CN110489820A - A kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method - Google Patents
A kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method Download PDFInfo
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Abstract
The analogy method of the invention discloses a kind of welding pool Microstructural Evolution based on Cellular Automata Method, specific step is as follows: consolidating condition to welding pool first and simplifies, then the nucleation and growth mode of dendrite is established, finally write computer program, alloy thermal physical property parameter and various welding conditions are inputted, carrying out calculating can be obtained analog result.The present invention can simulate growth morphology, the solute concentration distribution of dendrite in the variation of field of welding temperature and molten bath process of setting under transient condition, to play directive function to practical engineering application.
Description
Technical field
The invention belongs to Numerical Simulation of Microstructure Evolution fields in metal solidification process, and in particular to one kind is based on cellular
The welding pool Microstructural Evolution analogy method of automatic machine method.
Background technique
Welding is used as a kind of widely used processing method, is different from other processing methods with its salient feature, wherein
Most significant feature is exactly to issue physics and the chemistry change of raw various complexity in highly dynamic welding transient temperature field action
Change, these variations decide that the type of solidified structure, grain size etc. finally play decisive influence to the quality of processing.
In the research field of microstructure, conventional method is to be finally reached to determine complicated welding process through a large number of experiments
Amount and qualitatively understanding, it is often time-consuming and laborious, and also welding process is the process of a highly dynamic variation, only by experiment
Method is also difficult to make accurate anatomy to entire welding process.With the rapid development of computer technology with related thermodynamics,
Solidification theory constantly improve, and numerical simulation technology gradually shows the incomparable advantage of the experiment such as real-time, dynamic.
It is at present Phase Field and Cellular Automata Method, both of which using most methods in Microstructure Simulation field
Microstructure evolution can be calculated under the premise of coupling multiple physical field, and there are many successfully applications.But Phase Field is most
Big disadvantage be exactly it is computationally intensive, computational efficiency is low, and zoning is small, several crystal grain few in number can only be simulated, this greatly
Limit its development and application.In contrast, Cellular Automata Method physical basis is clear, there is considerable flexibility, and
The ability for showing complicated actual conditions, the canonical trend of crystal grain and actual die growth including various shape and size, meter
Calculation speed is faster than other methods, and reference area is big.
So establishing a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method seems especially heavy
It wants.
Summary of the invention
The welding pool Microstructural Evolution analogy method based on Cellular Automata Method that the object of the present invention is to provide a kind of,
Solve that Microstructure evolution existing in the prior art is computationally intensive, the low problem of computational efficiency.
The technical scheme adopted by the invention is that a kind of welding pool Microstructural Evolution mould based on Cellular Automata Method
Quasi- method, is specifically implemented according to the following steps:
Step 1, the welding pool curing condition for simplifying Cellular Automata Method；
Step 2 is based on heat transfer theory, constructs the transient state macro-temperature field model in welding process；
Step 3 is based on Interpolation Principle, and macroscopical field of welding temperature is changed into microcosmic temperature field needed for Microstructure evolution
Macro-Micro-Coupled Model；
Step 4, under the premise of obtaining microcosmic temperature field, building establishes transient condition undershoot based on grain nucleation and growth
Brilliant nucleation and growth mode；
Step 5, calculating and its visualization of result.
The features of the present invention also characterized in that:
The welding pool curing condition of simplified Cellular Automata Method includes: in step 1
Cellular is divided into liquid phase, solid phase and three kinds of interface state in simplified condition 1, entire process of setting；
Ignore kinetic undercooling in simplified condition 2, model；
Solid/liquid interfaces are in equilibrium state always in simplified condition 3, this model；
Simplified condition 4, cellular Domain relation use V.Neumann type neighborhood.
Step 2 is specifically implemented according to the following steps:
Simulated domain is divided into equal-sized square cellular, distribution of the temperature field on time and space can be with table
It is shown as:
T=T (x, y, z, t)
The governing equation of nonlinear transient heat conduction problem are as follows:
In formula: ρ is density of material；C is material specific heat capacity；T is thermo parameters method function；λ is thermal coefficient；For interior heat
Source strength；T is heat transfer time；
Transient heat conduct equation solve using centered finite difference methods:
In formula:For the temperature value of the position t moment (i, j, k) cellular, subscript indicates moment, the position that subscript indicates；
Δ x is cellular size；Δ t is time step；
Since cellular has internal and two kinds of surface distributing position, so deriving the cellular evolution rule of different location:
A, the evolution rule of internal cellular
B, the evolution rule of surface cellular
In formula: H is the convection transfer rate of weldment and air；Ai,j,kFor the contact area of center unit and air；T0For
Environment temperature；
After the temperature field evolution rule of cellular is set, need to be arranged moving heat source to simulate the shifting of actual welding heat source
It is dynamic, practical heat source is simulated using Gauss heat source, the mathematic(al) representation of Gauss heat source model is as follows:
In formula: qmFor the maximum heat flow density at source center；R is the distance apart from electric arc heated spot；rhHave for electric arc
Imitate heating radius；
Macro temperature field model construction is welded to complete.
Step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value for extracting macroscopical grid temperature field: a suitable computer capacity is chosen, finite element section is extracted
Temperature-time data on point；
Step 3.2, m- macro temperature field curve when being fitted to extracted data: by macro temperature field temperature-when
Between data be fitted to Temperature-time functional form；
Step 3.3 obtains microcosmic temperature field using interpolation method: using bilinear interpolation to macro temperature field interpolation, obtaining
Suitable for the microcosmic temperature field that microstructure calculates, specific mathematical expression is as follows:
In formula: Q11, Q12, Q21, Q22Represent the node of macro-scale grid；P is the grid node of micro-scale；T(Qij)
The corresponding temperature value of macro micro-scale node is respectively indicated with T (P)；
The building of field of welding temperature Macro-Micro-Coupled Model is completed.
Step 4 is specifically implemented according to the following steps:
The foundation of step 4.1, Nucleation Model
Using the forming core function based on Gaussian Profile, grain density n (Δ T) such as following formula are formed by under a certain degree of supercooling
It is shown:
And dn/d (Δ T) expression formula is as follows:
In formula: nmaxFor the maximum value of heterogeneous nucleation density；ΔTαFor standard curvature degree of supercooling；ΔTmaxFor maximum forming core
Degree of supercooling；
The foundation of step 4.2, growth model
It after nucleus is formed, needs under certain degree of supercooling, could continue to grow up to form crystal grain, Δ is subcooled by heat in degree of supercooling
Tt, constitutional supercooling Δ TcΔ T is subcooled with curvaturetIt constitutes:
Δ T=Δ Tt+ΔTc+ΔTr
tnThe equilibrium relation of moment solid/liquid interfaces are as follows:
In formula: TlWith T (tn) be alloy liquidus temperature and tnThe transient temperature at moment, mlFor liquidous slopes, CL0With
Cl(tn) be respectively alloy initial solute concentration and tnThe solute concentration at moment, Γ (θ) are Gibbs-Thompson coefficient,
For interface average curvature；
The propulsion of solid liquid interface, along with the variation of cellular unit solid rate, the growth of solid rate and interface speed are at just
Than that can be expressed from the next:
In formula: Δ x is size of mesh opening；Δ t is the step-length time；G is ortho position trellis state parameter；A is Discontinuous Factors；rand
() can generate a random number in [0,1]；
In formula: b is constant empirical parameter；Sm ' and sm " is respectively the state parameter of four closest cellulars, if
Adjacent cellular is that solid phase, sm ' and sm " value are 1, when adjacent cellular is liquid phase or interface, value 0；Interface cellular is being changed into
Before solid phase cellular, solid rate is continuously increased, in time t, the solid rate of a certain interface cellular are as follows:
In formula: N is the number of iterations；Δ t is time step.
Step 5 is specifically implemented according to the following steps:
Step 5.1: by based on step 1~3 constructed by based on grain nucleation and growth establish dendrite under transient condition
Nucleation and growth mode imports in simulation softward Matlab；
Step 5.2: input alloy thermal physical property parameter and various welding conditions, be calculated based on crystal grain
The analog result of the nucleation and growth mode of dendrite under transient condition is established in forming core and growth.
The beneficial effects of the present invention are:
(1) a kind of analogy method of welding pool Microstructural Evolution based on Cellular Automata Method is proposed, for research weldering
The process of setting for connecing molten bath provides a kind of new method；
It (2), can be to microcosmic group by carrying out visualization processing to the process of setting of entire welding pool on analog platform
Knitting evolution process has understanding more profound, provides support to improve welding quality；
(3) compared to experimental method, research cycle is short, at low cost, and environmentally protective.
Detailed description of the invention
Fig. 1 is a kind of process of the analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method of the present invention
Schematic diagram；
Fig. 2 is a kind of analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method of the present invention
V.Neumann neighborhood relationships schematic diagram；
Fig. 3 is a kind of space of the analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method of the present invention
Cellular divides schematic diagram；
Fig. 4 is a kind of Gauss of the analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method of the present invention
Heat source model schematic diagram；
Fig. 5 is a kind of two-wire of the analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method of the present invention
Property interpolation schematic diagram；
Fig. 6 is the Fe-0.4%C alloy transient field of welding temperature that embodiment 1 is simulated in the present invention；
Fig. 7 is the Fe-0.4%C alloy welding pool Microstructure evolution result that embodiment 1 is simulated in the present invention；
Fig. 8 is the Ti-45%Al alloy transient field of welding temperature that embodiment 2 is simulated in the present invention；
Fig. 9 is the Ti-45%Al alloy welding pool Microstructure evolution result that embodiment 2 is simulated in the present invention；
Figure 10 is the Al-4%Cu alloy transient field of welding temperature that embodiment 3 is simulated in the present invention；
Figure 11 is the Al-4%Cu alloy welding pool Microstructure evolution result that embodiment 3 is simulated in the present invention.
Specific embodiment
With reference to the accompanying drawing 1 and specific embodiment the present invention is described in detail.
Embodiment 1
A kind of analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method, as shown in Figure 1, specifically pressing
Implement according to following steps:
1. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method, which is characterized in that specific
It follows the steps below to implement:
Step 1, the welding pool curing condition for simplifying Cellular Automata Method；
Step 2 is based on heat transfer theory, constructs the transient state macro-temperature field model in welding process；
Step 3 is based on Interpolation Principle, and macroscopical field of welding temperature is changed into microcosmic temperature field needed for Microstructure evolution
Macro-Micro-Coupled Model；
Step 4, under the premise of obtaining microcosmic temperature field, building establishes transient condition undershoot based on grain nucleation and growth
Brilliant nucleation and growth mode；
Step 5, calculating and its visualization of result.
2. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the welding pool curing condition of simplified Cellular Automata Method includes: in the step 1
Cellular is divided into liquid phase, solid phase and three kinds of interface state in simplified condition 1, entire process of setting；
Ignore kinetic undercooling in simplified condition 2, model；
Solid/liquid interfaces are in equilibrium state always in simplified condition 3, this model；
Simplified condition 4, to simplify the calculation process, improve computational efficiency, and cellular Domain relation is adjacent using V.Neumann type
Domain, as shown in Figure 2.
3. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 2 is specifically implemented according to the following steps:
As shown in figure 3, simulated domain is divided into equal-sized square cellular, temperature field is on time and space
Distribution can indicate are as follows:
T=T (x, y, z, t)
Welding heat transfer problem belongs to typical nonlinear transient heat conduction problem, the control of nonlinear transient heat conduction problem
Equation are as follows:
In formula: ρ is density of material；C is material specific heat capacity；T is thermo parameters method function；λ is thermal coefficient；For interior heat
Source strength；T is heat transfer time；
Transient heat conduct equation solve using centered finite difference methods:
In formula:For the temperature value of the position t moment (i, j, k) cellular, subscript indicates moment, the position that subscript indicates；
Δ x is cellular size；Δ t is time step；
Since cellular has internal and two kinds of surface distributing position, so deriving the cellular evolution rule of different location:
A, the evolution rule of internal cellular
B, the evolution rule of surface cellular
In formula: H is the convection transfer rate of weldment and air；Ai,j,kFor the contact area of center unit and air；T0For
Environment temperature；
After the temperature field evolution rule of cellular is set, need to be arranged moving heat source to simulate the shifting of actual welding heat source
It is dynamic, practical heat source is simulated using Gauss heat source, as shown in figure 4, the mathematic(al) representation of Gauss heat source model is as follows:
In formula: qmFor the maximum heat flow density at source center；R is the distance apart from electric arc heated spot；rhHave for electric arc
Imitate heating radius；
Macro temperature field model construction is welded to complete.
4. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value for extracting macroscopical grid temperature field: a suitable computer capacity is chosen, finite element section is extracted
Temperature-time data on point；
Step 3.2, m- macro temperature field curve when being fitted to extracted data: by macro temperature field temperature-when
Between data be fitted to Temperature-time functional form, for self-programming establish coupling CA model be ready work；
Step 3.3 obtains microcosmic temperature field using interpolation method: using bilinear interpolation to macro temperature field interpolation, obtaining
Suitable for the microcosmic temperature field that microstructure calculates, Interpolation Principle is as shown in figure 5, specific mathematical expression is as follows:
In formula: Q11, Q12, Q21, Q22Represent the node of macro-scale grid；P is the grid node of micro-scale；T(Qij)
The corresponding temperature value of macro micro-scale node is respectively indicated with T (P)；
The building of field of welding temperature Macro-Micro-Coupled Model is completed.
Step 4 is specifically implemented according to the following steps:
The foundation of step 4.1, Nucleation Model
Using the forming core function based on Gaussian Profile, grain density n (Δ T) such as following formula are formed by under a certain degree of supercooling
It is shown:
And dn/d (Δ T) expression formula is as follows:
In formula: nmaxFor the maximum value of heterogeneous nucleation density；ΔTαFor standard curvature degree of supercooling；ΔTmaxFor maximum forming core
Degree of supercooling；
The foundation of step 4.2, growth model
It after nucleus is formed, needs under certain degree of supercooling, could continue to grow up to form crystal grain, Δ is subcooled by heat in degree of supercooling
Tt, constitutional supercooling Δ TcΔ T is subcooled with curvaturetIt constitutes:
Δ T=Δ Tt+ΔTc+ΔTr
tnThe equilibrium relation of moment solid/liquid interfaces are as follows:
In formula: TlWith T (tn) be alloy liquidus temperature and tnThe transient temperature at moment, mlFor liquidous slopes, CL0With
Cl(tn) be respectively alloy initial solute concentration and tnThe solute concentration at moment, Γ (θ) are Gibbs-Thompson coefficient,
For interface average curvature；
The propulsion of solid liquid interface, along with the variation of cellular unit solid rate, the growth of solid rate and interface speed are at just
Than that can be expressed from the next:
In formula: Δ x is size of mesh opening；Δ t is the step-length time；G is ortho position trellis state parameter；A is Discontinuous Factors；rand
() can generate a random number in [0,1]；
In formula: b is constant empirical parameter；Sm ' and sm " is respectively the state parameter of four closest cellulars, if
Adjacent cellular is that solid phase, sm ' and sm " value are 1, when adjacent cellular is liquid phase or interface, value 0；Interface cellular is being changed into
Before solid phase cellular, solid rate is continuously increased, in time t, the solid rate of a certain interface cellular are as follows:
In formula: N is the number of iterations；Δ t is time step；Work as fs(t)=1 when, interface cellular is solid phase by liquid phase,
When an Interface Element dysuria with lower abdominal colic becomes solid phase cellular, new liquid phase cellular is captured to be changed into new interface cellular, final to realize
The simulation of process of setting.
5. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 5 is specifically implemented according to the following steps:
Step 5.1: by based on step 1~3 constructed by based on grain nucleation and growth establish dendrite under transient condition
Nucleation and growth mode is written as computer program and imports in simulation softward Matlab；
Step 5.2: the thermal physical property parameter and various welding conditions for inputting alloy as shown in table 1 calculate
To the analog result for establishing the nucleation and growth mode of dendrite under transient condition based on grain nucleation and growth, obtained temperature field
The analog result difference of distribution and the dendrite morphology under its effect is as shown in Figure 6 and Figure 7.
The 1 main thermal physical property parameter of Fe-0.04%C alloy of table
Source center temperature highest as can be seen from Figure 6 is lower away from the remoter temperature of source center.
Melt tank edge has apparent column crystal to generate as can be seen from Figure 7, and molten bath is centrally generated a large amount of equiax crystal.
Embodiment 2
A kind of analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method, as shown in Figure 1, specifically pressing
Implement according to following steps:
Step 1, the welding pool curing condition for simplifying Cellular Automata Method；
Step 2 is based on heat transfer theory, constructs the transient state macro-temperature field model in welding process；
Step 3 is based on Interpolation Principle, and macroscopical field of welding temperature is changed into microcosmic temperature field needed for Microstructure evolution
Macro-Micro-Coupled Model；
Step 4, under the premise of obtaining microcosmic temperature field, building establishes transient condition undershoot based on grain nucleation and growth
Brilliant nucleation and growth mode；
Step 5, calculating and its visualization of result.
2. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the welding pool curing condition of simplified Cellular Automata Method includes: in the step 1
Cellular is divided into liquid phase, solid phase and three kinds of interface state in simplified condition 1, entire process of setting；
Ignore kinetic undercooling in simplified condition 2, model；
Solid/liquid interfaces are in equilibrium state always in simplified condition 3, this model；
Simplified condition 4, to simplify the calculation process, improve computational efficiency, and cellular Domain relation is adjacent using V.Neumann type
Domain, as shown in Figure 2.
3. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 2 is specifically implemented according to the following steps:
As shown in figure 3, simulated domain is divided into equal-sized square cellular, temperature field is on time and space
Distribution can indicate are as follows:
T=T (x, y, z, t)
Welding heat transfer problem belongs to typical nonlinear transient heat conduction problem, the control of nonlinear transient heat conduction problem
Equation are as follows:
In formula: ρ is density of material；C is material specific heat capacity；T is thermo parameters method function；λ is thermal coefficient；For interior heat
Source strength；T is heat transfer time；
Transient heat conduct equation solve using centered finite difference methods:
In formula:For the temperature value of the position t moment (i, j, k) cellular, subscript indicates moment, the position that subscript indicates；
Δ x is cellular size；Δ t is time step；
Since cellular has internal and two kinds of surface distributing position, so deriving the cellular evolution rule of different location:
A, the evolution rule of internal cellular
B, the evolution rule of surface cellular
In formula: H is the convection transfer rate of weldment and air；Ai,j,kFor the contact area of center unit and air；T0For
Environment temperature；
After the temperature field evolution rule of cellular is set, need to be arranged moving heat source to simulate the shifting of actual welding heat source
It is dynamic, practical heat source is simulated using Gauss heat source, as shown in figure 4, the mathematic(al) representation of Gauss heat source model is as follows:
In formula: qmFor the maximum heat flow density at source center；R is the distance apart from electric arc heated spot；rhHave for electric arc
Imitate heating radius；
Macro temperature field model construction is welded to complete.
4. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value for extracting macroscopical grid temperature field: a suitable computer capacity is chosen, finite element section is extracted
Temperature-time data on point；
Step 3.2, m- macro temperature field curve when being fitted to extracted data: by macro temperature field temperature-when
Between data be fitted to Temperature-time functional form, for self-programming establish coupling CA model be ready work；
Step 3.3 obtains microcosmic temperature field using interpolation method: using bilinear interpolation to macro temperature field interpolation, obtaining
Suitable for the microcosmic temperature field that microstructure calculates, Interpolation Principle is as shown in figure 5, specific mathematical expression is as follows:
In formula: Q11, Q12, Q21, Q22Represent the node of macro-scale grid；P is the grid node of micro-scale；T(Qij)
The corresponding temperature value of macro micro-scale node is respectively indicated with T (P)；
The building of field of welding temperature Macro-Micro-Coupled Model is completed.
5. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 4 is specifically implemented according to the following steps:
The foundation of step 4.1, Nucleation Model
Using the forming core function based on Gaussian Profile, grain density n (Δ T) such as following formula are formed by under a certain degree of supercooling
It is shown:
And dn/d (Δ T) expression formula is as follows:
In formula: nmaxFor the maximum value of heterogeneous nucleation density；ΔTαFor standard curvature degree of supercooling；ΔTmaxFor maximum forming core
Degree of supercooling；
The foundation of step 4.2, growth model
It after nucleus is formed, needs under certain degree of supercooling, could continue to grow up to form crystal grain, Δ is subcooled by heat in degree of supercooling
Tt, constitutional supercooling Δ TcΔ T is subcooled with curvaturetIt constitutes:
Δ T=Δ Tt+ΔTc+ΔTr
tnThe equilibrium relation of moment solid/liquid interfaces are as follows:
In formula: TlWith T (tn) be alloy liquidus temperature and tnThe transient temperature at moment, mlFor liquidous slopes, CL0With
Cl(tn) be respectively alloy initial solute concentration and tnThe solute concentration at moment, Γ (θ) are Gibbs-Thompson coefficient,
For interface average curvature；
The propulsion of solid liquid interface, along with the variation of cellular unit solid rate, the growth of solid rate and interface speed are at just
Than that can be expressed from the next:
In formula: Δ x is size of mesh opening；Δ t is the step-length time；G is ortho position trellis state parameter；A is Discontinuous Factors；rand
() can generate a random number in [0,1]；
In formula: b is constant empirical parameter；Sm ' and sm " is respectively the state parameter of four closest cellulars, if
Adjacent cellular is that solid phase, sm ' and sm " value are 1, when adjacent cellular is liquid phase or interface, value 0；Interface cellular is being changed into
Before solid phase cellular, solid rate is continuously increased, in time t, the solid rate of a certain interface cellular are as follows:
In formula: N is the number of iterations；Δ t is time step；Work as fs(t)=1 when, interface cellular is solid phase by liquid phase,
When an Interface Element dysuria with lower abdominal colic becomes solid phase cellular, new liquid phase cellular is captured to be changed into new interface cellular, final to realize
The simulation of process of setting.
5. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 5 is specifically implemented according to the following steps:
Step 5.1: by based on step 1~3 constructed by based on grain nucleation and growth establish dendrite under transient condition
Nucleation and growth mode is written as computer program and imports in simulation softward Matlab；
Step 5.2: the thermal physical property parameter and various welding conditions for inputting alloy as shown in table 1 calculate
To the analog result for establishing the nucleation and growth mode of dendrite under transient condition based on grain nucleation and growth, obtained temperature field
The analog result difference of distribution and the dendrite morphology under its effect is as shown in Figure 8 and Figure 9.
From figure 8, it is seen that source center temperature highest, the bulk temperature of heat source front end is lower than heat source rear end.
As can be seen from Figure 9 melt tank edge has a large amount of column crystals to generate, and equiax crystal generates after the center of molten bath, stops
The further growth of column crystal.
The 2 main thermal physical property parameter of Ti-45%Al alloy of table
Embodiment 3
A kind of analogy method of the welding pool Microstructural Evolution based on Cellular Automata Method, as shown in Figure 1, specifically pressing
Implement according to following steps:
1. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method, specifically according to following step
It is rapid to implement:
Step 1, the welding pool curing condition for simplifying Cellular Automata Method；
Step 2 is based on heat transfer theory, constructs the transient state macro-temperature field model in welding process；
Step 3 is based on Interpolation Principle, and macroscopical field of welding temperature is changed into microcosmic temperature field needed for Microstructure evolution
Macro-Micro-Coupled Model；
Step 4, under the premise of obtaining microcosmic temperature field, building establishes transient condition undershoot based on grain nucleation and growth
Brilliant nucleation and growth mode；
Step 5, calculating and its visualization of result.
2. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the welding pool curing condition of simplified Cellular Automata Method includes: in the step 1
Cellular is divided into liquid phase, solid phase and three kinds of interface state in simplified condition 1, entire process of setting；
Ignore kinetic undercooling in simplified condition 2, model；
Solid/liquid interfaces are in equilibrium state always in simplified condition 3, this model；
Simplified condition 4, to simplify the calculation process, improve computational efficiency, and cellular Domain relation is adjacent using V.Neumann type
Domain, as shown in Figure 2.
3. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 2 is specifically implemented according to the following steps:
As shown in figure 3, simulated domain is divided into equal-sized square cellular, temperature field is on time and space
Distribution can indicate are as follows:
T=T (x, y, z, t)
Welding heat transfer problem belongs to typical nonlinear transient heat conduction problem, the control of nonlinear transient heat conduction problem
Equation are as follows:
In formula: ρ is density of material；C is material specific heat capacity；T is thermo parameters method function；λ is thermal coefficient；For interior heat
Source strength；T is heat transfer time；
Transient heat conduct equation solve using centered finite difference methods:
In formula:For the temperature value of the position t moment (i, j, k) cellular, subscript indicates moment, the position that subscript indicates；
Δ x is cellular size；Δ t is time step；
Since cellular has internal and two kinds of surface distributing position, so deriving the cellular evolution rule of different location:
A, the evolution rule of internal cellular
B, the evolution rule of surface cellular
In formula: H is the convection transfer rate of weldment and air；Ai,j,kFor the contact area of center unit and air；T0For
Environment temperature；
After the temperature field evolution rule of cellular is set, need to be arranged moving heat source to simulate the shifting of actual welding heat source
It is dynamic, practical heat source is simulated using Gauss heat source, as shown in figure 4, the mathematic(al) representation of Gauss heat source model is as follows:
In formula: qmFor the maximum heat flow density at source center；R is the distance apart from electric arc heated spot；rhHave for electric arc
Imitate heating radius；
Macro temperature field model construction is welded to complete.
4. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value for extracting macroscopical grid temperature field: a suitable computer capacity is chosen, finite element section is extracted
Temperature-time data on point；
Step 3.2, m- macro temperature field curve when being fitted to extracted data: by macro temperature field temperature-when
Between data be fitted to Temperature-time functional form, for self-programming establish coupling CA model be ready work；
Step 3.3 obtains microcosmic temperature field using interpolation method: using bilinear interpolation to macro temperature field interpolation, obtaining
Suitable for the microcosmic temperature field that microstructure calculates, Interpolation Principle is as shown in figure 5, specific mathematical expression is as follows:
In formula: Q11, Q12, Q21, Q22Represent the node of macro-scale grid；P is the grid node of micro-scale；T(Qij)
The corresponding temperature value of macro micro-scale node is respectively indicated with T (P)；
The building of field of welding temperature Macro-Micro-Coupled Model is completed.
5. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 4 is specifically implemented according to the following steps:
The foundation of step 4.1, Nucleation Model
Using the forming core function based on Gaussian Profile, grain density n (Δ T) such as following formula are formed by under a certain degree of supercooling
It is shown:
And dn/d (Δ T) expression formula is as follows:
In formula: nmaxFor the maximum value of heterogeneous nucleation density；ΔTαFor standard curvature degree of supercooling；ΔTmaxFor maximum forming core
Degree of supercooling；
The foundation of step 4.2, growth model
It after nucleus is formed, needs under certain degree of supercooling, could continue to grow up to form crystal grain, Δ is subcooled by heat in degree of supercooling
Tt, constitutional supercooling Δ TcΔ T is subcooled with curvaturetIt constitutes:
Δ T=Δ Tt+ΔTc+ΔTr
tnThe equilibrium relation of moment solid/liquid interfaces are as follows:
In formula: TlWith T (tn) be alloy liquidus temperature and tnThe transient temperature at moment, mlFor liquidous slopes, CL0With
Cl(tn) be respectively alloy initial solute concentration and tnThe solute concentration at moment,For Gibbs-Thompson coefficient,For
Interface average curvature；
The propulsion of solid liquid interface, along with the variation of cellular unit solid rate, the growth of solid rate and interface speed are at just
Than that can be expressed from the next:
In formula: Δ x is size of mesh opening；Δ t is the step-length time；G is ortho position trellis state parameter；A is Discontinuous Factors；rand
() can generate a random number in [0,1]；
In formula: b is constant empirical parameter；Sm ' and sm " is respectively the state parameter of four closest cellulars, if
Adjacent cellular is that solid phase, sm ' and sm " value are 1, when adjacent cellular is liquid phase or interface, value 0；Interface cellular is being changed into
Before solid phase cellular, solid rate is continuously increased, in time t, the solid rate of a certain interface cellular are as follows:
In formula: N is the number of iterations；Δ t is time step；Work as fs(t)=1 when, interface cellular is solid phase by liquid phase,
When an Interface Element dysuria with lower abdominal colic becomes solid phase cellular, new liquid phase cellular is captured to be changed into new interface cellular, final to realize
The simulation of process of setting.
5. a kind of welding pool Microstructural Evolution simulation side based on Cellular Automata Method according to claim 1
Method, which is characterized in that the step 5 is specifically implemented according to the following steps:
Step 5.1: by based on step 1~3 constructed by based on grain nucleation and growth establish dendrite under transient condition
Nucleation and growth mode is written as computer program and imports in simulation softward Matlab；
Step 5.2: the thermal physical property parameter and various welding conditions for inputting alloy as shown in table 3 calculate
To the analog result for establishing the nucleation and growth mode of dendrite under transient condition based on grain nucleation and growth, obtained temperature field
The analog result difference of distribution and the dendrite morphology under its effect is as shown in Figure 10 and Figure 11.
The 3 main thermal physical property parameter of Al-4%Cu alloy of table
From fig. 10 it can be seen that source center temperature highest, the bulk temperature of heat source front end is lower than heat source rear end, temperature field
For the overall trend of variation to be higher apart from the nearlyr temperature of source center, the temperature gradient in source center region is significantly greater than peripheral region
Domain.
As can be seen from Figure 11 melt tank edge has a large amount of column crystals to generate, and after column crystal growth to a certain extent, melts
Just there is equiax crystal generation at pond center, and column crystal shared region in molten bath is significantly greater than equiax crystal.
It can be seen that field of welding temperature and its effect of the invention that can be simulated under transient condition from three embodiments of appeal
Under welding pool in dendritic growth, so that the adjustment for welding procedure in actual welding production process provides guidance.
Claims (6)
1. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method, which is characterized in that specifically according to
Following steps are implemented:
Step 1, the welding pool curing condition for simplifying Cellular Automata Method；
Step 2 is based on heat transfer theory, constructs the transient state macro-temperature field model in welding process；
Step 3 is based on Interpolation Principle, and macroscopical field of welding temperature is changed into the macro of microcosmic temperature field needed for Microstructure evolution
Microcosmic coupling model；
Step 4, under the premise of obtaining microcosmic temperature field, building based on grain nucleation and growth establish dendrite under transient condition
Nucleation and growth mode；
Step 5, calculating and its visualization of result.
2. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method according to claim 1,
It is characterized in that, the welding pool curing condition for simplifying Cellular Automata Method in the step 1 includes:
Cellular is divided into liquid phase, solid phase and three kinds of interface state in simplified condition 1, entire process of setting；
Ignore kinetic undercooling in simplified condition 2, model；
Solid/liquid interfaces are in equilibrium state always in simplified condition 3, this model；
Simplified condition 4, cellular Domain relation use V.Neumann type neighborhood.
3. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method according to claim 1,
It is characterized in that, the step 2 is specifically implemented according to the following steps:
Simulated domain is divided into equal-sized square cellular, distribution of the temperature field on time and space can indicate
Are as follows:
T=T (x, y, z, t)
The governing equation of nonlinear transient heat conduction problem are as follows:
In formula: ρ is density of material；C is material specific heat capacity；T is thermo parameters method function；λ is thermal coefficient；It is strong for inner heat source
Degree；T is heat transfer time；
Transient heat conduct equation solve using centered finite difference methods:
In formula:For the temperature value of the position t moment (i, j, k) cellular, subscript indicates moment, the position that subscript indicates；Δ x is
Cellular size；Δ t is time step；
Since cellular has internal and two kinds of surface distributing position, so deriving the cellular evolution rule of different location:
A, the evolution rule of internal cellular
B, the evolution rule of surface cellular
In formula: H is the convection transfer rate of weldment and air；Ai,j,kFor the contact area of center unit and air；T0For environment
Temperature；
After the temperature field evolution rule of cellular is set, needs to be arranged moving heat source to simulate the movement of actual welding heat source, adopt
Practical heat source is simulated with Gauss heat source, the mathematic(al) representation of Gauss heat source model is as follows:
In formula: qmFor the maximum heat flow density at source center；R is the distance apart from electric arc heated spot；rhIt is effectively hot for electric arc
Source radius；
Macro temperature field model construction is welded to complete.
4. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method according to claim 1,
It is characterized in that, the step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value for extracting macroscopical grid temperature field: a suitable computer capacity is chosen, is extracted on finite element node
Temperature-time data；
Step 3.2, m- macro temperature field curve when being fitted to extracted data: by the Temperature-time number of macro temperature field
According to being fitted to Temperature-time functional form；
Step 3.3 obtains microcosmic temperature field using interpolation method: using bilinear interpolation to macro temperature field interpolation, being applicable in
In the microcosmic temperature field that microstructure calculates, specific mathematical expression is as follows:
In formula: Q11, Q12, Q21, Q22Represent the node of macro-scale grid；P is the grid node of micro-scale；T(Qij) and T (P)
Respectively indicate the corresponding temperature value of macro micro-scale node；
The building of field of welding temperature Macro-Micro-Coupled Model is completed.
5. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method according to claim 1,
It is characterized in that, the step 4 is specifically implemented according to the following steps:
The foundation of step 4.1, Nucleation Model
Using the forming core function based on Gaussian Profile, grain density n (Δ T) such as following formula institute is formed by under a certain degree of supercooling
Show:
And dn/d (Δ T) expression formula is as follows:
In formula: nmaxFor the maximum value of heterogeneous nucleation density；ΔTαFor standard curvature degree of supercooling；ΔTmaxFor the supercooling of maximum forming core
Degree；
The foundation of step 4.2, growth model
It after nucleus is formed, needs under certain degree of supercooling, could continue to grow up to form crystal grain, Δ T is subcooled by heat in degree of supercoolingt, at
Divide supercooling Δ TcΔ T is subcooled with curvaturetIt constitutes:
Δ T=Δ Tt+ΔTc+ΔTr
tnThe equilibrium relation of moment solid/liquid interfaces are as follows:
In formula: TlWith T (tn) be alloy liquidus temperature and tnThe transient temperature at moment, mlFor liquidous slopes, CL0And Cl
(tn) be respectively alloy initial solute concentration and tnThe solute concentration at moment, Γ (θ) are Gibbs-Thompson coefficient,For
Interface average curvature；
The propulsion of solid liquid interface, along with the variation of cellular unit solid rate, the growth of solid rate is directly proportional to interface speed,
It can be expressed from the next:
In formula: Δ x is size of mesh opening；Δ t is the step-length time；G is ortho position trellis state parameter；A is Discontinuous Factors；Rand () energy
It is enough to generate a random number in [0,1]；
In formula: b is constant empirical parameter；Sm ' and sm " is respectively the state parameter of four closest cellulars, if adjacent
Cellular is that solid phase, sm ' and sm " value are 1, when adjacent cellular is liquid phase or interface, value 0；Interface cellular is being changed into solid phase
Before cellular, solid rate is continuously increased, in time t, the solid rate of a certain interface cellular are as follows:
In formula: N is the number of iterations；Δ t is time step.
6. a kind of welding pool Microstructural Evolution analogy method based on Cellular Automata Method according to claim 1,
It is characterized in that, the step 5 is specifically implemented according to the following steps:
Step 5.1: by based on step 1~3 constructed by the forming core of dendrite under transient condition established based on grain nucleation and growth
It is imported in simulation softward Matlab with growth model；
Step 5.2: input alloy thermal physical property parameter and various welding conditions, be calculated based on grain nucleation
The analog result of the nucleation and growth mode of dendrite under transient condition is established with growth.
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