CN102492882B - Capture and conversion rule for simulation of solidified microstructure of magnesium alloy - Google Patents
Capture and conversion rule for simulation of solidified microstructure of magnesium alloy Download PDFInfo
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- CN102492882B CN102492882B CN 201110400271 CN201110400271A CN102492882B CN 102492882 B CN102492882 B CN 102492882B CN 201110400271 CN201110400271 CN 201110400271 CN 201110400271 A CN201110400271 A CN 201110400271A CN 102492882 B CN102492882 B CN 102492882B
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- 238000004088 simulation Methods 0.000 title claims abstract description 14
- 229910000861 Mg alloy Inorganic materials 0.000 title claims abstract description 11
- 238000006243 chemical reaction Methods 0.000 title abstract 2
- 239000013078 crystal Substances 0.000 claims abstract description 21
- 239000007788 liquid Substances 0.000 claims abstract description 12
- 238000000034 method Methods 0.000 claims abstract description 9
- 238000007711 solidification Methods 0.000 claims abstract description 5
- 230000008023 solidification Effects 0.000 claims abstract description 5
- 230000001413 cellular effect Effects 0.000 claims description 66
- 230000009466 transformation Effects 0.000 claims description 5
- 238000013316 zoning Methods 0.000 claims description 2
- 238000005266 casting Methods 0.000 claims 1
- 230000006911 nucleation Effects 0.000 abstract 3
- 238000010899 nucleation Methods 0.000 abstract 3
- 238000004364 calculation method Methods 0.000 abstract 1
- 239000000463 material Substances 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 4
- 230000007704 transition Effects 0.000 description 3
- FYYHWMGAXLPEAU-UHFFFAOYSA-N Magnesium Chemical compound [Mg] FYYHWMGAXLPEAU-UHFFFAOYSA-N 0.000 description 2
- 210000001787 dendrite Anatomy 0.000 description 2
- 229910052749 magnesium Inorganic materials 0.000 description 2
- 239000011777 magnesium Substances 0.000 description 2
- 229910000838 Al alloy Inorganic materials 0.000 description 1
- 210000004027 cell Anatomy 0.000 description 1
- 238000001816 cooling Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000003913 materials processing Methods 0.000 description 1
- 229910052751 metal Inorganic materials 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 238000011160 research Methods 0.000 description 1
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Abstract
The invention discloses a capture and conversion rule for the simulation of a solidified microstructure of a magnesium alloy and belongs to the technical field of material processing. The rule is characterized in that: an orthohexagnal crystal nucleus is placed at the central position of a liquid cell which meets nucleation conditions; the crystal nucleus grows constantly along with the continuity of the solidification process; an adjacent cell is captured to serve as an interfacial cell when a corner of the crystal nucleus enters the adjacent cell, and an orthohexagnal crystal nucleus of which the crystal orientation is the same as that of a parent cell is placed at the corner so as to represent the nucleation of the adjacent cell; the cell does not participate in the nucleation and growth calculation when adjacent cells of the cell are all non-liquid; and the interfacial cell continues to capture other neighbor cells by the method. The rule has the advantages that: the growth of grains of the magnesium alloy at any angle can be realized under the configuration of a square cell and simple neighbors, and a simulation result can embody the anisotropy of grain growth; and the judgment required on the configuration of four adjacent cells is less than that of other adjacent cells during simulation, and the time required by iterative computation is short.
Description
Technical field
The invention belongs to the materials processing technology field, relate to the solidified structure simulation of magnesium alloy, particularly relate to a kind of seizure and transformation rule at the simulation of magnesium alloy solidification tissue.
Background technology
Cellular automata (Cellular Automaton is called for short CA) is at the beginning of the fifties in last century, and by the computer originator, famous mathematician Neumann proposes.Its basic thought is-primitive of individual cell or system, according to the situation of other primitive that is adjacent, decide own state by the rule of prior setting, thereby come the development law of the whole complexity of descriptive system by defining local simple rule.Cellular automata has four elements: (1) is found the solution the zone and is formed by the cellular with same size and geometry is regularly arranged, and under two-dimensional case, pros or hexagonal lattice are modal forms; (2) cellular has definite neighborhood; (3) each cellular has different state values or variate-value identifies; (4) state-transition of each cellular self is determined by predefined transition rule and adjacent born of the same parents' state.
The beginning of the nineties, people such as Rappaz was applied to the CA method solidified structure simulation of aluminium alloy first.Many scholars have improved this method on its basis subsequently.The common ground of these researchs is that seizure and the state transition rules of model only is applicable to the isometric system metal.Yet magnesium is close-packed hexagonal structure, and traditional method can not embody its anisotropy.Though have pertinent literature to develop the solidified structure of modeling magnesium alloy, still there is certain deficiency in model, as catch rule complicated, to dendrite adopted shape function approximate, can only realize the growth of some special angle crystal grain etc.
Summary of the invention
The purpose of this invention is to provide a kind of seizure and transformation rule at the simulation of magnesium alloy solidification tissue, make analog result can not only embody the sixfold symmetry of magnesium alloy, and can simulate the growth of arbitrarily angled crystal grain.
The present invention adopts following technical scheme:
This rule has following feature: (1) cellular is square.Neighbours are defined as von Neumann type, i.e. four neighbours up and down; (2) cellular has three kinds of states: liquid, interface and solid-state; (3) have only the predefined liquid forming core cellular ability forming core that is in, other cellulars can only be captured.Become the interface cellular after the cellular forming core; (4) only the interface cellular can catch neighbours' cellular; (5) being in liquid cellular just can be captured.Concrete seizure and state transition rules are as follows: as shown in Figure 1, the grid of zoning is square, and each square net is a cellular; A is the forming core cellular; Cellular B1～B4 is neighbours' cellular of cellular A.All cellular state of initial time are 0 (namely liquid), and temperature is identical.At moment t, when the condensate depression of cellular A during greater than the forming core condensate depression of this cellular, this cellular state changes (becoming interfacial state from liquid state), and it is the regular hexagon nucleus of θ that its center generates angle, a crystal orientation.Nucleus half cornerwise length variations can be by obtaining dendrite tip growth speed integration in a time step.Along with continuing of process of setting, the condensate depression of forming core cellular increases gradually, and nucleus is constantly grown up.Be example with adjacent born of the same parents B1, when certain angle point of nucleus entered adjacent born of the same parents B1, cellular B1 was captured and becomes the interface cellular.It is identical with female cellular A to generate angle, a crystal orientation simultaneously in cellular B1; The nucleus Ψ that the center overlaps with this angle point.When nucleus Ψ was enough big, cellular B1 can catch its liquid adjacent born of the same parents again.When neighbours' cellular state of cellular when all right and wrong are liquid, this cellular state becomes solid-state, no longer participates in forming core and growth.Along with forming core and the constantly repetition of seizure of cellular, simulate the solidified structure of foundry goods at last.
Nucleus has six angle points and neighbours' cellular has only four, and above-mentioned algorithm can not correctly catch under some extreme condition:
(1) two of nucleus angle points enter same neighbours' cellular (as B1 among Fig. 2 and B3) simultaneously.This situation appears when the angle, crystal orientation is smaller easily.One of them angle point of picked at random is as the germ nucleus of neighbours' cellular at this moment;
(2) neighbours' cellular can not be captured.As shown in Figure 3, the direction of arrow indication is the path of angle point in the nucleus growth process.Obvious two angle points can not enter adjacent born of the same parents B1, and adjacent born of the same parents B1 can not be captured.Use following additional seizure rule at this situation: when nucleus half cornerwise length L during greater than 2si (si is the cellular size), liquid neighbours' cellular of this nucleus all is transformed into the interface cellular.This moment, adjacent born of the same parents' germ nucleus overlapped with adjacent born of the same parents' center.Select 2si as the reason of critical length to be: neighbours' cellular of cellular all is within female born of the same parents' nucleus scope when L＞2si.
Effect of the present invention and benefit are that square cellular, simple neighbours dispose down the growth that can realize the arbitrarily angled crystal grain of magnesium alloy, and analog result can embody the anisotropy of grain growing.The square cellular compares the programming of regular hexagon cellular and aftertreatment all is easy to realize; Simple neighbours born of the same parents dispose required judgement than other adjacent born of the same parents and lack during simulation, and the iterative computation required time is short.
Description of drawings
Fig. 1 is that dendritic growth catches synoptic diagram.
Among Fig. 1: A is the forming core cellular; The angle, crystal orientation is θ; B1～B4 is neighbours' cellular of A.
Fig. 2 is the synoptic diagram that two angle points enter neighbours' cellular simultaneously.
Fig. 3 is the synoptic diagram that neighbours' cellular can not be captured.
Fig. 4 is the synoptic diagram with the single crystal grain analog result of different crystal orientations of the present invention's simulation.
Among Fig. 4: (a) 15 °; ° (b)-15.
Embodiment
Be described in detail the specific embodiment of the present invention below in conjunction with the technical scheme accompanying drawing.
Adopt seizure of the present invention and transformation rule simulated uniform temperature after the match the angle, crystal orientation be the growth of 15 ° and-15 ° of single crystal grain.The simulation yardstick is 1 * 1mm
2, cellular size si=20 μ m, rate of cooling is 1 ℃/s.Only define a forming core cellular at the center of computational fields during simulation, do not consider the forming core of other cellulars.As shown in Figure 4, analog result shows that crystal grain can keep its original crystal orientation all the time in growth process, and can not deflect, and has avoided " false anisotropy " of square net; Analog result can embody the close-packed hexagonal characteristic of magnesium; The growth of angle, crystal orientation crystal grain can realize arbitrarily.
Claims (1)
1. seizure and transformation rule at the simulation of magnesium alloy solidification tissue is characterized in that it comprises the steps: that the zoning is divided into the square cellular of even size; When the condensate depression of forming core cellular during greater than the required condensate depression of the forming core of this cellular, the cellular forming core is placed a regular hexagon nucleus at this cellular center; Along with ingot casting continue solidify, the condensate depression of forming core cellular increases gradually, nucleus is constantly grown; When the angle point of nucleus entered adjacent born of the same parents, adjacent born of the same parents were captured and become the interface cellular, placed the forming core that the crystal orientation regular hexagon nucleus identical with female born of the same parents represents adjacent born of the same parents simultaneously at this angle point place; As the adjacent born of the same parents of cellular when all right and wrong are liquid, this cellular just no longer participates in forming core and growth is calculated; The interface cellular continues to catch its adjacent born of the same parents according to the method described above;
When two angle points of nucleus entered in the same adjacent born of the same parents simultaneously, angle point of picked at random was as adjacent born of the same parents' germ nucleus;
When can not entering adjacent born of the same parents, uses the angle point of nucleus following additional seizure rule, namely when nucleus half cornerwise length
LGreater than 2
SiThe time,
SiBe the cellular size, the liquid adjacent born of the same parents of this nucleus all are transformed into the interface cellular; This moment, the center of adjacent born of the same parents' nucleus overlapped with adjacent born of the same parents center.
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