CN109522675A - The simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure - Google Patents
The simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure Download PDFInfo
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- 238000004458 analytical method Methods 0.000 title claims abstract description 34
- 238000004088 simulation Methods 0.000 title claims abstract description 29
- 239000006023 eutectic alloy Substances 0.000 title claims abstract description 23
- 239000000463 material Substances 0.000 claims abstract description 31
- 238000004364 calculation method Methods 0.000 claims abstract description 6
- 239000013078 crystal Substances 0.000 claims description 61
- 238000013508 migration Methods 0.000 claims description 53
- 230000005012 migration Effects 0.000 claims description 51
- 238000009792 diffusion process Methods 0.000 claims description 49
- 238000003491 array Methods 0.000 claims description 34
- 230000008859 change Effects 0.000 claims description 17
- XOFYZVNMUHMLCC-ZPOLXVRWSA-N prednisone Chemical compound O=C1C=C[C@]2(C)[C@H]3C(=O)C[C@](C)([C@@](CC4)(O)C(=O)CO)[C@@H]4[C@@H]3CCC2=C1 XOFYZVNMUHMLCC-ZPOLXVRWSA-N 0.000 claims description 17
- 239000011159 matrix material Substances 0.000 claims description 8
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- 230000005496 eutectics Effects 0.000 abstract description 27
- 238000000034 method Methods 0.000 abstract description 22
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- 238000000342 Monte Carlo simulation Methods 0.000 abstract description 3
- 238000001514 detection method Methods 0.000 abstract description 2
- 230000007812 deficiency Effects 0.000 abstract 1
- 239000012071 phase Substances 0.000 description 56
- 229910000679 solder Inorganic materials 0.000 description 11
- 230000008569 process Effects 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- ATJFFYVFTNAWJD-UHFFFAOYSA-N Tin Chemical compound [Sn] ATJFFYVFTNAWJD-UHFFFAOYSA-N 0.000 description 2
- 229910045601 alloy Inorganic materials 0.000 description 2
- 239000000956 alloy Substances 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000003466 welding Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000001413 cellular effect Effects 0.000 description 1
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- 239000007787 solid Substances 0.000 description 1
- 239000007790 solid phase Substances 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 238000001089 thermophoresis Methods 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
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Abstract
The invention discloses a kind of simulation of tinbase binary eutectic alloy microstructure and finite element solving analysis methods, are related to calculation material science field.The eutectic structure that this method is simulated and the eutectic structure shape that laboratory apparatus collects are very much like, and it can be in mainstream finite element CAE software and platform (such as ANSYS, MARC, ABAQUS, MSC/PATRAN, COMSOL etc.) realize eutectic structure load, solution and analysis；This method can make up the deficiency of existing tinbase binary eutectic alloy microstructure detection technique, realize the characterization of its microstructure physics and mechanical behavior.The method is by Monte Carlo Method in conjunction with finite element method, improve eutectic structure modeling efficiency, realize that the load of eutectic structure is solved and analyzed, a kind of new method is provided for eutectic structure signature analysis and fail-safe analysis, the very good solution problem of eutectic structure microstructure modeling and performance characterization.
Description
Technical field
The present invention relates to calculation material science fields, and in particular to a kind of tinbase binary eutectic alloy microstructure
Simulation and finite element solving analysis method.
Background technique
Tinbase binary eutectic alloy solder is widely used in electronic component and micro- interconnection solder joint of equipment.With
The trend of the continuous development of electronics industry middle-high density encapsulation technology, electronic device and system compact is more and more obvious, and is caused
The lasting reduction of welding spot size, solder joint solder matrix show apparent microstructure (binary eutectic tissue, two kinds of solid phase machines
The mixture of tool) inhomogeneities.Researchers at home and abroad are it is believed that solder joint is the weakest in electronic product and equipment
Part.It is obvious that research finds that binary eutectic structural heterogenity meeting butt welding point electromigration, thermophoresis and mechanics reliability etc. cause
It influences.However, due to the limitation of testing method and instrument detection accuracy, tiny area current density, temperature gradient and answer
The size of stress-strain etc. and the measurement of distribution and characterization are extremely difficult or even cannot achieve therefore micro- about binary eutectic tissue
The size of area's current density, temperature gradient or ess-strain etc. and the research of distribution and report are very deficient.
Due to the limitation of research technique, finite element method is used for microcell current density, temperature gradient or ess-strain
Deng size and distribution assessment.Conventional finite element modeling method is based on point, line, surface solid modelling, and user utilizes software circle
Face operation is ordered by determining that the coordinate relationship of point, line, surface and body establishes geometrical model, is then obtained by grid division
Finite element model.Either established in the Computer Aided Design Platforms such as AUTOCAD, UG, SOLIDWORKS and PRO/E
Geometrical model, is then introduced into finite element CAE software, and last grid division obtains finite element model.But binary eutectic tissue
Shape and structure are extremely complex, and conventional finite element modeling method to take a significant amount of time and energy, or even cannot achieve modeling.
Therefore, previously the processing of solder joint binary eutectic tissue homogeneity is not considered two kinds of eutectic phase (eutectic groups by most researchs
Phase in knitting) physical and mechanical properties difference.It has been reported and points out, Phase Field, Cellular Automata Method, Monte Carlo Method can
To realize the numerical modeling of complicated shape and structure binary eutectic tissue.However, these methods can not achieve to its complicated object
Solution analysis under reason and mechanical loading.
Summary of the invention
The purpose of the present invention is to provide a kind of simulation of tinbase binary eutectic alloy microstructure and finite element solvings point
Monte Carlo Method in conjunction with finite element method, is improved eutectic structure modeling efficiency, realizes eutectic group by analysis method, the method
The load knitted solves and analysis, provides a kind of new method, very good solution for eutectic structure signature analysis and fail-safe analysis
The problem of eutectic structure microstructure modeling and performance characterization.
The present invention solves its technical problem and adopts the following technical solutions to realize.
The present invention proposes the simulation and finite element solving analysis method of a kind of tinbase binary eutectic alloy microstructure,
Include:
S1: initial model is generated at random according to object Phase Proportion, it is believed that the energy of system can be determined by interface, and carried out
Energy balane is using no more than 5 × 5 range interface energy of part；
S2: maximum system energy is reduced by crystal boundary migration and long-range diffusion, passes through site and its randomly selected adjacent sites
Crystal boundary migration or long-range diffusion occur for orientation value symbol decision.
Probability when crystal boundary migration occurs are as follows:The probability of long-range diffusion occurs are as follows:A wherein preset value or random value of the η between section [0,1]；S3: noise is eliminated；Make to lead
Phase noise and the second phase noise are cancelled out each other, the noise not balanced out, and continue that long-range diffusion occurs, and long-range is required to spread
New noise is not generated；
S4: according to the element number of simple finite element model and arrangement mode, it is specified that pixel number and arrangement mode；
S5: generating the script file that finite element CAE software can identify, and contains the volume of each pixel in script file
Number and corresponding object phase information；
S6: reading script file with CAE software, assigns finite element mould according to the image information of each pixel of script file
The material properties of identical numbered cell and cell type information in type, generating includes different units type and material properties information
Complicated finite element model；
S7: the complicated finite element model comprising different units type and material properties information is loaded and is solved point
Analysis, obtains analog result.
In detail, in step sl, system capacity can be determined by interface, and carrying out interface in the following way can calculate:
S11: when calculating 5 × 5 region interface energy of part, consider anisotropy, vertical direction interface can be horizontally oriented boundary
3 times of face energy, diagonal interface can be horizontally oriented 2 times of interface energy；
S12: setting horizontal direction boundary interface can be E0, then the interface of vertical direction can be with the interface energy of diagonal
Respectively 3E0、2E0, then can formula according to interfaceCalculate energy.
In detail, in step s 2, crystal boundary migration carries out in the following way:
S21: when crystal boundary migration occurs, start to randomly choose a site i and 5 × 5 regions around it, if site i
Borderline region is fallen in, then the peripheral region of site i is less than 5 × 5 regions, calculates initial 5 × 5 regions or the boundary less than 5 × 5
It face can Eb1；
S22: compare the orientation value in the site i and around it the orientation value of a random adjacent sites j similarities and differences situation；If
When symbol identical value difference, the orientation value of this adjacent sites j is assigned to the site i, keeps the site i with j orientation value identical, so
The interface for calculating the regional area (i.e. 5 × 5 or smaller array) before changing and after changing afterwards can Eb1And Eb2, the change of interface energy
Measure Δ E=Eb2-Eb1If Δ E is less than or equal to zero, the probability P that crystal boundary migration occurs is 1, and otherwise, crystal boundary migration is not sent out
Raw, before keeping crystal boundary migration state.
In detail, in step s 2, long-range diffusion carries out in the following way:
S23: when long-range diffusion occurs, the orientation value of site i and a random adjacent sites j around it are randomly selected
When contrary sign occurs in orientation value, and make exchange position of the site i with adjacent sites j, i.e. site where i occur position it is mobile and
Can only be in distinct symbols, namely can only be moved in the site of out-phase, until encountering the same symbol, namely encounter same phase
Site and stop motion；
S24: the relatively variation delta E of front and back interface energy；If Δ E is less than or equal to zero, long-range diffusion occurs general
Rate is 1, and the probability otherwise occurred is η, wherein a preset value or random value of the η between section [0,1].
In detail, in step s3, noise is eliminated to carry out in the following way:
S31: if having the out-phase site of 5 or more (being more than half) in 8 adjacent sites in a site,
Then defining the site is noise, and circulation reads each site in matrix, and the noise of statistics available two kinds of phases out finally makes two kinds of phases
In noise constitute two one-dimensional noise arrays；
S32: the Partial Elements in two one-dimensional noise arrays are corresponded into exchange orientation value, so that in array element
The negative value in face becomes positive value, and positive value becomes negative value, keeps object phase conservation, then remaining part noise then continues through long-range
Diffusion is to eliminate.
In detail, step S32 is specifically carried out in the following way:
In the noise of two kinds of phases, A phase has a element, and B phase has b element, as a > b (a≤b), then taking two numbers
A element of b (a) corresponds exchange orientation value before group, and the negative value inside array element is allowed to become positive value, and positive value becomes negative value,
Object phase conservation is kept, a noise of remaining a-b (b-a) continues through long-range diffusion then to eliminate.
In detail, in step s 4, it is specified that pixel and arrangement mode carry out in the following way:
The element number and arrangement mode that simple finite element model is checked by CAE software, when the number and arrangement of unit
After rule determines, image pixel will be numbered and be arranged by the number and queueing discipline of unit, to make finite element model
In unit and pixel form mapping relations one by one.
In detail, in step s 6, the complicated finite element model comprising different units type and material properties information is generated
It carries out in the following manner:
By CAE software by script file material properties and cell type information transfer to corresponding to character combination
Unit, make the object phase information association of the unit of the same number of pixel, assigned or modified according to image information and is simple limited
Unit information in meta-model generates the finite element model comprising complex unit type and material properties information.
In detail, three-dimensionalreconstruction and cell node coupling are carried out by position corresponding relationship in the step s 7, applies boundary
Constraint condition may be implemented solution analysis of the complex model in finite element CAE software, obtain analog result.
The simulation of tinbase binary eutectic alloy microstructure and having for finite element solving analysis method of the embodiment of the present invention
Beneficial effect is:
(1) initial model generates at random according to true object Phase Proportion.
(2) think that the energy of system can be determined by interface, when calculating interface energy using no more than 5 × 5 models of part
Enclose interface can, rather than the interface of full scope can, improve computational efficiency.
(3) when long-range is spread, it is contemplated that final diffusion position neighbours' object phase environment.
(4) script file generated is pure file format, is programmed and easy to process, versatile, which can
By CAE software.
(5) eutectic structure modeling efficiency is improved, realizes that the quick load of eutectic structure is solved and analyzed.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below will be to needed in the embodiment
Attached drawing is briefly described, it should be understood that the following drawings illustrates only certain embodiments of the present invention, therefore is not to be seen as
It is the restriction to range, it for those of ordinary skill in the art, without creative efforts, can be with
Other relevant attached drawings are obtained according to these attached drawings.
Method flow diagram in Fig. 1 embodiment of the present invention；
The random matrix (interception part) generated in Fig. 2 embodiment of the present invention；
Initial model before heterogeneous microstructure develops in Fig. 3 embodiment of the present invention；
The monte-Carlo model figure of lattice is indicated in Fig. 4 embodiment of the present invention with site orientation value；
I falls in 5 × 5 array ranges of part of non-borderline region in Fig. 5 embodiment of the present invention；
I falls in the partial array range of borderline region in Fig. 6 embodiment of the present invention；
The crystal boundary migration of non-any 5 × 5 array of borderline region in Fig. 7 embodiment of the present invention；
The long-range diffusion simulations figure of non-any 5 × 5 array of borderline region in Fig. 8 embodiment of the present invention；
The crystal boundary migration simulation drawing of 3 × 3 array of borderline region in Fig. 9 embodiment of the present invention；
The crystal boundary migration simulation drawing of 3 × 4 array of borderline region in Figure 10 embodiment of the present invention；
The crystal boundary migration simulation drawing of 3 × 5 array of borderline region in Figure 11 embodiment of the present invention；
The crystal boundary migration simulation drawing of 4 × 4 array of borderline region in Figure 12 embodiment of the present invention；
Organizational Structure Evolution figure in Figure 13 embodiment of the present invention；
The arrangement mode schematic diagram of unit in Figure 14 embodiment of the present invention；
The finite element model for the eutectic alloy microstructure established in Figure 15 embodiment of the present invention；
The size of current density and distributed simulation result figure in Figure 16 embodiment of the present invention.
Specific embodiment
It in order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below will be in the embodiment of the present invention
Technical solution be clearly and completely described.The person that is not specified actual conditions in embodiment, according to normal conditions or manufacturer
It is recommended that condition carry out.Reagents or instruments used without specified manufacturer is the routine that can be obtained by commercially available purchase
Product.
Simulation to the tinbase binary eutectic alloy microstructure of the embodiment of the present invention and finite element solving analysis side below
Method is specifically described.
A kind of simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure comprising:
S1: initial model is generated at random according to object Phase Proportion, initial model is made of m n array site, wherein site
Indicate the domain with crystal lattice orientation, be endowed 1 to Q or -1 to-Q between random value (i.e. orientation value, Q are integer greater than 0)
To indicate specific lattice orientation.Indicating that the orientation value in the site of binary eutectic tissue main phase is probabilistically assigned is 1 to the closed interval Q
Interior positive integer indicates that the orientation value in the site of the second phase is probabilistically assigned as-Q to the negative integer in -1 closed interval；Introductory die
Object Phase Proportion in type generates at random according to object Phase Proportion true in microstructure.In Microstructure Simulation, polycrystalline material
In crystal grain can be gathered with the site with same orientation value to indicate.
Wherein, in an embodiment of the present invention, it is believed that system capacity can be determined by interface, can be calculated and be adopted at progress interface
It is no more than 5 × 5 array range interface energy of part；Computational efficiency can be improved in setting in this way, saves the time of calculating.
S2: thinking that maximum system energy can be determined by interface, interface energy is reduced according to specified rule, to simulate crystal grain
Grow up.When judging interface energy, the interface between identical two site of orientation value can be zero, two different positions of orientation value
There are interface energy between point.1 site i is randomly choosed, one adjacent sites j is then randomly choosed.Read the orientation of i and j
By certain probability crystal boundary occurs for value if identical (be positive together or the be negative together) value of i with j orientation value symbol is of different sizes
Migration, it is such as following a) shown；If i with j orientation value symbol is different, long-range diffusion occurs by certain probability, such as following b) institute
Show；When calculating the interface caused by crystal boundary migration or long-range diffusion can change, can change using localized interface rather than total
Body interface can change to reduce calculation amount, and the calculating that localized interface can change is divided into several situations as shown in c).The present invention
Embodiment in evolution rule it is as follows:
A) interface energy is reduced by crystal boundary migration.In the present invention, work as i, the symbol of the orientation value of j is identical but counts
When being worth of different sizes, crystal boundary migration will occur with certain probability P, i.e., the orientation value in the site j will be assigned to the site i, and make i, j
The orientation value of point is identical.Interface after calculating crystal boundary migration can E2It can E with the interface before crystal boundary migration1Interface can change (i.e.
Δ E=E2-E1), if interface can become smaller or constant, (i.e. Δ E≤0), the probability P that crystal boundary migration occurs at this time is 1, crystal boundary migration
It can occur, otherwise, probability P 0, crystal boundary migration cannot occur.
B) being spread by long-range reduces interface energy.If site i and j orientation value symbol is different, will be with certain probability
Long-range diffusion occurs for P, i.e. site where i occurs position movement and can only move in the site of distinct symbols (out-phase),
Until encountering the site of the same symbol (same to phase) and stop motion.Interface can E after calculating long-range diffusion2' with long-range diffusion before
Initial interface energy E1' interface can variation (i.e. Δ E=E2’-E1'), if interface can become smaller or constant, (i.e. Δ E≤0), this
The probability P of Shi Fasheng long-range diffusion is 1, and long-range diffusion can occur, and can only be that long-range occurs for η with certain probability P otherwise
It spreads, wherein a preset value or random value of the η between section [0,1].
C) calculating interface caused by being spread by crystal boundary migration or long-range can change.When the column locations of random selection site i
Meet 3≤L of condition≤m-2, and when 3≤C≤n-2, as shown in figure 5, passing through 5 × 5 partial arrays where calculating site i
Interface energy situation of change judges whether that crystal boundary migration or long-range diffusion occurs.When the column locations of random selection site i meet item
When part 1≤L≤2,1≤C≤2, m-1≤L≤m, n-1≤C≤n (randomly selected site i falls in borderline region), again
Refering to Fig. 5,5 × 5 array ranges of part when site i falls in non-borderline region in the embodiment of the present invention (i.e. 3≤L≤148, and
3≤C≤148).As shown in fig. 6, having chosen 3 × 3 partial arrays when random sites i falls in the 1st row the 1st column, i falls in the 1st
3 × 5 partial arrays, i when 3 × 4 partial arrays, i when row the 2nd arranges fall in the 1st row the 3rd column are fallen in when the 2nd row the 2nd arranges
4 × 4 partial arrays and i fall in 4 × 5 partial arrays when the 2nd row the 3rd column, discuss before calculating crystal boundary migration or long-range diffusion
The variation of interface energy afterwards judges that can crystal boundary migration or long-range diffusion occur.Random sites i can similarly be calculated and fall in lower-left
Crystal boundary migration and long-range propagation energy situation of change when Angle Position, upper right Angle Position, lower right position.
S3: m × n times are repeated according to step S2, and (sum in site, is defined as an illiteracy i.e. in the m n array of site
Special Caro step-length (Monte Carlo Step, MCS)), MCS N number of to model evolution.
S4: noise is eliminated.It determines noise, offsets noise (main phase noise and the second phase noise are offset).Unmatched noise is pressed
Long-range diffusion occurs according to step S2, and new noise cannot be formed after requiring long-range to spread.
S5: establishing simple finite element model corresponding with microstructure site array (m × n), right in an identical manner
Site array and cell array are numbered, and according to the object phase information of site array, generating finite element CAE software can be identified
Script file, the number in script file containing each site and the object phase information corresponding to it.
S6: reading script file with CAE software, and letter is assigned or modified according to the object phase information of each pixel of script file
The material properties of identical numbered cell and cell type information in single finite element model, generating includes different units type and material
Expect the complicated finite element model of attribute information；And realize that automatic load solves.
Feature and performance of the invention are described in further detail with reference to embodiments.
Embodiment 1
Shown in Fig. 1 specific as follows, the simulation and finite element solving analysis method of SnBi binary eutectic alloy microstructure,
Include the following steps:
S1: initial model is generated.Initial model is made of the site of 150 × 150 (i.e. m=150, n=150) arrays,
Middle site indicates the domain with crystal lattice orientation, is endowed the random value (i.e. Q=10) between 1 to 10 or -1 to -10 to indicate
The orientation of crystal grain.Indicate that the site of Sn phase is designated the orientation (that is, 1 to 10) that is positive.Indicate the site of Bi phase in -10 to -1 area
Between be assigned negative integer (that is, -10 to -1)；Then initial value model is generated at random according to true object Phase Proportion, due to SnBi
Volume ratio of two kinds of phases in eutectic structure be 1:1.03, it is specified that in program generate Sn phase probability be 49.26%, generate Bi
The probability of phase is 50.74%.The random matrix (part) of generation is as shown in Fig. 2, initial model is as shown in Figure 3.In this way we
Initial model can be generated at random according to true object Phase Proportion.
S2: in Microstructure Simulation, the identical region of orientation value can be understood as a crystal grain in polycrystalline material；
Interface is not present between the site of same orientation value, belongs to the same crystal grain, interface can be zero；Between different orientation value site
There are crystal boundary, interface can be not zero；Such as: the site that the site orientation value 1 that the 4th row the 4th arranges in Fig. 4 is arranged with the 4th row the 5th takes
To there is no interface energy between value 1；It is deposited between the site orientation value 1 and the 4th row the 11st column site orientation value 5 of 4th row the 10th column
In interface energy；When calculating interface energy, we are generally adopted by 5 × 5 range interface energy of part in random matrix.Such as Fig. 5
It is shown, if site i be located at array L row C column, then around it 5 × 5 arrays range is defined as: from L-2 to L+2 row and from
Array region where C-2 to C+2 column.If site i near zone cannot take part 5 × 5 arrays, as shown in fig. 6, if root
Row and array region from C-2 to C+2 in range from L-2 to L+2 are chosen according to actual conditions.Such as: when i falls in the 1st row
When 1 column position, 3 × 3 arrays are chosen；When i falls in the 1st 2 column position of row, 3 × 4 arrays are chosen；When i falls in the 1st row the 3rd
When column position, 3 × 5 arrays are chosen；When i falls in the 2nd 2 column position of row, 4 × 4 arrays are chosen；When i falls in the 2nd row the 3rd column
When position, 4 × 5 arrays are chosen.In our model, we consider anisotropy, vertical boundary interface can (Xiang Tonghang
Adjacent two column between interface can) be horizontal boundary interface can (interface can) between the adjacent rows of same column three
Times, diagonal boundary interface energy (interface energy between the site that two rows are adjacent and column are adjacent) is horizontal boundary interface energy
Twice；Such as: it is horizontal direction interface energy between i and L-1 row the column c site of L row column c site in Fig. 5；L row
It is vertical direction interface energy between column c site i and L row C-1 column site；L row column c site i and L-1 row
It is diagonal interface energy between C-1 column site.The interface energy calculation formula of local matrix where the i of site:
Wherein E (i, j) indicates position i, and the interface energy between j point, Z is neighbours' number of site i；N is the site part i battle array
The number of sites of column.
Evolution in the present invention is as follows: in 150 × 150 arrays, randomly choosing a site i, then randomly chooses it
One adjacent sites j.The orientation value of i and j is read, if value is or not i with j orientation value symbol identical (be positive together or be negative together)
Together, then crystal boundary migration occurs by certain probability, it is such as following a) shown；If i with j orientation value symbol is different, by certain probability
Long-range diffusion occurs, it is such as following b) shown；When calculating the interface caused by crystal boundary migration or long-range diffusion can change, use
Be that localized interface can change rather than total interface can change to reduce calculation amount, calculate localized interface and can change and is divided into as c)
Shown in several situations.Evolution rule of the invention is as follows:
A) the interface energy of system is reduced by crystal boundary migration.In the present invention, work as i, the orientation value symbol of j is identical but counts
When being worth of different sizes, crystal boundary migration will occur with certain probability P, i.e., the orientation value in the site j is assigned to the site i, make i and j
Point orientation value is identical.Interface after calculating crystal boundary migration can E2With the initial interface energy E before crystal boundary migration1(enable Δ E=E2-
E1), if energy becomes smaller or constant, (i.e. Δ E≤0), the probability P that crystal boundary migration occurs at this time is 1, and crystal boundary migration can be sent out
It is raw；Otherwise, probability P 0, crystal boundary migration cannot occur.As shown in Fig. 7, in taking for the site i that non-borderline region randomly selects
It is -5 to value, can is E according to the initial interface that formula (1) calculates 5 × 5 arrays in the site1=137E0, then randomly choose it
One adjacent sites j orientation value -1；Because -5 is different with -1 symbol identical value, -1 is assigned to and starts to randomly select
Site i, as shown in Fig. 7 (b), the interface after calculating crystal boundary migration can E2=132E0；The crystalline substance can be obtained by comparing front and back energy variation
Boundary's transition process can occur.B) being spread by long-range reduces interface energy.In the present invention, work as i, the orientation value symbol of j
When number difference, long-range diffusion will be occurred with certain probability P, i.e. it is mobile and can only be in distinct symbols that position occurs for site where i
It moves in site until encountering the site of the same symbol (same to phase) and stops moving.Interface after calculating long-range diffusion can E2' with
Initial interface energy E before long-range diffusion1' (enable Δ E=E2’-E1'), if energy becomes smaller or constant, (i.e. Δ E≤0) is sent out at this time
The probability P for growing journey diffusion is 1, and long-range diffusion can occur；Otherwise, occur long-range diffusion probability P be 0.1 (even η=
0.1).In embodiment as shown in figure 8, being -2 in the orientation value that non-borderline region randomly selects site i, according to formula (1), meter
The sum of two initial 5 × 5 array region interfaces energy before calculating the diffusion of the site i long-range as shown in Fig. 8 (a) E1'=115E0, so
After randomly choose one adjacent sites j1, orientation value 1, because of -2 and 1 contrary sign, site i and j1Place-exchange occurs
(orientation value exchange) is then until encountering orientation value by random walk diffusion in region of the orientation value as positive sign using probability P
The site (- 2) of negative sign, arrow indicates one of STOCHASTIC DIFFUSION path in Fig. 8 (a), site i respectively with site j1, site
j2, site j3, site j4, site j5, site j6, site j7Position is exchanged, is stopped until encountering the site of identical phase (- 2 or -4)
Only move；Two 5 × 5 array regions shown in partial array such as Fig. 8 (b) after long-range diffusion, after then calculating long-range diffusion
The sum of interface energy E2'=107E0, relatively front and back energy variation can obtain Δ E < 0, that is, occur the process probability P be 1.
C) 2 (a) more than, 2 (b) two steps be that can change and judge whether by 5 × 5 array interfaces of part where calculating site i
Crystal boundary migration or long-range diffusion occurs.If we discuss that calculating site i is located at the several of upper left corner area less than 5 × 5 arrays
Kind situation: as shown in figure 9, when random sites i falls in the 1st row the 1st column, 3 × 3 partial arrays is formed, are calculated by formula (1)
The initial interface energy of the partial array (a) are as follows: 40E0, the interface energy of partial array (b) after crystal boundary migration occurs are as follows: 39E0；Such as
Shown in Figure 10, when random sites i falls in the 1st row the 2nd column, 3 × 4 partial arrays is formed, which is calculated by formula (1)
Arrange the initial interface energy of (a) are as follows: 59E0, partial array (b) interface after crystal boundary migration occurs can are as follows: 57E0；Such as Figure 11 institute
Show, when random sites i falls in the 1st row the 3rd column, forms 3 × 5 partial arrays, which is calculated by formula (1)
Initial interface energy are as follows: 78E0, the interface energy of partial array (b) after crystal boundary migration occurs are as follows: 76E0；As shown in figure 12, when random
When site i falls in the 2nd row the 2nd column, 4 × 4 partial arrays are formed, the initial interface of the partial array (a) is calculated by formula (1)
It can are as follows: 84E0, the interface energy of partial array (b) after crystal boundary migration occurs are as follows: 81E0.It is attached in case of the site i of long-range diffusion
It cannot closely take 5 × 5 partial arrays (i falls in borderline region), then it is identical with crystal boundary migration situation, 3 are chosen according to the actual situation
× 3 arrays, 3 × 4 arrays, 3 × 5 arrays, 4 × 4 arrays, 4 × 5 arrays, then calculating front and back interface can situation of change.Similarly
The case where random sites i falls in lower left corner borderline region, upper right corner borderline region, lower right corner borderline region can be calculated.
Compare in order to facilitate observation of, by initial interface energy Eb1, the interface after crystal boundary migration can Eb2, it the results are shown in Table 1:
Crystal boundary migration interface occurs for 1 borderline region partial array (part) of table can situation of change
S3: 150 × 150 (sum in site, definition i.e. in 150 × 150 array of site are repeated according to step S2
For a Monte Carlo step-length (MCS)), as shown in figure 13, to model evolution 700,4900,9800,14700,19600,
24500 MCS.
S4: noise is eliminated.Circulation read matrix in each site, when a site more than half adjacent sites be it is different
When phase point (for example, having 5 or more in 8 adjacent sites is out-phase), it is possible to determine that the site is noise, is then counted
There is the orientation value of oneself in the noise of two kinds of phases out, each site, may be constructed two one-dimension arrays, if A phase has a element,
B phase has b element, as a > b (a≤b), then a element of b (a) before two arrays is taken to correspond exchange exchange orientation
Value allows the negative value inside array element to become positive value, and positive value becomes negative value, we can guarantee object phase conservation in this way, remaining
B-a (a-b) a noise occurs long-range diffusion according to step S2:(b), and cannot form new noise after requiring long-range to spread.
S5: the element number and arrangement mode of model pixel are provided；Simple finite element model list is checked in CAE software
Member is numbered and arrangement mode, is the unit arrangement mode of simple finite element model in embodiment, numerical value generation in figure shown in Figure 14
Table unit number；After the number and queueing discipline of unit determine, tinbase binary eutectic will be closed by element number and queueing discipline
Golden microstructure illustraton of model pixel carries out identical number and arrangement, to make the unit and image in finite element model
In pixel form mapping relations one by one.
S6: script file can be identified by generating finite element CAE software, the number in script file containing each pixel with
And its corresponding object phase information；Script file is made of a series of character combinations, in each character combination correspondence image
A pixel, the attribute number and material type number information of number, material comprising pixel；In embodiment, number i
The expression formula of character combination is that " expression formula of Fu Zuhe, wherein A, B, C are code, by the operational order of finite element CAE software
It determines, i is element number, and j is material properties number, and k is cell type number, for example, the pixel that number is 5 in embodiment
Tin phase is represented, material properties number is 2, and the cell type number of tin phase is 2, then it is to the foot that should apply in ANSYS software
In this document can be that " in the script file in part can be " middle number is attribute number and 2 ", the i.e. foot that A=is
In this document can be that " middle number is attribute number and material type number information；Implement；By identifying this array,
The material properties number for the unit that definition number is 5 by ANSYS software is 2, and cell type number is 2, is provided in embodiment single
The cell type that element type number is 2 is PLANE67；Language used in each character combination or code can be soft by ANSYS
Part identifies that material properties parameter is shown in Table 2 in embodiment.
The material properties of 2 tinbase binary eutectic alloy of table
S7: the complicated finite element model of inclusion not in-phase information is established.Script file is read with CAE software, according to foot
The object phase information of each pixel of this document modifies the material properties and cell type of identical numbered cell in simple finite element model
Information generates complicated finite element model as shown in figure 15 comprising different units type and material properties information；And it realizes automatic
Load solves, and obtains analog result.
It generates the complicated finite element model comprising different units type and material properties information to carry out in the following manner: logical
Cross CAE software by script file material properties and cell type information pass to unit corresponding to character combination, make picture
The object phase information association of the unit of the same number of element assigns the letter of the unit in simple finite element model according to object phase information
Breath generates the complicated finite element model comprising different units type and material properties information.
S8: solve analysis and obtain model result: the finite element model as shown in figure 14 obtained by (1)~(7) can be
Apply boundary condition in CAE software and load carries out solution analysis, coupled by node, applies edge-restraint condition, it can
It realizes solution analysis of the complex model in finite element CAE software, obtains analog result.In embodiment, to two-dimentional SnBi
When the voltage applied between the solder joint both ends of alloy finite element model is 0.001V, different tissues form can be studied (finely,
It is medium, coarse) current density situation, obtain simulation drawing shown in Figure 16；When to two-dimentional SnBi alloy finite element model
1 × 10 between solder joint both ends8A/m2Current density under when applying pressure, different opposite solder joint electromigration rows can be studied
For influence, obtain simulation drawing as shown in Figure 16, data result is arranged as shown in the following table 3 and table 4.
The current density (0.001V) of three solder joint of the table 3 under same application voltage
Table 4 is (1 × 10 under same application current density8A/m2) three solder joints current density
In conclusion the present invention provides a kind of new method for binary eutectic microstructure characteristics and fail-safe analysis, tool
Body surface is existing as follows:
(1) initial model generates at random according to true object Phase Proportion.
(2) think that the energy of system can be determined by interface, when calculating interface energy using no more than 5 × 5 models of part
Enclose interface can, rather than the interface of full scope can, improve computational efficiency.
(3) when long-range is spread, it is contemplated that final diffusion position neighbours' object phase environment.
(4) script file generated is pure file format, is programmed and easy to process, versatile, which can
By CAE software.
(5) eutectic structure modeling efficiency is improved, realizes that the quick load of eutectic structure is solved and analyzed.
Embodiments described above is a part of the embodiment of the present invention, instead of all the embodiments.Reality of the invention
The detailed description for applying example is not intended to limit the range of claimed invention, but is merely representative of selected reality of the invention
Apply example.Based on the embodiments of the present invention, those of ordinary skill in the art are obtained without creative efforts
Every other embodiment, shall fall within the protection scope of the present invention.
Claims (9)
1. the simulation and finite element solving analysis method of a kind of tinbase binary eutectic alloy microstructure, which is characterized in that it is wrapped
It includes:
S1: initial model is generated at random according to object Phase Proportion, it is believed that system capacity can be determined by interface, and made energy calculation
Using no more than 5 × 5 range interface energy of part；
S2: maximum system energy is reduced by crystal boundary migration and long-range diffusion, is orientated by site and its randomly selected adjacent sites
It is worth symbol decision and crystal boundary migration or long-range diffusion occurs；Probability when crystal boundary migration occurs are as follows:The probability of long-range diffusion occurs are as follows:Wherein η is section [0,1]
Between a preset value or random value；
S3: noise is eliminated；Main phase noise and the second phase noise is set to cancel out each other, the noise not balanced out continues that long-range occurs
Diffusion, and long-range diffusion is required not generate new noise；
S4: according to the element number of simple finite element model and arrangement mode, it is specified that pixel number and arrangement mode；
S5: generating the script file that finite element CAE software can identify, and contains the number of each pixel in the script file
And corresponding object phase information；
S6: reading the script file with CAE software, assigns finite element according to the image information of each pixel of the script file
The material properties of identical numbered cell and cell type information in model, generating includes different units type and material properties information
Complicated finite element model；
S7: the complicated finite element model comprising different units type and material properties information is loaded and is solved point
Analysis, obtains analog result.
2. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step sl, carrying out interface in the following way can calculate:
S11: when calculating 5 × 5 region interface energy of part, consider anisotropy, vertical direction interface can be horizontally oriented interface energy
3 times, diagonal interface can be horizontally oriented interface can 2 times；
S12: setting horizontal direction boundary interface can be E0, then the interface energy of vertical direction and the interface of diagonal can be respectively
3E0、2E0, then can formula according to interfaceCalculate interface energy.
3. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step s 2, the crystal boundary migration carries out in the following way:
S21: when crystal boundary migration occurs, start to randomly choose a site i and 5 × 5 regions around it, if site i is fallen in
Borderline region, then the peripheral region of site i is less than 5 × 5 regions, calculates initial 5 × 5 regions or the interface less than 5 × 5 regions
It can Eb1；
S22: compare the orientation value in the site i and around it the orientation value of a random adjacent sites j similarities and differences situation；If symbol phase
When with being worth different, the orientation value of this adjacent sites j being assigned to the site i, keeps the site i with j orientation value identical, then calculated and change
Regional area (i.e. 5 × 5 or smaller array) interface before becoming and after changing can Eb1And Eb2, the knots modification Δ E=E of interface energyb2-
Eb1If Δ E is less than or equal to zero, the probability P that crystal boundary migration occurs is 1, and otherwise, crystal boundary migration does not occur, and keeps crystal boundary
State before migration.
4. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step s 2, the long-range diffusion carries out in the following way:
S23: occur long-range diffusion when, randomly select the orientation value of site i and around it a random adjacent sites j orientation value
When there is contrary sign, and make the position that exchanges of the site i with adjacent sites j, i.e. site where i occurs position movement and can only be
Distinct symbols, namely can only be moved in the site of out-phase, until encountering the same symbol, namely encounter same phase site and
Stop motion；
S24: the relatively variation delta E of front and back interface energy；If Δ E is less than or equal to zero, the probability that long-range diffusion occurs is
1, the probability otherwise occurred is η, wherein a preset value or random value of the η between section [0,1].
5. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step s3, eliminating noise and carrying out in the following way:
S31: it if having the out-phase site of 5 or more (being more than half) in 8 adjacent sites in a site, defines
The site is noise, and circulation reads each site in matrix, and the noise of statistics available two kinds of phases out finally makes the noise in two kinds of phases
Constitute two one-dimensional noise arrays；
S32: corresponding exchange orientation value for the Partial Elements in two one-dimensional noise arrays, so that negative inside array element
Value becomes positive value, and positive value becomes negative value, keeps object phase conservation, and then remaining part noise continues through long-range diffusion then to disappear
It removes.
6. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, step S32 is specifically carried out in the following way:
In the noise of two kinds of phases, A phase has a element, and B phase has b element, as a > b (a≤b), then taking b before two arrays
(a) a element corresponds exchange orientation value, and the negative value inside array element is allowed to become positive value, and positive value becomes negative value, keeps object
Phase conservation, a noise of remaining a-b (b-a) continue through long-range diffusion then to eliminate.
7. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step s 4, it is specified that pixel and arrangement mode carry out in the following way:
The element number and arrangement mode that simple finite element model is checked by CAE software, when the number and queueing discipline of unit
After determination, image pixel will be numbered and be arranged by the number and queueing discipline of unit, to make in finite element model
Unit and pixel form mapping relations one by one.
8. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized in that, in step s 6, generate the complicated finite element model comprising different units type and material properties information press with
Under type carries out:
By CAE software by script file material properties and cell type information transfer to list corresponding to character combination
Member makes the object phase information association of the unit of the same number of pixel, assigns or modify simple finite element mould according to image information
Unit information in type generates the finite element model comprising complex unit type and material properties information.
9. the simulation and finite element solving analysis method of tinbase binary eutectic alloy microstructure according to claim 1,
It is characterized by:
Three-dimensionalreconstruction and cell node coupling are carried out by position corresponding relationship in the step s 7, apply edge-restraint condition, it can
To realize solution analysis of the complex model in finite element CAE software, analog result is obtained.
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Application publication date: 20190326 Assignee: Guilin Qunmei Technology Co.,Ltd. Assignor: GUILIN University OF ELECTRONIC TECHNOLOGY Contract record no.: X2023980044664 Denomination of invention: Simulation and finite element analysis method for microstructure of tin based binary eutectic alloy Granted publication date: 20220816 License type: Common License Record date: 20231031 |