CN116702505A - Nickel-based alloy three-dimensional columnar crystal growth numerical simulation method - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 95
- 239000013078 crystal Substances 0.000 title claims abstract description 68
- 229910045601 alloy Inorganic materials 0.000 title claims abstract description 48
- 239000000956 alloy Substances 0.000 title claims abstract description 48
- PXHVJJICTQNCMI-UHFFFAOYSA-N Nickel Chemical compound [Ni] PXHVJJICTQNCMI-UHFFFAOYSA-N 0.000 title claims abstract description 46
- 238000004088 simulation Methods 0.000 title claims abstract description 31
- 229910052759 nickel Inorganic materials 0.000 title claims abstract description 23
- 230000006911 nucleation Effects 0.000 claims abstract description 32
- 238000010899 nucleation Methods 0.000 claims abstract description 32
- 238000004781 supercooling Methods 0.000 claims abstract description 24
- 238000007711 solidification Methods 0.000 claims abstract description 22
- 230000008023 solidification Effects 0.000 claims abstract description 22
- 238000003466 welding Methods 0.000 claims abstract description 20
- 238000005253 cladding Methods 0.000 claims abstract description 17
- 238000009826 distribution Methods 0.000 claims abstract description 5
- 210000004027 cell Anatomy 0.000 claims description 66
- 239000007790 solid phase Substances 0.000 claims description 48
- 239000007791 liquid phase Substances 0.000 claims description 42
- 210000001787 dendrite Anatomy 0.000 claims description 27
- 238000009792 diffusion process Methods 0.000 claims description 18
- 239000007788 liquid Substances 0.000 claims description 18
- 238000006243 chemical reaction Methods 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000004590 computer program Methods 0.000 claims description 3
- 239000000155 melt Substances 0.000 claims description 3
- 238000005192 partition Methods 0.000 claims description 3
- 238000007712 rapid solidification Methods 0.000 claims description 3
- 239000007787 solid Substances 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
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- 229910001020 Au alloy Inorganic materials 0.000 description 1
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- 230000007423 decrease Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000003353 gold alloy Substances 0.000 description 1
- MSNOMDLPLDYDME-UHFFFAOYSA-N gold nickel Chemical class [Ni].[Au] MSNOMDLPLDYDME-UHFFFAOYSA-N 0.000 description 1
- 239000007769 metal material Substances 0.000 description 1
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Abstract
The invention discloses a numerical simulation method for the growth of three-dimensional columnar crystals of a nickel-based alloy, and provides a numerical simulation method for the growth of three-dimensional columnar crystals of the nickel-based alloy, aiming at the problems of nucleation and growth of columnar crystals in a molten pool during welding of the nickel-based alloy. The invention can simulate the growth morphology of columnar crystals and the distribution of solute components in the solidification process of the nickel-based alloy, and can simulate the influence of parameters such as solidification time, supercooling degree, thermal disturbance amplitude and the like on the growth of the columnar crystals, thereby playing a certain guiding role in improving the performance of the cladding layer of the nickel-based alloy.
Description
Technical Field
The invention belongs to the technical field of metal material welding numerical simulation, and particularly relates to a nickel-based alloy three-dimensional columnar crystal growth numerical simulation method.
Background
In order to more comprehensively study the dynamic evolution process of the microstructure of the cladding layer in the welding process, the whole appearance of the cladding layer in the microscale and the dynamic evolution process of the microstructure of the local area in the microscale molten pool are required to be subjected to multiscale simulation, and the influence of the cladding process on the microstructure appearance is further analyzed. Along with the development and gradual perfection of computer technology and simulation algorithm, the welding process is simulated by a numerical simulation method, and a high-precision simulation model is established to optimize technological parameters so as to obtain a good joint.
The existing growth simulation in the dendrite solidification process can only be displayed in a two-dimensional form, so that the growth process of dendrites cannot be seen in an omnibearing manner when the microscopic morphology of the cladding layer is observed.
Disclosure of Invention
The invention aims to provide a numerical simulation method for the growth of three-dimensional columnar crystals of a nickel-based alloy, which can obtain a comprehensive and clear three-dimensional growth model when observing the growth of columnar crystals of a microstructure of a cladding layer, and can further clearly solidify the growth rule of dendrites, thereby having an important guiding effect on actual production.
The technical scheme adopted by the invention is that the method for simulating the growth numerical value of the three-dimensional columnar crystal of the nickel-based alloy is implemented according to the following steps:
step 1, defining the shape of a molten pool, dividing the molten pool into grids by adopting a finite element method, and defining the conditions required when crystal grains are converted from a liquid phase to a solid phase;
step 2, defining crystal grains to solidify and grow in a segmented molten pool grid, and establishing a three-dimensional dendrite nucleation and growth model for the growth process;
step 3, establishing a solute distribution and diffusion model;
and 4, simulating calculation and result export.
The invention is also characterized in that:
the concrete process of defining the shape of the molten pool is as follows: modeling simplifies the cladding boundary into a smooth parabola, which can be expressed by the following equation:
wherein: a (i, j) represents coordinates of an arbitrary point; (i) 0 ,j 0 ) Representing the coordinates of the cladding layer apex or bottommost.
The conditions required to define the transformation of the grains from the liquid phase to the solid phase in step 1 include:
cell state: the cell of the whole simulation area only has three states, namely a solid phase, a liquid phase and a solid-liquid mixed interface;
neighborhood relationship: the whole simulation area is divided into a plurality of regular square cell grids, and two neighborhood relations are usually available for a square cell system, namely a Von Neumann type (four neighborhood) and a Moore type (eight neighborhood);
capturing rules: before the solidification process starts, all cells in the simulation area are defined as liquid, and after nucleation is generated by the nucleation model, cells forming the nucleation are assigned as solid phase, and cells adjacent to the nuclei are assigned as interface.
In the step 2, the crystal grains are required to be converted from a liquid phase to a solid phase in the solidification growth process in the divided molten pool grids, the conversion state of the cells is determined through a capturing rule in the conversion process, a propulsion model is determined according to the field relation, the solute of the middle cells is pushed to eight points around if the middle cells are solidified, and the like, the process is sequentially and outwards propelled, and whether the cells are converted from the liquid phase to the solid phase is determined according to the concentration of the solute discharged in the growth process, so that the growth is completed.
The specific process of establishing the three-dimensional dendrite nucleation and growth model in the growth process is as follows:
for a quasi-continuous nucleation model, the relationship between grain nucleation density and supercooling is:
wherein: n (N) max Representing the maximum non-valueUniformly nucleation the base number; delta T max A nucleation supercooling degree peak value is represented; delta T σ Representing standard curvature supercooling degree;
using the counting method proposed by Nastac, the interface curvature can be expressed as:
wherein: Δx represents cell size/cm; f (f) s (n) represents the solid phase fraction of n cells;
after nucleation, the crystal can continuously grow under the action of supercooling degree, and the concentration of discharged solute in the growth process is as follows:
wherein: d (D) l Is the liquid phase diffusion coefficient; Δt is the step time; dx is the mesh size;
solid fraction increment Δf after applying a perturbation function s Expressed as:
wherein: a represents the disturbance amplitude; rand () represents a random number within the [0,1] interval;
judging whether the cell is converted from a liquid phase to a solid phase, wherein a judgment formula is as follows:
f s n+1 ＝f s n+1 +Δf s ；
if f s n+1 >1 is converted to the solid phase, otherwise, not converted.
The specific process of the step 3 is as follows:
the most critical ring in establishing dendrite growth models is the problem of redistribution and diffusion of solutes, which ignores the flow of the melt due to the rapid solidification rate during the welding process; the partition coefficient of solute atoms at the solid-liquid interface is expressed as:
wherein: c (C) s Represents the concentration of solid phase solute; c (C) l For the previous cell liquid phase solute concentration;
the solid phase solute concentration of the interface cells per unit time is formulated:
wherein: c'. l For the latter cell liquid phase solute concentration, C' s Is the concentration of solid phase solute, f' s Fractional in solid phase, Δf s The solid phase fraction increase per unit time;
in the solidification process, the solute discharged from the interface cells inevitably increases the concentration of the solute in the solid-liquid front liquid phase cells, and generates a larger concentration gradient of the solute between the solid-liquid front liquid phase cells and the liquid phase cells at a longer distance from the solid-liquid interface, so that the solute is promoted to diffuse in the liquid phase cells, and the diffusion equation is as follows:
wherein: dl and Ds represent the liquid phase diffusion coefficient and the solid phase diffusion coefficient, respectively.
The specific process of the step 4 is as follows:
and (3) writing a computer program based on the molten pool grid, the conditions required by solid phase and the model obtained in the steps (1) to (3), guiding the programmed program into a simulation software Matlab, inputting the thermophysical parameters and various welding process parameters of the alloy, and calculating to obtain the three-dimensional columnar crystal growth numerical simulation result of the nickel base alloy.
The thermophysical parameters of the alloy include alloy density, heat conductivity coefficient and specific heat capacity.
Various welding process parameters include welding power, speed.
The beneficial effects of the invention are as follows:
(1) The method for simulating the growth numerical value of the three-dimensional columnar crystal of the nickel-based alloy provides a new research method for researching the microstructure of a nickel-gold alloy welding pool; the method can more clearly observe the rules of dendrite growth morphology and branch structure selection diversity in the alloy solidification process to a certain extent, obtain the complete growth evolution process of the three-dimensional dendrite in the solidification process, and has better guiding effect on actual production.
(2) The visual result of the solidification process of the nickel-based alloy cladding layer structure can be obtained, and the complex transformation in a molten pool in the nickel-based alloy welding process can be conveniently researched.
(3) Compared with experiments, the invention has the advantages of less resource consumption, short research period and the like.
Drawings
FIG. 1 is a flow chart of a method for simulating the growth of three-dimensional columnar crystals of a nickel-base alloy according to the invention;
FIG. 2 is a simplified schematic diagram of a molten pool of the numerical simulation method for the growth of three-dimensional columnar crystals of the nickel-base alloy according to the present invention;
FIG. 3 is a topography of a simulated nickel-based alloy cladding layer of example 1 of the present invention for three-dimensional columnar crystal growth at different times;
FIG. 4 is a morphology diagram of the growth of three-dimensional columnar crystals of the simulated nickel-based alloy cladding layer under different supercooling degrees in the embodiment 2 of the present invention;
FIG. 5 is a topography of a simulated nickel-based alloy cladding layer of example 3 of the present invention for three-dimensional columnar grain growth at different amplitudes of oversmall.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a numerical simulation method for three-dimensional columnar crystal growth in a nickel-based alloy welding process, which is shown in figure 1 and is specifically implemented according to the following steps:
step 1, defining the shape of a molten pool, dividing the molten pool into grids by adopting a finite element method, and defining the conditions required when crystal grains are converted from a liquid phase to a solid phase;
the concrete process for defining the shape of the molten pool is as follows: modeling simplifies the cladding boundary to a smooth parabola, as shown in FIG. 2, the parabolic equation can be represented by:
wherein: a (i, j) represents coordinates of an arbitrary point; (i) 0 ,j 0 ) Representing the coordinates of the cladding layer apex or bottommost.
The conditions required to define the transformation of a grain from a liquid phase to a solid phase include:
cell state: the cell of the whole simulation area only has three states, namely a solid phase, a liquid phase and a solid-liquid mixed interface;
neighborhood relationship: the whole simulation area is divided into a plurality of regular square cell grids, and two neighborhood relations are usually available for a square cell system, namely a Von Neumann type (four neighborhood) and a Moore type (eight neighborhood);
capturing rules: before the solidification process starts, all cells in the simulation area are defined as liquid, and after nucleation is generated by the nucleation model, cells forming the nucleation are assigned as solid phase, and cells adjacent to the nuclei are assigned as interface.
Step 2, defining crystal grains to solidify and grow in a segmented molten pool grid, and establishing a three-dimensional dendrite nucleation and growth model for the growth process;
in the process of solidification growth of the crystal grains in the divided molten pool grids, the crystal grains are required to be converted from a liquid phase to a solid phase, the conversion state of the cells is determined through a capturing rule in the conversion process, a propulsion model is determined according to the field relation, the solute of the middle cells is pushed to eight points around if the middle cells are solidified, and the like, the crystal grains are propelled outwards in sequence, and whether the cells are converted from the liquid phase to the solid phase is determined according to the concentration of the solute discharged in the growth process, so that the growth is completed.
The specific process of establishing the three-dimensional dendrite nucleation and growth model in the growth process is as follows:
for a quasi-continuous nucleation model, the relationship between grain nucleation density and supercooling is:
wherein: n (N) max Representing a maximum non-uniform nucleation base number; delta T max A nucleation supercooling degree peak value is represented; delta T σ Representing standard curvature supercooling degree;
using the counting method proposed by Nastac, the interface curvature can be expressed as:
wherein: Δx represents cell size/cm; f (f) s (n) represents the solid phase fraction of n cells;
after nucleation, the crystal can continuously grow under the action of supercooling degree, and the concentration of discharged solute in the growth process is as follows:
wherein: d (D) l Is the liquid phase diffusion coefficient; Δt is the step time; dx is the mesh size;
solid fraction increment Δf after applying a perturbation function s Expressed as:
wherein: a represents the disturbance amplitude; rand () represents a random number within the [0,1] interval;
judging whether the cell is converted from a liquid phase to a solid phase, wherein a judgment formula is as follows:
f s n+1 ＝f s n+1 +Δf s ；
if f s n+1 >1 is converted to the solid phase, otherwise, not converted.
Step 3, establishing a solute distribution and diffusion model; the specific process is as follows:
the most critical ring in establishing dendrite growth models is the problem of redistribution and diffusion of solutes, which ignores the flow of the melt due to the rapid solidification rate during the welding process; the partition coefficient of solute atoms at the solid-liquid interface is expressed as:
wherein: c (C) s Represents the concentration of solid phase solute; c (C) l For the previous cell liquid phase solute concentration;
the solid phase solute concentration of the interface cells per unit time is formulated:
wherein: c'. l For the latter cell liquid phase solute concentration, C' s Is the concentration of solid phase solute, f' s Fractional in solid phase, Δf s The solid phase fraction increase per unit time;
in the solidification process, the solute discharged from the interface cells inevitably increases the concentration of the solute in the solid-liquid front liquid phase cells, and generates a larger concentration gradient of the solute between the solid-liquid front liquid phase cells and the liquid phase cells at a longer distance from the solid-liquid interface, so that the solute is promoted to diffuse in the liquid phase cells, and the diffusion equation is as follows:
wherein: dl and Ds represent the liquid phase diffusion coefficient and the solid phase diffusion coefficient, respectively.
And 4, simulating calculation and result export. The specific process is as follows:
writing a computer program based on the molten pool grid, the conditions required by solid phase and the model obtained in the steps 1-3, introducing the programmed program into a simulation software Matlab, and inputting the thermophysical parameters of the alloy and various welding technological parameters, wherein the thermophysical parameters of the alloy comprise alloy density, heat conduction coefficient and specific heat capacity; various welding process parameters include welding power, speed; and calculating to obtain a nickel-based alloy three-dimensional columnar crystal growth numerical simulation result.
The steps are carried out according to the above steps,
example 1
By adopting the numerical simulation method for the growth of the three-dimensional columnar crystals of the nickel-base alloy, which is disclosed by the invention, the supercooling degree is set to be 10 ℃, the thermal disturbance amplitude is set to be 0.2, and the solidification time is calculated to be 2.5s, 5s and 7.5s respectively, so that the schematic diagram of the simulation result of the growth of the three-dimensional columnar crystals in the molten pool is shown in fig. 3. It can be observed from fig. 3 a that primary dendrites grow in a preferential direction and form primary dendrite arms, and grains grow simultaneously in the lateral and longitudinal directions. In fig. 3, B is a columnar crystal morphology at a solidification time of 5s, and is generated on the primary dendrite arm spindle under the action of supercooling of components, and the space for growth of secondary dendrites is also large, so that rapid growth is obtained. Meanwhile, the growth of the columnar crystal transverse dendrite arm main axis is blocked and stops, so that the crystal growth has obvious directivity. In FIG. 3, C is the morphology of columnar crystal growth at 7.5s solidification time, and the lateral growth has been substantially stopped at this time, and the crystal grows longitudinally in the direction of the temperature gradient.
Example 2
By adopting the numerical simulation method for the growth of the three-dimensional columnar crystals of the nickel-base alloy, provided by the invention, the setting time is set to be 5 seconds, the thermal disturbance amplitude is set to be 0.2, the supercooling degree is set to be 5 ℃ and 10 ℃ respectively, the growth morphology of the columnar crystals in a molten pool is shown as a graph in fig. 4, and the observation from the graph in fig. 4 shows that the growth speed of the crystals is obviously increased and the columnar crystals are obviously grown in the same setting time along with the increase of the supercooling degree. In fig. 4, a is a columnar crystal morphology at a supercooling degree of 5 ℃, primary dendrite grows in a preferential direction when the supercooling degree is small, and secondary dendrite growth is not obvious. In fig. 4, B is a columnar crystal morphology at a supercooling degree of 10 ℃, and it was observed that the growth rate of the crystal was increased, and significant secondary dendrites were generated on the primary dendrite arms. In fig. 4, C is a columnar crystal morphology at a supercooling degree of 15 ℃, and lateral growth is substantially stopped, and secondary dendrites generated on primary dendrite arms are more numerous and more dense than the fastest growth of crystals in fig. 4 a and fig. 4B.
Example 3
By adopting the numerical simulation method for the growth of the three-dimensional columnar crystals of the nickel-base alloy, provided by the invention, the solidification time is set to be 5s, the supercooling degree is set to be 10 ℃, and the growth morphology of the columnar crystals in the molten pool is shown as figure 5 when the thermal disturbance amplitudes are respectively 0.01, 0.1 and 0.2, and can be observed from figure 5. During the same solidification time, the growth rate of the crystal increases slightly as the amplitude of the thermal disturbance increases gradually. By comparing FIG. 5AB C, the primary dendrite arms are smoother with little secondary dendrite present at smaller amplitudes of thermal disturbance. When the amplitude of the applied disturbance increases again, the growth rate of the columnar crystals increases slightly, and the lateral growth time of the columnar crystals decreases.
By the mode, the invention provides the numerical simulation method for the growth of the three-dimensional columnar crystals of the nickel-base alloy, which aims at the problems of nucleation and growth of the columnar crystals in a molten pool in the welding process of the nickel-base alloy. The invention simulates the growth morphology of columnar crystals and the distribution of solute components in the solidification process of the nickel-based alloy, and can simulate the influence of parameters such as solidification time, supercooling degree, thermal disturbance amplitude and the like on the growth of the columnar crystals, thereby playing a certain guiding role in improving the performance of the cladding layer of the nickel-based alloy.
Claims (9)
1. The nickel-based alloy three-dimensional columnar crystal growth numerical simulation method is characterized by comprising the following steps of:
step 1, defining the shape of a molten pool, dividing the molten pool into grids by adopting a finite element method, and defining the conditions required when crystal grains are converted from a liquid phase to a solid phase;
step 2, defining crystal grains to solidify and grow in a segmented molten pool grid, and establishing a three-dimensional dendrite nucleation and growth model for the growth process;
step 3, establishing a solute distribution and diffusion model;
and 4, simulating calculation and result export.
2. The method for simulating the growth of three-dimensional columnar crystals of the nickel-base alloy according to claim 1, wherein the specific process of defining the shape of a molten pool is as follows: modeling simplifies the cladding boundary into a smooth parabola, which can be expressed by the following equation:
wherein: a (i, j) represents coordinates of an arbitrary point; (i) 0 ,j 0 ) Representing the coordinates of the cladding layer apex or bottommost.
3. The method for simulating the growth of three-dimensional columnar crystals of a nickel-base alloy according to claim 1, wherein the conditions required for defining the transformation of grains from a liquid phase to a solid phase in step 1 include:
cell state: the cell of the whole simulation area only has three states, namely a solid phase, a liquid phase and a solid-liquid mixed interface;
neighborhood relationship: the whole simulation area is divided into a plurality of regular square cell grids, and two neighborhood relations are usually available for a square cell system, namely a Von Neumann type (four neighborhood) and a Moore type (eight neighborhood);
capturing rules: before the solidification process starts, all cells in the simulation area are defined as liquid, and after nucleation is generated by the nucleation model, cells forming the nucleation are assigned as solid phase, and cells adjacent to the nuclei are assigned as interface.
4. A method for simulating the growth of three-dimensional columnar crystals of a nickel-base alloy according to claim 3, wherein in the step 2, the crystal grains are required to be converted from a liquid phase to a solid phase in the process of solidification growth in a divided molten pool grid, the conversion state of the cells is determined through a capturing rule in the conversion process, a propulsion model is determined according to a field relation, the solute of the intermediate cells is pushed to eight points around if the intermediate cells are solidified, and the like, the process is sequentially and outwardly propelled, and whether the cells are converted from the liquid phase to the solid phase is determined according to the concentration of the solute discharged in the growth process, so that the growth is completed.
5. The method for simulating the growth of three-dimensional columnar crystals of nickel-base alloy according to claim 4, wherein the specific process of establishing a three-dimensional dendrite nucleation and growth model for the growth process is as follows:
for a quasi-continuous nucleation model, the relationship between grain nucleation density and supercooling is:
wherein: n (N) max Representing a maximum non-uniform nucleation base number; delta T max A nucleation supercooling degree peak value is represented; delta T σ Representing standard curvature supercooling degree;
using the counting method proposed by Nastac, the interface curvature can be expressed as:
wherein: Δx represents cell size/cm; f (f) s (n) represents the solid phase fraction of n cells;
after nucleation, the crystal can continuously grow under the action of supercooling degree, and the concentration of discharged solute in the growth process is as follows:
wherein: d (D) l Is the liquid phase diffusion coefficient; Δt is the step time; dx is the mesh size;
solid fraction increment Δf after applying a perturbation function s Expressed as:
wherein: a represents the disturbance amplitude; rand () represents a random number within the [0,1] interval;
judging whether the cell is converted from a liquid phase to a solid phase, wherein a judgment formula is as follows:
if it isThen it will be converted to the solid phase and otherwise not converted.
6. The method for simulating the growth of the three-dimensional columnar crystal of the nickel-base alloy according to claim 1, wherein the specific process of the step 3 is as follows:
the most critical ring in establishing dendrite growth models is the problem of redistribution and diffusion of solutes, which ignores the flow of the melt due to the rapid solidification rate during the welding process; the partition coefficient of solute atoms at the solid-liquid interface is expressed as:
wherein: c (C) s Represents the concentration of solid phase solute; c (C) l For the previous cell liquid phase solute concentration;
the solid phase solute concentration of the interface cells per unit time is formulated:
wherein: c'. l For the latter cell liquid phase solute concentration, C' s Is the concentration of solid phase solute, f' s Fractional in solid phase, Δf s The solid phase fraction increase per unit time;
in the solidification process, the solute discharged from the interface cells inevitably increases the concentration of the solute in the solid-liquid front liquid phase cells, and generates a larger concentration gradient of the solute between the solid-liquid front liquid phase cells and the liquid phase cells at a longer distance from the solid-liquid interface, so that the solute is promoted to diffuse in the liquid phase cells, and the diffusion equation is as follows:
wherein: dl and Ds represent the liquid phase diffusion coefficient and the solid phase diffusion coefficient, respectively.
7. The method for simulating the growth of the three-dimensional columnar crystal of the nickel-base alloy according to claim 1, wherein the specific process of the step 4 is as follows:
and (3) writing a computer program based on the molten pool grid, the conditions required by solid phase and the model obtained in the steps (1) to (3), guiding the programmed program into a simulation software Matlab, inputting the thermophysical parameters and various welding process parameters of the alloy, and calculating to obtain the three-dimensional columnar crystal growth numerical simulation result of the nickel base alloy.
8. The method for simulating the growth of three-dimensional columnar crystals of a nickel-base alloy according to claim 7, wherein the thermophysical parameters of the alloy comprise alloy density, heat conductivity coefficient and specific heat capacity.
9. The method for simulating the growth of three-dimensional columnar crystals of a nickel-base alloy according to claim 7, wherein the various welding process parameters comprise welding power and speed.
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