic strength, different cooling speeds and the like on the growth morphology of dendrites, and the prior art can only analyze the final structure and morphology of the alloy through metallographic experiments, and can not predict and analyze the morphology of dendrites at any time point in the solidification process. According to the invention, the influence of each technological parameter on the simulation result is quantitatively analyzed by contrast simulation so as to determine more excellent technological parameters, thereby obtaining the alloy with more excellent performance. For example, a great number of simulation results obtained by comparing and simulating for many times and carrying out statistical analysis can be used for selecting the process parameters corresponding to the optimal dendrite morphology from the simulation results so as to guide the actual production, thereby obtaining the alloy with more excellent performances.
Claims (1)
1. A numerical simulation method for a directional solidification process of Ti-45% Al alloy is characterized by comprising the following steps:
step 1, simplifying the model establishment conditions;
the step 1 simplified model establishment condition comprises the following steps:
simplifying the condition 1, wherein the whole solidification process only has three cell states of liquid phase, solid phase and interface;
simplifying condition 2, adopting V.Neumann type neighborhood, namely four neighborhood, as cell neighborhood relation;
simplifying condition 3, neglecting dynamic supercooling, only considering temperature supercooling, component supercooling and curvature supercooling;
simplifying condition 4, dividing the simulation area into square grids, wherein each grid is a cell;
step 2, establishing a nucleation and growth model;
the step 2 is implemented according to the following specific steps:
the whole simulation area is defined as liquid phase cell, a plurality of solid phase cell are defined at the solidification starting position to be used as initial crystal nucleus cell for solidification, and the liquid phase cell around the initial crystal nucleus is defined as interface cell;
as known from the theory of solidification of metals, the liquid metal must have a supercooling degree to solidify, and the total supercooling degree can be calculated by formula (1):
wherein: t (T) l Is the liquidus temperature; t is the current cell temperature; m is m l Is the liquidus slope of the solute; c (C) 0 Is the initial concentration of solute; c (C) l * Balance the liquid phase fraction at the interface; ΓK is Gibbs-Thompson coefficient; epsilon is the strength of the surface energy anisotropy; theta is the included angle between the normal direction and the horizontal direction of the interface, and theta 0 An included angle between a preferred growth direction of the crystal and a horizontal direction;
given the degree of supercooling, the equilibrium liquid phase fraction at the interface can be calculated by equation (2):
when excess solute is discharged between the interface cell and the liquid-phase cell through the interface area Δx, the solute discharged during Δt time can be calculated by the formula (3):
wherein: d (D) l Is the liquid phase diffusion coefficient; Δx is the mesh size selected for simulation; Δt is unit time; nb is the liquid phase cell of the interface cell; c (C) nb Liquid adjacent cell concentration;
at this time, the solid phase fraction of interface cells increases by Δf s Can be calculated from equation (4):
wherein: a is a disturbance factor; k (k) 0 Distributing coefficients for balancing; rand () can be at [0,1]Generating a random number;
step 3, establishing a solute redistribution and diffusion model;
the step 3 is specifically implemented according to the following steps:
when there is Δf in the next time step of solidification s When the liquid phase of (a) is changed to the solid phase, the solute discharged during Δt can be determined by the formula (5):
wherein: f (f) s Is a solid phase fraction; c (C) l For the diffusion of the solutes in the liquid phase cells, which are discharged during the growth of interface cells, the concentration of the solutes in the liquid phase around dendrites is increased, the diffusion of the solutes in the liquid phase cells can be calculated by the formula (6):
wherein: d (D) l Is a liquid phase diffusion coefficient, n is the number of interface cells;
step 4, defining a capturing rule;
the step 4 is specifically implemented according to the following steps:
step 4: selecting an initial crystal nucleus cell, carrying out solid phase fraction solving and judging on interface cells around the initial crystal nucleus cell, if the solid phase fraction of the interface cells is greater than 1, converting the interface cells into solid phase cells, and capturing liquid phase cells around the newly converted cell into new interface cells;
solving and judging the solid phase fraction of the interface cells around the newly transformed solid phase cells, transforming the interface cells into solid phase cells if the solid phase fraction of the interface cells is more than 1, capturing the liquid phase cells around the newly transformed solid phase cells into new interface cells, and the like until all the liquid phase cells are transformed into solid phase cells;
step 5, analog calculation and result export;
the step 5 is implemented according to the following steps:
step 5.1: programming based on the Ti-45% Al alloy directional solidification process model constructed in the steps 1-4;
step 5.2: and (3) introducing the programmed program into a simulation software Matlab, and inputting the thermophysical parameters of the Ti-45% Al alloy to obtain a simulation result of the directional solidification process of the Ti-45% Al alloy.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010929261.7A CN112185474B (en) | 2020-09-07 | 2020-09-07 | Numerical simulation method for directional solidification process of Ti-45% Al alloy |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010929261.7A CN112185474B (en) | 2020-09-07 | 2020-09-07 | Numerical simulation method for directional solidification process of Ti-45% Al alloy |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112185474A CN112185474A (en) | 2021-01-05 |
| CN112185474B true CN112185474B (en) | 2024-02-06 |
Family
ID=73925232
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010929261.7A Active CN112185474B (en) | 2020-09-07 | 2020-09-07 | Numerical simulation method for directional solidification process of Ti-45% Al alloy |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112185474B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113192565A (en) * | 2021-04-15 | 2021-07-30 | 西安理工大学 | Three-dimensional numerical simulation method for grain growth in directional solidification process of titanium-aluminum alloy |
| CN113284570B (en) * | 2021-05-25 | 2024-03-19 | 西安理工大学 | Simulation method for microstructure of aluminum alloy welding pool |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2143866A1 (en) * | 1970-09-08 | 1972-03-09 | Battelle Memorial Institute | Process for the production of a permanent agnet material |
| CN110321604A (en) * | 2019-06-18 | 2019-10-11 | 西安理工大学 | A kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification |
| CN110489821A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of nickel alloy cladding molten bath Numerical Simulation of Dendrite method |
| CN110489818A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of ternary alloy three-partalloy welding pool columnar dendrite growth method for numerical simulation |
| CN110489820A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method |
| CN110968954A (en) * | 2019-12-02 | 2020-04-07 | 哈尔滨理工大学 | BGA tin-lead solder ball solidification process simulation method based on cellular automaton |
| CN111339670A (en) * | 2020-02-28 | 2020-06-26 | 西安理工大学 | Dendritic crystal growth numerical simulation method in nickel-based alloy laser cladding process |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI589373B (en) * | 2015-11-20 | 2017-07-01 | Metal Ind Res & Dev Ct | Metal solidification microstructure prediction method for continuous casting process |
-
2020
- 2020-09-07 CN CN202010929261.7A patent/CN112185474B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE2143866A1 (en) * | 1970-09-08 | 1972-03-09 | Battelle Memorial Institute | Process for the production of a permanent agnet material |
| CN110321604A (en) * | 2019-06-18 | 2019-10-11 | 西安理工大学 | A kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification |
| CN110489821A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of nickel alloy cladding molten bath Numerical Simulation of Dendrite method |
| CN110489818A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of ternary alloy three-partalloy welding pool columnar dendrite growth method for numerical simulation |
| CN110489820A (en) * | 2019-07-29 | 2019-11-22 | 西安理工大学 | A kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method |
| CN110968954A (en) * | 2019-12-02 | 2020-04-07 | 哈尔滨理工大学 | BGA tin-lead solder ball solidification process simulation method based on cellular automaton |
| CN111339670A (en) * | 2020-02-28 | 2020-06-26 | 西安理工大学 | Dendritic crystal growth numerical simulation method in nickel-based alloy laser cladding process |
Non-Patent Citations (9)
| Title |
|---|
| 张俊婷 ; 崔小朝 ; 王宥宏 ; .CA法模拟各向异性和Gibbs-Thomson参数对枝晶生长的影响.中北大学学报(自然科学版).2013,(第02期),全文. * |
| 张敏 ; 张喜兵 ; 吕金波 ; 席敏敏 ; .焊接熔池凝固组织中等轴晶生长的模拟.焊管.2011,(第12期),全文. * |
| 张敏 ; 徐蔼彦 ; 汪强 ; 李露露 ; .Al-4%Cu凝固过程枝晶生长的数值模拟.材料工程.2016,(第06期),全文. * |
| 张敏 ; 薛覃 ; 李露露 ; 李继红 ; .Ti-Al合金凝固过程中的枝晶生长研究.兵器材料科学与工程.2016,(第03期),全文. * |
| 杨莹莹 ; 李日 ; 周靖超 ; 赵朝阳 ; .CA-LBM模型模拟Al-4.7%Cu固溶体合金成分分布和枝晶形貌.材料热处理学报.2016,(第10期),全文. * |
| 石玉峰 ; 许庆彦 ; 柳百成 ; .对流作用下枝晶形貌演化的数值模拟和实验研究.物理学报.2011,(第12期),全文. * |
| 郭钊 ; 周建新 ; 沈旭 ; 殷亚军 ; 计效园 ; 王圣 ; .改进元胞自动机法数值模拟高温合金凝固过程枝晶生长行为.机械工程材料.2020,(第02期),全文. * |
| 骈松 ; 张照 ; 包羽冲 ; 刘林 ; 李日 ; .基于三维LBM-CA模型模拟Al-4.7%Cu合金的枝晶形貌和成分分布.材料导报.2017,(第20期),全文. * |
| 黄建峰 ; 杨屹 ; 李羽晨 ; 杨军 ; 吴钋冰 ; 姚进 ; .基于元胞自动机法的铝合金定向凝固过程微观组织数值模拟.四川大学学报(工程科学版).2010,(第06期),全文. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112185474A (en) | 2021-01-05 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112185474B (en) | Numerical simulation method for directional solidification process of Ti-45% Al alloy | |
| CN101075287B (en) | Physical simulating method and device during continuous-casting billet coagulation tissue growth process | |
| CN110489821B (en) | Nickel-based alloy surfacing molten pool dendritic crystal growth numerical simulation method | |
| CN110489820B (en) | Welding pool microstructure evolution simulation method based on cellular automaton method | |
| Gandin et al. | Three-dimensional probabilistic simulation of solidification grain structures: Application to superalloy precision castings | |
| CN110489818B (en) | Numerical simulation method for growth of columnar dendrite of ternary alloy welding pool | |
| CN110321604B (en) | Numerical simulation method for growth of single dendrite during solidification of ternary alloy | |
| CN112784424B (en) | Three-dimensional numerical simulation method for grain growth of titanium alloy welding pool | |
| CN105057642B (en) | Casting crystalline grain organizes the formation of the analogy method of correlation values | |
| CN102508965B (en) | Adaptive variable-speed drawing simulation method for directional solidification blade production | |
| CN110619157A (en) | Method for simulating microstructure evolution of titanium alloy welding pool | |
| CN102426622B (en) | Adaptive variable-speed drawing simulation method for production of single-crystal blade | |
| Liu et al. | Numerical simulation of EBCHM for the large-scale TC4 alloy slab ingot during the solidification process | |
| CN113284570B (en) | Simulation method for microstructure of aluminum alloy welding pool | |
| CN111339670B (en) | Dendrite growth numerical simulation method in nickel-based alloy laser cladding process | |
| Liu et al. | Microstructure evolution of large-scale titanium slab ingot based on CAFE method during EBCHM | |
| CN113192565A (en) | Three-dimensional numerical simulation method for grain growth in directional solidification process of titanium-aluminum alloy | |
| Tsai et al. | A three dimensional cellular automaton model for the prediction of solidification morphologies of brass alloy by horizontal continuous casting and its experimental verification | |
| CN109719241A (en) | A kind of short-flow casting forging integral process of steel | |
| CN113343524A (en) | Fe-Al-Ta ternary alloy directional solidification process optimization method based on simulation | |
| CN116702505A (en) | Nickel-based alloy three-dimensional columnar crystal growth numerical simulation method | |
| CN105740537A (en) | Two-dimensional computer simulation method for air hole forming and evolution in welding process | |
| Pan et al. | Numerical simulation of directional solidification of single crystal turbine blade casting | |
| CN113770383B (en) | Method for determining additive manufacturing forming process parameters based on grain morphology prediction | |
| CN110910967A (en) | Method for predicting CrN precipitation condition in molten steel solidification process |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |