CN113139254B - Method for describing columnar crystal morphology in 6xxx series aluminum alloy melting welding pool - Google Patents

Method for describing columnar crystal morphology in 6xxx series aluminum alloy melting welding pool Download PDF

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CN113139254B
CN113139254B CN202110527948.2A CN202110527948A CN113139254B CN 113139254 B CN113139254 B CN 113139254B CN 202110527948 A CN202110527948 A CN 202110527948A CN 113139254 B CN113139254 B CN 113139254B
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张庆宇
陈宇
王晓南
沈鑫珺
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Abstract

The invention discloses a method for describing the morphology of columnar crystals in a 6xxx series aluminum alloy fusion welding molten pool, which comprises the steps of establishing and initializing a CA-FD model of the 6xxx series aluminum alloy, and setting a solid phase region in a calculation region of the CA-FD model to simulate the morphology of the molten pool; calculating the evolution process of the temperature field along with the time t by an analytic method along with the accumulation of the time t, storing temperature data, calculating solid phase fraction increment by a solid phase fraction increment formula in a CA-FD model, storing solid phase position data, calculating redistribution of a concentration field and a solute by a solute diffusion equation in the CA-FD model, storing concentration data and outputting the stored data; and repeating the output until the iteration termination condition is reached to obtain the columnar crystal morphology of the 6xxx series aluminum alloy in the welding pool. According to the invention, the dendritic crystal growth phenomenon during welding and solidification of the 6xxx series aluminum alloy is reproduced by the CA-FD and the analytic method, the efficiency is high, the application range is wide, and a basis is provided for optimizing the welding process.

Description

Method for describing columnar crystal morphology in 6xxx series aluminum alloy melting welding pool
Technical Field
The invention relates to the technical field of fusion welding analysis of 6xxx series aluminum alloy, in particular to a method for describing the morphology of columnar crystals in a fusion welding pool of 6xxx series aluminum alloy.
Background
The 6xxx series aluminum alloy (the components are Al, mg and Si, al is a solvent, and solute elements of Mg and Si are added into liquid Al to be solidified into the 6xxx series aluminum alloy) is widely applied to the fields of transportation, buildings and the like at present due to the good comprehensive performance of the 6xxx series aluminum alloy. In the production of 6xxx series aluminum alloys, fusion welding is one of the primary means of joining. In the fusion welding process, the 6xxx series aluminum alloy welding joint can generate solid-liquid-solid complex phase change, wherein the solidification process from liquid phase to solid phase can influence the microstructure appearance, and further influences the mechanical property of the welding joint.
Therefore, the solidification process of the liquid phase to the solid phase is an important part in the fusion welding process. However, the prior art does not study the evolution process of the solidification structure of the 6xxx series aluminum alloy, moreover, the process is difficult to observe in real time in the process of fusion welding or experiment, and a scientific basis cannot be provided for optimizing the welding process.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the defects in the prior art, and provide a method for describing the appearance of columnar crystals in a 6xxx series aluminum alloy melting welding pool, wherein the phenomenon of dendritic crystal growth in the welding and solidification process of the 6xxx series aluminum alloy is reproduced by a numerical simulation method of a computer, and a scientific basis is provided for optimizing a welding process.
In order to solve the technical problem, the invention provides a method for describing the morphology of columnar crystals in a 6xxx series aluminum alloy fusion welding pool, which comprises the following steps:
step 1: establishing a CA-FD model of the 6xxx series aluminum alloy by adopting a coupled cellular automaton-finite difference method, initializing model parameters, and setting a solid phase region simulation molten pool morphology in a calculation region of the CA-FD model;
step 2: the temperature of the temperature field is reduced along with the accumulation of the time t, the evolution process of the temperature field along with the time t is calculated through an analytical method, and temperature data are stored;
and step 3: the method comprises the following steps of (1) growing the columnar dendritic crystal along with the accumulation of time t, calculating solid phase fraction increment through thermodynamic data and a solid phase fraction increment formula in a CA-FD model, marking the position of the columnar dendritic crystal and storing solid phase position data;
and 4, step 4: along with the accumulation of time t, the solute in the solid phase is discharged to a solid-liquid interface, the solute is uniformly distributed into the liquid phase, a concentration field and solute redistribution are calculated through a solute diffusion equation in a CA-FD model, concentration data are stored, and the temperature data, the solid phase position data and the concentration data are output;
and 5: and (5) repeating the step (2) to the step (4) until a preset iteration end condition is reached and the calculation is terminated to obtain the columnar crystal morphology of the 6xxx series aluminum alloy in the welding pool.
Further, the method for calculating the temperature field in the step 2 comprises the following steps:
Figure GDA0003953078030000021
wherein T is the temperature of the simulation zone, T 0 Is the initial temperature, q is the effective thermal power, lambda is the thermal conductivity, v is the welding speed, a is the thermal conductivity coefficient,
Figure GDA0003953078030000022
the distance between the current point and the center of the heat source is shown, and x, y and z are the relative positions of the current point and the center of the heat source.
Further, the increase of solid phase fraction Δ f in said step 3 α The calculation formula of (c) is:
Figure GDA0003953078030000023
wherein Δ f α For solid phase fraction increase of single interfacial cells,. DELTA.x is cell size, G is shape adjustment factor related to adjacent cell state, Δ t is a time step, V α Is the dendrite growth rate.
Further, the shape adjustment factor G related to the state of the neighboring cells is calculated by:
Figure GDA0003953078030000031
wherein S Ⅰ And S Ⅱ The state parameters of 4 grids of nearest neighbor and 4 grids of next neighbor in the calculation area are respectively calculated, and m is the mark of the neighbor grid.
Further, the dendrite growth velocity V α The calculation formula of (2) is as follows:
Figure GDA0003953078030000032
wherein
Figure GDA0003953078030000033
Is the mean interfacial kinetic coefficient, δ α Is powerThe degree of the chemical anisotropy is determined by the degree of the chemical anisotropy,
Figure GDA0003953078030000034
at a growth angle of theta α,0 Δ T being the preferred growth direction α Is the local supercooling degree.
Further, the local supercooling degree Δ T α The calculation method of (A) is as follows:
Figure GDA0003953078030000035
wherein
Figure GDA0003953078030000036
To balance the liquidus temperature, T * Is the local actual temperature of the interface,
Figure GDA0003953078030000037
for the average Gibbs-Thomson coefficient, K is the average curvature,
Figure GDA0003953078030000038
is a surface anisotropy function;
the curvature K is calculated as:
Figure GDA0003953078030000039
wherein
Figure GDA00039530780300000310
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure GDA00039530780300000311
is the partial derivative of the solid phase fraction in the direction of the simulation coordinate axis x;
anisotropy of a film
Figure GDA00039530780300000312
The calculation method is as follows:
Figure GDA00039530780300000313
whereinε is the degree of surface anisotropy.
Further, the growth angle
Figure GDA0003953078030000041
The calculation method is as follows:
Figure GDA0003953078030000042
wherein
Figure GDA0003953078030000043
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure GDA0003953078030000044
is the partial derivative of the solid phase fraction in the direction of the simulation coordinate axis x.
Further, the solute diffusion equation in the CA-FD model in step 4 is:
Figure GDA0003953078030000045
wherein X represents Mg or Si solute, k represents alpha phase or l liquid phase, C k (X) represents the solute concentration, D k (X) represents a diffusion coefficient, R k (X) is the distribution source term of Si and Mg solutes at the liquid-solid interface in one time step, t is the actual solidification time,
Figure GDA0003953078030000046
is the laplacian operator.
Further, the distribution source terms R of Si and Mg solutes at the liquid-solid interface within one time step k The calculation mode (X) is as follows:
Figure GDA0003953078030000047
wherein
Figure GDA0003953078030000048
Is the local actual liquid phase concentration of the Si or Mg solute at the liquid-solid interface,
Figure GDA0003953078030000049
is the local concentration of Si or Mg solute in the alpha phase, Δ f α As an increase in solid fraction.
Further, the iteration ending condition preset in the step 5 is specifically that the solid fraction of the 6xxx series aluminum alloy is greater than 85% or the sum of the elapsed time steps is greater than a preset total time step.
Compared with the prior art, the technical scheme of the invention has the following advantages:
(1) Simulating the evolution of columnar crystal morphology and the diffusion process of solute by adopting a coupled cellular automaton-finite difference method, and performing simulation calculation on columnar crystals in a 6xxx series aluminum alloy melting and welding pool; and the temperature field in the welding molten pool is calculated by adopting an analytic method, and the CA-FD model is combined with the analytic method temperature field, so that the calculation efficiency is high.
(2) The temperature field in the welding molten pool is calculated by adopting an analytical method, the evolution rule of the columnar crystal morphology in the welding molten pool is simulated by combining thermodynamic data, the columnar crystal morphology at different molten pool positions and under different welding parameters can be described, and the application range is wide.
(3) The dendritic crystal growth phenomenon in the welding and solidification process of the 6xxx series aluminum alloy can be reproduced, the microstructure evolution process is observed in real time, and the possible microscopic defects are predicted by analyzing the simulated microstructure morphology and the solute concentration distribution, so that theoretical guidance is provided for the actual welding process.
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In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.
FIG. 1 is a flow chart of the calculation of the evolution process of the morphology of columnar crystals in a CA-FD model simulation molten pool in the invention.
FIG. 2 is a schematic diagram of the temperature field of the entire weld pool of the cross section of the weld joint under the temperature field of the analytic method of the CA-FD model simulation in the embodiment of the invention.
FIG. 3 is a graph showing the simulation result of the columnar crystal morphology at the dotted line box I in FIG. 2 when the calculation area is set to 200 × 600, each grid is 0.5 μm, the welding speed is 0.01m/s, and the welding power is 2627w when the columnar crystal morphology at different weld positions is simulated in the embodiment of the present invention.
Fig. 4 is a simulation result diagram of the columnar crystal morphology at the dashed box ii in fig. 2 when the calculation region 600 × 200 is set, each grid is 0.5 μm, the welding speed is 0.01m/s, and the welding power is 2627w when the columnar crystal morphology at different weld positions is simulated in the embodiment of the present invention.
FIG. 5 is a graph showing the simulation result of the columnar crystal morphology at the dotted line box I in FIG. 2 when the welding speed is set to 0.005m/s, the area is calculated to be 200 × 600, and the welding power is 2627w for each lattice when the columnar crystal morphology and the concentration field distribution under different welding parameters are simulated in the embodiment of the present invention.
Fig. 6 is a graph showing simulation results of the columnar crystal morphology at the dashed box ii in fig. 2 when the welding speed is set to 0.005m/s, the area is calculated to be 600 × 200, each lattice is 0.5 μm, and the welding power is 2627w when the columnar crystal morphology and the concentration field distribution under different welding parameters are simulated in the embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the drawings and the embodiments so that those skilled in the art can better understand the present invention and can carry out the present invention, but the embodiments are not to be construed as limiting the present invention.
In the description of the present invention, it should be understood that the term "comprises/comprising" is intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to the listed steps or elements but may alternatively include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to the flowchart of fig. 1, an embodiment of a method of describing columnar grain morphology in a molten weld pool of a 6xxx series aluminum alloy in accordance with the present invention includes the steps of:
step 1: a CA-FD model of the 6xxx series aluminum alloy is established by adopting a coupled cellular automation-finite difference (CA-FD) method, and model parameters are initialized, wherein the model parameters comprise grid size, calculation area size, temperature field, concentration field, dendritic crystal growth preferred orientation and the like. And setting a solid phase region to simulate the appearance of a molten pool in a calculation region of the CA-FD model.
And 2, step: and (3) the temperature of the temperature field is reduced along with the accumulation of the time t, the evolution process of the temperature field along with the time t is calculated by an analytical method, and the temperature data is stored.
The calculation method of the temperature field comprises the following steps:
Figure GDA0003953078030000061
wherein T is the temperature of the simulation zone, T 0 Is the initial temperature, q is the effective thermal power, lambda is the thermal conductivity, v is the welding speed, a is the thermal conductivity coefficient,
Figure GDA0003953078030000062
the distance between the current point and the center of the heat source is shown, and x, y and z are the relative positions of the current point and the center of the heat source.
And 3, step 3: and (3) growing the columnar dendrite along with the accumulation of the time t, calculating solid phase fraction increment through thermodynamic data and a solid phase fraction increment formula in a CA-FD model, marking the position of the columnar dendrite and storing solid phase position data.
Solid phase fraction increase Δ f in CA-FD model α The calculation formula of (2) is as follows:
Figure GDA0003953078030000071
wherein Δ f α For solid phase fraction increase of single interfacial cells,. DELTA.x is cell size, G is shape adjustment factor related to adjacent cell state, Δ t is a time step, V α Is the dendrite growth rate.
The calculation formula of the shape adjustment factor G related to the states of the adjacent cells is as follows:
Figure GDA0003953078030000072
wherein S Ⅰ And S Ⅱ The state parameters of 4 grids of nearest neighbor and 4 grids of next neighbor in the calculation area are respectively calculated, and m is the mark of the neighbor grid. The growth velocity V of the dendrite α The calculation formula of (2) is as follows:
Figure GDA0003953078030000073
wherein
Figure GDA0003953078030000074
Is the mean interfacial kinetic coefficient, δ α Is the degree of the dynamic anisotropy, and,
Figure GDA0003953078030000075
at a growth angle of theta α,0 Δ T as a preferred growth direction α Is the local supercooling degree.
The local supercooling degree DeltaT α The calculation method of (A) is as follows:
Figure GDA0003953078030000076
wherein
Figure GDA0003953078030000077
In order to balance the liquidus temperature of the liquid,
Figure GDA0003953078030000078
obtained by calculation of thermodynamic data according to the local liquid phase composition, T * Is the local actual temperature of the interface,
Figure GDA0003953078030000079
for the average Gibbs-Thomson coefficient, K is the average curvature,
Figure GDA00039530780300000710
is a function of the surface anisotropy. The temperature field in the welding molten pool is calculated by adopting an analytical method, the evolution rule of the columnar crystal morphology in the welding molten pool is simulated by combining thermodynamic data, the columnar crystal morphology at different molten pool positions and under different welding parameters can be described, and the application range is wide; heating powerChemical data were obtained by PanEngine, each alloy having its own thermodynamic data.
The curvature K is calculated as:
Figure GDA00039530780300000711
wherein
Figure GDA00039530780300000712
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure GDA00039530780300000713
is the partial derivative of the solid phase fraction in the direction of the simulation coordinate axis x. Anisotropy of a film
Figure GDA00039530780300000714
The calculation method of (A) is as follows:
Figure GDA00039530780300000715
where epsilon is the degree of surface anisotropy.
The growth angle
Figure GDA0003953078030000081
The calculation method is as follows:
Figure GDA0003953078030000082
wherein
Figure GDA0003953078030000083
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure GDA0003953078030000084
is the partial derivative of the solid phase fraction in the x direction of the simulation coordinate axis.
And 4, step 4: and (3) discharging the solute in the solid phase to a solid-liquid interface along with the accumulation of the time t, uniformly distributing the solute into the liquid phase, calculating a concentration field and solute redistribution through a solute diffusion equation in a CA-FD model, storing concentration data, and outputting the temperature data, the solid phase position data and the concentration data.
The solute diffusion equation in the CA-FD model is:
Figure GDA0003953078030000085
wherein X represents Mg or Si solute, k represents alpha phase or l liquid phase, C k (X) represents the solute concentration, D k (X) represents a diffusion coefficient, R k (X) is the distribution source term of Si and Mg solutes at the liquid-solid interface in one time step, t is the actual solidification time,
Figure GDA0003953078030000086
is the laplacian operator.
Distribution source term R of Si and Mg solutes at the liquid-solid interface within a time step k The calculation method of (X) is as follows:
Figure GDA0003953078030000087
wherein
Figure GDA0003953078030000088
Is the local actual liquid phase concentration of the Si or Mg solute at the liquid-solid interface,
Figure GDA0003953078030000089
is the local concentration of Si or Mg solute in the alpha phase, Δ f α As an increase in solid fraction.
And 5: and (4) repeating the steps 2 to 4 within a preset total time, and terminating the calculation until the solid fraction of the 6xxx series aluminum alloy is more than 85 percent or the sum of the elapsed time steps is more than the preset total time step to obtain the columnar crystal morphology of the 6xxx series aluminum alloy in the welding pool. The total time step is large, and the purpose of setting the total time step is to ensure that the dendrite has enough time to grow; setting a finishing judgment condition to stop the simulation program after enough dendrites are obtained; the simulation program will stop regardless of whether the total time step is exceeded or the solid fraction exceeds 85%.
To further illustrate the beneficial effects of the present invention, the welding process of the 6xxx series aluminum alloy (Al-Mg-Si) was simulated in this example under the established CA-FD model. FIG. 2 is a schematic diagram of the whole weld pool temperature field under the analytic method temperature field of CA-FD model simulation. The dotted boxes i, ii in fig. 2 are simulated areas. And respectively simulating the columnar crystal morphology and the concentration field distribution of the region I and the region II under different welding parameters.
When the columnar crystal shapes at different welding seam positions are simulated, and the calculation area is set to be 200 multiplied by 600, each grid is 0.5 micrometer, the welding speed is 0.01m/s, the welding power is 2627w, and the simulation position is a dotted line frame I at the bottom position of the welding seam center in fig. 2. The calculation results are shown in fig. 3, in which (a) in fig. 3 is a graph showing the evolution of the columnar morphology and the distribution of the Mg concentration at a solid phase fraction of 0.2 and a time t =0.053s, (b) in fig. 3 is a graph showing the evolution of the columnar morphology and the distribution of the Mg concentration at a solid phase fraction of 0.4 and a time t =0.069s, and (c) in fig. 3 is a graph showing the evolution of the columnar morphology and the distribution of the Mg concentration at a solid phase fraction of 0.5 and a time t =0.076 s. Fig. 3 (d) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.2 and a time t =0.053s, fig. 3 (e) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.4 and a time t =0.069s, and fig. 3 (f) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.5 and a time t =0.076 s. It can be seen from fig. 3 that there is a secondary dendrite arm generation. Because Mg and Si solutes are discharged in the process of dendritic crystal solidification, the Mg and Si concentrations around the dendritic crystal are higher than those at positions far away from the dendritic crystal. The color in the figure clearly shows that the position with the highest Mg and Si concentration is the root of the columnar crystal, and the concentration is gradually reduced from the root to the tip. The dendrites continually grow and draw out solute resulting in solute accumulation with a higher concentration at the root than at the tip. The initial content of Si is higher than the initial content of Mg, resulting in a higher Si concentration than Mg concentration at the same location.
When the columnar crystal morphology at different welding seam positions is simulated, when a calculation area is set to be 600 multiplied by 200, each grid is 0.5 micrometer, the welding speed is 0.01m/s, the welding power is 2627w, and the simulation position is a dotted line frame II at the leftmost molten pool position of the cross section of the welding seam in the graph 2. The columnar crystal morphology of the weld pool at the weld surface is shown in fig. 4, (a) in fig. 4 is a schematic diagram of the columnar crystal morphology evolution and the Mg concentration distribution at a solid fraction of 0.2 and a time t =0.055s, (b) in fig. 4 is a schematic diagram of the columnar crystal morphology evolution and the Mg concentration distribution at a solid fraction of 0.4 and a time t =0.073s, and (c) in fig. 4 is a schematic diagram of the columnar crystal morphology evolution and the Mg concentration distribution at a solid fraction of 0.5 and a time t =0.081 s. Fig. 4 (d) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.2 and a time t =0.055s, fig. 3 (e) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.4 and a time t =0.073s, and fig. 3 (f) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.5 and a time t =0.081 s. It can be seen from fig. 4 that there is a secondary dendrite wall created and that there are significantly more secondary dendrite arms than in fig. 3 because the location of fig. 4 is further from the heat source than in fig. 3, and the secondary dendrite arms are more easily created because they cool faster. The distribution of Mg and Si concentration in FIG. 4 is similar to that in FIG. 3.
When the columnar crystal morphology and the concentration field distribution under different welding parameters are simulated, the welding speed is set to be 0.005m/s, and when the area is calculated to be 200 multiplied by 600, each grid is 0.5 micron, and the welding power is 2627w. The simulation result of the histogram at the dotted line box i in fig. 2 is shown in fig. 5, (a) in fig. 5 is a graph showing the evolution of the histogram and the Mg concentration distribution at a solid fraction of 0.2 and a time t =0.130s, (b) in fig. 5 is a graph showing the evolution of the histogram and the Mg concentration distribution at a solid fraction of 0.4 and a time t =0.174s, and (c) in fig. 5 is a graph showing the evolution of the histogram and the Mg concentration distribution at a solid fraction of 0.5 and a time t =0.189 s. Fig. 5 (d) is a graph showing the evolution of the columnar crystal morphology and the Si concentration distribution at a solid phase fraction of 0.2 and a time t =0.130s, fig. 5 (e) is a graph showing the evolution of the columnar crystal morphology and the Si concentration distribution at a solid phase fraction of 0.4 and a time t =0.174s, and fig. 5 (f) is a graph showing the evolution of the columnar crystal morphology and the Si concentration distribution at a solid phase fraction of 0.5 and a time t =0.189 s.
The welding speed was set to 0.005m/s, and the welding power 2627w was calculated for the region 600 × 200, 0.5 μm per cell. The simulation result of the columnar crystal morphology at the dotted line box ii in fig. 2 is shown in fig. 6, (a) in fig. 6 is a graph showing the columnar crystal morphology evolution and the Mg concentration distribution at the solid phase fraction of 0.2 and the time t =0.122s, (b) in fig. 6 is a graph showing the columnar crystal morphology evolution and the Mg concentration distribution at the solid phase fraction of 0.4 and the time t =0.159s, and (c) in fig. 6 is a graph showing the columnar crystal morphology evolution and the Mg concentration distribution at the solid phase fraction of 0.5 and the time t =0.173 s. Fig. 6 (d) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.2 and a time t =0.122s, fig. 6 (e) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.4 and a time t =0.159s, and fig. 6 (f) is a graph showing the evolution of the columnar morphology and the Si concentration distribution at a solid phase fraction of 0.5 and a time t =0.173 s.
It can be seen from fig. 5 and 6 that the initialization directions of the columnar crystals are not consistent, and a strong competitive growth phenomenon exists; the reduction of the welding speed results in the reduction of the cooling rate and the increase of the average dendrite spacing (5 columnar crystals exist at the welding speed of 0.01m/s and 4 columnar crystals exist at the welding speed of 0.005 m/s), thereby influencing the final microstructure morphology. The simulation results are in line with reality. In fig. 3 to 6, wt.% is represented by mass fraction, and the vertical direction is a simulation region i, and the horizontal direction is a simulation region ii, which are located at different bath positions.
Compared with the prior art, the technical scheme of the invention has the following advantages: (1) Simulating the evolution of columnar crystal morphology and the diffusion process of solute by adopting a coupled cellular automaton-finite difference method, and performing simulation calculation on columnar crystals in a 6xxx series aluminum alloy melting and welding pool; and the temperature field in the welding molten pool is calculated by adopting an analytic method, and the CA-FD model is combined with the analytic method temperature field, so that the calculation efficiency is high. (2) The temperature field in the welding molten pool is calculated by adopting an analytical method, the evolution rule of the columnar crystal morphology in the welding molten pool is simulated by combining thermodynamic data, the columnar crystal morphology at different molten pool positions and under different welding parameters can be described, and the application range is wide. (3) The dendritic crystal growth phenomenon in the welding and solidification process of the 6xxx series aluminum alloy can be reproduced, the microstructure evolution process is observed in real time, and the possible microscopic defects are predicted by analyzing the simulated microstructure morphology and the solute concentration distribution, so that theoretical guidance is provided for the actual welding process.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.

Claims (2)

1. A method for describing columnar crystal morphology in a 6xxx series aluminum alloy fusion welding pool is characterized by comprising the following steps:
step 1: establishing a CA-FD model of the 6xxx series aluminum alloy by adopting a coupled cellular automaton-finite difference method, initializing model parameters, and setting a solid phase region simulation molten pool morphology in a calculation region of the CA-FD model;
and 2, step: the temperature of the temperature field is reduced along with the accumulation of the time t, the evolution process of the temperature field along with the time t is calculated through an analytical method, and temperature data are stored;
the calculation method of the temperature field comprises the following steps:
Figure FDA0003953078020000011
where T is the temperature of the simulated region, T 0 Is the initial temperature, q is the effective thermal power, lambda is the thermal conductivity, v is the welding speed, a is the thermal conductivity coefficient,
Figure FDA0003953078020000012
the distance between the current point and the center of the heat source is shown, and x, y and z are the relative positions of the current point and the center of the heat source;
and 3, step 3: the method comprises the following steps of (1) growing the columnar dendritic crystal along with the accumulation of time t, calculating solid phase fraction increment through thermodynamic data and a solid phase fraction increment formula in a CA-FD model, marking the position of the columnar dendritic crystal and storing solid phase position data;
increase in solid phase fraction Δ f α The calculation formula of (c) is:
Figure FDA0003953078020000013
wherein Δ f α For solid phase fraction increase of single interfacial cells,. DELTA.x is cell size, G is shape adjustment factor related to adjacent cell state, Δ t is a time step, V α The growth speed of the dendrite;
the calculation formula of the shape adjustment factor G related to the states of the adjacent cells is as follows:
Figure FDA0003953078020000021
wherein S Ⅰ And S Ⅱ Respectively calculating state parameters of 4 nearest neighbor grids and 4 next nearest neighbor grids in the area, wherein m is a mark of the nearest neighbor grids;
the growth velocity V of the dendrite α The calculation formula of (2) is as follows:
Figure FDA0003953078020000022
wherein
Figure FDA0003953078020000023
Is the mean interfacial kinetic coefficient, δ α Is the degree of the dynamic anisotropy, and,
Figure FDA00039530780200000214
at a growth angle of theta α,0 Δ T as a preferred growth direction α Local supercooling degree;
the local supercooling degree Delta T α The calculation method is as follows:
Figure FDA0003953078020000024
wherein
Figure FDA0003953078020000025
To balance the liquidus temperature, T * Is the local actual temperature of the interface,
Figure FDA0003953078020000026
for the average Gibbs-Thomson coefficient, K is the average curvature,
Figure FDA0003953078020000027
is a surface anisotropy function;
the curvature K is calculated as:
Figure FDA0003953078020000028
wherein
Figure FDA0003953078020000029
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure FDA00039530780200000210
is the partial derivative of the solid phase fraction in the x direction of the simulation coordinate axis;
anisotropy of property
Figure FDA00039530780200000211
The calculation method is as follows:
Figure FDA00039530780200000212
wherein ε is the degree of surface anisotropy;
the growth angle
Figure FDA00039530780200000213
The calculation method is as follows:
Figure FDA0003953078020000031
wherein
Figure FDA0003953078020000032
Is the partial derivative of the solid phase fraction in the y direction of the simulation coordinate axis,
Figure FDA0003953078020000033
is the partial derivative of the solid phase fraction in the direction of the simulation coordinate axis x;
and 4, step 4: along with the accumulation of time t, the solute in the solid phase is discharged to a solid-liquid interface, the solute is uniformly distributed into the liquid phase, a concentration field and solute redistribution are calculated through a solute diffusion equation in a CA-FD model, concentration data are stored, and the temperature data, the solid phase position data and the concentration data are output;
the solute diffusion equation in the CA-FD model is:
Figure FDA0003953078020000034
wherein X represents Mg or Si solute, k represents alpha phase or l liquid phase, C k (X) represents the solute concentration, D k (X) represents a diffusion coefficient, R k (X) is the distribution source term of Si and Mg solutes at the liquid-solid interface within one time step, t is the actual solidification time,
Figure FDA0003953078020000035
is Laplace operator;
distribution source term R of Si and Mg solutes at the liquid-solid interface within a time step k The calculation method (X) is as follows:
Figure FDA0003953078020000036
wherein
Figure FDA0003953078020000037
Is the local actual liquid phase concentration of the Si or Mg solute at the liquid-solid interface,
Figure FDA0003953078020000038
is the local concentration of Si or Mg solute in the alpha phase, Δ f α As solid fraction increase;
and 5: and (5) repeating the step (2) to the step (4) until a preset iteration end condition is reached and the calculation is terminated to obtain the columnar crystal morphology of the 6xxx series aluminum alloy in the welding pool.
2. The method of describing columnar grain morphology in a 6xxx series aluminum alloy fusion weld pool, as set forth in claim 1, wherein: the iteration end condition preset in the step 5 is specifically that the solid fraction of the 6xxx series aluminum alloy is greater than 85% or the sum of the elapsed time steps is greater than a preset total time step.
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