CN110321604A - A kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification - Google Patents
A kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification Download PDFInfo
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Abstract
The invention discloses a kind of methods of the single Numerical Simulation of Dendrite of Development in Ternary Alloy Solidification.Specific step is as follows: simplifying curing condition and simultaneously establishes Dendrite Growth Model and solute redistribution and diffusion model, writes computer program based on the model established and import simulation softward and calculated, finally obtain the analog result of process of setting dendritic growth.The present invention can simulate the distribution of the growth morphology of dendrite and solute constituent element in Development in Ternary Alloy Solidification, influence of the factors such as degree of supercooling, response excursion, strength of anisotropy to process of setting can also be simulated simultaneously, to play directive function to practical engineering application.
Description
Technical field
The invention belongs to Metal Material Welding technique numerical simulation technology technical fields, and in particular to a kind of ternary alloy three-partalloy is solidifying
Gu the single Numerical Simulation of Dendrite method of process.
Background technique
Welding pool has the characteristics that high temperature, instantaneous, dynamic, therefore traditional experimental method is difficult to melt transient changing
Pond process of setting is studied.With the fast development of computer technology, numerical simulation is molten as a kind of emerging research welding
The technology of pond process of setting, can various phenomenons accurate, in quantization alloy graining process and Evolution, compensate for traditional real
The shortcomings that proved recipe method.
The method for numerical simulation of welding pool process of setting have Deterministic Methods, Monte Carlo Method (MC), Phase Field (PF),
Cellular Automata Method (CA) etc..Wherein Cellular Automata Method is based on the random thought of " probability ", while being based on grain nucleation again
With growth physical mechanism, therefore physical basis is clear, and has considerable flexibility, and shows the ability of complicated actual conditions.
It currently, the CA model of solidified structure is primarily adapted for use in bianry alloy, but is generally ternary in Practical Project and application
Alloy, and it is then less for the report of ternary alloy three-partalloy solidified structure numerical simulation.Therefore, a kind of ternary alloy three-partalloy dendritic growth is established
CA model is particularly important.
Summary of the invention
The object of the present invention is to provide a kind of single Numerical Simulation of Dendrite methods of Development in Ternary Alloy Solidification, solve
The problem of lacking suitable for ternary alloy three-partalloy solidified structure CA model existing in the prior art.
The technical scheme adopted by the invention is that a kind of single Numerical Simulation of Dendrite side of Development in Ternary Alloy Solidification
Method is specifically implemented according to the following steps:
Step 1: simplified model condition；
Step 2: capture rule definition；
Step 3: growth model is established；
Step 4: solute redistribution and diffusion model are established；
Step 5: calculating and result exports.
The features of the present invention also characterized in that:
Step 1 simplified model condition includes:
Entire process of setting is divided into liquid phase, solid phase and interface (solid-liquid) three kinds of states；
Ignore kinetic undercooling in model, only considers temperature supercooling, constitutional supercooling and curvature supercooling；
Solute constituent element B and C is set in Development in Ternary Alloy Solidification, ignores the counterdiffusion between solute, only considers solute
Self-diffusion；
In order to which analog result is more accurate, cellular neighborhood relationships use eight neighborhood (Moore neighborhood).
Step 2 is specifically implemented according to the following steps:
Simulated domain is divided into square net by step 2.1, each grid is a cellular；
Step 2.2,8 neighbours' cellulars in advance around one solid phase cellular of molten bath center definition, cellular are then interface
Cellular, remaining cellular are in liquid phase state；
Step 2.3, the selected resulting solid phase cellular of step 2.2, when solidification starts, to the solid phase cellular surrounding neighbours member
Born of the same parents carry out fraction solid solution and determine, the fraction solid of neighbours' cellular is greater than 1, then the cellular is changed into solid phase cellular, week
The liquid phase cellular enclosed is then captured in as new interface cellular；
Step 2.4 carries out fraction solid solution to the interface cellular around solid phase cellular new obtained by step 2.3 and sentences
Fixed, the fraction solid of neighbours' cellular is greater than 1, then the cellular is changed into solid phase cellular, and surrounding liquid phase cellular is then captured in
For new interface cellular, and so on, until entire molten bath solidifies completely.
Step 3 is specifically implemented according to the following steps:
The calculating of step 3.1, total degree of supercooling, tnTotal degree of supercooling at moment can be obtained by following formula:
ΔT(tn)=Tl-T(tn)+ml1×(Cl1(tn)-C1)+ml2×(Cl2(tn)-C2)-Γ(θ)×k(tn)
In formula: TlFor liquidus temperature；T(tn) it is tnThe temperature of moment liquid metal；ml1、ml2Respectively solute constituent element B,
The liquidous slopes of C；Cl1(tn)、Cl2(tn) it is respectively solute constituent element B, C in tnThe liquid phase solute concentration at moment；C1, C2 difference
For the initial solute concentration of solute constituent element B, C；Γ (θ) is Gibbs-Thompson coefficient；k(tn) it is tnThe interface curvature at moment；
Step 3.2 is based on step 3.1 gained tnTotal degree of supercooling at moment, to v (tn) the dentrite tip speed of growth counted
It calculates, is shown below:
v(tn)=μk(θ)×ΔT(tn)
In formula: μk(θ) is interface kinetics coefficient；
Step 3.3 is based on the resulting v (t of step 3.2n), to Δ fsThe increment of interface cellular fraction solid is calculated, such as
Shown in following formula:
In formula: G is ortho position trellis state parameter；Δ t is time step；A is Discontinuous Factors；Rand () can be in [0,1]
Generate the function of a random number；
Step 3.4 is based on the resulting Δ f of step 3.3s, to fs nThe fraction solid of interface cellular is calculated, such as following formula institute
Show:
fs n+1=fs n+Δfs
In formula: fs n+1For the fraction solid of subsequent time interface cellular；fs nFor the fraction solid of current time interface cellular.
Step 4 is specifically implemented according to the following steps:
Step 4.1 is based on the resulting f of step 3.3s n, to Δ CiInterface Element dysuria with lower abdominal colic becomes the extra molten of solid phase cellular discharge
Matter is calculated, and is shown below:
ΔCi=Cli×(1-ki)×Δfs
In formula: CliIndicate the liquid phase solute concentration of i (B or C) constituent element；kiIndicate the solute balance distribution coefficient of i constituent element；
Step 4.2 is based on the resulting Δ f of step 3.3sWith the resulting f of step 3.4s n, the solid-phase component solidified is carried out
It calculates, is shown below:
In formula: CsiIndicate the solid phase solute concentration of i constituent element；
Step 4.3 is based on the resulting Δ C of step 4.1iWith the resulting Cs of step 4.2i, the diffusion of solute constituent element is counted
It calculates, is shown below:
In formula: Dli、DsiRespectively indicate the Liquid Diffusion Coefficient and solid phase diffusion welding of i constituent element.
Step 5 is specifically implemented according to the following steps:
Step 5.1, the model established based on step 3 and step 4 write computer program；
Step 5.2 is calculated according to the resulting computer program of step 5.1 and exports result.
The beneficial effects of the present invention are: on the basis of bianry alloy CA model, proposes a kind of ternary alloy three-partalloy and solidified
The method for numerical simulation of the single dendritic growth of journey, the present invention can simulate in Development in Ternary Alloy Solidification the growth morphology of dendrite and
The distribution of solute constituent element, while the factors such as degree of supercooling, response excursion, strength of anisotropy can also be simulated to process of setting
Influence, to play directive function to practical engineering application.
Detailed description of the invention
Fig. 1 is the solidification for inventing a kind of simulation model of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification
Process Microstructure Simulation flow chart；
Fig. 2 is the sky for inventing a kind of simulation model of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification
Between, cellular schematic diagram after state discrete；
Al constituent element liquid phase when being 0 ° that Fig. 3 is embodiment 1 is simulated in the present invention Ti-6Al-4V alloy selecting excellence evaluation
Solute concentration distribution state and dendritic growth shape appearance figure；
V constituent element liquid phase when being 0 ° that Fig. 4 is embodiment 1 is simulated in the present invention Ti-6Al-4V alloy selecting excellence evaluation
Solute concentration distribution state and dendritic growth shape appearance figure；
Fig. 5 is embodiment 1 is simulated in the present invention Ti-6Al-4V alloy selecting excellence evaluation Al constituent element liquid when being 30 °
Phase solute concentration distribution state and dendritic growth shape appearance figure；
V constituent element liquid phase when being 30 ° that Fig. 6 is embodiment 1 is simulated in the present invention Ti-6Al-4V alloy selecting excellence evaluation
Solute concentration distribution state and dendritic growth shape appearance figure；
Fig. 7 is embodiment 2 is simulated in the present invention Fe-0.8%C-0.3%Si alloy strength of anisotropy Al when being 0
Constituent element liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
V group when being 0 that Fig. 8 is embodiment 2 is simulated in the present invention Fe-0.8%C-0.3%Si alloy strength of anisotropy
First liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
Fig. 9 is embodiment 2 is simulated in the present invention Fe-0.8%C-0.3%Si alloy strength of anisotropy when being 0.2
Al constituent element liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
Figure 10 is embodiment 2 is simulated in the present invention Fe-0.8%C-0.3%Si alloy strength of anisotropy when being 0.2
V constituent element liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
Figure 11 is embodiment 3 is simulated in the present invention Fe-0.6%C-0.4%Si alloy degree of supercooling Al constituent element when being 5K
Liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
Figure 12 is embodiment 3 is simulated in the present invention Fe-0.6%C-0.4%Si alloy degree of supercooling V constituent element liquid when being 5K
Phase solute concentration distribution state and dendritic growth shape appearance figure；
Figure 13 is embodiment 3 is simulated in the present invention Fe-0.6%C-0.4%Si alloy degree of supercooling Al constituent element when being 10K
Liquid phase solute concentration distribution state and dendritic growth shape appearance figure；
Figure 14 is embodiment 3 is simulated in the present invention Fe-0.6%C-0.4%Si alloy degree of supercooling V constituent element when being 10K
Liquid phase solute concentration distribution state and dendritic growth shape appearance figure.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification of the present invention, specific steps as shown in Figure 1,
Step 1: simplified model condition；
Entire process of setting is divided into liquid phase, solid phase and interface (solid-liquid) three kinds of states；
Ignore kinetic undercooling in model, only considers temperature supercooling, constitutional supercooling and curvature supercooling；
Solute constituent element B and C is set in Development in Ternary Alloy Solidification, ignores the counterdiffusion between solute, only considers solute
Self-diffusion；
In order to which analog result is more accurate, cellular neighborhood relationships use eight neighborhood (Moore neighborhood).
Step 2: capture rule definition is specifically implemented according to the following steps:
Simulated domain is divided into square net by step 2.1, each grid is a cellular；
Step 2.2,8 neighbours' cellulars in advance around one solid phase cellular of molten bath center definition, cellular are then interface
Cellular, remaining cellular are in liquid phase state, as shown in Figure 2；
Step 2.3, the selected resulting solid phase cellular of step 2.2, when solidification starts, to the solid phase cellular surrounding neighbours member
Born of the same parents carry out fraction solid solution and determine, the fraction solid of neighbours' cellular is greater than 1, then the cellular is changed into solid phase cellular, week
The liquid phase cellular enclosed is then captured in as new interface cellular；
Step 2.4 carries out fraction solid solution to the interface cellular around solid phase cellular new obtained by step 2.3 and sentences
Fixed, the fraction solid of neighbours' cellular is greater than 1, then the cellular is changed into solid phase cellular, and surrounding liquid phase cellular is then captured in
For new interface cellular, and so on, until entire molten bath solidifies completely.
Step 3: growth model is established, and is specifically implemented according to the following steps:
The calculating of step 3.1, total degree of supercooling, tnTotal degree of supercooling at moment can be obtained by following formula:
ΔT(tn)=Tl-T(tn)+ml1×(Cl1(tn)-C1)+ml2×(Cl2(tn)-C2)-Γ(θ)×k(tn)
In formula: TlFor liquidus temperature；T(tn) it is tnThe temperature of moment liquid metal；ml1、ml2Respectively solute constituent element B,
The liquidous slopes of C；Cl1(tn)、Cl2(tn) it is respectively solute constituent element B, C in tnThe liquid phase solute concentration at moment；C1, C2 difference
For the initial solute concentration of solute constituent element B, C；Γ (θ) is Gibbs-Thompson coefficient；k(tn) it is tnThe interface curvature at moment；
Step 3.2 is based on step 3.1 gained tnTotal degree of supercooling at moment, to v (tn) the dentrite tip speed of growth counted
It calculates, is shown below:
v(tn)=μk(θ)×ΔT(tn)
In formula: μk(θ) is interface kinetics coefficient；
Step 3.3 is based on the resulting v (t of step 3.2n), to Δ fsThe increment of interface cellular fraction solid is calculated, such as
Shown in following formula:
In formula: G is ortho position trellis state parameter；Δ t is time step；A is Discontinuous Factors；Rand () can be in [0,1]
Generate the function of a random number；
Step 3.4, be based on the resulting Δ f of step 3.3s, to fs nThe fraction solid of interface cellular is calculated, such as following formula
It is shown:
fs n+1=fs n+Δfs
In formula: fs n+1For the fraction solid of subsequent time interface cellular；fs nFor the fraction solid of current time interface cellular.
Step 4: solute redistribution and diffusion model are established, and are specifically implemented according to the following steps:
Step 4.1 is based on the resulting f of step 3.3s n, to Δ CiInterface Element dysuria with lower abdominal colic becomes the extra molten of solid phase cellular discharge
Matter is calculated, and is shown below:
ΔCi=Cli×(1-ki)×Δfs
In formula: CliIndicate the liquid phase solute concentration of i (B or C) constituent element；kiIndicate the solute balance distribution coefficient of i constituent element；
Step 4.2 is based on the resulting Δ f of step 3.3sWith the resulting f of step 3.4s n, the solid-phase component solidified is carried out
It calculates, is shown below:
In formula: CsiIndicate the solid phase solute concentration of i constituent element；
Step 4.3 is based on the resulting Δ C of step 4.1iWith the resulting Cs of step 4.2i, the diffusion of solute constituent element is counted
It calculates, is shown below:
In formula: Dli、DsiRespectively indicate the Liquid Diffusion Coefficient and solid phase diffusion welding of i constituent element.
Step 5: it calculates and result exports, be specifically implemented according to the following steps:
Step 5.1, the model established based on step 3 and step 4 write computer program；
Step 5.2 is calculated according to the resulting computer program of step 5.1 and exports result.
Embodiment 1
By taking Ti-6Al-4V ternary alloy three-partalloy as an example, simulation test carried out to method of the invention, when simulation alloy heat used
Physical parameter is as shown in table 1:
Table 1
Table 1 is that Ti-6Al-4V alloy calculates thermal physical property parameter used when simulating.
Analog result as shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6, it can be seen from the figure that selecting excellence evaluation be 0 ° when, once
Secondary dendrite in dendritic arm is undeveloped, only a small amount of tiny secondary dendrite, and when selecting excellence evaluation is 30 °, primary tiller
Coarse secondary dendrite has been grown on brilliant arm.And diffusion layer of the Al element on interface is greater than diffusion layer of the V element on interface.
Embodiment 2
By taking Fe-0.8%C-0.3%Si ternary alloy three-partalloy as an example, simulation test carried out to method of the invention, when simulation is used
Alloy thermal physical property parameter it is as shown in table 2:
Table 2
Table 2 is that Fe-0.8%C-0.3%Si alloy calculates thermal physical property parameter used when simulating.
Analog result as shown in Fig. 7, Fig. 8, Fig. 9, Figure 10, it can be seen from the figure that anisotropy be 0 when, equiax crystal
Using original grain as starting point, primary tiller crystal orientation surrounding homoepitaxial, there are many secondary dendrite, whole dendrite morphologies in dendritic arm
In flakes.When anisotropy is 0.2, a dendrite is not in dispersion growth around at this time, but it is raw to defer to crystal structure
It is long, and flourishing two, three times dendrite are observed that in a dendritic arm.
Embodiment 3
By taking Fe -0.6%C -0.4%Si ternary alloy three-partalloy as an example, simulation test carried out to method of the invention, when simulation is used
Alloy thermal physical property parameter it is as shown in table 3:
Table 3
Table 3 is that Fe -0.6%C -0.4%Si alloy calculates thermal physical property parameter used when simulating.
Analog result as shown in Figure 11, Figure 12, Figure 13, Figure 14, it can be seen from the figure that when degree of supercooling be 5K when, once
Dendritic arm is shorter, and the secondary dendrite negligible amounts in a dendritic arm, secondary dendrite are undeveloped at this time.When degree of supercooling is 8K
When, one time dendrite significantly increases, and has flourishing secondary dendrite in a dendritic arm.
From above three embodiments as can be seen that the present invention can successfully simulate dendrite in Development in Ternary Alloy Solidification
Growth morphology, solute Distribution state and crystal preferred orientation, strength of anisotropy, degree of supercooling is to the shadow of dendritic growth pattern
It rings.
Claims (6)
1. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification, which is characterized in that specifically according to following step
It is rapid to implement:
Step 1: simplified model condition；
Step 2: capture rule definition；
Step 3: growth model is established；
Step 4: solute redistribution and diffusion model are established；
Step 5: calculating and result exports.
2. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification according to claim 1, feature
It is, the step 1 simplified model condition includes:
Entire process of setting is divided into liquid phase, solid phase and three kinds of interface state；
Ignore kinetic undercooling in model, only considers temperature supercooling, constitutional supercooling and curvature supercooling；
Solute constituent element B and C is set in Development in Ternary Alloy Solidification, ignores the counterdiffusion between solute, only considers expanding certainly for solute
It dissipates；
In order to which analog result is more accurate, cellular neighborhood relationships use eight neighborhood.
3. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification according to claim 1, feature
It is, the step 2 is specifically implemented according to the following steps:
Simulated domain is divided into square net by step 2.1, each grid is a cellular；
Step 2.2,8 neighbours' cellulars in advance around one solid phase cellular of molten bath center definition, cellular are then interface cellular,
Remaining cellular is in liquid phase state；
Step 2.3, the selected resulting solid phase cellular of step 2.2, when solidification starts, carry out the solid phase cellular surrounding neighbours cellular
Fraction solid solves and determines, the fraction solid of neighbours' cellular is greater than 1, then the cellular is changed into solid phase cellular, surrounding liquid
Phase cellular is then captured in as new interface cellular；
Step 2.4 carries out fraction solid solution to the interface cellular around solid phase cellular new obtained by step 2.3 and determines, adjacent
The fraction solid for occupying cellular is greater than 1, then the cellular is changed into solid phase cellular, and it is new that surrounding liquid phase cellular, which is then captured in,
Interface cellular, and so on, until entire molten bath solidifies completely.
4. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification according to claim 1, feature
It is, the step 3 is specifically implemented according to the following steps:
The calculating of step 3.1, total degree of supercooling, tnTotal degree of supercooling at moment can be obtained by following formula:
ΔT(tn)=Tl-T(tn)+ml1×(Cl1(tn)-C1)+ml2×(Cl2(tn)-C2)-Γ(θ)×k(tn)
In formula: TlFor liquidus temperature；T(tn) it is tnThe temperature of moment liquid metal；ml1、ml2Respectively solute constituent element B, C
Liquidous slopes；Cl1(tn)、Cl2(tn) it is respectively solute constituent element B, C in tnThe liquid phase solute concentration at moment；C1, C2 are respectively molten
The initial solute concentration of matter constituent element B, C；Γ (θ) is Gibbs-Thompson coefficient；k(tn) it is tnThe interface curvature at moment；
Step 3.2 is based on step 3.1 gained tnTotal degree of supercooling at moment, to v (tn) the dentrite tip speed of growth calculated, such as
Shown in following formula:
v(tn)=μk(θ)×ΔT(tn)
In formula: μk(θ) is interface kinetics coefficient；
Step 3.3 is based on the resulting v (t of step 3.2n), to Δ fsThe increment of interface cellular fraction solid is calculated, such as following formula
It is shown:
In formula: G is ortho position trellis state parameter；Δ t is time step；A is Discontinuous Factors；Rand () can be generated in [0,1]
The function of one random number；
Step 3.4 is based on the resulting Δ f of step 3.3s, to fs nThe fraction solid of interface cellular is calculated, and is shown below:
fs n+1=fs n+Δfs
In formula: fs n+1For the fraction solid of subsequent time interface cellular；fs nFor the fraction solid of current time interface cellular.
5. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification according to claim 1, feature
It is, the step 4 is specifically implemented according to the following steps:
Step 4.1 is based on the resulting f of step 3.3s n, to Δ CiInterface Element dysuria with lower abdominal colic become solid phase cellular discharge extra solute into
Row calculates, and is shown below:
ΔCi=Cli×(1-ki)×Δfs
In formula: CliIndicate the liquid phase solute concentration of i (B or C) constituent element；kiIndicate the solute balance distribution coefficient of i constituent element；
Step 4.2 is based on the resulting Δ f of step 3.3sWith the resulting f of step 3.4s n, the solid-phase component solidified is counted
It calculates, is shown below:
In formula: CsiIndicate the solid phase solute concentration of i constituent element；
Step 4.3 is based on the resulting Δ C of step 4.1iWith the resulting Cs of step 4.2i, the diffusion of solute constituent element is calculated,
It is shown below:
In formula: Dli、DsiRespectively indicate the Liquid Diffusion Coefficient and solid phase diffusion welding of i constituent element.
6. a kind of single Numerical Simulation of Dendrite method of Development in Ternary Alloy Solidification according to claim 1, feature
It is, the step 5 is specifically implemented according to the following steps:
Step 5.1, the model established based on step 3 and step 4 write computer program；
Step 5.2 is calculated according to the resulting computer program of step 5.1 and exports result.
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| 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 |
| CN111339670B (en) * | 2020-02-28 | 2024-04-09 | 西安理工大学 | Dendrite growth numerical simulation method in nickel-based alloy laser cladding process |
| CN111640469A (en) * | 2020-05-18 | 2020-09-08 | 苏州大学 | Three-dimensional simulation method for dendrite coarsening |
| CN112185474A (en) * | 2020-09-07 | 2021-01-05 | 西安理工大学 | Numerical simulation method for directional solidification process of Ti-45% Al alloy |
| CN112185474B (en) * | 2020-09-07 | 2024-02-06 | 西安理工大学 | Numerical simulation method for directional solidification process of Ti-45% Al alloy |
| CN112115634A (en) * | 2020-09-21 | 2020-12-22 | 哈尔滨理工大学 | Three-dimensional numerical prediction method for grain structure in unidirectional solidification process of molten metal |
| CN112115634B (en) * | 2020-09-21 | 2021-04-06 | 哈尔滨理工大学 | Three-dimensional numerical prediction method for grain structure in unidirectional solidification process of molten metal |
| CN112784424A (en) * | 2021-01-28 | 2021-05-11 | 西安理工大学 | Three-dimensional numerical simulation method for grain growth of titanium alloy welding pool |
| CN112784424B (en) * | 2021-01-28 | 2024-04-09 | 西安理工大学 | Three-dimensional numerical simulation method for grain growth of titanium alloy welding pool |
| CN113823357A (en) * | 2021-08-09 | 2021-12-21 | 西安理工大学 | Numerical simulation method for isometric crystal growth in quaternary alloy solidification process |
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