CN110263418A - A kind of body centred cubic alloy microsegregation Numerical Predicting Method - Google Patents
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Abstract
A kind of body centred cubic alloy microsegregation Numerical Predicting Method, the present invention relates to body centred cubic alloy microsegregation Numerical Predicting Methods.The purpose of the present invention is to solve existing method can not Accurate Prediction body centred cubic alloy microsegregation formation the problem of.Process are as follows: one, progress micro-scale mesh generation；Two, 3 grids of square net and surrounding are one group；Three, dendritic growth is completed；Four, the state of grid is determined；Five, kinetic coefficient is determined；Six, 4 local calculation domains are further divided into；Seven, the forming core in local calculation domain is calculated；Eight, certain group pairing grid is randomly choosed in local calculation domain, judges whether the group occurs forming core phenomenon；Nine, 4 groups of neighbours match grid around female boundary fitting capture；Ten, calculating parameter；11, it calculates solutes accumulation equation: 12, repeating seven~11, export solute component distributed data file；Estimate heat treatment time.The present invention is used for body centred cubic alloy microsegregation numerical prediction field.
Description
Technical Field
The invention relates to a body centered cubic alloy microsegregation numerical prediction method.
Background
The energy consumption is high in the casting production process, and the environment is polluted by the emission of waste residues and dust. The improvement of the casting yield needs to start from the research of the casting defect forming mechanism. Segregation is a phenomenon in which the internal components of a casting are not uniform after the casting is solidified, and is divided into macroscale segregation, i.e., macroscale segregation and microscale segregation, i.e., 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. The formulation of a plurality of heat treatment processes is proposed according to a method of 'one furnace, a plurality of 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 shows the solidification process in real time by means of computational graphics, thereby being beneficial to capturing the micro segregation formation details and analyzing the 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 numerical simulation method is adopted to predict the formation of the microsegregation, the calculation based on the dendritic crystal morphology is required, and the cooling speed, the grain size and the interaction among different dendritic crystals can influence the formation of the microsegregation. 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 solve the problem that the prior method cannot accurately predict the formation of the microsegregation of the body-centered cubic alloy, and provides a method for predicting the microsegregation numerical value 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, 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, a square grid (j, k) and 3 surrounding grids (j-1, k), (j, k-1) and (j-1, k-1) are in a group, namely, 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 that 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 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 coefficientUnits are m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is givenUnit ℃/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
Wherein, TLIs the liquidus temperature of the alloy, and the unit is DEG C, i belongs to [1,4 ]]4 different local calculation domains are shown, and different cooling speeds are adopted in the different local calculation domains;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;
wherein N isnｕcleiRepresents the nucleation density in units of 1/m3；NmaxRepresents the maximum nucleation density in units of 1/m3I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta TmeanRepresents the maximum nucleation supercooling in units of ℃; delta TσIndicating standard deviation nucleation supercooling;andrespectively representing the nucleation density, N, at time t and at time t-DeltatnucleiDenotes nucleation density, N at 0snｕclei＝0；Andrespectively representing the nucleation supercooling degree, Delta T, at the time T and the time T-Delta TnucleiIndicating the degree of nucleation supercooling,. DELTA.Tnuclei＝TM+mlCl-T, Δ T at 0snuclei＝0；
TMThe melting point of pure magnesium is measured in units of ℃; m islIs the slope of the liquidus in deg.C/wt%; clIs 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:
wherein S issubareaFor local calculation of the domain area, Ssubarea＝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 of each grid in the group is 0 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 varies as follows:
fraction of solid phase fs＝1，Cs＝Cokpar，Cl＝0，Caver＝Csfs+Cl(1-fs)，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein f issIs the solid phase fraction, the minimum value of 0 represents the liquid phase, and the maximum value of 1 represents the solid phase; csIs a solid phase component; clIs a liquid phase component; coIs an alloy initial component; caverThe unit of the component is weight percent and is the average component; k is a radical ofparThe coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different crystal 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)mothMother core grid (j, k)mothCapturing 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)sonWill change from liquid to growth state, i.e. state (j, k)sonChange from 0 to 1, mesh (j, k) capturedsonWith and mother core grid (j, k)mothThe same icolor and growth theta values indicate belonging to the same dendrite;
if a certain grid fs1, but of the paired meshess<1, the lattice will also remain in the growth state (state 1) until f of the paired latticesWhen the state of the four grids is 1, the 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) is 1 and fs(j, k) ═ 1, no computation is performed, and the search continues in the computation domain for state (j, k) ═ 1 and fs(j, k) a grid not equal to 1;
for state (j, k) 1 and fsGrid calculation solid-liquid interface curvature k with (j, k) ≠ 1curveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T and growth speed VtipA solid phase fraction fs, a liquid phase component ClAnd a solid phase component Cs；
Wherein, deltakThe gamma is a Gibbs coefficient unit of C m;
when f iss<When 1, counting the number of grids with state 0 in the neighbor 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), left upper (j-1, k +1), right upper (j +1, k +1), left lower (j-1, k-1) and right lower (j +1, k-1) grids; for the mesh (j, k), solute exclusion amount Δ C, liquid phase component ClHarmonizing and fixingPhase component CsThe calculation is as follows:
when f issWhen 1, the liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
Cl＝0
wherein, delta t is a time step length, and t-delta t is the last moment; at 0s, Cs＝0，fs＝0，Cl＝Co；
The liquid phase composition of the lattice having 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) lattices is increased
Step eleven for only state (j, k) 0 and state (j, k) 1 and fs(j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
wherein D islIs the diffusion coefficient of solute element in liquid phase;
calculating the solute diffusion equation in the solid phase for a grid with state (j, k) 2:
wherein D issIs the diffusion coefficient of solute element in solid phase; the unit of the diffusion coefficient is m2/s；
Step twelve, repeating the step seven to the step eleven until the temperature of all the grids is less than the solidus temperature TsIf yes, the calculation is terminated, and a solute component distribution data file is output;
based on the calculated micro segregation distribution, three points P1, P2 and P3 are selected in the calculation domain, and the components are respectively C1、C2And C3The distance between point P1 and point P2 is equal to the distance Len between point P2 and point P3; the heat treatment time was estimated using the following formula:
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 treatmentEstimate the heat treatment time theat。
The invention has the beneficial effects that:
in the invention, the microstructure and the microsegregation of the micro dendrite are calculated at the same time, and the prediction of the heat treatment time depends on the microsegregation distribution obtained by calculation based on the microstructure of the micro dendrite, thereby being 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 be used for predicting the formation of the microsegregation more quickly, provides theoretical support for the 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 comparing a solid phase fraction and a temperature change curve of Al-7 wt% Si alloy calculated based on a Charles formula with a solid phase fraction and a temperature change curve obtained based on a cellular automaton method, wherein the abscissa is the solid phase fraction and the ordinate is the temperature;
FIG. 2a is a graph showing experimental results of a solidification structure obtained when the cooling rate of the Al-7 wt% Si alloy is 5.0 ℃/s.
Fig. 2b is a graph of the solidification structure result of the Al-7 wt% Si alloy at a cooling rate of 5.0 ℃/s based on a mesh pairing algorithm, with a mesh size Δ len of 2 μm;
fig. 3a is a graph of a solidification structure of an Al-7 wt% Si alloy simulated based on a paired lattice algorithm at a cooling rate of 10.0 ℃/s with a lattice size Δ len of 2 μm;
FIG. 3b is a solidification structure diagram obtained by simulation of Al-7 wt% Si alloy based on solid-liquid interface geometric factor algorithm under the condition that the mesh size is 2 μm when the cooling rate is 10.0 ℃/s;
fig. 4a is a graph of a solidification structure of an Al-7 wt% Si alloy obtained by simulation at 1s of solidification based on a paired lattice algorithm, with a lattice size Δ len of 4 μm at a cooling rate of 10.0 ℃/s;
fig. 4a1 shows a solidification structure diagram obtained by simulation of Al-7 wt% Si alloy at a cooling rate of 10.0 ℃/s with a mesh size Δ len of 4 μm at 1s of solidification based on the solid-liquid interface geometry factor algorithm;
fig. 4b is a graph of a solidification structure of an Al-7 wt% Si alloy simulated at 3s of solidification based on a paired lattice algorithm with a lattice size Δ len of 4 μm at a cooling rate of 10.0 ℃/s;
fig. 4b1 is a solidification structure diagram obtained by simulation of the Al-7 wt% Si alloy at 3s of solidification based on the solid-liquid interface geometry factor algorithm, with a mesh size Δ len of 4 μm at a cooling rate of 10.0 ℃/s;
fig. 5a is a microsegregation profile of an Al-7 wt% Si alloy simulated at 3s solidification based on a paired-lattice algorithm at a cooling rate of 10.0 ℃/s with a lattice size Δ len of 4 μm;
FIG. 5b is a microsegregation distribution diagram of Al-7 wt% Si alloy obtained by simulation of solidification for 3s based on the solid-liquid interface geometry factor algorithm at a cooling rate of 10.0 ℃/s and a mesh size Δ len of 4 μm;
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 embodiment 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 the dendrite growth calculation domain has m multiplied by n grids;
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) form 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 assigned with the same pairing identifier, and the pairing identifier is represented by pd, so that pd (j, k) ═ pd (j-1, k) ═ pd (j, k-1) ═ pd (j-1, k-1) ═ j/2+ k/2+1 (the value can be decimal number or 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 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 coefficientUnits are m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is givenUnit ℃/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
Wherein, TLIs the liquidus temperature of the alloy, and the unit is DEG C, i belongs to [1,4 ]]4 different local calculation domains are shown, and different cooling speeds are adopted in the different local calculation domains;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;
wherein N isnucleiRepresents the nucleation density in units of 1/m3；NmaxRepresents the maximum nucleation density in units of 1/m3I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta TmeanRepresents the maximum nucleation supercooling in units of ℃; delta TσIndicating standard deviation nucleation supercooling;andrespectively representing the nucleation density, N, at time t and at time t-DeltatnucleiDenotes nucleation density, N at 0snuclei＝0；Andrespectively representing the nucleation supercooling degree, Delta T, at the time T and the time T-Delta TnucleiIndicating the degree of nucleation supercooling,. DELTA.Tnuclei＝TM+mlCl-T, Δ T at 0snuclei＝0；
TMThe melting point of pure magnesium is measured in units of ℃; m islIs the slope of the liquidus in deg.C/wt%; clIs 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:
wherein S issubareaFor local calculation of the domain area, Ssubarea＝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 of each grid in the group is 0, 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 exists, and 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 varies as follows:
fraction of solid phase fs＝1，Cs＝Cokpar，Cl＝0，Caver＝Csfs+Cl(1-fs)，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein f issIs the solid phase fraction, the minimum value of 0 represents the liquid phase, and the maximum value of 1 represents the solid phase; csIs a solid phase component; clIs a liquid phase component; coIs an alloy initial component; caverThe unit of the component is weight percent and is the average component; k is a radical ofparThe coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different crystal 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)mothMother core grid (j, k)mothCapturing 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)sonWill change from liquid toGrowth state, i.e. state (j, k)sonChange from 0 to 1, mesh (j, k) capturedsonWith and mother core grid (j, k)mothThe same icolor and growth theta values indicate belonging to the same dendrite; grids (j, k are the same) with the same pairing index, requiring that the state becomes 2 at the same time;
if a certain grid fs1, but of the paired meshess<1, the lattice will also remain in the growth state (state 1) until f of the paired latticesWhen the state of the four grids is 1, the 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) is 1 and fs(j, k) ═ 1, no computation is performed, and the search continues in the computation domain for state (j, k) ═ 1 and fs(j, k) a grid not equal to 1;
for state (j, k) 1 and fsGrid calculation solid-liquid interface curvature k with (j, k) ≠ 1curveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T and growth speed VtipSolid phase fraction fsLiquid phase component ClAnd a solid phase component Cs；
Wherein,the value is provided by step five; deltakThe gamma is a Gibbs coefficient unit of C m;
when f iss<When 1, counting the number of grids with state 0 in the neighbor 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), left upper (j-1, k +1), right upper (j +1, k +1), left lower (j-1, k-1) and right lower (j +1, k-1) grids; for the mesh (j, k), solute exclusion amount Δ C, liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
when f issWhen 1, the liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
Cl＝0
(step five simulates the summer solidification condition, no solute is diffused in the liquid phase, and the solutes are instantly and uniformly mixed in the liquid phase, but the solute is diffused in the liquid phase and cannot be instantly and uniformly mixed by simulating the growth of dendrites at present, so that the released solutes can be only distributed between the (j, k) grid and the adjacent grid around the (j, k) grid.)
Wherein, delta t is a time step length, and t-delta t is the last moment; at 0s, Cs＝0，fs＝0，Cl＝Co；
The liquid phase composition of the lattice having 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) lattices is increased
Step eleven for only state (j, k) 0 and state (j, k) 1 and fs(j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
wherein D islIs the diffusion coefficient of solute element in liquid phase;
calculating the solute diffusion equation in the solid phase for a grid with state (j, k) 2:
wherein D issIs the diffusion coefficient of solute element in solid phase; the unit of the diffusion coefficient is m2/s；
Step twelve, repeating the step seven to the step eleven until the temperature of all the grids is less than the solidus temperature TsIf 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, (the diffusion equation of solute in liquid phase and solid phase solved in the step eleven obtains component distribution, the nonuniformity of the component distribution is called microsegregation), three points P1, P2 and P3 are selected in the calculation domain, and the components are respectively C1、C2And C3The distance between point P1 and point P2 is equal to the distance Len between point P2 and point P3; the heat treatment time was estimated using the following formula:
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 treatmentEstimate the heat treatment time theat。
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 fileb-heatThe distance Len between the points; and component C after heat treatmenta-heatProvided 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 with the labels of (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 dendritic crystal 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 mesh group is composed of four meshes (j, k), (j-1, k), (j, k-1) and (j-1, k-1), then the first group of neighbor meshes is composed of (j-2, k), (j-3, k), (j-2, k-1) and (j-3, k-1), the second group of neighbor meshes is composed of (j +2, k), (j +3, k), (j +2, k-1) and (j +3, k-1), the third group of neighbor meshes is composed of (j, k-2), (j-1, k-2), (j, k-3) and (j-1, k-3), the fourth group of neighbor meshes is composed 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)sonWill change from liquid to growth state, i.e. state (j, k)sonFrom 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, that is, state (j, k) is 0, and state (j, k) is the state of the grid; the remaining trellis may have three states:
when f issWhen (j, k) is 0, the liquid state is obtained, and state (j, k) is 0;
when 0 is present<fs(j,k)<1, state (j, k) is 1;
when f issWhen (j, k) is 1 and f of the paired gridssAlso equal to 1, then transition to solid state, state (j, k) 2;
fs(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 stepUnits 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:
wherein f iss-scheilTo calculate the resulting solid phase fraction, T, using the Charles formulamIs the melting point of the alloy, TLIs the alloy liquidus temperature, kparEquilibrium partition coefficient, T, for the alloyscheilAt a certain cooling speed, the melt temperature, Tscheil＝TL-10 × t, the cooling rate is chosen to be 10 ℃/s, t is the cooling time, increasing from 0s to 6 s;
by calculation ofCan obtain fs-scheil～TscheilA curve;
step five (2), simulating a curve of solid phase fraction changing along with temperature under the summer solidification condition based on a cellular automata method;
step five (2-1), setting (m/2, n/2) as a nucleation core grid, namely fs(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)scheilCharacterised by variation, i.e. T ═ TL-10 × t, t increasing from 0s to 6 s;
step five (2-3) and the grid with state (j, k) equal to 2 change the state values of the upper, lower, left and right grids to 1 (to a growth state), that is, state (j, k +1) equal to 1, state (j, k-1) equal to 1, state (j-1, k) equal to 1, and state (j +1, k) equal to 1;
when the cooling time is t, the solid-liquid interface curvature k is calculated for a grid with state 1curveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T and growth speed VtipSolid phase fraction fsLiquid phase component ClAnd a solid phase component Cs；
Wherein, TMThe melting point of pure magnesium is measured in units of ℃; m islIs the slope of the liquidus in deg.C/wt%; clIs a liquid phase component; t is the grid temperature; gamma is Gibbs coefficient, unit is C m; theta is an angle; deltakIn order to be a coefficient of the dynamic anisotropy,is the derivative in the X-axis direction of the rectangular coordinate system;is the derivative in the Y-axis direction of the rectangular coordinate system;is the average dendrite growth kinetic coefficient, in cm/s/DEG C;selecting between 0.01 and 0.5, and firstly selecting 0.01; growth theta is an isometric dendritic crystal growth orientation angle, and a value is randomly selected between 0 and 90 degrees;
when f iss<1 hour, liquid phase component ClAnd a solid phase component CsAnd the solute Δ C discharged from the solid-liquid interface was calculated as follows:
wherein,the liquid phase component is t-delta t at the last moment;a solid phase component at time t- Δ t;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 ofparThe coefficients are distributed for balance; f. ofsIs the solid phase fraction;representing the solid phase fraction at the current time t; in the same way, ClAnd CsRespectively 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 Liquid phase solutes, namely, the calculation domain has m multiplied by n grids, if the grids with the state-0 at the moment have Liquid _ num, the Liquid phase component of each grid with the state-0 is increased by deltaC/Liquid _ num;
when f issWhen 1, the liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
Cl＝0
at 0s, Cs＝0，fs＝0，Cl＝Co，CoIs 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 ClSolid phase component CsFraction of solid phase fsCurvature k of solid-liquid interfacecurveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T, growth speed VtipTemperature T, average dendrite growth kinetic coefficient
Step five (2-4), the time is increased from 0s to 6s, the step five (2-2) and the step five (2-3) are repeated, and a solid phase fraction-temperature curve is obtained (the time step is generally a smaller value which can be 0.001 s.);
mean dendrite growth kinetics coefficient at this time
F obtained by solving the Charles formula and the solid phase fraction-temperature curves-scheil～TscheilComparing the curves, verifying the selectionThe 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. | fs-fs-scheil|<0.01, then selectReasonable otherwiseIncreasing the temperature by 0.01 cm/s/DEG C, and repeating the step five (2-1) to the step five (2-4) until the | fs-fs-scheil|<0.01, selecting reasonable average dendritic crystal growth kinetic coefficient May be 0.01,0.02,0.03,0.04, until a value is chosen that ensures that the curve calculated on the basis of the cells matches well with the curve calculated on the basis of the summer formula, i calculate thatAt 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 the 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 [1, n/2] of j and the value range [ m/2+1, m ] of k are calculated;
in the second calculation domain, the value range of j [ n/2+1, n ], and 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 ], and 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:
al-7 wt% Si alloy is selected as a research object, α -Al dendrite structure and micro segregation formation are simulated by adopting a cellular automaton model based on a square pairing grid group, the square pairing grid group consists of 300 multiplied by 300 square grids, and the related parameters of physical property parameters required by calculation and parameters required by numerical simulation are listed in Table 1.
TABLE 1 Al-7 wt% Si alloy numerical simulation thermophysical property parameters and calculation parameters
(1) In FIG. 1, cellular automata is used to simulate the summer freezing condition when the average dendrite growth kinetic coefficient Then, the obtained solid phase fraction-temperature change rule (shown by a circle) is well consistent with the solid phase fraction-temperature change rule (solid line) calculated based on the Charles formula. Thus, for Al-7 wt% Si alloys, the growth kinetic coefficient was determined to be 0.06 cm/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, the nucleation parameter selects a numerical value corresponding to "local region 1" in table 1, the white region is a dendrite, corresponds to a negative microsegregation region, and the interdendritic region is a positive microsegregation region. The calculation result is well matched with the experimental result.
(3) In fig. 3a and 3b, when the size of the mesh is small (2 μm), reasonable dendrite morphology can be obtained based on the mesh pairing algorithm fig. 3a and the solid-liquid interface geometric factor algorithm fig. 3b, that is, the dendrite arms are perpendicular to each other.
(4) In fig. 4a, 4a1, 4b1, when the grid size is large (4 μm), reasonable dendrite morphology can be obtained based on a paired grid algorithm (fig. 4a, 4b), and some dendrite growth morphology is unreasonable based on a solid-liquid interface geometric factor algorithm (fig. 4a1, 4b1), that is, an included angle between a secondary arm and a primary arm is not 90 °, primary dendrite arms are not mutually perpendicular, and when the dendrite growth orientation is greater than 60 ° or less than 30 °, such a phenomenon occurs, which indicates that the solid-liquid interface geometric factor algorithm is sensitive to the selection of the grid size, and the 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 geometry factor algorithm is shown in fig. 5 b; 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 small 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 1-4, when the heat treatment time is 500 ℃, the distances (Len) are 18 μm, 30 μm, 66 μm and 87 μm respectively, and the average heat treatment time is 323s, 415s, 2275s and 3946 s. Four different tissue morphologies and microsegregation distributions can be obtained through one calculation, and more choices are provided for the formulation of 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, a square grid (j, k) and 3 surrounding grids (j-1, k), (j, k-1) and (j-1, k-1) are in a group, namely, 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 that 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 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 coefficientUnits are m/s/DEG C;
step six, further dividing the calculation domain into 4 local calculation domains;
step seven, a certain cooling speed is givenUnit ℃/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
Wherein, TLIs the liquidus temperature of the alloy, and the unit is DEG C, i belongs to [1,4 ]]4 different local calculation domains are shown, and different cooling speeds are adopted in the different local calculation domains;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;
wherein N isnucleiRepresents the nucleation density in units of 1/m3；NmaxRepresents the maximum nucleation density in units of 1/m3I represents 4 different local calculation domains, and different local calculation domains adopt different maximum nucleation supercooling and maximum nucleation densities; delta TmeanRepresents the maximum nucleation supercooling in units of ℃; delta TσIndicating standard deviation nucleation supercooling;andrespectively representing the nucleation density, N, at time t and at time t-DeltatnucleiDenotes nucleation density, N at 0snuclei＝0；Andrespectively representing the nucleation supercooling degree, Delta T, at the time T and the time T-Delta TnucleiIndicating the degree of nucleation supercooling,. DELTA.Tnuclei＝TM+mlCl-T, Δ T at 0snuclei＝0；
TMThe melting point of pure magnesium is measured in units of ℃; m islIs the slope of the liquidus in deg.C/wt%; clIs 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:
wherein S issubareaFor local calculation of the domain area, Ssubarea＝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 of each grid in the group is 0 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 varies as follows:
fraction of solid phase fs＝1，Cs＝Cokpar，Cl＝0，Caver＝Csfs+Cl(1-fs)，state＝2，icolor＝Random[1,Neg[i]]，growthθ＝Random[0,90°]；
Wherein f issIs the solid phase fraction, the minimum value of 0 represents the liquid phase, and the maximum value of 1 represents the solid phase; csIs a solid phase component; clIs a liquid phase component; coIs an alloy initial component; caverThe unit of the component is weight percent and is the average component; k is a radical ofparThe coefficients are distributed for balance;
each nucleation core is assigned a label icolor for distinguishing different crystal 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)mothMother and sonCore grid (j, k)mothCapturing 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)sonWill change from liquid to growth state, i.e. state (j, k)sonChange from 0 to 1, mesh (j, k) capturedsonWith and mother core grid (j, k)mothThe same icolor and growth theta values indicate belonging to the same dendrite;
if a certain grid fs1, but of the paired meshess<1, the lattice will also remain in the growth state (state 1) until f of the paired latticesWhen the state of the four grids is 1, the 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) is 1 and fs(j, k) ═ 1, no computation is performed, and the search continues in the computation domain for state (j, k) ═ 1 and fs(j, k) a grid not equal to 1;
for state (j, k) 1 and fsGrid calculation solid-liquid interface curvature k with (j, k) ≠ 1curveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T and growth speed VtipSolid phase fraction fsLiquid phase component ClAnd a solid phase component Cs；
Wherein, deltakIs a dynamic anisotropy coefficient, and gamma is a Gibbs coefficient with the unit of DEG C m;
when f iss<When 1, counting the number of grids with state 0 in the neighbor 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), left upper (j-1, k +1), right upper (j +1, k +1), left lower (j-1, k-1) and right lower (j +1, k-1) grids; for the mesh (j, k), solute exclusion amount Δ C, liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
when f issWhen 1, the liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
Cl＝0
wherein, delta t is a time step length, and t-delta t is the last moment; at 0s, Cs＝0，fs＝0，Cl＝Co；
Upper (j, k +1) Liquid phase composition of the mesh with state 0 in the lower (j, k-1), left (j-1, k), right (j +1, k +1), upper left (j +1, k +1), lower left (j-1, k-1), and lower right (j +1, k-1) meshes is increased
Step eleven for only state (j, k) 0 and state (j, k) 1 and fs(j, k) solute diffusion equation in liquid phase calculated for grid of ≠ 1:
wherein D islIs the diffusion coefficient of solute element in liquid phase;
calculating the solute diffusion equation in the solid phase for a grid with state (j, k) 2:
wherein D issIs the diffusion coefficient of solute element in solid phase; the unit of the diffusion coefficient is m2/s；
Step twelve, repeating the step seven to the step eleven until the temperature of all the grids is less than the solidus temperature TsIf yes, the calculation is terminated, and a solute component distribution data file is output;
based on the calculated micro segregation distribution, three points P1, P2 and P3 are selected in the calculation domain, and the components are respectively C1、C2And C3The distance between point P1 and point P2 is equal to the distance Len between point P2 and point P3; the heat treatment time was estimated using the following formula:
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 treatmentEstimate the heat treatment time theat。
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 with the labels of (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 dendritic crystal 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 mesh group is composed of four meshes (j, k), (j-1, k), (j, k-1) and (j-1, k-1), then the first group of neighbor meshes is composed of (j-2, k), (j-3, k), (j-2, k-1) and (j-3, k-1), the second group of neighbor meshes is composed of (j +2, k), (j +3, k), (j +2, k-1) and (j +3, k-1), the third group of neighbor meshes is composed of (j, k-2), (j-1, k-2), (j, k-3) and (j-1, k-3), the fourth group of neighbor meshes is composed 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)sonWill change from liquid to growth state, i.e. state (j, k)sonFrom 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, that is, state (j, k) is 0, and state (j, k) is the state of the grid; the remaining trellis may have three states:
when f issWhen (j, k) is 0, the liquid state is obtained, and state (j, k) is 0;
when 0 is present<fs(j,k)<1, state (j, k) is 1;
when f issWhen (j, k) is 1 and f of the paired gridssAlso equal to 1, then transition to solid state, state (j, k) 2;
fs(j, k) is the fraction of solid phase in the square grid (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 stepUnits 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:
wherein f iss-ｓcｈeilTo calculate the resulting solid phase fraction, T, using the Charles formulamIs the melting point of the alloy, TLIs the alloy liquidus temperature, kparEquilibrium partition coefficient, T, for the alloyscheilAt a certain cooling speed, the melt temperature, Tscheil＝TＬ-10 × t, the cooling rate is chosen to be 10 ℃/s, t is the cooling time, increasing from 0s to 6 s;
f can be obtained by calculations-scheil～TscheilA curve;
step five (2), simulating a curve of solid phase fraction changing along with temperature under the summer solidification condition based on a cellular automata method;
step five (2-1), setting (m/2, n/2) as a nucleation core grid, namely fs(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)scheilCharacterised by variation, i.e. T ═ TL-10 × t, t increasing from 0s to 6 s;
step five (2-3) and the grid with the state (j, k) ═ 2 change the state values of the upper, lower, left and right grids to 1, namely, the state (j, k +1) ═ 1, the state (j, k-1) ═ 1, the state (j-1, k) ═ 1 and the state (j +1, k) ═ 1;
when the cooling time is t, the solid-liquid interface curvature k is calculated for a grid with state 1curveNormal angle of solid-liquid interfaceGrowth supercooling degree delta T and growth speed VtipSolid phase fraction fsLiquid phase component ClAnd a solid phase component Cs；
Wherein, TMThe melting point of pure magnesium is measured in units of ℃; m islIs the slope of the liquidus in deg.C/wt%; clIs a liquid phase component; t is the grid temperature; gamma is Gibbs coefficient, unit is C m; theta is an angle; deltakIn order to be a coefficient of the dynamic anisotropy,is the derivative in the X-axis direction of the rectangular coordinate system;is the derivative in the Y-axis direction of the rectangular coordinate system;is the average dendrite growth kinetic coefficient, in cm/s/DEG C;selecting between 0.01 and 0.5, and firstly selecting 0.01; growth theta is an isometric dendritic crystal growth orientation angle, and a value is randomly selected between 0 and 90 degrees;
when f iss<1 hour, liquid phase component ClAnd a solid phase component CsAnd the solute Δ C discharged from the solid-liquid interface was calculated as follows:
wherein,the liquid phase component is t-delta t at the last moment;a solid phase component at time t- Δ t;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 ofparThe coefficients are distributed for balance; f. ofsIs the solid phase fraction;representing the solid phase fraction at the current time t; in the same way, ClAnd CsRespectively 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 Liquid phase solutes, namely, the calculation domain has m multiplied by n grids, if the grids with the state-0 at the moment have Liquid _ num, the Liquid phase component of each grid with the state-0 is increased by deltaC/Liquid _ num;
when f issWhen 1, the liquid phase component ClAnd a solid phase component CsThe calculation is as follows:
Cl＝0
at 0s, Cs＝0，fs＝0，Cl＝Co，CoIs 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
F obtained by solving the Charles formula and the solid phase fraction-temperature curves-scheil～TscheilComparing the curves, verifying the selectionThe 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. | fs-fs-scheil|<0.01, then selectReasonable otherwiseIncreasing the temperature by 0.01 cm/s/DEG C, and repeating the step five (2-1) to the step five (2-4) until the | fs-fs-scheil|<0.01, selecting reasonable average dendritic crystal growth kinetic coefficient
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 [1, n/2] of j and the value range [ m/2+1, m ] of k are calculated;
in the second calculation domain, the value range of j [ n/2+1, n ], and 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 ], and the value range of k [1, m/2 ].
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