CN110263418B - Body-centered cubic alloy microsegregation numerical prediction method - Google Patents

Body-centered cubic alloy microsegregation numerical prediction method Download PDF

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CN110263418B
CN110263418B CN201910522224.1A CN201910522224A CN110263418B CN 110263418 B CN110263418 B CN 110263418B CN 201910522224 A CN201910522224 A CN 201910522224A CN 110263418 B CN110263418 B CN 110263418B
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刘东戎
浦震鹏
赵红晨
赵思聪
郭二军
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Harbin University of Science and Technology
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Abstract

The invention discloses a body-centered cubic alloy microsegregation numerical prediction method, and relates to a body-centered cubic alloy microsegregation numerical prediction method. The invention aims to solve the problem that the prior method cannot accurately predict the formation of the microsegregation of the body-centered cubic alloy. The process is as follows: 1. carrying out micro-scale mesh generation; 2. the square grids and the surrounding 3 grids form a group; 3. finishing the growth of the dendrite; 4. determining a state of a grid; 5. determining a kinetic coefficient; 6. further dividing the calculation domain into 4 local calculation domains; 7. calculating a kernel in a local computation domain; 8. randomly selecting a certain group of paired grids in a local computing domain, and judging whether the group generates a nucleation phenomenon; 9. the mother core grid captures 4 groups of neighbor pairing grids around; 10. calculating parameters; 11. calculating a solute diffusion equation: 12. seventy to eleven times are repeated, and solute component distribution data files are output; the heat treatment time was estimated. The method is used for the field of body-centered cubic alloy microsegregation numerical prediction.

Description

Body-centered cubic alloy microsegregation numerical prediction method
Technical Field
The invention relates to a body centered cubic alloy microsegregation numerical prediction method.
Background
The energy consumption is very high in the casting production process, and the emission of waste residue and dust causes pollution to the environment. The improvement of the casting yield needs to start from the research of the casting defect forming mechanism. Segregation refers to a phenomenon that the internal components of a casting are not uniform after the casting is solidified and is divided into macroscale segregation, namely macrosegregation, and microscale segregation, namely microscale segregation. Macrosegregation, if not present in the riser or on the surface of the casting, can lead to direct scrap of the casting. The microsegregation is the origin of the thermal cracks, and most researches show that the heat treatment process can effectively reduce the microsegregation, thereby reducing the possibility of the occurrence of the thermal cracks. The heat treatment time and the heat treatment temperature are important heat treatment process parameters, the heat treatment time is short, the temperature is low, the microsegregation cannot be reduced, the heat treatment time is long, the temperature is high, the microsegregation can be eliminated, but the excessive time and temperature can cause the coarsening of crystal grains, and the energy is wasted. Many heat treatment processes are developed according to the method of 'one furnace, multiple samples and stage observation', namely, a plurality of samples obtained under the same solidification condition are simultaneously put into a heat treatment furnace, a heat treatment temperature is set, the samples are taken out at different times, the metallographic structure of the samples is compared, and reasonable heat treatment time is obtained. The experimental method has certain blindness and uncertainty, and consumes a large amount of manpower, material resources and financial resources.
Compared with an experimental method, the numerical simulation adopts a numerical algorithm to solve a theoretical equation, and the solidification process is shown in real time by means of computational graphics, so that the method is beneficial to capturing micro segregation formation details and analyzing a formation mechanism. Therefore, the method adopts a numerical simulation means to analyze the micro segregation forming process so as to estimate the heat treatment process parameters, and has important significance for proposing the heat treatment process parameters, shortening the heat treatment period of the castings and increasing the finished product rate of the castings.
The micro segregation is not only formed on the dendrite precipitated first but also exists between dendrites and dendrite arms, and the segregation in this region is positive micro segregation. The primary purpose of the heat treatment is to mitigate the degree of positive microsegregation between dendrites and dendrite arms. At present, most of numerical prediction about microsegregation focuses on analytical solution by adopting a theoretical formula, the influence of dendrite morphology is neglected, and the randomness of a solidification process cannot be considered in a calculation result. Therefore, the calculation based on the dendrite morphology is required for predicting the microsegregation by adopting a numerical simulation method, and the microsegregation formation can be influenced by the cooling speed, the grain size and the interaction among different dendrites. Many cast alloys have a body centered cubic structure, such as cast aluminum, tin-lead, and the like. In the numerical calculation of the dendrite growth of the body-centered cubic alloy, a solid-liquid interface geometric factor is introduced by a cellular automaton method in order to reproduce growth anisotropy (the crystal grains grow in any direction after nucleation), the parameter lacks physical meaning, and the calculation result is sensitive to the selection of grid size. Meanwhile, when the cellular automata method is used for treating the growth of a solid-liquid interface, the determination method of the growth kinetic coefficient is not clear. The phase field method can better reproduce the dendritic crystal morphology, although the solid-liquid interface geometric factor is not required to be introduced, the method requires that the grid size is smaller than the thickness of the solid-liquid interface, the calculation time is long, and the calculation efficiency is not high. Meanwhile, the calculation domain only has one cooling speed and fixed nucleation parameters, and only one set of dendrite structure evolution information can be obtained by calculation once. If the calculation is carried out once, multiple groups of information about the dendritic structures can be obtained, and the establishment of the parameters of the subsequent heat treatment process is facilitated.
Disclosure of Invention
The invention aims to provide a body-centered cubic alloy microsegregation numerical prediction method for solving the problem that the existing method cannot accurately predict the formation of the microsegregation of the body-centered cubic alloy.
The method for predicting the microsegregation numerical value of the body-centered cubic alloy comprises the following specific processes:
step one, enabling a dendritic crystal growth calculation domain to be in a rectangular coordinate system, performing micro-scale mesh subdivision on the dendritic crystal growth calculation domain, and adopting square meshes with side length size delta len, wherein each square mesh is marked by (j, k);
j represents a coordinate along the X-axis direction of the rectangular coordinate system, k represents a coordinate along the Y-axis direction of the rectangular coordinate system, the value range of j is [1, n ], and the value range of k is [1, m ]; j and k are integers, and m and n are even numbers, so that the dendrite growth calculation domain has m multiplied by n grids;
step two, the square grid (j, k) and the surrounding 3 grids (j-1, k), (j, k-1) and (j-1, k-1) form a group, that is, the square grids (j, k), (j-1, k), (j, k-1) and (j-1, k-1) are mutually paired grids, the four grids are endowed with the same pairing identifier, and the pairing identifier is represented by pd, so pd (j, k) = pd (j-1, k) = pd (j, k-1) = pd (j-1, k-1) = j/2+ k/2+1;
pairing each grid in the dendrite growth calculation domain, then each grid pd (j, k) value will be greater than 1;
step three, endowing a neighbor object for each group of matching grids in the dendritic crystal growth calculation domain, and finishing dendritic crystal growth by capturing the neighbor object;
step four, determining the state of each square grid in the solidification process;
step five, determining the average dendritic crystal growth kinetic coefficient
Figure BDA0002097082220000021
Units are m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is given
Figure BDA0002097082220000022
Unit ℃/s, each grid in the local calculation domain has the same temperature;
when the solidification time is t, the temperature corresponding to the grid is
Figure BDA0002097082220000023
Wherein, T L Is the liquidus temperature of the alloy, and the unit is the temperature i belongs to [1,4 ]]4 different local calculation domains are shown, and different cooling speeds are adopted in the different local calculation domains;
Figure BDA0002097082220000024
the cooling rate is; t is time in units of s;
calculating nucleation in local calculation domains by adopting a Gaussian nucleation distribution formula, wherein different nucleation parameters are adopted in different local calculation domains;
Figure BDA0002097082220000031
Figure BDA0002097082220000032
wherein N is nｕclei Represents the nucleation density in units of 1/m 3 ；N max Represents the maximum nucleation density in units of 1/m 3 I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta T mean Represents the maximum nucleation supercooling in units of ℃; delta T σ Indicating standard deviation nucleation supercooling;
Figure BDA0002097082220000033
and
Figure BDA0002097082220000034
representing the nucleation density, N, at time t and at time t- Δ t, respectively nuclei Represents nucleation density, N at 0s nｕclei ＝0；
Figure BDA0002097082220000035
And
Figure BDA0002097082220000036
respectively representing the nucleation supercooling degree, delta T, at the time T and the time T-Delta T nuclei Indicating the degree of nucleation supercooling,. DELTA.T nuclei ＝T M +m l C l -T, Δ T at 0s nuclei ＝0；
T M The melting point of pure magnesium is measured in units of ℃; m is a unit of l Is the slope of the liquidus in deg.C/wt%; c l Is a liquid phase component; t is the grid temperature;
the relationship between the nucleation number Neg and the nucleation density at the time t is as follows:
Figure BDA0002097082220000037
wherein S is subarea For local calculation of the domain area, S subarea ＝Nucell[i]×Δlen×Δlen，Nucell[i]Calculating the number of square grids in the domain i for local part, wherein delta len is the side length of each square grid;
step eight, in the local calculation domain i, randomly selecting a certain group of paired grids, if the state =0 of each grid in the group and comparing two random numbers num1 and num2 of each grid, and if 1 grid exists, meeting the condition that num1 is more than or equal to num2, the group does not generate the nucleation phenomenon; if all grids satisfy num1< num2, the nucleation phenomenon occurs in the group, and the physical quantity corresponding to each grid in the group of grids changes as follows:
fraction of solid phase f s ＝1，C s ＝C o k par ，C l ＝0，C aver ＝C s f s +C l (1-f s )，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein, f s Is the solid phase fraction, the minimum value of 0 represents the liquid phase, and the maximum value of 1 represents the solid phase; c s Is a solid phase component; c l Is a liquid phase component; c o Is an alloy initial component; c aver The unit of the component is weight percent and is the average component; k is a radical of par The coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different grains, random [1, neg ], [ i ] ] indicates that a Random number is selected from 1 to Neg [ i ]; growth theta is the growth orientation angle of the core, and a value is randomly selected between 0 and 90 degrees; state is state;
step nine, the grid solidified by nucleation is called the mother core grid (j, k) moth Mother core grid (j, k) moth Capturing 4 surrounding neighbor pairing grids, if the state corresponding to each grid in a certain set of neighbor grids is equal to 0, capturing the grids, and capturing the grids (j, k) son Will change from liquid to growth state, i.e. state (j, k) son Change from 0 to 1, mesh (j, k) captured son With and mother core grid (j, k) moth The same icolor and growth theta values indicate that they belong to the same dendrite;
if a certain grid f s =1, but f of the mating mesh s <1, then the lattice will also remain in the growing state (state = 1) until f of the mating lattice s When =1, thisThe states of the four grids are changed into solid states at the same time;
step ten, at a certain time t, if the grid state (j, k) =1 and f s (j, k) =1, no computation is performed, and the search for state (j, k) =1 and f continues in the computation domain s (j, k) grid not equal to 1;
for state (j, k) =1 and f s Grid calculation solid-liquid interface curvature k of (j, k) ≠ 1 curve Normal angle of solid-liquid interface
Figure BDA0002097082220000046
Growth supercooling degree delta T and growth speed V tip A solid phase fraction fs, a liquid phase component C l And a solid phase component C s ；
Figure BDA0002097082220000041
Figure BDA0002097082220000042
Figure BDA0002097082220000043
Figure BDA0002097082220000044
Figure BDA0002097082220000045
Wherein, delta k The gamma is a Gibbs coefficient unit of C m;
when f is s <When 1, counting the number of grids with state =0 in the adjacent grids of the grid, namely the total number Nzero of grids with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids; to is directed atGrid (j, k), solute exclusion amount Δ C, liquid phase component C l And a solid phase component C s The calculation is as follows:
Figure BDA0002097082220000051
Figure BDA0002097082220000052
Figure BDA0002097082220000053
when f is s When =1, the liquid phase component C l And a solid phase component C s The calculation is as follows:
C l ＝0
Figure BDA0002097082220000054
wherein, delta t is a time step length, and t-delta t is the last moment; at 0s, C s ＝0，f s ＝0，C l ＝C o ；
The liquid phase composition of the grid with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids is increased
Figure BDA0002097082220000055
Step eleven, for state (j, k) =0 and state (j, k) =1 and f s (j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
Figure BDA0002097082220000056
wherein D is l Is the diffusion coefficient of solute element in liquid phase;
the solute diffusion equation in the solid phase is calculated for the grid of state (j, k) = 2:
Figure BDA0002097082220000057
wherein D is s Is the diffusion coefficient of solute element in solid phase; the unit of the diffusion coefficient is m 2 /s；
Step twelve, repeating the step seven to the step eleven until the temperature of all grids is less than the solidus temperature T s If so, stopping the calculation and outputting a solute component distribution data file;
based on the calculated microsegregation distribution, three points P1, P2 and P3 are selected in the calculation domain, and the components are respectively C 1 、C 2 And C 3 The distance between the point P1 and the point P2 is equal to the distance Len between the point P2 and the point P3; the heat treatment time was estimated using the following formula:
Figure BDA0002097082220000058
wherein, a-heat represents the state after heat treatment, and b-heat represents the state before heat treatment, namely the solidification is finished;
composition based on P2 point after given heat treatment
Figure BDA0002097082220000059
Estimating the heat treatment time t heat 。
The beneficial effects of the invention are as follows:
in the invention, the microstructure and the microsegregation of the micro dendrites are calculated at the same time, and the heat treatment time prediction depends on the microsegregation distribution obtained based on the microstructure calculation of the micro dendrites, so that the method is more practical. The calculation domain is divided into a plurality of local calculation domains, the morphology and component distribution information of a plurality of groups of dendritic crystal structures can be obtained through one-time calculation, and the calculation of the heat treatment time can be aimed at different cooling conditions, so that a plurality of groups of process parameters can be provided.
According to the invention, the numerical simulation is carried out on the micro segregation formation in the solidification process of the body-centered cubic alloy, the growth anisotropy of dendrites is reproduced based on the matched square grid group, the influence of the grid size on the calculation result is eliminated to a certain extent, and the calculation efficiency is improved; in the calculation domain, different nucleation rates and cooling speeds are adopted at different local positions, so that the purpose of obtaining different tissue evolution results through one-time calculation is achieved. And estimating the heat treatment time based on the calculation result, providing a plurality of reference data for the formulation of the heat treatment process, and shortening the process development period.
The method is suitable for predicting the formation of the microsegregation in the solidification process of the body-centered cubic alloy, and a reasonable heat treatment process can be formulated based on the microsegregation obtained by prediction. The method can predict the formation of microsegregation more quickly, provides theoretical support for development and improvement of a heat treatment process from multiple aspects, has huge market application potential, and has the output value of more than billions of yuan once being widely adopted. The method solves the problem that the formation of the microsegregation of the body-centered cubic alloy cannot be accurately predicted at present.
Drawings
FIG. 1 is a graph of a solid phase fraction and temperature change curve of an Al-7wt% Si alloy calculated based on the Charles formula in comparison with a solid phase fraction and temperature change curve obtained based on the cellular automata method, the abscissa being the solid phase fraction and the ordinate being the temperature;
FIG. 2a is a graph showing the results of an experiment on the solidification structure of an Al-7wt% Si alloy at a cooling rate of 5.0 ℃/s.
FIG. 2b is a graph of the result of the Al-7wt% Si alloy on the basis of the paired lattice algorithm at a cooling rate of 5.0 ℃/s, with a lattice size of Δ len =2 μm;
FIG. 3a is a graph of Al-7wt% Si alloy obtained by simulating the solidification structure based on a paired lattice algorithm at a lattice size of Δ len =2 μm at a cooling rate of 10.0 ℃/s;
FIG. 3b is a graph of Al-7wt% Si alloy obtained by simulating a solidification structure based on a solid-liquid interface geometry factor algorithm when the mesh size is Δ len =2 μm at a cooling rate of 10.0 ℃/s;
FIG. 4a is a graph of a solidification structure of an Al-7wt% Si alloy obtained by simulation of solidification at 1s based on a paired lattice algorithm, when the lattice size is Δ len =4 μm at a cooling rate of 10.0 ℃/s;
FIG. 4a1 is a graph of a solidification structure obtained by simulating solidification of an Al-7wt% Si alloy at 1s based on the solid-liquid interface geometry algorithm, when the mesh size is Δ len =4 μm at a cooling rate of 10.0 ℃/s;
FIG. 4b is a graph of a solidification structure of an Al-7wt% Si alloy obtained by simulation at 3s of solidification based on a paired lattice algorithm, when the lattice size is Δ len =4 μm at a cooling rate of 10.0 ℃/s;
FIG. 4b1 is a graph of a solidification structure obtained by simulating solidification of an Al-7wt% Si alloy at a cooling rate of 10.0 ℃/s and a mesh size of Δ len =4 μm for 3s based on a solid-liquid interface geometry factor algorithm;
FIG. 5a is a graph of Al-7wt% Si alloy obtained by simulating a microsegregation profile at 3s solidification based on a paired lattice algorithm, with a lattice size Δ len =4 μm at a cooling rate of 10.0 ℃/s;
FIG. 5b is a graph showing a microsegregation distribution of an Al-7wt% Si alloy obtained by simulation at 3s of solidification based on the solid-liquid interface geometry algorithm, when the mesh size is Δ len =4 μm at a cooling rate of 10.0 ℃/s;
FIG. 6 is a micro segregation distribution diagram obtained by dividing a calculation domain into 4 parts, and adopting parameters from local area 1 to local area 4 in Table 1, and after solidification is finished based on a paired grid algorithm.
Detailed Description
The first specific implementation way is as follows: the method for predicting the microsegregation numerical value of the body-centered cubic alloy comprises the following specific steps:
step one, a dendrite growth calculation domain is positioned in a rectangular coordinate system, the dendrite growth calculation domain (determined) is subjected to micro-scale grid subdivision, square grids with the side length size of delta len are adopted, and each square grid is marked by (j, k);
j represents a coordinate along the X-axis direction of the rectangular coordinate system, k represents a coordinate along the Y-axis direction of the rectangular coordinate system, the value range of j is [1, n ], and the value range of k is [1, m ]; j and k are integers, and m and n are even numbers, so that m multiplied by n grids are in total in a dendritic crystal growth calculation domain;
and step two, in order to overcome the influence of grid anisotropy on dendritic crystal growth calculation, pairing between square grids is required. The pairing between the meshes cannot be randomly selected as the coagulation progresses, and the pairing is completed before the coagulation starts, i.e. the paired meshes of the same group do not change as the coagulation progresses.
The square grid (j, k) and the surrounding 3 grids (j-1, k), (j, k-1) and (j-1, k-1) are in a group, that is, the square grids (j, k), (j-1, k), (j, k-1) and (j-1, k-1) are paired grids, the four grids are endowed with the same pairing identifier, and the pairing identifier is represented by pd, so pd (j, k) = pd (j-1, k) = pd (j, k-1) = pd (j-1, k-1) = j/2 k/2 decimal (the value can be decimal number, and can also be an integer);
pairing each grid in the dendrite growth calculation domain, then each grid pd (j, k) value will be greater than 1; the grids with the same pairing identification have the same state change at the same time although the growth speed is high or low;
step three, endowing a neighbor object for each group of matching grids in the dendritic crystal growth calculation domain, and finishing dendritic crystal growth by capturing the neighbor object;
step four, determining the state of each square grid in the solidification process;
step five, determining the average dendritic crystal growth kinetic coefficient
Figure BDA0002097082220000071
In m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is given
Figure BDA0002097082220000081
Unit ℃/s, each grid in the local computation domain has the same temperature;
when the solidification time is t, the temperature corresponding to the grid is
Figure BDA0002097082220000082
Wherein, T L Is the liquidus temperature of the alloy, and the unit is DEG C, i belongs to [1,4 ]]Representing 4 different local computation domains, notDifferent cooling speeds are adopted in the same local calculation domain;
Figure BDA0002097082220000083
the cooling rate is; t is time in units of s;
calculating nucleation in local calculation domains by adopting a Gaussian nucleation distribution formula, wherein different nucleation parameters are adopted in different local calculation domains;
Figure BDA0002097082220000084
Figure BDA0002097082220000085
wherein N is nuclei Represents the nucleation density in units of 1/m 3 ；N max Represents the maximum nucleation density in units of 1/m 3 I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta T mean Represents the maximum nucleation supercooling in units of ℃; delta T σ Indicating standard deviation nucleation supercooling;
Figure BDA0002097082220000086
and
Figure BDA0002097082220000087
representing the nucleation density, N, at time t and at time t- Δ t, respectively nuclei Denotes nucleation density, N at 0s nuclei ＝0；
Figure BDA0002097082220000088
And
Figure BDA0002097082220000089
respectively represents nucleation supercooling degree, delta T, at time T and time T-delta T nuclei Denotes nucleation supercooling degree, Δ T nuclei ＝T M +m l C l -T, Δ T at 0s nuclei ＝0；
T M The melting point of pure magnesium is measured in units of ℃; m is l Is the slope of the liquidus in deg.C/wt%; c l Is a liquid phase component; t is the grid temperature;
the relationship between the nucleation number Neg and the nucleation density at the time t is as follows:
Figure BDA00020970822200000810
wherein S is subarea For local calculation of the domain area, S subarea ＝Nucell[i]×Δlen×Δlen，Nucell[i]Calculating the number of square grids in the domain i locally, wherein delta len is the side length of each square grid;
step eight, in a local calculation domain i, randomly selecting a certain group of paired grids, if the state =0 of each grid in the group and comparing two Random numbers num1 and num2 of each grid (the Random numbers are obtained from Random [1, (m × n) ], wherein each grid has two Random numbers), and if 1 grid meets the condition that num1 is more than or equal to num2, the group does not generate a nucleation phenomenon; if all grids satisfy num1< num2, the nucleation phenomenon occurs in the group, and the physical quantity corresponding to each grid in the group of grids changes as follows:
fraction of solid phase f s ＝1，C s ＝C o k par ，C l ＝0，C aver ＝C s f s +C l (1-f s )，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein, f s Is the solid phase fraction, the minimum value is 0 to represent the liquid phase, and the maximum value is 1 to represent the solid phase; c s Is a solid phase component; c l Is a liquid phase component; c o Is an alloy initial component; c aver The unit of the component is weight percent and is the average component; k is a radical of par The coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different grains, random [1, neg ], [ i ] ] indicates that a Random number is selected from 1 to Neg [ i ]; growing theta is the growth orientation angle of the core, and a value is randomly selected between 0 and 90 degrees; state is state;
step nine, the grid solidified by nucleation is called the mother core grid (j, k) moth Mother core grid (j, k) moth Capturing 4 surrounding sets of neighbor pairing grids, if the state corresponding to each grid in a certain set of neighbor grids is equal to 0, capturing the grids, and capturing the grids (j, k) son Will change from liquid to growth state, i.e. state (j, k) son Change from 0 to 1, mesh (j, k) captured son With and mother core grid (j, k) moth The same icolor and growth theta values indicate that they belong to the same dendrite; grids (j, k are the same) with the same pairing index require that the state becomes 2 at the same time;
if a certain grid f s =1, but f of the mating mesh s <1, then the lattice will also remain in the growing state (state = 1) until f of the mating lattice s When =1, the states of the four grids simultaneously become solid;
step ten, at a certain time t, if the grid state (j, k) =1 and f s (j, k) =1, no computation is performed, and the search for state (j, k) =1 and f continues in the computation domain s (j, k) grid not equal to 1;
for state (j, k) =1 and f s Grid calculation solid-liquid interface curvature k with (j, k) ≠ 1 curve Normal angle of solid-liquid interface
Figure BDA0002097082220000094
Supercooling degree delta T and growth speed V tip Solid phase fraction f s Liquid phase component C l And a solid phase component C s ；
Figure BDA0002097082220000091
Figure BDA0002097082220000092
Figure BDA0002097082220000093
Figure BDA0002097082220000101
Figure BDA0002097082220000102
Wherein the content of the first and second substances,
Figure BDA0002097082220000103
the value is provided by step five; delta. For the preparation of a coating k The gamma is a Gibbs coefficient unit of C m;
when f is s <When 1, counting the number of grids with state =0 in the adjacent grids of the grid, namely the total number Nzero of grids with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids; for the mesh (j, k), solute exclusion amount Δ C, liquid phase component C l And a solid phase component C s The calculation is as follows:
Figure BDA0002097082220000104
Figure BDA0002097082220000105
Figure BDA0002097082220000106
when f is s When =1, the liquid phase component C l And a solid phase component C s The calculation is as follows:
C l ＝0
Figure BDA0002097082220000107
( Simulating the summer solidification condition in the fifth step, wherein no solute is diffused in the liquid phase, and the solute is instantly and uniformly mixed in the liquid phase. And the simulated dendritic growth can not be instantly mixed uniformly because the solute is diffused in the liquid phase, so that the released solute can be only distributed between the (j, k) grid and the adjacent grid around the (j, k) grid. )
Wherein, the delta t is a time step length, and t-delta t is the last moment; at 0s, C s ＝0，f s ＝0，C l ＝C o ；
The liquid phase composition of the grid with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids is increased
Figure BDA0002097082220000108
Step eleven, for state (j, k) =0 and state (j, k) =1 and f s (j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
Figure BDA0002097082220000109
wherein D is l Is the diffusion coefficient of solute element in liquid phase;
the solute diffusion equation in the solid phase is calculated for a grid of state (j, k) = 2:
Figure BDA0002097082220000111
wherein D is s Is the diffusion coefficient of solute elements in solid phase; the unit of the diffusion coefficient is m 2 /s；
Step twelve, repeating the step seven to the step eleven until the temperature of all the grids is less than the solidus temperature T s If yes, the calculation is terminated, and a solute component distribution data file is output; (the solidus is determined from the phase diagram and is an input parameter, known value)
Based on the calculated microsegregation distribution, (component distribution is obtained by solving solute diffusion equations in the liquid phase and the solid phase in the step eleven, and the nonuniformity of the component distribution is called microsegregation) three points P1, P2 and P3 are selected in the calculation domain, wherein the components are respectively C 1 、C 2 And C 3 The distance between the point P1 and the point P2 is equal to the distance Len between the point P2 and the point P3; the heat treatment time was estimated using the following formula:
Figure BDA0002097082220000112
wherein, a-heat represents the state after heat treatment, and b-heat represents the state before heat treatment, namely the solidification is finished;
composition based on P2 point after given heat treatment
Figure BDA0002097082220000113
Estimating the heat treatment time t heat 。
In step twelve, after the computation is terminated, a data file about the solute component distribution is obtained, and some positions, which are the points, can be selected in the data file, and the components, namely C, corresponding to the points can be obtained through the data file b-heat The distance Len between the points; and component C after heat treatment a-heat Provided by the designer or engineer according to factory production standards.
The second embodiment is as follows: the difference between the present embodiment and the first embodiment is that, in the third step, a neighbor object is given to each group of matching grids in the dendrite growth calculation domain, and the dendrite growth is completed by capturing the neighbor object; the process is as follows:
grids marked by (j belongs to [1,2], k belongs to [1, m ]), (j belongs to [ n-1, n ], k belongs to [1, m ]), (j belongs to [3, n-2], k belongs to [1,2 ]), (j belongs to [3, n-2) ], and k belongs to [ m-1, m ]) are defined as boundary grids, do not participate in dendrite growth, and therefore do not need to be endowed with neighbor objects;
each of the other paired meshes has 4 paired neighbor meshes: when the paired grid set consists of four grids (j, k), (j-1, k), (j, k-1) and (j-1, k-1), then the first set of neighboring grids consists of (j-2, k), (j-3, k), (j-2, k-1) and (j-3, k-1), the second set of neighboring grids consists of (j +2, k), (j +3, k), (j +2, k-1) and (j +3, k-1), the third set of neighboring grids consists of (j, k-2), (j-1, k-2), (j, k-3) and (j-1, k-3), and the fourth set of neighboring grids consists of (j, k + 2), (j-1, k-2), (j, k + 3) and (j-1, k + 3);
if a certain group of neighbor grids cannot be captured as long as the state corresponding to one grid is not equal to 0; if the state corresponding to each grid in a certain group of neighbor grids is equal to 0, the group of neighbor grids are captured and captured as the grid (j, k) son Will change from liquid to growth state, i.e. state (j, k) son From 0 to 1.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the difference between the present embodiment and the first or second embodiment is that, in the fourth step, the state of each square grid in the solidification process is determined; the process is as follows:
the boundary grid defined in step three can only be in a liquid state, i.e. state (j, k) =0, and state (j, k) is the state of the grid; the remaining trellis may have three states:
when f is s When (j, k) =0, the state (j, k) =0;
when 0 is present<f s (j,k)<1, in the growth state, state (j, k) =1;
when f is s (j, k) =1 and f of the paired meshes s Also equal to 1, then transition to solid state, state (j, k) =2;
f s (j, k) is the solidus fraction of the square mesh (j, k) (the solidus fraction of the square mesh (j, k) that is micro-scale meshing of the dendrite growth computation domain (already determined)).
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: in this embodiment, unlike one of the first to third embodiments, the average dendrite growth kinetic coefficient is determined in the fifth step
Figure BDA0002097082220000121
Units are m/s/DEG C; the specific process is as follows:
step five (1), calculating a curve of solid phase fraction changing with temperature under the summer solidification condition; the process is as follows:
summer solidification, i.e. no diffusion of solute in the solid phase and uniform mixing of solute components in the liquid phase; under the summer solidification condition, the relation of the solid phase fraction along with the temperature change is as follows:
Figure BDA0002097082220000122
wherein f is s-scheil To calculate the resulting solid phase fraction, T, using the Charles formula m Is the melting point of the alloy, T L Is the alloy liquidus temperature, k par Equilibrium partition coefficient, T, for the alloy scheil At a certain cooling speed, the melt temperature, T scheil ＝T L -10 × t, the cooling rate being chosen to be 10 ℃/s, t being the cooling time, increasing from 0s to 6s;
f can be obtained by calculation s-scheil ～T scheil A curve;
step five (2) simulating a curve of solid phase fraction changing with temperature under the summer solidification condition based on a cellular automation method;
step five (2-1), setting (m/2, n/2) as a nucleation core grid, namely f s (m/2, n/2) =1 and state (m/2, n/2) =2;
step five (2-2), calculating the change of the grid temperature T at a certain cooling speed to follow the temperature T in the step five (1) scheil Characteristic of variation, i.e. T = T L -10 × t, t increasing from 0s to 6s;
step five (2-3), the grid of state (j, k) =2 will change the state values of the upper, lower, left and right grids to 1 (to growth state), namely state (j, k + 1) =1, state (j, k-1) =1, state (j-1, k) =1, state (j +1, k) =1;
when the cooling time is t, the solid-liquid interface curvature k is calculated for a state =1 grid curve Normal angle of solid-liquid interface
Figure BDA0002097082220000123
Supercooling degree delta T and growth speed V tip Solid phase fraction f s Liquid phase component C l And a solid phase component C s ；
Figure BDA0002097082220000131
Figure BDA0002097082220000132
Figure BDA0002097082220000133
Figure BDA0002097082220000134
Figure BDA0002097082220000135
Wherein, T M The melting point of pure magnesium is measured in units of ℃; m is l Is the slope of the liquidus in deg.C/wt%; c l Is a liquid phase component; t is the grid temperature; gamma is Gibbs coefficient, unit is C m; theta is an angle; delta k In order to be a coefficient of the dynamic anisotropy,
Figure BDA0002097082220000136
is the derivative in the X-axis direction of a rectangular coordinate system;
Figure BDA0002097082220000137
is the derivative in the Y-axis direction of the rectangular coordinate system;
Figure BDA0002097082220000138
is the average dendrite growth kinetic coefficient, in cm/s/DEG C;
Figure BDA0002097082220000139
selecting between 0.01 and 0.5, and firstly selecting 0.01; the growth theta is the growth orientation angle of the equiaxed dendritic crystal, and a value is randomly selected between 0 and 90 degrees;
when f is s <1 hour, liquid phase component C l Solid phase component C s And the solute Δ C discharged from the solid-liquid interface is calculated as follows:
Figure BDA00020970822200001310
Figure BDA00020970822200001311
Figure BDA00020970822200001312
wherein the content of the first and second substances,
Figure BDA00020970822200001313
the liquid phase component is t-delta t at the last moment;
Figure BDA00020970822200001314
a solid phase component at time t- Δ t;
Figure BDA00020970822200001315
the solid phase fraction is t-delta t at the last moment, delta t is the time step length, and t-delta t is the last moment; k is a radical of par The coefficients are distributed for balance; f. of s Is the solid phase fraction;
Figure BDA00020970822200001316
representing the solid phase fraction at the current time t; in the same way, C l And C s Respectively representing a liquid phase component and a solid phase component at the current time t;
evenly distributing the Δ C to all state =0 grids in the calculation domain, so as to complete the process of uniformly mixing the Liquid phase solutes, namely, the calculation domain has m × n grids, and if the grids of the state =0 have Liquid _ num at the moment, the Liquid phase component of each grid of the state =0 is increased by Δ C/Liquid _ num;
when f is s When =1, the liquid phase component C l And a solid phase component C s The calculation is as follows:
C l ＝0
Figure BDA0002097082220000141
at 0s, C s ＝0，f s ＝0，C l ＝C o ，C o Is an alloy initial component;
note: step five (2-3) and step eight, step ten, step eleven are all based on the calculation of the cellular automata method, so the calculated physical quantities adopt the same names: the discharged mass of the solution is Δ C, and the liquid phase component C l Solid phase component C s Fraction of solid phase f s Curvature k of solid-liquid interface curve Normal angle of solid-liquid interface
Figure BDA0002097082220000142
Growth supercooling degree delta T, growth speed V tip Temperature T, average dendrite growth kinetic coefficient
Figure BDA0002097082220000143
Step five (2-4), increasing the time from 0s to 6s, repeating the step five (2-2) and the step five (2-3) to obtain a solid phase fraction-temperature curve, (the time step is generally a small value, and can be 0.001 s.);
mean dendrite growth kinetics coefficient at this time
Figure BDA0002097082220000144
F obtained by solving Charles formula and the curve of solid phase fraction-temperature s-scheil ～T scheil Comparing the curves, verifying the selection
Figure BDA0002097082220000145
The rationality of the value; if the absolute value of the difference between the solid phase fraction obtained based on the cellular automata method and the solid phase fraction obtained by the Charles equation is not more than 0.01 at the same temperature, i.e. | f s -f s-scheil |<0.01, then select
Figure BDA0002097082220000146
Reasonable otherwise
Figure BDA0002097082220000147
Adding 0.01 cm/s/DEG C, and repeating the steps five (2-1) to five (2-4) until | f s -f s-scheil |<0.01, selecting reasonable average dendritic crystal growth kinetic coefficient
Figure BDA0002097082220000148
Figure BDA0002097082220000149
May be 0.01,0.02,0.03,0.04, until a value is selected that ensures that the curve calculated based on the cells matches well with the curve calculated based on the summer formula, i calculated to
Figure BDA00020970822200001410
At 0.06, the two curves match well.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is that, in the sixth step, the calculation domain is further divided into 4 local calculation domains; the specific process is as follows:
in the first calculation domain, the value range of j [1, n/2], the value range of k [ m/2+1, m ];
in the second calculation domain, the value range of j [ n/2+1, n ], the value range of k [ m/2+1, m ];
in the third calculation domain, the value range [1, n/2] of j and the value range [1, m/2] of k are calculated;
in the fourth calculation domain, the value range of j [ n/2+1, n ], the value range of k [1, m/2].
Other steps and parameters are the same as in one of the first to fourth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the preparation method comprises the following steps:
selecting Al-7wt% Si alloy as research object, and simulating alpha-Al dendritic structure and micro segregation formation by using cellular automata model based on square paired grid group, wherein the square paired grid group consists of 300 × 300 square grids. The relevant parameters for calculating the required input physical property parameters and for numerical simulation are listed in table 1.
TABLE 1 Al-7wt% Si alloy numerical simulation thermophysical parameters and calculated parameters
Figure BDA0002097082220000151
(1) In FIG. 1, cellular automata is used to simulate the summer freezing condition when the average dendrite growth kinetic coefficient
Figure BDA0002097082220000152
Figure BDA0002097082220000153
Then, the obtained solid phase fraction-temperature change rule (shown by a circle) is better matched with the solid phase fraction-temperature change rule (solid line) calculated based on the Charles formula. Thus for Al-7wt% Si alloy, the growth kinetic coefficient was determined to be 0.06cm/s/K;
(2) FIG. 2a is a metallographic photograph obtained by an electrochemical corrosion experiment, wherein different colors represent different dendrites, the dendrite is a negative microsegregation region, and a black gray region between dendrites is a positive microsegregation region. Fig. 2b is a calculation result based on the mesh pairing algorithm, where the nucleation parameter selects a value corresponding to "local region 1" in table 1, the white region is a dendrite, corresponds to a negative micro-segregation region, and the interdendritic region is a positive micro-segregation region. The calculation result is well matched with the experimental result.
(3) In fig. 3a and 3b, when the grid size is small (2 μm), reasonable dendrite morphology can be obtained based on both the matching grid algorithm fig. 3a and the solid-liquid interface geometric factor algorithm fig. 3b, i.e. the dendrite arms are perpendicular to each other.
(4) In fig. 4a, 4a1, 4b, and 4b1, when the grid size is large (4 μm), a reasonable dendrite morphology can be obtained based on a paired grid algorithm (fig. 4a and 4 b), and some dendrite growth morphologies are not reasonable based on a solid-liquid interface geometric factor algorithm (fig. 4a1 and 4b 1), that is, an included angle between a secondary arm and a primary arm is not 90 °, primary dendrite arms are not perpendicular to each other, and when the dendrite growth orientation is greater than 60 ° or less than 30 °, this phenomenon occurs, which indicates that the solid-liquid interface geometric factor algorithm is sensitive to the selection of the grid size, and this method is not suitable for the simulation calculation of a large calculation domain.
(5) In fig. 5, the microsegregation distribution is given for fig. 4b and 4b1, the result based on the paired grid algorithm is shown in fig. 5a, and the result based on the solid-liquid interface geometric factor algorithm is shown in fig. 5b; in FIGS. 5a and 5b, the dendrite is a negative micro-segregation zone and the interdendritic region is a positive segregation zone; the segregation degree is reasonable, namely the minimum value of the composition is more than or equal to 0.91, and the maximum value of the composition is less than or equal to 16.38. However, the dendrite morphology in FIG. 5b is not reasonable.
(6) In fig. 6, the calculation domain is divided into four parts, the nucleation parameters and the cooling rate of each region are different (see table 1), and the local region 1 corresponds to the conditions of high nucleation density, high cooling rate and low nucleation supercooling, so that the structure is fine, and the size of the micro segregation region between dendrites is small. The local region 4 corresponds to the case of low nucleation density, small cooling rate and large nucleation undercooling, so that the structure is relatively coarse and the size of the micro-segregation region between dendrites is relatively large. For the local calculation domains 1 to 4, when the heat treatment time was 500 ℃, the distances (Len) were 18 μm, 30 μm, 66 μm, and 87 μm, respectively, and the average heat treatment times were 323s, 415s, 2275s, and 3946s. Four different tissue morphologies and micro segregation distributions can be obtained by one calculation, and more choices are provided for formulating the heat treatment process.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (5)

1. A body centered cubic alloy microsegregation numerical prediction method is characterized by comprising the following steps: the method comprises the following specific processes:
step one, a dendrite growth calculation domain is positioned in a rectangular coordinate system, microscopic scale grid subdivision is carried out on the dendrite growth calculation domain, square grids with the side length size of delta len are adopted, and each square grid is marked by (j, k);
j represents a coordinate along the X-axis direction of the rectangular coordinate system, k represents a coordinate along the Y-axis direction of the rectangular coordinate system, the value range of j is [1, n ], and the value range of k is [1, m ]; j and k are integers, and m and n are even numbers, so that the dendrite growth calculation domain has m multiplied by n grids;
step two, the square grid (j, k) and the surrounding 3 grids (j-1, k), (j, k-1) and (j-1, k-1) are grouped into a group, that is, the square grids (j, k), (j-1, k), (j, k-1) and (j-1, k-1) are paired grids, the four grids are endowed with the same pairing identifier, and the pairing identifier is represented by pd, so pd (j, k) = pd (j-1, k) = pd (j, k-1) = pd (j-1, k-1) = j/2+ k/2+ p 1;
pairing each grid in the dendrite growth calculation domain, then each grid pd (j, k) value will be greater than 1;
step three, endowing a neighbor object to each group of matched grids in the dendrite growth calculation domain, and finishing dendrite growth by capturing the neighbor object;
step four, determining the state of each square grid in the solidification process;
step five, determining the average dendritic crystal growth kinetic coefficient
Figure FDA0003827897790000011
Units are m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is given
Figure FDA0003827897790000012
Unit ℃/s, each grid in the local computation domain has the same temperature;
when the solidification time is t, the temperature corresponding to the grid is
Figure FDA0003827897790000013
Wherein, T L Is the liquidus temperature of the alloy, and the unit is the temperature i belongs to [1,4 ]]4 different local calculation domains are represented, and different cooling speeds are adopted in the different local calculation domains;
Figure FDA0003827897790000014
the cooling rate is; t is time in units of s;
calculating the nucleation in a local calculation domain by adopting a Gaussian nucleation distribution formula, wherein different nucleation parameters are adopted in different local calculation domains;
Figure FDA0003827897790000015
Figure FDA0003827897790000016
wherein N is nuclei Represents the nucleation density in units of 1/m 3 ；N max Represents the maximum nucleation density in units of 1/m 3 I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta T mean Represents the maximum nucleation supercooling in units of ℃; delta T σ Indicating standard deviation nucleation supercooling;
Figure FDA0003827897790000021
and
Figure FDA0003827897790000022
respectively at time t and at time t- Δ tNucleation density of, N at 0s nuclei ＝0；
Figure FDA0003827897790000023
And
Figure FDA0003827897790000024
respectively representing the nucleation supercooling degree, delta T, at the time T and the time T-Delta T nuclei Indicating the degree of nucleation supercooling,. DELTA.T nuclei ＝T M +m l C l -T, Δ T at 0s nuclei ＝0；
T M The melting point of pure magnesium is measured in units of ℃; m is l Is the slope of the liquidus in deg.C/wt%; c l Is a liquid phase component; t is the grid temperature;
the relationship between the nucleation number Neg and the nucleation density at the time t is as follows:
Figure FDA0003827897790000025
wherein S is subarea For local calculation of the domain area, S subarea ＝Nucell[i]×Δlen×Δlen，Nucell[i]Calculating the number of square grids in the domain i locally, wherein delta len is the side length of each square grid;
step eight, in the local calculation domain i, randomly selecting a certain group of paired grids, if the state =0 of each grid in the group and comparing two random numbers num1 and num2 of each grid, and if 1 grid exists, meeting the condition that num1 is more than or equal to num2, the group does not generate the nucleation phenomenon; if all grids satisfy num1< num2, the nucleation phenomenon occurs in the group, and the physical quantity corresponding to each grid in the group of grids changes as follows:
fraction of solid phase f s ＝1，C s ＝C o k par ，C l ＝0，C aver ＝C s f s +C l (1-f s )，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein f is s Is the solid phase fraction, the minimum value is 0 representing the liquidPhase, maximum 1 represents solid phase; c s Is a solid phase component; c l Is a liquid phase component; c o Is an alloy initial component; c aver The unit of the component is weight percent and is the average component; k is a radical of formula par The coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different grains, random [1, neg ], [ i ] ] indicates that a Random number is selected from 1 to Neg [ i ]; growth theta is the growth orientation angle of the core, and a value is randomly selected between 0 and 90 degrees; state is a state;
step nine, the grid solidified by nucleation is called the mother core grid (j, k) moth Mother core grid (j, k) moth Capturing 4 surrounding neighbor pairing grids, if the state corresponding to each grid in a certain set of neighbor grids is equal to 0, capturing the grids, and capturing the grids (j, k) son Will change from liquid to growth state, i.e. state (j, k) son Change from 0 to 1, mesh (j, k) captured son With and mother core grid (j, k) moth The same icolor and growth theta values indicate that they belong to the same dendrite;
if a certain grid f s =1, but f of the mating mesh s < 1, then the grid will also remain in growth state =1 until f of the mating grid s When =1, the states of the four grids simultaneously become solid;
step ten, at a certain time t, if the grid state (j, k) =1 and f s (j, k) =1, no computation is performed, and the search for state (j, k) =1 and f continues in the computation domain s (j, k) a grid not equal to 1;
for state (j, k) =1 and f s Grid calculation solid-liquid interface curvature k with (j, k) ≠ 1 curve Normal angle of solid-liquid interface
Figure FDA00038278977900000313
Growth supercooling degree delta T and growth speed V tip Solid phase fraction f s Liquid phase component C l And a solid phase component C s ；
Figure FDA0003827897790000031
Figure FDA0003827897790000032
Figure FDA0003827897790000033
Figure FDA0003827897790000034
Figure FDA0003827897790000035
Wherein, delta k Is a dynamic anisotropy coefficient, and gamma is a Gibbs coefficient with the unit of DEG C m;
Figure FDA0003827897790000036
is the solid phase fraction of t-delta t at the last moment,
Figure FDA0003827897790000037
representing the solid phase fraction at the current time t;
when f is s When the sum is less than 1, counting the number of grids with state =0 in the adjacent grids of the grid, namely the total number Nzero of grids with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids; for the mesh (j, k), solute exclusion amount Δ C, liquid phase component C l And a solid phase component C s The calculation is as follows:
Figure FDA0003827897790000038
Figure FDA0003827897790000039
Figure FDA00038278977900000310
when f is s =1, liquid phase component C l And a solid phase component C s The calculation is as follows:
C l ＝0
Figure FDA00038278977900000311
wherein, the delta t is a time step length, and t-delta t is the last moment; at 0s, C s ＝0，f s ＝0，C l ＝C o ；
Figure FDA00038278977900000312
The liquid phase component is t-delta t at the last moment;
Figure FDA0003827897790000041
a solid phase component at time t- Δ t;
the liquid phase composition of the grid with state =0 in the upper (j, k + 1), lower (j, k-1), left (j-1, k), right (j +1, k), upper left (j-1, k + 1), upper right (j +1, k + 1), lower left (j-1, k-1) and lower right (j +1, k-1) grids is increased
Figure FDA0003827897790000042
Step eleven for only state (j, k) =0 and state (j, k) =1 and f s (j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
Figure FDA0003827897790000043
wherein D is l Is the diffusion coefficient of solute element in liquid phase;
the solute diffusion equation in the solid phase is calculated for the grid of state (j, k) = 2:
Figure FDA0003827897790000044
wherein D is s Is the diffusion coefficient of solute element in solid phase; the unit of the diffusion coefficient is m 2 /s；
Step twelve, repeating the step seven to the step eleven until the temperature of all grids is less than the solidus temperature T s If yes, the calculation is terminated, and a solute component distribution data file is output;
based on the calculated microsegregation distribution, three points P1, P2 and P3 are selected in the calculation domain, and the components are respectively
Figure FDA0003827897790000045
C 2 And C 3 The distance between the point P1 and the point P2 is equal to the distance Len between the point P2 and the point P3; the heat treatment time was estimated using the following formula:
Figure FDA0003827897790000046
wherein, a-heat represents after heat treatment, b-heat represents before heat treatment, namely the solidification end state;
composition based on P2 point after given heat treatment
Figure FDA0003827897790000047
Estimating the heat treatment time t heat 。
2. The method of claim 1, wherein the method comprises the steps of: in the third step, each group of matching grids in the dendrite growth calculation domain is endowed with a neighbor object, and the dendrite growth is completed by capturing the neighbor object; the process is as follows:
grids marked by (j belongs to [1,2], k belongs to [1, m ]), (j belongs to [ n-1, n ], k belongs to [1, m ]), (j belongs to [3, n-2], k belongs to [1,2 ]), (j belongs to [3, n-2) ], and k belongs to [ m-1, m ]) are defined as boundary grids, do not participate in dendrite growth, and therefore do not need to be endowed with neighbor objects;
each of the other paired meshes has 4 paired neighbor meshes: when the paired grid set consists of four grids of (j, k), (j-1, k), (j, k-1) and (j-1, k-1), then the first set of neighbor grids consists of (j-2, k), (j-3, k), (j-2, k-1) and (j-3, k-1), the second set of neighbor grids consists of (j +2, k), (j +3, k), (j +2, k-1) and (j +3, k-1), the third set of neighbor grids consists of (j, k-2), (j-1, k-2), (j, k-3) and (j-1, k-3), and the fourth set of neighbor grids consists of (j, k + 2), (j-1, k + 2), (j, k + 3) and (j-1, k + 3);
if the state corresponding to one grid in a certain group of neighbor grids is not equal to 0, the group of neighbor grids can not be captured; if the state corresponding to each grid in a certain group of neighbor grids is equal to 0, the group of neighbor grids are captured and captured as the grid (j, k) son Will change from liquid to growth state, i.e. state (j, k) son From 0 to 1.
3. The method of claim 2, wherein the method comprises the steps of: determining the state of each square grid in the solidification process in the fourth step; the process is as follows:
the boundary grid defined in step three can only be in a liquid state, i.e. state (j, k) =0, and state (j, k) is the state of the grid; the remaining trellis may have three states:
when f is s When (j, k) =0, the state (j, k) =0;
when 0 < f s When (j, k) < 1, it is in the growth state, state (j, k) =1;
when f is s (j, k) =1 and f of the paired meshes s Also equal to 1, then transition to solid state, state (j, k) =2;
f s (j, k) is the fraction of solid phase in the square lattice (j, k).
4. The method of claim 3, wherein the method comprises the steps of: determining the average dendrite growth kinetic coefficient in the fifth step
Figure FDA0003827897790000051
Units are m/s/DEG C; the specific process is as follows:
step five (1), calculating a curve of solid phase fraction changing with temperature under the summer solidification condition; the process is as follows:
summer solidification, i.e. no diffusion of solute in the solid phase and uniform mixing of solute components in the liquid phase; under the summer solidification condition, the solid phase fraction changes with the temperature according to the relation formula:
Figure FDA0003827897790000052
wherein f is s-scheil To calculate the resulting solid phase fraction, T, using the Charles formula m Is the melting point of the alloy, T L Is the alloy liquidus temperature, k par Equilibrium partition coefficient, T, for the alloy scheil At a certain cooling speed, the melt temperature, T scheil ＝T L -10 × t, the cooling rate is chosen to be 10 ℃/s, t is the cooling time, increasing from 0s to 6s;
f can be obtained by calculation s-scheil ～T scheil A curve;
step five (2) simulating a curve of solid phase fraction changing with temperature under the summer solidification condition based on a cellular automation method;
step five (2-1), setting (m/2, n/2) as a nucleation core grid, namely f s (m/2, n/2) =1 and state (m/2, n/2) =2;
step five (2-2), calculating the change of the grid temperature T at a certain cooling speed to follow the temperature T in the step five (1) scheil Characteristic of variation, i.e. T = T L -10 × t, t increasing from 0s to 6s;
step five (2-3), the grid of state (j, k) =2 will change the state values of the upper, lower, left and right grids to 1, namely state (j, k + 1) =1, state (j, k-1) =1, state (j-1, k) =1, state (j +1, k) =1;
when the cooling time is t, the solid-liquid interface curvature k is calculated for a state =1 grid curve Normal angle of solid-liquid interface
Figure FDA00038278977900000617
Growth supercooling degree delta T and growth speed V tip Solid phase fraction f s Liquid phase component C l And a solid phase component C s ；
Figure FDA0003827897790000061
Figure FDA0003827897790000062
Figure FDA0003827897790000063
Figure FDA0003827897790000064
Figure FDA0003827897790000065
Wherein, T M The melting point of pure magnesium is measured in units of ℃; m is a unit of l Is the slope of the liquidus in deg.C/wt%; c l Is a liquid phase component; t is the grid temperature; gamma is a Gibbs coefficient, with the unit being m DEG C; theta is an angle; delta k In order to be a coefficient of the dynamic anisotropy,
Figure FDA0003827897790000066
is the derivative in the X-axis direction of the rectangular coordinate system;
Figure FDA0003827897790000067
is the derivative in the Y-axis direction of the rectangular coordinate system;
Figure FDA0003827897790000068
is the average dendrite growth kinetic coefficient, in cm/s/DEG C;
Figure FDA0003827897790000069
selecting between 0.01 and 0.5; growth theta is an isometric dendritic crystal growth orientation angle, and a value is randomly selected between 0 and 90 degrees;
when f is s When < 1, the liquid phase component C l Solid phase component C s And the solute Δ C discharged from the solid-liquid interface was calculated as follows:
Figure FDA00038278977900000610
Figure FDA00038278977900000611
Figure FDA00038278977900000612
wherein the content of the first and second substances,
Figure FDA00038278977900000613
the liquid phase component is t-delta t at the last moment;
Figure FDA00038278977900000614
a solid phase component at time t- Δ t;
Figure FDA00038278977900000615
the solid phase fraction is t-delta t at the last moment, delta t is the time step length, and t-delta t is the last moment; k is a radical of par The coefficients are distributed for balance; f. of s Is the solid phase fraction;
Figure FDA00038278977900000616
representing the solid phase fraction at the current time t; for the same reason, C l And C s Respectively representing a liquid phase component and a solid phase component at the current time t;
evenly distributing the deltaC into all state =0 grids in a calculation domain, thereby completing the process of uniformly mixing the Liquid phase solutes, namely, the calculation domain has m multiplied by n grids, if at the moment, the grids of the state =0 have Liquid _ num, the Liquid phase component of each grid of the state =0 is increased by deltaC/Liquid _ num;
when f is s When =1, the liquid phase component C l And a solid phase component C s The calculation is as follows:
C l ＝0
Figure FDA0003827897790000071
at 0s, C s ＝0，f s ＝0，C l ＝C o ，C o Is an alloy initial component;
step five (2-4), increasing the time from 0s to 6s, repeating the step five (2-2) and the step five (2-3), and obtaining a solid phase fraction-temperature curve;
mean dendrite growth kinetics coefficient at this time
Figure FDA0003827897790000072
F obtained by solving the Charles formula and the solid phase fraction-temperature curve s-scheil ～T scheil Comparing the curves, verifying the selection
Figure FDA0003827897790000073
The rationality of the value; if the absolute value of the difference between the solid phase fraction obtained based on the cellular automata method and the solid phase fraction obtained by the Charles equation is not more than 0.01 at the same temperature, i.e. | f s -f s-scheil If | is less than 0.01, then select
Figure FDA0003827897790000074
Reasonable otherwise
Figure FDA0003827897790000075
Increasing the temperature by 0.01 cm/s/DEG C, and repeating the step five (2-1) to the step five (2-4) until the | f s -f s-scheil Less than 0.01, and selecting reasonable average dendrite growth kinetic coefficient
Figure FDA0003827897790000076
5. The method of claim 4, wherein the method comprises the steps of: in the sixth step, the calculation domain is further divided into 4 local calculation domains; the specific process is as follows:
in the first calculation domain, the value range of j [1, n/2], the value range of k [ m/2+1, m ];
in the second calculation domain, the value range of j [ n/2+1, n ], the value range of k [ m/2+1, m ];
in the third calculation domain, the value range of j [1, n/2], and the value range of k [1, m/2];
in the fourth calculation domain, the value range of j [ n/2+1, n ], and the value range of k [1, m/2].
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