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Determination of dendritic coherency in solidifying melts by rheological measurements
Materials Science and Engineering, A 173 (1993) 101-103
101
Determination of dendritic coherency in solidifying melts by rheological measurements L. Arnberg Department of Metallurgy, NorwegianInstitute of Technology, N- 7034 Trondheim (Norway)
G. Chai Department of Inorganic Chemistry, Universityof Stockholm, Arrhenius Laboratory, 106 91 Stockholm (Sweden)
L. Backerud SinterCast Inc., 1000North Opdyke Road, Auburn Hills, M148057 (USA)
Abstract The instant, during equiaxed solidification, when the dendrites start to impinge and form a network is called the dendritic coherency point. The paper presents a method for measuring the dendritic coherency point. The method utilizes the fact that the shear strength of the solidifying material increases sharply at the coherency point. A probe is slowly rotated in the melt during controlled solidification and the torque and temperature are measured. The coherency point can be deduced from the derivative of the torque/temperature curve. Coherency measurements of solidifying aluminium alloys have shown that the coherency point for a given alloy is reproducible for given cooling conditions, but varies greatly with alloying composition, grain refinement and cooling rate. It has been found that the fraction solid at which coherency occurs varies between less than 0.1 for poorly grain refined AI foundry alloys and more than 0.5 for fine grained AI alloys.
1. Introduction
Casting defects during equiaxed dendritic growth
(e.g. macrosegregation, shrinkage, porosity and hot tearing) start to develop at the point where the dendrites impinge and a continuous network becomes coherent. Determination of this point can result in a better understanding of these defects. Dendritic coherency has been studied by thermal analysis with two thermocouples, one of which is placed in contact with the inner mould wall and the other in the sample centre [1]. The temperature difference between the two thermocouples shows a distinct decrease at the coherency point because of improved thermal contact through the solid dendrite network [1]. Other methods are based on rheology and utilize the fact that the shear strength of the solidifying material increases sharply at the coherency point [2-3]. Claxton [4] measured the yield strength at different temperatures in commercial aluminium alloys by rotating a graphite cylinder in the slowly solidifying alloys. These experiments were, however, tedious since a series of measurements was required to establish the coherency point for each alloy. The present paper presents a new method to determine the dendritic coherency point of an alloy in a single experiment. The method is based on the same 0921-5093/93/$6.00
principle as Claxton's experiment but differs in that the stirrer is rotated at a very low speed, which makes continuous torque measurements during solidification possible without mechanically disturbing the solidifying material. Coherency studies of several binary aluminium base alloys have been made at varying cooling rates. In addition, the coherency point has been established for a number of commercial aluminium foundry alloys. The paper gives some examples of these results.
2. Experimental details
Figure 1 shows schematically the experimental setup for torque measurements. The stirrer is made from steel and mounted to the axis of a commercial viscosimeter (Physica MC 10). At the appropriate melt superheat (typically 100 K) the furnace is turned off and the melt is cooled within the furnace (0.3 K s-l), freely in air by removing the furnace (1 K s -1) or by compressed air (3 K s-t). The stirrer is rotated at 0.05 rev min- 1 during the solidification, and the torque and temperature are continuously measured. Figure 2(a) shows the temperature and torque curves of an A1-Mg alloy. The fraction solid can be calculated from the © 1993 - Elsevier Sequoia. All rights reserved
L. Arnberg et al.
102
/
Determination o[ dendritic coherency TABLE 1. Chemical composition and fraction of solid at the dendritic coherency point for some AI foundry alloys. TA and RM denote thermal analysis and rheological measurements, respectively
stirrer thermocouple --
~
1
furnace
Alloy xxx www vvv
le.,enO
x x x
^ ^ ^
x×× xx× xxx wwv
Fig. 1 Schematic drawing of the experimental set-up (dimensions are in millimetres).
900
680
8OO\,\
660
700
620
400"
~
i
\
4o
0
Mg
0.02 5.10 6.70 6.80 9.10 17.4 11.4 0.10 0.12
0.01 4.10 0.28 0.10 1.00 0.01 0.44 0.01 0.30 0.08 0.04 0.35 1.00 3.20 0.34 0.74 4.80 0.56 0.46 0.09 0.18 0.16 0.01 7.60 0.55 0.74 0.44
Zn
Ti
TA
RM
0.19 0.09 0.01 0.15
25 17 12 18 11 10 8 21 34
24-28 13-17 12-15 13-19 12-16 9-10 11-14 16-23 23-25
1.10 0.06 1.10 7.5(/ 0.15
so
lao
16o
260
Solidificationtime (s)
240
~
as0
18 20116
560
540 32O
I
iI 0.7
14
3. Results and discussion
&
580
200 !
(a)
Fe
23% fraction solid is well defined. The shape of the torque curve after coherency depends on other factors and will not be discussed here.
600 ~
300 100!
Si
-64o ~"
T
600 D" 500
Cu
Coherency(%)
700
--
1000
201 355 356 A356 A380 B390 413 518 713
Element(wt.%)
Table 1 shows the chemical compositions and dendritic coherency points, determined by rheological measurements and by thermal analysis, for some aluminium foundry alloys. It can be seen that there is a fair agreement between the two sets of data. As a general trend it can be seen that the AI-Si alloys (300 and 400 series) become coherent earlier during solidification than the AI-Cu, Al-Mg and A1-Zn alloys. When dendrites become coherent, grains form. If the grain radius is R, the thermal balance at the scale of a grain can be written as [5]:
t0.6
12
/
dfs/dt
~0.5
4:zR~Q~xt
=4~ R3 p G - 3
At
-L
At ]
0.4 "o
81 /
(b)
:l'
0.3
2~
0.1
o
0,2
Io
2o
~o
4o
go
go
Fraction solid (%)
io
so
9o
0.0 100
Fig. 2. Rheological and thermal data from a solidifying A1 alloy: (a) torque and temperature vs. time; (b) derivative of torque and temperature vs. calculated fraction of solid.
where Qext is the external heat flux, p is the density of the melt, L is the heat of fusion, Cp is the specific heat of the melt, Afs is the fraction solid at the coherency point, AT is the temperature difference between the nucleation temperature and coherency temperature and At is the time from nucleation to coherency. For aluminium alloys one can assume that the dendrites are pure A1 and the equation becomes: R
At
-K Qext 2.06At +O.32Afs cooling curve according to Backerud et al. [1]. Figure 2(b) shows the derivatives of the torque and temperature ws. fraction solid curve. It can be seen that the sharp increase of the torque derivative curve at about
where K is a constant. Figure 3 shows the relation between grain size and At/(2.06At+O.32Afs) for the foundry alloys. It can be seen that most of the alloys fall
L. Arnberg et al.
/
103
Determination of dendritic coherency
TABLE 2. Influenceof coolingrate on fraction solid at dendritic coherency,in aluminiumfoundry alloy 355 -4-
413 5-
380 -t-
j/ /-/"
E~. 4 ///" •¢-
J
./.
i
3/"
0
/
/
518
"/.+.
-4-
356
/
Coolingrate (%)
Fraction solid (%)
0.3 1 3
13-17 12-15 9-12
./
A356 ,,,4- t .t/-/'355 / 201 /- . / 713 ,/+1
2
-p
3
4
5
6
7
8
9
10
t / ( 2*AT + 0.3*fs)
Fig. 3. Relation between grain size and fraction solidfs, temperature differenceA T and time t at the dendritic coherencypoint.
Table 2 shows the effect of cooling rate on coherency for the A1-Si foundry alloy 355. It can be seen that the fraction solid at the coherency point decreases with increasing cooling rate. This can be explained by the fact that the growth rate of the dendrite arms increases with increasing cooling rate and dominates over the slight decrease in grain size.
21" 0.0011i
4. Conclusions
18 0.00511 15.
Q
129-
Torque experiments make it possible to determine the dendritic coherency during equiaxed dendritic solidification. The alloy composition affects the dendritic coherency point; an increase of alloying elements will cause dendrites to become coherent earlier. Grain refinement will delay the dendritic coherency, while an increase of cooling rate will cause an earlier dendritic coherency point.
0.01Ti 0.051i 0.113 /
o.2"ri 6-
3-
0
0
lO
2'0
30
4'0
s'o
80
io
8'0
9'0
loo
Fraction solid (%)
Fig. 4. Torque vs. fraction solid in A1-4Cu-xTi samples, showing the effectof grain refinementon dendritic coherency.
on a straight line. The scatter can be explained by the fact that alloys A380, 413 and 518 do not contain any Ti for grain refinement and the growth is more or less columnar. The profound effect of grain size on dendrite coherency can be seen in Fig. 4, which shows some binary A1-4wt% Cu alloys which have been grainrefined to different grain sizes by Ti additions. It can be seen that the coherency point is delayed up to more than 50% fraction solid in the alloy with the highest Ti concentration and thus smallest grain size.
Acknowledgments The work was sponsored by Hydro Aluminium, Elkem Aluminium, Norsk Hydro, Magnesium Division and B~eckerud Innovation AB.
References 1 L. Backerud, G. Chai and J. Tamminen,Solidification Characteristics of Aluminium Alloys, Foundry Alloys, Vol. 2, AFS, Scanaluminium,Oslo, 1990. 2 S.A.Metz and M.C. Flemings,AE~ Trans., 78 (1970) 453. 3 D.B. Spencer, R. Mehrabian and M.C. Flemings, Metal Trans., 3 (1972) 1925. 4 R.J. Claxton,J. MetaL, Feb (1975) 14. 5 M. Rappaz and P. Thevoz, Acta MetaL, 35 (1987) 1487.
101
Determination of dendritic coherency in solidifying melts by rheological measurements L. Arnberg Department of Metallurgy, NorwegianInstitute of Technology, N- 7034 Trondheim (Norway)
G. Chai Department of Inorganic Chemistry, Universityof Stockholm, Arrhenius Laboratory, 106 91 Stockholm (Sweden)
L. Backerud SinterCast Inc., 1000North Opdyke Road, Auburn Hills, M148057 (USA)
Abstract The instant, during equiaxed solidification, when the dendrites start to impinge and form a network is called the dendritic coherency point. The paper presents a method for measuring the dendritic coherency point. The method utilizes the fact that the shear strength of the solidifying material increases sharply at the coherency point. A probe is slowly rotated in the melt during controlled solidification and the torque and temperature are measured. The coherency point can be deduced from the derivative of the torque/temperature curve. Coherency measurements of solidifying aluminium alloys have shown that the coherency point for a given alloy is reproducible for given cooling conditions, but varies greatly with alloying composition, grain refinement and cooling rate. It has been found that the fraction solid at which coherency occurs varies between less than 0.1 for poorly grain refined AI foundry alloys and more than 0.5 for fine grained AI alloys.
1. Introduction
Casting defects during equiaxed dendritic growth
(e.g. macrosegregation, shrinkage, porosity and hot tearing) start to develop at the point where the dendrites impinge and a continuous network becomes coherent. Determination of this point can result in a better understanding of these defects. Dendritic coherency has been studied by thermal analysis with two thermocouples, one of which is placed in contact with the inner mould wall and the other in the sample centre [1]. The temperature difference between the two thermocouples shows a distinct decrease at the coherency point because of improved thermal contact through the solid dendrite network [1]. Other methods are based on rheology and utilize the fact that the shear strength of the solidifying material increases sharply at the coherency point [2-3]. Claxton [4] measured the yield strength at different temperatures in commercial aluminium alloys by rotating a graphite cylinder in the slowly solidifying alloys. These experiments were, however, tedious since a series of measurements was required to establish the coherency point for each alloy. The present paper presents a new method to determine the dendritic coherency point of an alloy in a single experiment. The method is based on the same 0921-5093/93/$6.00
principle as Claxton's experiment but differs in that the stirrer is rotated at a very low speed, which makes continuous torque measurements during solidification possible without mechanically disturbing the solidifying material. Coherency studies of several binary aluminium base alloys have been made at varying cooling rates. In addition, the coherency point has been established for a number of commercial aluminium foundry alloys. The paper gives some examples of these results.
2. Experimental details
Figure 1 shows schematically the experimental setup for torque measurements. The stirrer is made from steel and mounted to the axis of a commercial viscosimeter (Physica MC 10). At the appropriate melt superheat (typically 100 K) the furnace is turned off and the melt is cooled within the furnace (0.3 K s-l), freely in air by removing the furnace (1 K s -1) or by compressed air (3 K s-t). The stirrer is rotated at 0.05 rev min- 1 during the solidification, and the torque and temperature are continuously measured. Figure 2(a) shows the temperature and torque curves of an A1-Mg alloy. The fraction solid can be calculated from the © 1993 - Elsevier Sequoia. All rights reserved
L. Arnberg et al.
102
/
Determination o[ dendritic coherency TABLE 1. Chemical composition and fraction of solid at the dendritic coherency point for some AI foundry alloys. TA and RM denote thermal analysis and rheological measurements, respectively
stirrer thermocouple --
~
1
furnace
Alloy xxx www vvv
le.,enO
x x x
^ ^ ^
x×× xx× xxx wwv
Fig. 1 Schematic drawing of the experimental set-up (dimensions are in millimetres).
900
680
8OO\,\
660
700
620
400"
~
i
\
4o
0
Mg
0.02 5.10 6.70 6.80 9.10 17.4 11.4 0.10 0.12
0.01 4.10 0.28 0.10 1.00 0.01 0.44 0.01 0.30 0.08 0.04 0.35 1.00 3.20 0.34 0.74 4.80 0.56 0.46 0.09 0.18 0.16 0.01 7.60 0.55 0.74 0.44
Zn
Ti
TA
RM
0.19 0.09 0.01 0.15
25 17 12 18 11 10 8 21 34
24-28 13-17 12-15 13-19 12-16 9-10 11-14 16-23 23-25
1.10 0.06 1.10 7.5(/ 0.15
so
lao
16o
260
Solidificationtime (s)
240
~
as0
18 20116
560
540 32O
I
iI 0.7
14
3. Results and discussion
&
580
200 !
(a)
Fe
23% fraction solid is well defined. The shape of the torque curve after coherency depends on other factors and will not be discussed here.
600 ~
300 100!
Si
-64o ~"
T
600 D" 500
Cu
Coherency(%)
700
--
1000
201 355 356 A356 A380 B390 413 518 713
Element(wt.%)
Table 1 shows the chemical compositions and dendritic coherency points, determined by rheological measurements and by thermal analysis, for some aluminium foundry alloys. It can be seen that there is a fair agreement between the two sets of data. As a general trend it can be seen that the AI-Si alloys (300 and 400 series) become coherent earlier during solidification than the AI-Cu, Al-Mg and A1-Zn alloys. When dendrites become coherent, grains form. If the grain radius is R, the thermal balance at the scale of a grain can be written as [5]:
t0.6
12
/
dfs/dt
~0.5
4:zR~Q~xt
=4~ R3 p G - 3
At
-L
At ]
0.4 "o
81 /
(b)
:l'
0.3
2~
0.1
o
0,2
Io
2o
~o
4o
go
go
Fraction solid (%)
io
so
9o
0.0 100
Fig. 2. Rheological and thermal data from a solidifying A1 alloy: (a) torque and temperature vs. time; (b) derivative of torque and temperature vs. calculated fraction of solid.
where Qext is the external heat flux, p is the density of the melt, L is the heat of fusion, Cp is the specific heat of the melt, Afs is the fraction solid at the coherency point, AT is the temperature difference between the nucleation temperature and coherency temperature and At is the time from nucleation to coherency. For aluminium alloys one can assume that the dendrites are pure A1 and the equation becomes: R
At
-K Qext 2.06At +O.32Afs cooling curve according to Backerud et al. [1]. Figure 2(b) shows the derivatives of the torque and temperature ws. fraction solid curve. It can be seen that the sharp increase of the torque derivative curve at about
where K is a constant. Figure 3 shows the relation between grain size and At/(2.06At+O.32Afs) for the foundry alloys. It can be seen that most of the alloys fall
L. Arnberg et al.
/
103
Determination of dendritic coherency
TABLE 2. Influenceof coolingrate on fraction solid at dendritic coherency,in aluminiumfoundry alloy 355 -4-
413 5-
380 -t-
j/ /-/"
E~. 4 ///" •¢-
J
./.
i
3/"
0
/
/
518
"/.+.
-4-
356
/
Coolingrate (%)
Fraction solid (%)
0.3 1 3
13-17 12-15 9-12
./
A356 ,,,4- t .t/-/'355 / 201 /- . / 713 ,/+1
2
-p
3
4
5
6
7
8
9
10
t / ( 2*AT + 0.3*fs)
Fig. 3. Relation between grain size and fraction solidfs, temperature differenceA T and time t at the dendritic coherencypoint.
Table 2 shows the effect of cooling rate on coherency for the A1-Si foundry alloy 355. It can be seen that the fraction solid at the coherency point decreases with increasing cooling rate. This can be explained by the fact that the growth rate of the dendrite arms increases with increasing cooling rate and dominates over the slight decrease in grain size.
21" 0.0011i
4. Conclusions
18 0.00511 15.
Q
129-
Torque experiments make it possible to determine the dendritic coherency during equiaxed dendritic solidification. The alloy composition affects the dendritic coherency point; an increase of alloying elements will cause dendrites to become coherent earlier. Grain refinement will delay the dendritic coherency, while an increase of cooling rate will cause an earlier dendritic coherency point.
0.01Ti 0.051i 0.113 /
o.2"ri 6-
3-
0
0
lO
2'0
30
4'0
s'o
80
io
8'0
9'0
loo
Fraction solid (%)
Fig. 4. Torque vs. fraction solid in A1-4Cu-xTi samples, showing the effectof grain refinementon dendritic coherency.
on a straight line. The scatter can be explained by the fact that alloys A380, 413 and 518 do not contain any Ti for grain refinement and the growth is more or less columnar. The profound effect of grain size on dendrite coherency can be seen in Fig. 4, which shows some binary A1-4wt% Cu alloys which have been grainrefined to different grain sizes by Ti additions. It can be seen that the coherency point is delayed up to more than 50% fraction solid in the alloy with the highest Ti concentration and thus smallest grain size.
Acknowledgments The work was sponsored by Hydro Aluminium, Elkem Aluminium, Norsk Hydro, Magnesium Division and B~eckerud Innovation AB.
References 1 L. Backerud, G. Chai and J. Tamminen,Solidification Characteristics of Aluminium Alloys, Foundry Alloys, Vol. 2, AFS, Scanaluminium,Oslo, 1990. 2 S.A.Metz and M.C. Flemings,AE~ Trans., 78 (1970) 453. 3 D.B. Spencer, R. Mehrabian and M.C. Flemings, Metal Trans., 3 (1972) 1925. 4 R.J. Claxton,J. MetaL, Feb (1975) 14. 5 M. Rappaz and P. Thevoz, Acta MetaL, 35 (1987) 1487.