CN102156184A - Method for predicting space between aluminium-silicon alloy eutectic structure lamellas - Google Patents

Method for predicting space between aluminium-silicon alloy eutectic structure lamellas Download PDF

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CN102156184A
CN102156184A CN2010105661163A CN201010566116A CN102156184A CN 102156184 A CN102156184 A CN 102156184A CN 2010105661163 A CN2010105661163 A CN 2010105661163A CN 201010566116 A CN201010566116 A CN 201010566116A CN 102156184 A CN102156184 A CN 102156184A
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eutectic
solute
diffusion
coefficient
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CN102156184B (en
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李强
曲迎东
李荣德
张超逸
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Shenyang University of Technology
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Abstract

The invention relates to a method for predicting space between aluminium-silicon alloy eutectic structure lamellas; the method is characterized in that an experimental period can be greatly shortened by using a numerical simulation method to predict the space between aluminium-silicon alloy eutectic lamellas; the cost is low, and the prediction result is not limited by the experimental conditions; and the influences of a certain single factor to the space between the aluminium-silicon alloy eutectic structure lamellas can be inspected. The shortages that the cost of the existing experimental method for measuring the space between aluminium-silicon alloy eutectic structure lamellas is relatively high, the experimental period is long and the experiment results are influenced obviously by the experimental conditions are overcome; the computation is fast; the error is small; and the quantitative prediction to the space between eutectic lamellas can be realized.

Description

Alpax eutectic structure sheet interlayer spacing Forecasting Methodology
One, technical field:
The invention belongs to metallurgical technology field, relate generally to a kind of Forecasting Methodology of eutectic structure sheet interlayer spacing, particularly at the Forecasting Methodology of Alpax eutectic structure sheet interlayer spacing.
Two, background technology:
Alpax is one of most widely used aluminium alloy, and it is widely used in fields such as automobile, electric power, aviation.Casting is a main method of Alpax moulding.But in casting process, the al-si eutectic tissue is a kind of typical solidified structure pattern.The sheet interlayer spacing of al-si eutectic tissue is a principal element that is directly connected to the cast product mechanical property, eutectic sheet interlayer spacing at Alpax adopted experimental technique to measure more in the past, but the sheet interlayer spacing cost of determination of experimental method al-si eutectic tissue is higher, experimental period is long, and experimental result is influenced significantly by experiment condition.
Three, summary of the invention:
1, goal of the invention:
The present invention is directed to the less present situation of Al-Si eutectic structure sheet interlayer spacing Quantitative study, a kind of Alpax eutectic structure sheet interlayer spacing Forecasting Methodology is proposed, solve the existing problem of present determination of experimental method al-si eutectic tissue lamellar spacing, for Alpax eutectic structure performance prediction from now on provides theoretical direction, and can be applied directly to the casting technique improvement, realize the sheet interlayer spacing of refinement al-si eutectic tissue.
2, technical scheme:
The present invention is achieved through the following technical solutions:
A kind of Alpax eutectic structure sheet interlayer spacing Forecasting Methodology is characterized in that: dope eutectic structure sheet interlayer spacing after Alpax solidifies under this cooling velocity and the thermograde according to the cooling velocity of actual measurement and local thermograde, step is as follows:
(1), set up silicon eutectic structure sheet interlayer spacing forecast model:
At first true origin is got
Figure 2010105661163100002DEST_PATH_IMAGE002
The center of phase is determined therefrom yWith zCoordinate.The y axle is positioned on the solid-liquid interface, and vertical with lamella.Problem reduction is become two-dimensional state, because the symmetry of diffusion, it is separated
Figure 2010105661163100002DEST_PATH_IMAGE004
In the zone.Solid-liquid interface with
Figure 2010105661163100002DEST_PATH_IMAGE006
Speed stable growth on the z direction, this moment diffusion equation be:
Figure 2010105661163100002DEST_PATH_IMAGE008
(1)
Wherein,
Figure 2010105661163100002DEST_PATH_IMAGE010
Be the silicon solute concentration, Coefficient of diffusion for solute in the liquid phase.
Because in process of setting, temperature has certain influence to the solute coefficient of diffusion of liquid phase, therefore to predict the eutectic sheet interlayer spacing accurately, temperature must be taken into account the influence of solute coefficient of diffusion.
(2), calculate the solute coefficient of diffusion:
（2）
In the formula D 0 ---Equilibrium state solute coefficient of diffusion;
Q---The atom diffusion activation energy;
R g ---The air constant;
T---Temperature.
Because here D 0, QWith R g Be constant, wherein D 0=8 10 -9
Figure 2010105661163100002DEST_PATH_IMAGE018
=-2856; These two data substitution formula (2) are obtained the solute coefficient of diffusion is:
Figure 2010105661163100002DEST_PATH_IMAGE020
(3), calculate the eutectic structure sheet interlayer spacing
Figure 2010105661163100002DEST_PATH_IMAGE022
:
Periodic change condition according to eutectic composition can get:
Figure 2010105661163100002DEST_PATH_IMAGE024
(3)
Wherein, Be the balance eutectic composition,
Figure 2010105661163100002DEST_PATH_IMAGE028
Be the eutectic growth speed on the z direction, A, BAll be constant, it is worth by formula (4), and (5) calculate:
Figure 2010105661163100002DEST_PATH_IMAGE030
(4)
Figure 2010105661163100002DEST_PATH_IMAGE032
(5)
Wherein
Figure 2010105661163100002DEST_PATH_IMAGE034
Be eutectic line length.
(4),
Figure 449276DEST_PATH_IMAGE002
Mutually and
Figure 2010105661163100002DEST_PATH_IMAGE036
The constitutional supercooling degree of phase
Figure 2010105661163100002DEST_PATH_IMAGE038
With
Figure 2010105661163100002DEST_PATH_IMAGE040
For:
Figure 2010105661163100002DEST_PATH_IMAGE042
(6)
Figure 2010105661163100002DEST_PATH_IMAGE044
(7)
Wherein, For
Figure 879600DEST_PATH_IMAGE002
The slope of phase liquidus curve,
Figure 2010105661163100002DEST_PATH_IMAGE048
For
Figure 597020DEST_PATH_IMAGE036
The slope of phase liquidus curve.In process of setting, the speed of growth at interface exerts an influence to solute distribution coefficient, adopts continuity model to calculate in the method
Figure 929913DEST_PATH_IMAGE002
Mutually and
Figure 681968DEST_PATH_IMAGE036
Its expression formula of solute redistribution factor of phase is as follows:
Figure 2010105661163100002DEST_PATH_IMAGE050
（8）
Figure 2010105661163100002DEST_PATH_IMAGE052
（9）
Wherein
Figure 2010105661163100002DEST_PATH_IMAGE054
Figure 2010105661163100002DEST_PATH_IMAGE056
---Equilibrium state α phase liquidus curve slope;
Figure 2010105661163100002DEST_PATH_IMAGE058
---Equilibrium state β phase liquidus curve slope;
k 0a ---Nonequilibrium condition solute redistribution factor;
k 0 β ---Nonequilibrium condition solute redistribution factor;
D L ---Non-equilibrium solute coefficient of diffusion.
(5), in the eutectic growth process,
Figure 68212DEST_PATH_IMAGE002
Mutually and The curvature of phase is cold excessively With For:
Figure 2010105661163100002DEST_PATH_IMAGE064
(10)
Figure 2010105661163100002DEST_PATH_IMAGE066
(11)
Wherein,
Figure 2010105661163100002DEST_PATH_IMAGE068
For
Figure 97928DEST_PATH_IMAGE002
The contact angle of phase solid-liquid phase, For
Figure 642173DEST_PATH_IMAGE036
The contact angle of phase solid-liquid phase,
Figure 2010105661163100002DEST_PATH_IMAGE072
For Phase Gibbs-Thomson free energy coefficient For
Figure 202915DEST_PATH_IMAGE036
Phase Gibbs-Thomson free energy coefficient.
(6), the degree of supercooling of each phase is:
(12)
Figure 2010105661163100002DEST_PATH_IMAGE078
(13)
Will
Figure 2010105661163100002DEST_PATH_IMAGE080
, Obtain:
Figure 2010105661163100002DEST_PATH_IMAGE084
(14)
Degree of supercooling can be write as in the eutectic growth process:
Figure 2010105661163100002DEST_PATH_IMAGE086
(15)
Wherein
Figure 2010105661163100002DEST_PATH_IMAGE088
(16)
Figure 2010105661163100002DEST_PATH_IMAGE090
(17)
Right according to equation (15)
Figure 305039DEST_PATH_IMAGE022
Ask local derviation, when obtaining minimum subcooled temperature
Figure 766107DEST_PATH_IMAGE022
Value:
Figure 2010105661163100002DEST_PATH_IMAGE092
（18）
(16) and (17) are brought in the equation (18) and can obtain:
(19)
(20)
Wherein
Figure 2010105661163100002DEST_PATH_IMAGE098
(21)
(22)
Wherein,
Figure 2010105661163100002DEST_PATH_IMAGE102
,
Figure 2010105661163100002DEST_PATH_IMAGE104
Can draw the al-si eutectic sheet interlayer spacing shown in Fig. 1 and Fig. 2 and degree of supercooling and speed of growth relation by above-mentioned equation.
3, advantage and effect:
A kind of Alpax eutectic structure sheet interlayer spacing Forecasting Methodology that the present invention proposes, this method has following advantage:
Adopt method for numerical simulation prediction Alpax eutectic sheet interlayer spacing to shorten experimental period greatly, and cost is low, predicts the outcome not limited by experiment condition, and can investigates of the influence of a certain single technological factor Alpax eutectic structure sheet interlayer spacing.Calculating is quick, and error is less, and the relative error of this method of observation and result of calculation contrast discovery can realize the quantification prediction to the eutectic sheet interlayer spacing less than 5% by experiment.
Four, description of drawings:
Fig. 1 is Al-Si eutectic sheet interlayer spacing and the degree of supercooling and the speed of growth
Figure DEST_PATH_IMAGE106
Concern synoptic diagram;
Fig. 2 is an Al-Si eutectic theory
Figure DEST_PATH_IMAGE108
Concern synoptic diagram.
Five, embodiment:
Eutectic structure is a kind of the most common solidified structure pattern, and wherein the sheet interlayer spacing of eutectic structure pattern and eutectic structure is the principal element of the final eutectic cast properties of influence.Alpax is the most frequently used casting alloy, and it has advantages of good casting, therefore is widely used in fields such as automobile, electric power, machinery.According to classical H all-Pitch formula, the size of crystal grain and the relation of mechanical property as can be known, crystal grain is tiny more, its mechanical property is high more.But in the eutectic structure of solidifying, the eutectic sheet interlayer spacing is tiny more, and the mechanical property of eutectic structure is good more.Therefore the refining eutectic sheet interlayer spacing is main contents of research and control eutectic structure pattern.
The present invention is described further below in conjunction with specific embodiment:
A kind of Alpax eutectic structure sheet interlayer spacing Forecasting Methodology is characterized in that: dope eutectic structure sheet interlayer spacing after Alpax solidifies under this cooling velocity and the thermograde according to the cooling velocity of actual measurement and local thermograde, step is as follows:
(1), set up silicon eutectic structure sheet interlayer spacing forecast model:
At first true origin is got
Figure 510466DEST_PATH_IMAGE002
The center of phase is determined therefrom yWith zCoordinate.The y axle is positioned on the solid-liquid interface, and vertical with lamella.Problem reduction is become two-dimensional state, because the symmetry of diffusion, it is separated In the zone.Solid-liquid interface with
Figure 964898DEST_PATH_IMAGE006
Speed stable growth on the z direction, this moment diffusion equation be:
Figure 546052DEST_PATH_IMAGE008
(1)
Wherein,
Figure 818902DEST_PATH_IMAGE010
Be the silicon solute concentration, Coefficient of diffusion for solute in the liquid phase.
Because in process of setting, temperature has certain influence to the solute coefficient of diffusion of liquid phase, therefore to predict the eutectic sheet interlayer spacing accurately, temperature must be taken into account the influence of solute coefficient of diffusion.
(2), calculate the solute coefficient of diffusion:
Figure 564321DEST_PATH_IMAGE014
（2）
In the formula D 0 ---Equilibrium state solute coefficient of diffusion;
Q---The atom diffusion activation energy;
R g ---The air constant;
T---Temperature.
Because here D 0, QWith R g Be constant, wherein D 0=8
Figure 999981DEST_PATH_IMAGE016
10 -9
Figure 709311DEST_PATH_IMAGE018
=-2856; These two data substitution formula (2) are obtained the solute coefficient of diffusion is:
Figure 597633DEST_PATH_IMAGE020
(3), calculate the eutectic structure sheet interlayer spacing :
Periodic change condition according to eutectic composition can get:
Figure 770305DEST_PATH_IMAGE024
(3)
Wherein,
Figure 650537DEST_PATH_IMAGE026
Be the balance eutectic composition, Be the eutectic growth speed on the z direction, A, BAll be constant, it is worth by formula (4), and (5) calculate:
(4)
Figure 857024DEST_PATH_IMAGE032
(5)
Wherein
Figure 908157DEST_PATH_IMAGE034
Be eutectic line length.
(4),
Figure 771071DEST_PATH_IMAGE002
Mutually and The constitutional supercooling degree of phase With
Figure 40811DEST_PATH_IMAGE040
For:
Figure 391021DEST_PATH_IMAGE042
(6)
Figure 356703DEST_PATH_IMAGE044
(7)
Wherein,
Figure 475969DEST_PATH_IMAGE046
For
Figure 665642DEST_PATH_IMAGE002
The slope of phase liquidus curve, For
Figure 6941DEST_PATH_IMAGE036
The slope of phase liquidus curve.In process of setting, the speed of growth at interface exerts an influence to solute distribution coefficient, adopts continuity model to calculate in the method
Figure 246293DEST_PATH_IMAGE002
Mutually and
Figure 544550DEST_PATH_IMAGE036
Its expression formula of solute redistribution factor of phase is as follows:
Figure 869352DEST_PATH_IMAGE050
（8）
Figure 239154DEST_PATH_IMAGE052
（9）
Wherein
Figure 802170DEST_PATH_IMAGE056
---Equilibrium state α phase liquidus curve slope;
Figure 348689DEST_PATH_IMAGE058
---Equilibrium state β phase liquidus curve slope;
k 0a ---Nonequilibrium condition solute redistribution factor;
k 0 β ---Nonequilibrium condition solute redistribution factor;
D L ---Non-equilibrium solute coefficient of diffusion.
(5), in the eutectic growth process,
Figure 459865DEST_PATH_IMAGE002
Mutually and The curvature of phase is cold excessively
Figure 376185DEST_PATH_IMAGE060
With
Figure 410000DEST_PATH_IMAGE062
For:
Figure 59287DEST_PATH_IMAGE064
(10)
Figure 862158DEST_PATH_IMAGE066
(11)
Wherein,
Figure 1016DEST_PATH_IMAGE068
For The contact angle of phase solid-liquid phase,
Figure 709526DEST_PATH_IMAGE070
For
Figure 632482DEST_PATH_IMAGE036
The contact angle of phase solid-liquid phase,
Figure 942241DEST_PATH_IMAGE072
For
Figure 950648DEST_PATH_IMAGE002
Phase Gibbs-Thomson free energy coefficient
Figure 941738DEST_PATH_IMAGE074
For
Figure 719201DEST_PATH_IMAGE036
Phase Gibbs-Thomson free energy coefficient.
(6), the degree of supercooling of each phase is:
Figure 137544DEST_PATH_IMAGE076
(12)
Figure 429985DEST_PATH_IMAGE078
(13)
Will ,
Figure 856735DEST_PATH_IMAGE082
Obtain:
Figure 445980DEST_PATH_IMAGE084
(14)
Degree of supercooling can be write as in the eutectic growth process:
Figure 491296DEST_PATH_IMAGE086
(15)
Wherein
Figure 824188DEST_PATH_IMAGE088
(16)
(17)
Right according to equation (15)
Figure 336389DEST_PATH_IMAGE022
Ask local derviation, when obtaining minimum subcooled temperature
Figure 541106DEST_PATH_IMAGE022
Value:
Figure 677689DEST_PATH_IMAGE092
（18）
(16) and (17) are brought in the equation (18) and can obtain:
Figure 80989DEST_PATH_IMAGE094
(19)
Figure 265896DEST_PATH_IMAGE096
(20)
Wherein
Figure 957908DEST_PATH_IMAGE098
(21)
Figure 632603DEST_PATH_IMAGE100
(22)
Wherein,
Figure 93672DEST_PATH_IMAGE102
,
Figure 523516DEST_PATH_IMAGE104
Go out the al-si eutectic sheet interlayer spacing shown in Fig. 1 and Fig. 2 and degree of supercooling and speed of growth relation by above-mentioned Equation for Calculating.
Embodiment:
Said method material therefor parameter is as follows: Al-12.6mass%Si, liquidus curve are 577 ℃, and eutectic composition is 12.6%,
Figure 437245DEST_PATH_IMAGE056
=-7.5,
Figure 915631DEST_PATH_IMAGE058
=17.5, k 0a =0.13, k 0 β =2 * 10 -4,
Figure DEST_PATH_IMAGE110
=8.9 * 10 -3,
Figure DEST_PATH_IMAGE112
,
Figure DEST_PATH_IMAGE114
, ,
Figure DEST_PATH_IMAGE118
,
Figure DEST_PATH_IMAGE120
, , the pouring temperature of alloy is 700 ℃, mold temperature is 300 ℃.
On the metallographic structure photo that obtains that experimentizes according to above-mentioned steps Phase size and eutectic sheet interlayer spacing are measured.
What adopt is Metering system,
Figure 208783DEST_PATH_IMAGE124
Be that line is measured on the vertical direction of lamella, repeated measurement is averaged for 10 times.
Table 1 analog result and experimental result are relatively
The sheet interlayer spacing of analog computation is 13.9 as can be seen from Table 1
Figure DEST_PATH_IMAGE127
, the sheet interlayer spacing of the al-si eutectic tissue of practical measurement is 14.6
Figure 750754DEST_PATH_IMAGE127
, error is 0.7
Figure 767251DEST_PATH_IMAGE127
, relative error is 5% only, illustrates that Model Calculation is reliable.
Can dope eutectic structure sheet interlayer spacing after Alpax solidifies under this cooling velocity and the thermograde according to the cooling velocity of actual measurement and local thermograde; And added the influence of temperature and cooling velocity in the prediction al-si eutectic tissue lamellar spacing model to the material thermal physical property parameter, mainly be temperature and cooling velocity to the influence of the liquidus curve slope of the coefficient of diffusion of silicon in aluminium liquid, aluminium silicon phasor, thereby having guaranteed that model can be implemented in wider temperature range and the bigger cooling velocity interval realize prediction accuracy.
The inventive method is equally applicable to the sheet interlayer spacing prediction of the eutectic freezing tissue of other alloys, the thermograde and the cooling velocity that can obtain by actual monitoring, the sheet interlayer spacing of prediction eutectic.
This Alpax eutectic structure sheet interlayer spacing Forecasting Methodology provided by the invention, adopt method for numerical simulation prediction Alpax eutectic sheet interlayer spacing to shorten experimental period greatly, and cost is low, predicting the outcome not limited by experiment condition, and can investigate the influence of a certain single factors to Alpax eutectic structure sheet interlayer spacing.Calculate fast, error is less, is suitable for commercial Application.

Claims (2)

1. Alpax eutectic structure sheet interlayer spacing Forecasting Methodology, it is characterized in that: dope eutectic structure sheet interlayer spacing after Alpax solidifies under this cooling velocity and the thermograde according to the cooling velocity of actual measurement and local thermograde, step is as follows:
(1), set up silicon eutectic structure sheet interlayer spacing forecast model:
At first true origin is got
Figure DEST_PATH_IMAGE002
The center of phase is determined thus yWith zCoordinate; yAxle is positioned on the solid-liquid interface, and vertical with lamella; Problem reduction is become two-dimensional state; Because the symmetry of diffusion, it is separated
Figure DEST_PATH_IMAGE004
In the zone; Solid-liquid interface is with speed
Figure DEST_PATH_IMAGE006
Stable growth on the z direction, the diffusion equation of this moment is:
Figure DEST_PATH_IMAGE008
（1）
In the formula (1),
Figure DEST_PATH_IMAGE010
Be the silicon solute concentration,
Figure DEST_PATH_IMAGE012
Coefficient of diffusion for solute in the liquid phase;
(2), calculate the solute coefficient of diffusion:
Figure DEST_PATH_IMAGE014
（2）
In the formula (2): D 0 ---Equilibrium state solute coefficient of diffusion;
Q---The atom diffusion activation energy;
R g ---The air constant;
T---Temperature;
Because D 0, QWith R g Be constant, wherein D 0=8
Figure DEST_PATH_IMAGE016
10 -9
Figure DEST_PATH_IMAGE018
=-2856; These two data substitution formula (2) are obtained the solute coefficient of diffusion is:
(3), calculate the eutectic structure sheet interlayer spacing :
Periodic change condition according to eutectic composition can get:
(3)
Wherein,
Figure DEST_PATH_IMAGE026
Be the balance eutectic composition, Be the eutectic growth speed on the z direction, A, BAll be constant, its value is calculated by formula (4), (5):
Figure DEST_PATH_IMAGE030
(4)
Figure DEST_PATH_IMAGE032
(5)
Wherein
Figure DEST_PATH_IMAGE034
Be eutectic line length;
(4), Mutually and
Figure DEST_PATH_IMAGE036
The constitutional supercooling degree of phase
Figure DEST_PATH_IMAGE038
With For:
(6)
Figure DEST_PATH_IMAGE044
(7)
Wherein,
Figure DEST_PATH_IMAGE046
For
Figure 908546DEST_PATH_IMAGE002
The slope of phase liquidus curve, For
Figure 563649DEST_PATH_IMAGE036
The slope of phase liquidus curve;
(5), in the eutectic growth process,
Figure 771908DEST_PATH_IMAGE002
Mutually and
Figure 648597DEST_PATH_IMAGE036
The curvature of phase is cold excessively With
Figure DEST_PATH_IMAGE052
For:
(10)
Figure DEST_PATH_IMAGE056
(11)
Wherein,
Figure DEST_PATH_IMAGE058
For The contact angle of phase solid-liquid phase,
Figure DEST_PATH_IMAGE060
For The contact angle of phase solid-liquid phase,
Figure DEST_PATH_IMAGE062
For
Figure 313824DEST_PATH_IMAGE002
Phase Gibbs-Thomson free energy coefficient
Figure DEST_PATH_IMAGE064
For
Figure 858069DEST_PATH_IMAGE036
Phase Gibbs-Thomson free energy coefficient;
(6), the degree of supercooling of each phase is:
Figure DEST_PATH_IMAGE066
(12)
Figure DEST_PATH_IMAGE068
(13)
Will , Obtain:
Figure DEST_PATH_IMAGE074
(14)
Degree of supercooling is in the eutectic growth process:
Figure DEST_PATH_IMAGE076
(15)
Wherein
Figure DEST_PATH_IMAGE078
(16)
Figure DEST_PATH_IMAGE080
(17)
Right according to equation (15)
Figure 216545DEST_PATH_IMAGE022
Ask local derviation, when drawing minimum subcooled temperature
Figure 783924DEST_PATH_IMAGE022
Value:
Figure DEST_PATH_IMAGE082
（18）
Formula (16) and formula (17) are brought in the equation (18) and can obtain:
Figure DEST_PATH_IMAGE084
(19)
Figure DEST_PATH_IMAGE086
(20)
Wherein
(21)
Figure DEST_PATH_IMAGE090
(22)
Wherein,
Figure DEST_PATH_IMAGE092
,
Figure DEST_PATH_IMAGE094
Can calculate al-si eutectic sheet interlayer spacing and degree of supercooling and speed of growth relation by above-mentioned equation.
2. Alpax eutectic structure sheet interlayer spacing Forecasting Methodology according to claim 1, it is characterized in that: in process of setting, the speed of growth at interface exerts an influence to solute distribution coefficient, adopts continuity model to calculate Mutually and
Figure 483469DEST_PATH_IMAGE036
The solute redistribution factor of phase, its expression formula is as follows:
Figure DEST_PATH_IMAGE096
（8）
Figure DEST_PATH_IMAGE098
（9）
Wherein
Figure DEST_PATH_IMAGE100
---Equilibrium state α phase liquidus curve slope;
Figure DEST_PATH_IMAGE104
---Equilibrium state β phase liquidus curve slope;
k 0a ---Nonequilibrium condition solute redistribution factor;
k 0 β ---Nonequilibrium condition solute redistribution factor;
D L ---Non-equilibrium solute coefficient of diffusion.
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