CN115270573A - Simulation method and system for solidification and coarsening of metal additive manufacturing grain structure - Google Patents
Simulation method and system for solidification and coarsening of metal additive manufacturing grain structure Download PDFInfo
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Abstract
The invention relates to a simulation method and a simulation system for solidification and coarsening of a metal additive manufacturing grain structure, wherein the method comprises the following steps: carrying out grid division on a calculation domain of a metal material; and calculating the temperature distribution at the current moment, determining the area where each unit of metal material is positioned, and further simulating solidification and coarsening of the molten pool area and the heat affected area unit by adopting a cellular automaton method and a Monte Carlo method respectively. In the invention, the cellular automata method and the Monte Carlo method are strongly coupled, so that the solidification and coarsening of the grain structure can be considered simultaneously, the simulation result is more accurate, the advantages of the two algorithms are fused, and the calculation efficiency is improved while the more complete physical basis is realized.
Description
Technical Field
The invention relates to the technical field of metal additive manufacturing, in particular to a method and a system for simulating solidification and coarsening of a metal additive manufacturing grain structure.
Background
Metal additive manufacturing technology (also known as metal 3D printing technology) melts an additional metal material into a liquid state and forms a molten pool by a high power heat beam (laser or electron beam). The molten material is solidified to form a deposition layer, and the molten material is piled up layer by layer one by one, so that the manufacturing and forming of the three-dimensional part in any shape can be realized, and the metal additive manufacturing technology is a low-cost, short-period, design and manufacturing integrated revolutionary manufacturing technology. Compared with the traditional manufacturing technology, the method is mainly characterized in that high temperature gradient and periodic cycle thermal history cause complex metallurgical change, form complex grain structure and finally influence the mechanical property of the formed part. The method is a well-known relationship of manufacturing process-structure-mechanical property, and the grain structure is used as a bridge of the process-property, so that accurate prediction and modeling have important significance.
The whole additive manufacturing process comprises a plurality of complex metallurgical phenomena, common metallurgical phenomena are shown in figure 1, nucleation of equiaxial crystals, epitaxial and competitive growth of a molten pool boundary and grain coarsening of a heat affected zone around the molten pool, which occur in two adjacent zones simultaneously and mutually affect each other, and the final complex grain morphology is caused together.
Existing simulation techniques include cellular automata and monte carlo. The prior art has advantages and disadvantages when simulating solidification of a molten pool and coarsening of crystal grains in a heat affected zone in additive manufacturing: the cellular automation method is based on the solidification theory, has unique advantages in simulating a molten pool solidification structure, but has relatively large calculated amount, and the Monte Carlo method is based on mathematical probability, has high coarsening calculation efficiency in a simulated heat affected zone, but lacks physical foundation, such as crystal orientation information and the like. The two metallurgical phenomena will occur in adjacent spaces at the same time physically and mutually affect each other. Therefore, in order to simulate the grain structure of additive manufacturing more accurately, the invention provides a method and a system for simulating solidification and coarsening of the grain structure of metal additive manufacturing, and more specifically, the method couples a cellular automaton method and a Monte Carlo method, so that the solidification and coarsening of the grain structure can be considered simultaneously, the simulation result is more accurate, the advantages of two algorithms are fused, and the calculation efficiency is improved while the physical basis is more complete.
Disclosure of Invention
The invention aims to provide a method and a system for simulating solidification and coarsening of a metal additive manufacturing grain structure, which can simultaneously simulate solidification in a molten pool and grain coarsening in a heat affected zone on the basis of more physical foundations (such as considering the influence of crystal orientation on competitive growth and coarsening and considering physical time evolution), and more accurately simulate the grain structure of additive manufacturing.
In order to achieve the purpose, the invention provides the following scheme:
a simulation method of solidification and coarsening of a metal additive manufacturing grain structure, comprising:
performing grid division on a calculation domain of a metal material, giving an initial grain identifier and a crystal orientation to a unit metal material of each grid unit, selecting a preset number of unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degree to each potential nucleation point according to Gaussian distribution;
calculating the temperature field distribution of the calculation domain at the current moment t;
determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-influence area is an area outside the heat-influence area and the molten pool area;
selecting each unit metal material one by one for all the unit metal materials in the molten pool area, simulating the growth and capture process according to the states and temperatures of the unit metal materials and the neighboring unit metal materials by using a cellular automation method, and simulating the nucleation process by using whether the unit metal materials are the potential nucleation points and the critical supercooling degrees thereof;
selecting each unit metal material one by one for all the unit metal materials in the heat affected zone, and simulating a coarsening process by using a Monte Carlo method;
when the unit metal material is in the non-affected zone, the current unit metal material does not need to be subjected to simulation treatment;
judging whether the temperature of each unit metal material is less than the lower limit temperature of a heat affected zone or not to obtain a first judgment result;
if the first judgment result is negative, making t = t + Δ t, and returning to the step of calculating the temperature field distribution of the calculation domain at the time t;
and if the first judgment result is yes, completing the simulation of solidification and coarsening.
A simulation system for solidification and coarsening of a metal additive manufacturing grain structure, comprising:
the calculation domain initialization module is used for carrying out grid division on the calculation domain of the metal material, endowing an initial grain identifier and a crystal orientation to the unit metal material of each grid unit, selecting a preset number of the unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degrees to each potential nucleation point according to Gaussian distribution;
the state area determining module is used for calculating the temperature field distribution of the calculation area at the moment t; determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-influence area is an area outside the heat-influence area and the molten pool area;
the solidification process simulation module is used for selecting each unit metal material one by one for all the unit metal materials in the molten pool area, simulating the growth and capture processes according to the states and temperatures of the unit metal materials and the adjacent unit metal materials by using a cellular automation method, and simulating the nucleation process by using whether the unit metal materials are the potential nucleation points and the critical supercooling degree;
the coarsening process simulation module is used for selecting each unit metal material one by one for all the unit metal materials in the heat affected zone and simulating a coarsening process by utilizing a Monte Carlo method;
the judging module is used for judging whether the temperature of each unit metal material is less than the lower limit temperature of the heat affected zone or not to obtain a first judging result;
if the first judgment result is negative, making t = t + delta t, and returning to the step of calculating the temperature field distribution of the calculation domain at the current moment t;
and if the first judgment result is yes, completing the simulation of solidification and coarsening.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention relates to a simulation method and a simulation system for solidification and coarsening of a metal additive manufacturing grain structure, and aims to solve the problem that the solidification and coarsening of a molten pool cannot be considered simultaneously when the metal additive manufacturing grain structure is simulated by the conventional method. The simulation includes: carrying out grid division on a calculation domain of a metal material; determining the region where the state of each unit metal material is located based on the current temperature field distribution; performing solidification simulation by using a cellular automation method and coarsening simulation by using a Monte Carlo method according to the area where the unit metal material is located; until the temperature of each unit metal material is judged to be less than the lower limit temperature of the heat affected zone. The cellular automata method is coupled with the Monte Carlo method, so that the solidification and coarsening of the grain structure can be considered at the same time, the simulation result is more accurate, the advantages of the two algorithms are combined, and the calculation efficiency is improved while the physical basis is more complete.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the embodiments will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic view of an additive manufacturing process microstructure evolution process provided by the present invention;
FIG. 2 is a two-dimensional schematic diagram of the envelope growth and capture of the cellular automaton method provided by the present invention;
FIG. 3 is a schematic diagram of a Monte Carlo method randomly modifying a center unit die identifier according to the present invention;
fig. 4 is a flowchart of a simulation method for solidification and coarsening of a grain structure in metal additive manufacturing according to embodiment 1 of the present invention;
FIG. 5 is a schematic view of an octahedral envelope provided in example 1 of the present invention;
fig. 6 is a block diagram of a simulation system for solidification and coarsening of a grain structure in metal additive manufacturing provided in embodiment 2 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The cellular automation method is based on a solidification theory and a random nucleation model, has good physical basis, and can accurately simulate the solidification process in a molten pool. The kinetic monte carlo method can simulate the grain coarsening process in the heat affected zone by modifying the grain identifiers to minimize the local grain boundary energy through a random algorithm. Two methods will be described below:
cellular automata method: cellular automata discretizes a computational domain into a number of tiny units, each unit representing a local material point at which the unit is located, and comprising a series of variables: unit state, grain identifier, crystal orientation, unit temperature, octahedral envelope, and the like. The algorithm generates new crystal nucleuses which are randomly distributed according to the nucleation model, and determines the growth speed of the tips of the crystal nucleuses according to the growth kinetics of the tips of the dendrites. The nucleation model generally employs a continuous nucleation model that randomly selects potential nucleation points of a given density in the computational domain and assigns a critical degree of supercooling to each nucleation point. When no envelope exists in the center of the nucleation point unit and the degree of supercooling of the nucleation point unit reaches the critical degree of supercooling criterion, the unit nucleates and generates a randomly oriented octahedral envelope in the center of the unit. The envelope of the nucleation cell (called parent cell) is then grown continuously according to its own supercooling degree, and when the envelope exceeds the center of the neighboring cell, the neighboring cell (called child cell) is captured and a child envelope inheriting the parent cell envelope orientation is generated in the neighboring cell according to an off-center growth algorithm. Growth and capture of the envelope as shown in fig. 2, fig. 2 (a) shows the envelope growth and fig. 2 (b) shows the neighbor cells captured. The continuous growth and capture process of the unit envelope is a solidification process that solid crystal nuclei continuously consume surrounding liquid units. As can be seen from the algorithm, the model comprises a nucleation model and a dendrite tip dynamic model, so that the method has complete physical significance. However, the algorithm can only simulate the solidification process and neglect the grain coarsening process of the heat affected zone around the molten pool.
Kinetic monte carlo method: the monte carlo method is a stochastic algorithm based on interface energy minimization. The algorithm discretizes the computational domain into small units and assigns a grain identifier to each unit. Two adjacent cells, if they have different grain identifiers, constitute a grain boundary pair. For a three-dimensional model, a cell has 26 neighbor cells, and thus a maximum of 26 grain boundary pairs. The monte carlo method randomly selects a unit on the grain boundary each time, and randomly changes the grain identifier of the unit to the grain identifier of a neighbor unit, as shown in fig. 3, wherein a solid black line represents the modified grain boundary. Assuming that the pairs of grain boundary pairs of the central unit before and after modification are m and n, respectively, this modification causes the change in the grain boundary energy of the system to be Δ E = (m-n) E, (where E is the grain boundary energy that one grain boundary pair has). Since the driving force for grain coarsening is that the system grain boundary energy is minimized, the Monte Carlo method receives this modification with a probability of
When the delta E is larger than or equal to 0, the modification is completely received, when the delta E is smaller than 0, the modification is received according to a certain probability, and the larger the delta E is, the lower the receiving probability is. Therefore, as the algorithm is continuously carried out, the grain boundary can be gradually reduced, and the effect of simulating grain coarsening is achieved. The Monte Carlo method modifies the grain boundary based on probability, and can well simulate the grain coarsening process, but the algorithm cannot simulate the solidification process. In response to this problem, while there have been attempts by researchers to improve upon the monte carlo method to enable it to simulate coagulation, the monte carlo method still lacks a physical basis, such as: the Monte Carlo method ignores the crystal orientation, so that the competitive growth process of crystal grains with different crystal orientations in the solidification process is difficult to simulate; the basic unit of time in the Monte Carlo method is the Monte Carlo time step lacking physical significance, not physical time.
The invention aims to provide a method and a system for simulating solidification and coarsening of a metal additive manufacturing grain structure, which can simultaneously simulate solidification in a molten pool and grain coarsening in a heat affected zone on the basis of more physical foundations (such as considering the influence of crystal orientation on competitive growth and coarsening and considering physical time evolution), and more accurately simulate the grain structure of additive manufacturing.
In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Example 1
As shown in fig. 4, the present embodiment provides a simulation method for solidification and coarsening of a metal additive manufacturing grain structure, including:
s1: the method comprises the steps of carrying out grid division on a calculation domain of a metal material, giving an initial grain identifier and a crystal orientation to a unit metal material of each grid unit, selecting a preset number of unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degree delta T to each potential nucleation point according to Gaussian distribution c 。
S2: calculating the temperature field distribution of the calculation domain at the current moment t; determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-affected zone is an area outside the range of the heat-affected zone.
In step S2, the expression for calculating the temperature field distribution of the calculation domain at time t is:
wherein, T 0 Is the starting temperature; q and v are the power and speed of the heat source; r (y, z) is the distance from the grid cell to the heat source path; λ is the thermal conductivity; α is thermal diffusivity; ξ = x-vt is the distance of the grid cell from the center of the heat source in the scan direction; x, y and z are coordinate values of the center of the grid cell.
In this embodiment, the temperature field may be calculated by other methods, such as a finite element method, a finite volume method, a finite difference method, a lattice boltzmann method, and the like.
Wherein the state of the metal material in each unit in the step S2 is in the molten pool area, and the criteria of the heat affected zone and the non-affected zone are as follows:
if T > = T s The unit metal material is located in the molten bath, wherein T s Is the solid phase limit temperature of the material.
If T is s ＞T＞＝T HAZ The unit metal material is located in the heat affected zone, where T HAZ The lower temperature of the heat affected zone of the material.
If T < T HAZ If the unit metal material is located in the non-affected zone, the current unit metal material is not required to be subjected to simulation processing.
The specific judgment process is as follows:
the determining, based on the temperature field distribution, a region in which the state of each unit metal material is located specifically includes:
for each unit metal material, judging whether the temperature T of the unit metal material is more than or equal to the solid phase limit temperature T of the material or not s Obtaining a second judgment result;
when the second judgment result is yes, determining that the state of the unit metal material is in the molten pool area;
when the second judgment result is negative, judging whether the temperature T of the unit metal material is more than or equal to the heat affected zone of the material or notLower limit temperature T of HAZ If yes, determining that the current state of the unit metal material is in the heat affected zone. If not, the state of the unit metal material is in a region outside the heat affected zone, namely a non-affected zone.
S3: and selecting each unit metal material one by one for all the unit metal materials in the molten pool area, simulating the growth and capture process according to the states and temperatures of the unit metal materials and the metal materials of the neighboring units thereof by using a cellular automation method, and simulating the nucleation process by using whether the unit metal materials are the potential nucleation points and the critical supercooling degrees thereof. This step is completed by the time all the unit metal materials are selected once.
Wherein, step S3 specifically includes:
step S31: and calculating the supercooling degree of the unit metal material according to the current temperature of the unit metal material and the material liquid phase limit temperature. Δ T = T l -T，T l Is the material liquid phase limit temperature.
Step S32: and judging the state of each unit metal material according to the supercooling degree.
(1) And when the supercooling degree delta T is less than 0 and the unit metal material is overheated, deleting the central envelope of the unit metal material and changing the state of the unit metal material into a liquid state.
(2) And when the supercooling degree delta T is more than or equal to 0, supercooling the unit metal material, and performing nucleation process simulation and growth and capture process simulation according to the state of the unit metal material and whether the unit metal material is the potential nucleation point.
Specifically, when the state of the unit metal material is liquid (that is, no envelope exists in the unit metal material), and the unit metal material is the potential nucleation point, it is determined whether the supercooling degree of the unit metal material is greater than or equal to the critical supercooling degree, and a third determination result is obtained. And when the condition that the unit metal material is the potential nucleation point is not met, performing nucleation process simulation on other unit metal materials.
If the third determination result is yes, an octahedral envelope with random orientation is generated in the center of the current unit metal material, as shown in fig. 5, the envelope orientation represents the orientation of crystal grains, and the envelope size is controlled by the semi-diagonal length thereof, and the initial length of the envelope is 0. The generation envelope is the process of forming crystal nucleus.
And if the third judgment result is negative, the unit metal material cannot be nucleated currently, namely, the nucleation process simulation is not carried out.
When the state of the unit metal material is solid (that is, an envelope exists in the unit metal material), judging whether liquid exists in the states of the neighboring unit metal materials of the unit metal material (whether more than one liquid unit exists in the neighboring unit metal material), and obtaining a fourth judgment result;
if the fourth judgment result is that the envelope in the unit metal material starts to grow, updating the size of the envelope in the unit metal material; the update formula is:
L t+Δt ＝L t +v(ΔT)Δt
v(ΔT)＝a 1 ΔT+a 2 ΔT 2 +a 3 ΔT 3
wherein L is t And L t+Δt The envelope size modules are respectively at t moment and t + delta t moment; v (Δ T) is the envelope growth rate; a is 1 ，a 2 ，a 3 Is a fitting parameter; delta T is the supercooling degree; Δ t is the time increment of the current time iteration step of the cellular automaton model.
When the center of the liquid neighbor cell metal material is within the envelope in the cell metal material, the liquid neighbor cell metal material is captured by the envelope in the cell metal material. And generating an envelope with the same orientation as the envelope at the center of the metal material of the neighboring unit so as to inherit the growth direction of the envelope.
If the fourth judgment result is negative, updating the size of the envelope in the unit metal material, and stopping the growth of the envelope in the unit metal material.
S4: and selecting each unit metal material one by one for all the unit metal materials in the heat affected zone, and simulating the coarsening process by utilizing a Monte Carlo method. The monte carlo method applied in this embodiment is to associate the coarsening time step in the conventional monte carlo method with the real physical time, and introduce the grain boundary migration probability in the probability calculation of whether the grain identifier is modified.
Step S4 specifically includes:
step S41: calculating a coarsening time step t C And calculating a coarsening time step increment delta t within the time increment delta t according to the coarsening time step C (t) and its maximum value Deltat C max (t) of (d). Coarsening time step t C The method is used for coarsening the iteration time step in the simulation, and the meaning of the method is iteration times and has no physical significance. And delta t is the time increment in the cellular automata and is real physical time.
The calculation formula of the coarsening time step is as follows:
wherein, K 1 And n 1 Is a model constant; k and n are respectively an index pre-factor and a grain coarsening index (which can be obtained by experimental measurement or theoretical calculation); r is a gas constant; t (T) is the current time temperature, L 0 Is the initial grain size, d cell For mesh size, Q is the activation energy.
The coarsening time step increment corresponding to the time increment Δ t is:
Δt C (t)＝t C (t)-t C (t-Δt)。
within a time increment Δ t, an iteration Δ t is required for each unit metallic material C (t) times, Δ t for different unit metal materials for any time due to non-isothermal process of additive manufacturing C (t) is different, therefore, for all the unit metal materials in the heat affected zone, each unit metal material is selected one by one, and the coarsening time step increment delta t is calculated C (t) and obtaining Δ t C (t) maximum value Δ t C max (t) of (d). The time increment is delta t, each unit metal material of the heat affected zone is traversed and subjected to coarsening simulation calculation, when each unit is traversed and calculated once and recorded as a coarsening time step, the total coarsening time step is delta t C max (t)。
Step S42: and selecting each unit metal material one by one for all the unit metal materials in the heat affected zone, and judging whether the current unit metal material is positioned in a grain boundary (namely whether the grain identifier of the current unit metal material is consistent with the grain identifiers of all the corresponding neighbor unit metal materials) to obtain a fifth judgment result. When all the unit metal materials in the heat affected zone are selected once, the roughening time step is increased once, and the process returns to "determining whether the number of roughening time steps of the heat affected zone within the time increment Δ t is the maximum number of iterations" in step S46.
Step S43: if the fifth determination result is yes, the unit metal material is not located at the grain boundary, the grain identifier of the current unit metal material is not modified, and the next metal material is continuously traversed and the process returns to "determine whether the current unit metal material is located at the grain boundary (i.e. whether the grain identifier of the current unit metal material is consistent with the grain identifiers of all the corresponding neighboring unit metal materials)" in step S42.
Step S44: if the fifth judgment result is negative, the unit metal material is positioned at the grain boundary, and the grain identifier of the unit metal material is pre-modified to be the target grain identifier; the target grain identifier is the grain identifier of any one of the neighboring unit metallic materials that is not consistent with the grain identifier of the current unit metallic material. The pre-modification is understood to be a pre-modification, not a final modification, and whether the pre-modification is accepted or not is judged based on the acceptance probability, so that the final modification result can be determined.
Step S45: and calculating the acceptance probability according to the boundary energy difference, the temperature influence probability and the grain boundary migration probability before and after the crystal grain identifier is modified, and determining whether the pre-modification of the crystal grain identifier is accepted according to the acceptance probability.
Wherein, the calculation formula of the acceptance probability is as follows:
wherein, P is the acceptance probability; p is a radical of m As the grain boundary migration probability associated with the grain boundary misorientation,
θ ij is poor grain boundary orientation; theta.theta. m The boundary value of a large-angle crystal boundary and a small-angle crystal boundary is obtained; delta E is the boundary energy difference before and after the crystal grain identifier is modified; k is a model constant used to reduce anisotropy introduced by the cubic lattice. p is a radical of T For the temperature influence probability, for taking into account the influence of different temperatures at different spatial positions on the coarsening of the tissue, p T The calculation formula of (c) is:
wherein, Δ t C (t) is the coarsening time step increment; Δ t C max (t) is the maximum value of the coarsening time step increment.
Since the pre-modification grain identifier is random, the modification may not conform to the physical law (i.e. grain coarsening proceeds toward the direction of reducing the free energy of the system), so it is necessary to judge the rationality of the modification according to the energy variation of the pre-modification, and modify the modification result by the acceptance probability (i.e. reasonable pre-modification has a greater probability of being accepted, and unreasonable pre-modification has a greater probability of being rejected), and the pre-modification is rejected and then the modification is cancelled.
Step S46: judging whether the coarsening time step number of the heat affected zone in the time increment delta t is the maximum iteration number or not to obtain a sixth judgment result; the maximum iteration number is the maximum value delta t of the coarsening time step increment C max (t)。
Step S47: if the sixth determination result is negative, the process returns to "select each unit metal material one by one for all the unit metal materials in the heat affected zone" in step S42.
Step S48: and if the sixth judgment result is yes, finishing the grain coarsening simulation at the current moment.
S5: and judging whether the temperature of each unit metal material is less than the lower limit temperature of the heat affected zone or not to obtain a first judgment result.
And if the first judgment result is negative, enabling t = t + delta t, and returning to the step S2.
And if the first judgment result is yes, completing the simulation of solidification and coarsening.
The solidification process of the metal material occurs between the solidus and liquidus temperatures, and the coarsening process occurs between the lower limit temperature of the heat affected zone and the solidus temperature, so when all the cell temperatures in the calculation region are cooled below the lower limit temperature of the heat affected zone, that is, the solidification and coarsening processes are completed, the simulation process is finished.
In this embodiment, (1) a cellular automation method and a monte carlo method are coupled, and the coupling algorithm can simultaneously consider solidification in the molten bath and grain coarsening of a heat affected zone, that is, solidification simulation and coarsening simulation can be simultaneously performed in one method flow. (2) The iteration time step of coarsening the crystal grains without physical significance is coupled with the physical time of the cellular automaton, the solidification simulation and the coarsening simulation are carried out in the same physical time scale, and the simulation result is more accurate. (3) The advantages of the two algorithms are fused, namely the calculation efficiency is improved, and meanwhile, a more complete physical basis is achieved.
Example 2
As shown in fig. 6, the present embodiment provides a simulation system for solidification and coarsening of a grain structure in metal additive manufacturing, including:
the calculation domain initialization module M1 is used for carrying out grid division on a calculation domain of a metal material, endowing an initial grain identifier and a crystal orientation to a unit metal material of each grid unit, selecting a preset number of unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degrees to each potential nucleation point according to Gaussian distribution;
the state area determining module M2 is used for calculating the temperature field distribution of the calculation area at the current moment t; determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-influence area is an area outside the range of the heat-influence area;
a solidification process simulation module M3, which is used for selecting each unit metal material one by one for all the unit metal materials in the molten pool area, carrying out growth and capture process simulation according to the states and temperatures of the unit metal materials and the adjacent unit metal materials by using a cellular automation method, and carrying out nucleation process simulation according to whether the unit metal materials are the potential nucleation points and the critical supercooling degrees of the unit metal materials;
the coarsening process simulation module M4 is used for selecting each unit metal material one by one for all the unit metal materials in the heat affected zone and simulating a coarsening process by utilizing a Monte Carlo method;
the judging module M5 is used for judging whether the temperature of each unit metal material is less than the lower limit temperature of the heat affected zone or not to obtain a first judging result;
if the first judgment result is negative, making t = t + Δ t, and returning to the step of calculating the temperature field distribution of the calculation domain at the current moment t;
and if the first judgment result is yes, completing the simulation of solidification and coarsening.
For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A simulation method for solidification and coarsening of a metal additive manufacturing grain structure is characterized by comprising the following steps:
performing grid division on a calculation domain of a metal material, giving an initial grain identifier and a crystal orientation to a unit metal material of each grid unit, selecting a preset number of unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degree to each potential nucleation point according to Gaussian distribution;
calculating the temperature field distribution of the calculation domain at the current moment t;
determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-influence area is an area outside the range of the heat-influence area;
selecting each unit metal material one by one for all the unit metal materials in the molten pool area, simulating the growth and capture process according to the states and temperatures of the unit metal materials and the metal materials of the neighboring units by using a cellular automation method, and simulating the nucleation process by using whether the unit metal materials are the potential nucleation points and the critical supercooling degrees of the unit metal materials;
selecting each unit metal material one by one for all the unit metal materials in the heat affected zone, and simulating a coarsening process by using a Monte Carlo method;
when the unit metal material is in the non-affected zone, the current unit metal material is not required to be subjected to simulation treatment;
judging whether the temperature of each unit metal material is less than the lower limit temperature of a heat affected zone or not to obtain a first judgment result;
if the first judgment result is negative, making t = t + delta t, and returning to the step of calculating the temperature field distribution of the calculation domain at the time t;
and if the first judgment result is yes, completing the simulation of solidification and coarsening.
2. The method of claim 1, wherein the expression for calculating the temperature field distribution of the calculation domain at a current time t is:
wherein, T 0 Is the starting temperature; q and v are the power and speed of the heat source; r (y, z) is the distance from the grid cell to the heat source path; λ is the thermal conductivity; α is thermal diffusivity; ξ = x-vt is the distance of the grid cell from the center of the heat source in the scan direction; x, y and z are coordinate values of the center of the grid cell.
3. The method according to claim 2, wherein the determining the region where the state of each of the unit metal materials is based on the temperature field distribution specifically comprises:
for each unit metal material, judging whether the temperature of the unit metal material is greater than or equal to the solid phase limit temperature of the material or not to obtain a second judgment result;
when the second judgment result is yes, determining that the unit metal material is in the molten pool area;
when the second judgment result is negative, judging whether the temperature of the unit metal material is greater than or equal to the lower limit temperature of the material heat affected zone; if so, determining that the current state of the unit metal material is in the heat affected zone, and if not, determining that the current state of the unit metal material is in the non-affected zone.
4. The method of claim 1, wherein the simulating the growth and capture process according to the states and temperatures of the unit metallic material and the neighboring unit metallic materials by using the cellular automata method, and the simulating the nucleation process according to whether the unit metallic material is the potential nucleation point and the critical supercooling degree thereof comprise:
calculating the supercooling degree of the unit metal material according to the current temperature of the unit metal material and the material liquid phase limit temperature;
for each unit metal material, judging the state of the unit metal material according to the supercooling degree;
when the supercooling degree is less than 0, deleting the central envelope of the unit metal material and changing the state of the unit metal material into a liquid state;
and when the supercooling degree is more than or equal to 0, performing nucleation process simulation and growth and capture process simulation according to the state of the unit metal material and whether the unit metal material is the potential nucleation point.
5. The method of claim 4, wherein the performing nucleation process simulation and growth and capture process simulation based on the state of the unit metallic material and whether the unit metallic material is the potential nucleation point comprises:
when the unit metal material is in a liquid state and the unit metal material is the potential nucleation point, judging whether the supercooling degree of the unit metal material is greater than or equal to the critical supercooling degree to obtain a third judgment result;
if the third judgment result is yes, generating an octahedral envelope with random orientation in the center of the current unit metal material;
if the third judgment result is negative, the current unit metal material does not carry out nucleation process simulation;
when the state of the unit metal material is solid, judging whether liquid exists in the states of the neighboring unit metal materials of the unit metal material to obtain a fourth judgment result;
if the fourth judgment result is yes, updating the size of the envelope in the unit metal material; when the center of the liquid neighbor unit metal material is positioned in the envelope of the unit metal material, the liquid neighbor unit metal material is captured by the envelope of the unit metal material;
if the fourth judgment result is negative, updating the size of the envelope in the unit metal material, and stopping the growth of the envelope in the unit metal material.
6. The method according to claim 5, wherein the updating the size of the envelope in the unit metal material comprises:
L t+Δt ＝L t +u(ΔT)Δt
u(ΔT)＝a 1 ΔT+a 2 ΔT 2 +a 3 ΔT 3
wherein L is t And L t+Δt The envelope size modules are respectively at t moment and t + delta t moment; v (Δ T) is the envelope growth rate; a is a 1 ，a 2 ，a 3 Is a fitting parameter; delta T is the supercooling degree; Δ t is the time increment of the current time iteration step of the cellular automaton model.
7. The method according to claim 1, wherein the simulation of the coarsening process using the monte carlo method specifically comprises:
calculating a coarsening time step, and calculating a coarsening time step increment in a time increment in a cellular automaton method according to the coarsening time step;
selecting each unit metal material one by one for all the unit metal materials in the heat affected zone; for each unit metal material, judging whether the grain identifiers of the current unit metal material are consistent with the grain identifiers of the corresponding neighbor unit metal material or not, and obtaining a fifth judgment result 2
If the fifth judgment result is yes, the unit metal material is not located at the grain boundary, and the grain identifier of the current unit metal material is not modified;
if the fifth judgment result is negative, the unit metal material is positioned at the grain boundary, and the grain identifier of the unit metal material is pre-modified to be the target grain identifier; the target grain identifier is any one of the grain identifiers of the neighbor unit metal materials which are inconsistent with the grain identifier of the current unit metal material;
calculating an acceptance probability according to the boundary energy difference, the temperature influence probability and the grain boundary migration probability before and after the crystal grain identifier is modified, and determining whether the pre-modification of the crystal grain identifier is accepted according to the acceptance probability;
judging whether the coarsening traversal time of the heat affected zone in the time increment delta t is the maximum iteration time or not to obtain a sixth judgment result; the maximum iteration number is the maximum value of the coarsening time step increment;
if the sixth judgment result is negative, returning to the step of selecting each unit metal material one by one for all the unit metal materials in the heat affected zone;
and if the sixth judgment result is yes, finishing the grain coarsening simulation at the current moment.
8. The method of claim 7, wherein the acceptance probability is calculated by:
wherein, P is the acceptance probability; p is a radical of m As the grain boundary migration probability associated with the grain boundary misorientation,
θ ij is poor grain boundary orientation; theta m The boundary value of a large-angle crystal boundary and a small-angle crystal boundary is obtained; delta E is the boundary energy difference before and after the crystal grain identifier is modified; k is the model constant.
9. The method of claim 7, wherein the temperature influence probability is calculated by:
wherein, Δ t C (t) is the coarsening time step increment; Δ t C max (t) is the maximum value of the coarsening time step increment.
10. A system based on the method of any one of claims 1 to 9, comprising:
the calculation domain initialization module is used for carrying out grid division on the calculation domain of the metal material, endowing an initial grain identifier and a crystal orientation to the unit metal material of each grid unit, selecting a preset number of the unit metal materials as potential nucleation points according to nucleation density, and distributing critical supercooling degrees to the potential nucleation points according to Gaussian distribution;
the state area determining module is used for calculating the temperature field distribution of the calculation area at the current moment t; determining the region where the state of each unit metal material is located based on the current temperature field distribution; the area is a molten pool area, a heat affected area or a non-affected area; the non-influence area is an area outside the range of the heat-influence area;
the solidification process simulation module is used for simulating the growth and capture process and the nucleation process by utilizing a cellular automation method according to the states and temperatures of the unit metal material and the neighboring unit metal material thereof, whether the unit metal material is the potential nucleation point and the critical supercooling degree thereof when the unit metal material is in the molten pool area;
the coarsening process simulation module is used for simulating a coarsening process by utilizing a Monte Carlo method when the unit metal material is in the heat affected zone;
the judging module is used for judging whether the temperature of each unit metal material is less than the lower limit temperature of the heat affected zone or not to obtain a first judging result;
if the first judgment result is negative, making t = t + Δ t, and returning to the step of calculating the temperature field distribution of the calculation domain at the current moment t;
and if the first judgment result is yes, completing the simulation of solidification and coarsening.
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