Bull. Mater. Sci., Vol. 3, Number I, February 1981, pp. 37-55. (~) Printed in India. Computation and application of local solidification times of grey cast iron cast in metallic moulds MALUR N SRINIVASAN Dopaxtment of Mechanical Emgineoxing, Indian Institute of Sciemee, Bangalore 560 012, India MS received 5 August 1980 Abstract. Heat conduction equations applicable to the solidification of grey cast iron east in moulds of the same material were solved for the cases of plate and cylindrical shaped castings made by pouring the metal at different tornperatures into moulds of different wall thicknesses preheated to different temperatures, when the heat transfer coefficient at the casting-mould interface was assumed to have differemt values. An explicit finite difference method was used to solve the equations- with the aid of a digital computer. Local solidification times at different nodal points wern determined from the solutions and a relationship between the local solidification time and the location in a 'casting' was established. The application of local solidification times for predicting the microstructure and estimating the ultimate tensile strength of these "castings" cast in metallic moulds has beext demonstrated. Keywords. Permanent moulding; grey east iron; cooling rate; solidification; finite difference method; heat conduction; undercool~ graphite; flake graphite; fnrrita; poaxlito, tensile strength. 1. Introduction The application of permanent moulding process to the production of cast iron castings has been rather limited despite the many advantages offered by this process as compared to sand casting process. One of the important reasons for this situa- tion is the di[tieulty in controlling the structure and properties of permanent mould cast iron casting~ in view of their extreme sensitivity to the composition, the cooling rate of the casting and the melt treatment, if any. Knowledge of the influence of these factors upon the structtue and properties of the castings would be very helpful in obviating this difficulty. Since it is known that the structure and properties in the as-cast state are consequences of the solidification process, it would be of value to understaud the effect of composition, cooling rate and melt treatment upon the solidification of castings. Thermal analysis of castings has been recognised as a valuable tool to provide information on these aspects. Thermal analysis can be carried out using both experimental and analytical techniques. While experimental methods are well-suited for generating infor- mation on the effects of composition and melt treatment in a small volume ~f 37
Transcript
Bull. Mater. Sci., Vol. 3, Number I, February 1981, pp. 37-55. (~) Printed in India.
Computation and application of local solidification times of grey cast iron cast in metallic moulds
M A L U R N SRINIVASAN Dopaxtment of Mechanical Emgineoxing, Indian Institute of Sciemee, Bangalore 560 012, India
MS received 5 August 1980
Abstract. Heat conduction equations applicable to the solidification of grey cast iron east in moulds of the same material were solved for the cases of plate and cylindrical shaped castings made by pouring the metal at different tornperatures into moulds of different wall thicknesses preheated to different temperatures, when the heat transfer coefficient at the casting-mould interface was assumed to have differemt values. An explicit finite difference method was used to solve the equations- with the aid of a digital computer. Local solidification times at different nodal points wern determined from the solutions and a relationship between the local solidification time and the location in a 'casting' was established. The application of local solidification times for predicting the microstructure and estimating the ultimate tensile strength of these "castings" cast in metallic moulds has beext demonstrated.
The application of permanent moulding process to the product ion of cast i ron castings has been rather limited despite the many advantages offered by this process as compared to sand casting process. One o f the impor tant reasons for this situa- t ion is the di[tieulty in controlling the structure and properties of permanent mould cast i ron casting~ in view of their extreme sensitivity to the composit ion, the cooling rate of the casting and the melt treatment, i f any. Knowledge o f the influence of these factors upon the structtue and properties of the castings would be very helpful in obviating this difficulty. Since it is known that the structure and properties in the as-cast state are consequences of the solidification process, it would be of value to understaud the effect of composit ion, cooling rate and melt t reatment upon the solidification of castings. Thermal analysis of castings has been recognised as a valuable tool to provide information on these aspects.
The rmal analysis can be carried out using both experimental and analytical techniques. While experimental methods are well-suited for generating infor- mation on the effects of composit ion and melt t reatment in a small volume ~ f
37
38 Malur N Srinivasan
material, they are as a rule expensive to provide information on the effect of cooling rate in different p~rts of a casting. An additional difficulty is the possi- bility of the solidification mechanism being altered considerably with the use of too many semory devices in different parts of the casting. On the other hand the effect of cooling rate can be adequately considered in an analytical model provided the physical conditions prevailing during solidification of the casting are satisfactorily taken into account in the analytical model. It has been recog- nised that numerical methods are well-suited for this purpose.
In earlier experimental work of the present author and his associates (Rama Prasad et al 1980; Rarna Prasad 1976) relationships have been established between the total solidification time of a permanent mould grey cast iron casting, and the structure and tensile strength of the casting. The total solidification time in each ease was measured experimentally and for the reason already mentioned it was not possible to assess the local solidification times at diffrent parts of the casting using this experimental technique. However, if the latter information is known, it would be possible to estimate the magnitude of the tensile strength and predict the microstructure at different locations in the casting, from the relationship established experimentally. With this in view computation of the local solidi- fication times of various permanent mould grey cast iron castings was carried out with the aid of a digital computer, using a tinite-difference network.
2. Statement and solution of the problem
Although details have been published earlier (Srinivasan 1975) they are again presented here for clarity. The alloy chosen for this study is hypereutectie cast iron with a carbon equivalence of 4.7 (which is known to be suitable for pro- ducing chill-free castings) cast into grey cast iron moulds without any treatment. The variable affecting the cooling rate of castings are as follows :
Casting shape
Casting size
Mould wall thickness
Pouring temperature (o C)
Initial mould temperature (°C)
Hgat transfer coefficient at the cooling-mould interface
The initial conditions a r e :
Plate and cylinder
1.27, 1.90, 2.54, and 3 .18cm thick plates
3.84, 6.36, 8.88 and 11.40 em diameter cylinders
1.28, 1.92 and 2.56 era.
I set II set III set
1350 1300 1250
250 200 150
0.01, 0.02, 0-03, 0.04 0.05 cal/sec, cm~C
(i) The casting, when completely filled in the mould, is at a uniform temperature of 1350, 1300 or 1250 ° C.
(ii) The initial mould temperature when the casting is completely failed is 250 ° C when the metal temperature is 1350 ° C, 200 ° C when the metal tempe- rature is 1300° C and 150°C when the metal temperature is 1250 ° C.
60 f8 z 0 1 60) and ~ = a I,~-~ + r 6r_ for cylinders.
Typical finite difference networks employed are shown in figure 1. difference eqttations applicable in each case are as follows.
aN(It --- [M(I) {0 (I + 1) + 0 ( I - 1}1 + [{1 - 2M(/)} 0 (It]
for the interior points in the casting and the mould
aN(C) = O(C) + [ 2 n f c ) { a ( C - 1) --O(C}]
_ V2h A x : M(C) 1)}] L K(C) {0 (c) - 0 ( c +
for the outer surface of the casting.
ON(D) --- 0 (D) + [2M(D) {0 (D + 1) - 0 (D)}]
['2h ~_x: M(D) {0 (D - 1) - 0 (D)}] + L K(D)
Casting - m o u l d Outer surface of casting interface of mould
(at
i ,c3-I ~ . . Costing - mould . / ~ interface
~ ~Outer surface of
/ // , . , ,
(b)
L Sehnmati¢ tnpr~nlation of tTpieal tinite diff~x~¢o nntwork,
Local solidification of grey cast iron 39
The boundary conditions are :
(it I-Ieat flow across the casting-mould interface is governed by a heat transfer coefficient h.
(ii) The outer surface of the mould loses heat by convection and radiation to the surrounding atmosphere.
The heat conduction equations considered a r e :
b0 030 for plates (1)
(2)
The finite
O)
40 Malur N Srinivasan
for the inner surface of the mould, a M
+ [{ 1 - 2M (L)} 0 (L)]
or the outer surface of the mould.
(4)
Cylinder shaped castings
The respective equations a r e :
,N,,, _- 0 " + , ) }+ ,,} ]
+ [{1 - 2M (a) o (t)] (7)
corresponding to equation (3),
ON(C) = O(C) + [2M(C){O(C - I) - 0(C)}]
2 C + 1 2 h A r M ( C ) ] 2C " K(C) {0 (C) - 0 (C + 1)} (8)
corresponding to equation (4),
ON(D) = 0 (n) + [2M(D) {0 (O + 1) - 0 (O)}]
+ E 2 2 ~ 1 .2hArM(O)¢,,...K_(_ff)) ~ t , - - - 1) - O(D)}] (9)
corresponding to equation (5), and
[ [ 2 L + l 2 h c , . A r ) ] ON(L) = M(L) 2 0 ( L - 1 ) - I[ 2L " K(L) ( O ( L ) - AT)
+ [{1 - 2M(L))O(L)] (10)
corresponding to equation (6). In the~e equations, thermal property values obtained from Angus (1960) are
substituted according to the values of temperatures and the modulus at each mesh point is determined from a knowledge of the thermal properties as well as the chosen spatial and time incrementM values.
The heat transfer coefficient at the casting-mould interface is chosen to have tire different values (0.01, 0"02, 0.03, 0-04 and 0.05 C.G.S. units) for each casting-mould combination. In practical problems this value is dependent upon m~ny factors such as the net contraction or expansion of the casting during solidi- tieation, the expansion of the mould and the type of mould coating employed etc. However, the range c'~osen fairly represents the values encountered in practice.
It is ~ssumed in the present problem that there is no liqnidus arrest and that euteetic freezing occurs at a constant temperature of 1150 ° C. At the eut¢ctic temperature, the temperature at each nodal point is made .to remain constant until
Local solidification of grey cast iron 41
the latent heat is liberated according to the method originally suggested by Eyers etal (1946) and Dusinberre (1949).
The computer program was written in Fortran IV language and calculations were performed mainly with the aid of IBM 360/44 computer at the Indian Insti- tute of Science. In all, 360 '" castings" were examined.
& Results and discussion
In flgume 2 typical temperature variation curves are shown at different locations in a given" casting" from which the solidification time at each location was determined. In the author's earlier publication (Srinivasan 1975) the following observations had been made on total solidification time (solidification time of the last part cf the casting to solidify) in respect of the 120 "castings " examined in that paper.
(i) In a given casting the total solidification time decreases as the heat transfer coefficient at the casting-mould interface increases, but this decrease is less marked at higher values of the coefficient.
(ii) When solidifying in a mould of a given wall thickness and for a given value of the heat transMer coefficient, the total solidification time of a plate" shaped casting is higher than that of a compatible cylindrical casting.
Cylindrical casting : 11.4 cm dia. Pouring temp. ' 1300°C Initial mould temp. : 2QO°C Mould wallthickness : 1.28 cm Heat transfer co-efficient : -- Q.01 CGS
1300 0,1 ,2 ,3 ,4 ,5 ,6 Loc~tions (Ref. Fig. l ]
~ 1 2 0 0
g 0
loooJ I I t 0 200 4 0 0 600
Time (sec)
42 Malur N Srinivasan
(iii) The extent of decrease in solidification time when the shape is changed from plate to cylirtder is higher irt the case of thin-walled moulds compared to thick-walled moulds.
These observations are equally valid in respect of the additional 240 "cas t ings" examined in this paper. In addition, the following observation is also found to be valid.
In a given casting the totaI solidification time decreases as the pouring tempe- rature and the initial mould temperature are decreased, at a given value of the heat transfer coefficient.
In the earlier paper (Srinivasan 1975) the local solidification times at different locations in each casting had not been considered and this aspect has been examined in detail in the present paper.
Figure 3 shows typical plots of the local solidification times with respect to the relevant loeatiorts. It is observed that appreciable changes in slope occur near the centre of the castings in all cases and near the surface of the castings in some cases. However, in the interior region of the casting, the relationship between the local solidification time and the distance of that location from the sttrface of the casting is approximately linear in all the "castings " examined. The eqttations of these linear relationships (T = Cal + C~) were determined by the least square method and the values of the slopes and intercepts have been tabulated irt tables 1 to 6. The deviations of the solidification times at the surface
1000
750 "G
E t - O
8 50O
25O
0
Computed curves
Lees! square approximation for the interior locations
/ > '
f / C ~ g S : 11.4cm clio - / . ,o" Pouri.~g temp. ~3~o~
/ ~ : ~ ~o~e~. 250~c / , !t ic ftss - .2sc
r ~ Heat tronsfer "~ 00. f l or curve 1 co-efficient J O.05for curve 2
I I I I t I 6 5 4 3 2 1 0
Location (Ref. Fig.l)
Figere 3, Solidification times at different locations in the ¢a~tings.
Tab
le
1.
Pla
te
sha
pe
d
cast
ing
s.
Po
uri
ng
te
mp
era
ture
1
35
0°C
, In
itia
l m
ou
ld
tem
pe
ratu
re-2
50
°C.
i
Ca
stin
g C
oef
fici
ent
Mo
uld
wal
l th
ick
nes
s "
1.2
8 c
m
Mo
uld
wat
t th
ick
nes
s 1
.92
cm
M
ou
ld w
all
thic
kn
ess
2" 5
6 c
m
thic
kn
ess
C.G
.S.
- .
..
..
..
¢m
Ca
C2
Dj
D,
Ca
Cs
D s
D o
C
1 C
j D
s D
, t~
E
1 "2
7
1.¸9
0
2"5
4
3"1
8
0.0
1
60
.06
0.0
2
35
.85
0.0
3
29
.16
0'0
4
24
.03
0"0
5
21
.55
0"0
1
74
"90
0"0
2
47
-08
0'0
3
37
"64
0.0
4
33
-05
O" 0
5
30
" 3
7
0.0
1
93
.43
0.0
2
61
.33
0.0
3
51
.62
0.0
4
45
.06
0.0
5
41
.88
O'O
I 1
17
-68
0.0
2
81
.00
O. 0
3
68
- 3
2
0.0
4
62
-!3
0-0
5
58
.53
23
"15
+
5
.78
--
5
"12
5
5.8
7
11
"85
+
4
"61
--
4
"61
3
3-9
4
7"4
8
+
8"0
5
--
5"4
4
26
"88
5"9
5
--
1"1
3
--
4"7
0
23
"09
4"7
7
--
8"2
8
--
4"6
3
20
'99
35
-24
÷
8
-63
--
4
"76
6
5"9
7
17
-68
+
5
-81
--
4
"36
4
2"1
!
11
"57
--
0
.74
--
4
"25
3
4"0
7
8"3
5
--
7"5
8
--
4"4
6
30
"11
6"4
3
--
14"0
1 --
4
"71
2
7"8
2
47
"16
+
1
2"7
4
--
4'2
5
77
"52
22
"69
+
8
"19
--
3
"71
5
1-7
1
13
"35
+
4
"69
--
4
"55
4
2-5
5
9-6
7
--
7"0
0
--
3"7
7
38
-33
6"8
3
--
7"4
8
--
3-9
9
35
"84
58
"36
+
!9
"21
--
3
"62
9
0-7
8
26
-04
+
1
5-2
7
--
2"5
3
61
"97
14
"60
+
9
"04
--
2
"16
5
2"5
7
8"6
1
+
16
"05
--
2
"01
4
7-9
1
4"7
9
+
47
"16
--
2
'02
4
5"1
6
23
"07
+
4
-30
--
5
"13
5
4-5
3
1!'
93
+
2
"88
--
4
"82
3
3-5
6
8.0
4
+
0-5
2
--
4-7
6
26
"51
6"1
1
--
4"5
3
--
5-0
3
23
"07
4"8
1
--
9"0
4
--
4.9
7
20
-97
35
"05
+
5
"40
--
4
"87
6
2"9
0
17
.81
q-
2
"01
--
4"
7•
40
"58
11
"83
--
4
-46
--
4
"73
3
3"1
7
8"7
6
--
12
"60
--
5
"02
2
9-6
0
6'8
5
--
19
"28
--
5
"20
2
7"4
4
47
"02
+
6
"61
--
4
"62
7
!'8
7
23
"40
--
0
"03
--
4
"47
4
8"0
1
15
"09
--
9
"40
--
4
-69
4
0-3
4
10
"70
--
1
7"0
9
--
5"0
2
36
-51
8'0
2
--
21
"21
--
5
"33
3
4'4
0
59
"08
+
7
-99
--
4
"27
8
1"8
4
28
"39
--
!'
76
--
4
-07
3
2"8
0
17
"46
--
1
1"9
5
--
4"4
1
25
-55
11
"80
--
16
"06
--
4-7
2
21
-91
8"2
6
--
15
"40
--
5
"03
1
9"6
7
23
"11
+
3
"86
--
5"1
6
12"0
,1
+
2'2
0
--4
.90
8"1
0
--
0
"22
--
4.8
2
6"1
1
--
4
"53
--
4"9
8
4"8
2
--
9"2
3
--5
"29
35
"09
+
4
-41
--
4-9
3
18
"03
q-
0
-42
--
4"7
8
12
"02
--
5
.97
--
4"9
5
8"8
4
--
13
-39
--
5"2
9
6'8
9
--
19
"75
--
5"5
8
47
"03
+
4
"65
--
4-7
4
23
"76
--
2
"31
--
4-7
3
15
"50
--
1
2-1
9
--5
"10
11
"14
--
2
0-3
7
--5
"42
8-4
1
--
24
"86
--
5.8
7
59
.17
+
4
.64
-4
-49
8"2
9
- 5
.72
-4
.62
5"1
5
- 1
6.6
3
-5-0
3
3-9
3
--
23
-27
--
5-4
6
2'9
2
--
24
"54
--
5"8
5
~t
Tab
le 2
. P
late
sh
aped
ca
stin
gs.
P
ou
tin
g
tem
pe
ratu
re
13
00
° C
, In
itia
l m
ou
ld
tem
pe
ratu
re
20
0 °
C.
4~
Ca
stin
g
Co
effi
cien
t
thic
kn
ess
C.G
.S.
Mo
uld
wa
r th
ick
nes
s 1-
28
em
M
ou
ld w
all
lhic
lmes
s 1
' 92
cm
M
ou
ld w
all
thic
kn
ess
2.5
6 e
m
c~
c.
Do
D.
C,
C~
D.
D.
6"1
C~
D.
D.
1"2
7
1"90
2"5
4
3"1
8
0.0
1
0.0
2
0.0
3
0.0
4
0.0
5
0.0
1
0.0
2
0.0
3
0-0
4
0.0
5
0.0
1
0,0
2
0-0
3
0,0
4
0.0
5
0"0
1
O' 0
2
0"0
3
0"0
4
0-0
5
54
"33
32
"80
25
"55
21
"91
19
"67
66
.26
4!.
74
33
.56
29
.47
27
"18
79
-83
52
"42
43
'22
38
"71
35
"94
96
"74
65
.87
55
"55
50
"28
47
"15
16
-61
+
6
-82
--
5
"47
8"2
9
+
4"8
1
--
5"1
6
5"1
5
+
5"0
1
--
3"7
4
3'9
3
--
5"6
7
--
5"1
0
2"9
2
--
8"4
2
--
5-1
0
24
"64
+
9
"73
--
5
"10
11
"79
+
3
"58
--
4
"72
7"3
2
--
3-7
0
--
4"8
4
4'9
5
--
6-7
0
--
5"0
1
3"4
7
--
5"4
5
--
5"3
7
32
"08
+
1
2"8
8
--
4"5
1
14
"34
+
4
"67
--
4
"21
8"0
6
+
1"7
7
--
4"4
i
4"8
7
+
9"7
9
--
4"6
1
2-8
2
+
35
.74
--
4
"95
38
"37
+
1
8"1
3
--
3"8
9
15
"35
+
1
2-0
3
--
3"3
5
7"2
0
+2
8"2
8
--
3"3
3
2"8
9
41
06
"05
--
3
"57
0"4
0
49
93
-75
--
3
"70
51
"48
31
"46
24
-78
21
"36
19
"45
60
"10
38
'54
31
-26
27
"82
25
"65
69
-47
46
"09
38
'43
34
-61
32
'39
79
"85
54
"79
4
62
46
42
"33
39
"89
16
"79
+
4
"95
--
5
"54
8-3
9
+
2-8
4
--
5"2
2
5"5
3
--
2-2
1
--
5-2
5
4"0
2
--
7-7
9
--
5"4
3
3-0
7
--
12
-89
--
5
"55
24
-74
+
6
-84
--
5
"10
•2"0
8 +
0
"10
--
5"
•9
7"6
2
--
8"2
9
--
5"2
3
5"2
7
--
12
"37
--
5
"67
3-8
1
--
13
"88
--
5
"94
32
"58
+
6
"87
--
4
"98
15
-20
--
3
-26
--
4
"95
9"0
1
--
8"9
6
--
5-2
9
5"7
7
--
7"3
3
--
5"5
3
3"7
7
+
1"5
4
--
6"0
9
39
"91
+
7
"18
--
4
"62
17
"38
--
3
"50
--
4
"71
9"4
1
--
2"5
0
--
5"1
2
5"2
8
+
13
"94
--
5
-46
2"7
8
+
57
-37
--
5
"81
50
"53
31
"27
24
-78
21
-36
19
"45
57
"93
37
"51
30
"88
27
.44
25
"52
65
"74
44
"18
37
"08
33
"73
31
"53
73
"89
51
"28
43
;86
40
"19
37
"98
16
"88
+
4
"39
--
5"5
4
8'4
3
+
2"3
5
--5
"37
5"5
3
--
2"2
1
--5
"81
4"0
2
--
7"7
9
--5
"43
3.0
7
--
12
"89
--
5"3
5
25
"13
+
4
"70
--
5"3
2
12
"28
--
1
"53
--
5"1
7
7"7
2
--
9.4
8
--5
"54
5.3
7
--
14
"00
--
5"8
5
3"8
5
--
14
"78
--
6"0
9
33
"00
+
4
"58
--
5"1
7
15
"56
--
5
"49
--
5-2
7
9"3
6
--
12
"36
--
5"5
9
6"0
6
--
11
-77
--
6"1
8
4"0
7
--
5"95
--
6"3
4
40
"57
+
3
"79
--
4"9
2
18
"18
--
8
"09
--
5"1
5
10
"24
--
1
0"4
0
--5
"61
6"0
5
--
0-5
6
--6
"08
3-5
1
+
24
"64
--
6"5
1
4°
Tab
le 3
. P
late
sh
aped
ca
stin
gs.
P
ou
rin
g
tean
per
atu
ro
12
50
°C,
Init
ial
mo
uld
te
mp
erat
ure
1
50
°C.
Cas
tin
g
Co
effi
cien
t
thic
kn
ess
C.G
.S.
Mo
uld
wal
l th
ick
nes
s 1
"28
em
M
ou
ld w
all
thic
kn
oss
1
.92
cm
Ca
C~
D s
D
o C
x C
2 D
s
D.
Mo
uld
wal
l th
ick
nes
s 2"
56
cm
C1
Cz
D~
D.
g,
1 "2
7
1"90
2" 5
4
3"1
8
0"01
0
"02
0
-03
0
"04
0
"05
0"01
0
"02
0
"03
0"0
4
0"0
5
0'0
1
0"0
2
0"0
3
0-0
4
0"0
5
0-0
1
0"0
2
0"0
3
0-0
4
0"0
5
49
"77
3
0-!
3
23
"64
20
"21
18"3
0
10-9
1 +
8
"05
--
6
-07
5
"14
+
5
'21
--
5
-49
3
-16
0
"0
--
5"4
9
2"1
4
--
0"61
--
5
"58
1,
'55
+
1"94
--
6"
01
59"2
1 37
"51
30
-24
26
"54
2
4"3
7
15
"38
+
11
"93
--
5"4
9
6"71
+
5
"95
--
5
"18
3"
71
+
8"0
9
--
5"3
9
2.•5
+
24
"37
--
5
"58
1"
24
+
61
-69
--
5"
77
69
"76
19
"07
+
15
"02
--
5"
01
45
"90
7
-29
+
1
5"8
6
--
4"81
37
"95
3.2
0
+
50
"0
--
5"0
5
33
'73
1"
14
+1
82
-46
--
5"
07
31
-05
--
0
"04
+
60
25
"0
--
5"1
4
81
"92
2
1.4
8
+
21
"07
--
4"
31
55"7
1 6
"46
+
4
9"5
5
--
4"1
2
46
"69
1"
37
+3
03
"58
--
4
-17
4
1-9
5
--
t'1
0
+4
42
"45
--
4"
11
39"
05
--
2" 5
9 +
20
7"
92
--
~4"
08
47"
86
29-
36
23"
07
20"
03
18
"30
10
"99
+
6"
71
--
6"1
4
5"2
7
+
2"6
2
--
5"8
5
3"2
6
--
3"07
--
5
"80
2-1
8
--
2"4
3
--
5"9
2
t.5
5
+
1"94
--
6"
01
54"
21
35
"47
28
" 97
25"
65
'23"
61
16"2
8 +
4"
51
--
5-0
4
7"0
6
+
0"6
9
--
5-6
4
3"93
+
2
"04
--
5
"89
2
"33
+
1
4"7
6
--
6"18
1"38
+
4
5"2
9
--
6"27
62
"96
42
" 07
34
" 98
31
" 34
29
' 03
19"9
5 +
7
"82
--
5
.43
8
"08
+
4
"53
--
5
"53
3-9
3
+
22
"14
--
5
.87
1
-86
+
7
3-1
2
--
6-0
8
0"61
+
28
8"5
2
--
6"15
71
-30
2
3-3
3
+
8"35
--
5
"05
4
9"0
6
8"2
2
+
16
"83
--
5"
25
41"-
49
3-0
6
+
81
"28
--
5"
51
37
.37
0
-55
+
58
4"9
1
--
5-6
5
34"~
92
--
0"9
5
+3
94
"21
--
5"
69
47"
29
29
-17
23
" 07
20
" 03
1
8"3
0
11
"09
+
5
"74
--
6"1
3
5"31
+
1
-85
--
5.7
8
3"2
6
--
3.0
7
--5
'80
2"1
8
--
2"43
--
5"9
2
1-'5
5 +
1"
94
--6
-01
53
"85
3
4"9
6
28
"71
2
5-
32
23
-48
16
'03
+
6
.14
--
5"9
2
7"2
0
--
1"26
--
5"7
4
4"0
2
--
0"2
5
>6
-20
2'4
4
+
9"5
9
--5
-92
1"
42
+
41
"20
--
6"4
5
60
'47
2
0"4
4
+
4-9
4
--5
"65
4
0"8
2
8"4
7
--
0"28
--
5"7
8
34"2
1 4
"22
+
13
"74
--6
"17
3
0.6
7
2"1
4
+
50
-47
--
6"2
6
28
"65
0
"75
+
21
6"0
--
6'5
9
67
-48
2
4-1
3
+
4.2
5
-5-3
6
46
.92
8
.92
+
7
.63
-5
-69
3
9.8
9
3.6
9
+
49
.84
-6
.01
3
6-2
2
1.0
8
+2
48
.80
-6
.26
3
3-9
3
--
0"5
5
+6
08
"18
--
6.3
5
o~
.g.
Ta
ble
4
. C
yli
nd
ric
al
ca
stin
gs.
P
ou
rin
g
tem
pe
ratu
re
13
50
°C,
Init
ial
mo
uld
te
mp
era
ture
2
50
°C.
Ca
stin
g
Dia
me
ter
c~n
Co
effa
eiea
t
C.G
,S.
Mo
uld
w
all
th
ick
ne
ss
1.2
8 e
m
Mo
uld
w
all
th
ick
ne
ss
1.9
2 c
m
Mo
uld
w
all
th
ick
ne
ss
2-
56
can
c~
c,
1),
D,
cl
c,
1),
D,
c~
c,
1),
D°
3"
84
6"
36
8'88
11"4
0
0.0
1
44
.19
4
2-0
0
- 1
3.2
0
- 9
.22
3
9"8
n
40
.93
-
13
.83
-
9.0
6
38
-43
4
0.8
4
- 1
4.2
2
- 8
.75
0.0
2
31
-67
1
9.9
6
- 1
9.7
9
- 9
.87
2
8.7
8
20
-00
-
21
.01
-
9.6
2
28
.02
2
0-2
5
- 2
1.7
9
- 9
.30
0"0
3
29
-85
1
0-8
4
--
12
-23
--
1
4"8
2
24
-68
1
2"6
7
--
27
"28
--
9
"85
2
4-3
1
12"8
3 --
27
-84
--
1
0-0
7
0"0
4
24
"53
8
-73
--
2
7-3
7
--
10
-11
2
2"6
6
9"1
1
--
30
"56
--
1
0"5
0
22
"41
9"
26
--
47
-18
--
1
0"3
2
0"0
5
23
"17
6
"44
--
2
7"8
4
--
10
"24
2
1"5
0
6-7
8
--
32
"09
--
1
0-5
3
20
"89
7
"07
--
6
0"6
4
--
!0"9
7
0"0
1
0"0
2
0"0
3
0"0
4
0"0
5
71
"40
55
"90
50
"16
47
"14
45
"21
71
"77
--
1
7"2
3
--
9"8
3
58
-42
6
~'4
9
--
17
'68
--
9
-46
5
3-8
4
67
"32
--
1
9"3
8
--
9.3
6
29
"62
--
2
0"3
5
--
10
"24
4
4"9
4
30
"58
--
2
6-1
3
--
10
"01
4
1"5
9
31
"09
--
2
7.3
2
--
10
"15
15
"22
--
1
3"6
5
--
10
"46
4
0"1
7
17
"64
--
2
6-8
1
--
10
"40
3
7"1
9
!8"5
9
--
30
.74
--
1
0"5
2
8-0
7
+
8"0
2
--
10
"57
3
7"6
5
!1"2
5
--
22
"57
--
1
0"6
7
34
"76
1
2"4
9
--
31
.94
--
1
1.3
3
3-7
5
+7
0"7
8
--
10
"66
3
5"9
5
7"5
8
--
16
"86
--
1
1-0
1
33
-20
8
"99
--
2
9"7
9
--
11
"12
0'0
1
15
9"9
4
14
7"4
1
--
23
"16
--
1
1"7
3
11
2"0
0
11
7-3
5
--
21
"12
--
1
0"4
1
93
"19
1
13
"99
--
2
3"8
f --
1
0"1
5
0"0
2
15
4-8
1
28
'76
+
2
7-4
3
--
12
-86
9
7"2
1
31
"47
+
7
"71
--
1
0-8
2
78
"34
3
9"1
9
--
16
"92
--
1
0'6
6
0"0
3
15
3"8
5
--
17
-75
+
20
7"8
7
--
13
"34
9
1"8
2
2"1
9
+7
39
"64
--
1
0-9
4
72
"70
1
4"4
1
+
26
"59
--
1
0"9
1
0"0
4
15
2-6
5
--4
2-5
7
+1
28
"52
--
1
3-4
4
~8
"73
--
1
2-6
2
+2
01
"53
--
1
1"1
2
69
"53
2
"06
+
/-4
67
.14
--
1
0"9
2
0"0
5
15
1"2
4
--
57
"86
+
11
4-6
9
--
13
-90
8
6~
54
--
2
2"4
1
+1
41
'20
--
1
1"2
7
67
"64
--
5
"49
+
25
4"6
7
--
10
"94
0"0
1
11
2"0
2
10
1"2
5
--
15
"07
--
1
0"6
2
81
"89
9
4"0
9
--
20
"19
--
9
"97
7
1"7
8
91
"99
--
2
2"0
7
--
9.7
9
0"0
2
97
"75
2
8-3
0
q-
7"3
5
--
10
"95
6
6"7
4
35
-88
--
2
0"7
9
--
10
"42
5
7"8
3
38
"14
--
2
6"6
4
--
10
"37
0"0
3
92
"77
1
-84
+
79
5"8
3
--
11
"04
6
1"2
6
16
"01
--
1
"26
--
1
0-7
7
52
"81
1
9"9
3
--
20
"61
--
1
0"7
4
0.1
)4
90
"05
--
1
1-5
0
+1
92
-20
--
1
1"1
2
58
"26
6
"~2
+
6
5"8
9
--
10
-91
5
0"0
3
11
"09
--
5
-76
--
1
0"9
0
0"0
5
88
"18
--
1
9"5
0
+1
38
-64
--
1
1-0
5
56
"33
0
"42
+
7
9"4
1
--
12
"12
4
8"2
8
5"6
9
q-
32
"19
--
1
1"1
3
Cas
tin
g
dia
met
er
cm
Co
et~
cien
t
C.G
.S.
Tab
le
5.
Cy
lin
dri
cal
cast
ing
s.
Po
uri
ng
te
mp
erat
ure
1
30
0°C
, In
itia
l m
ou
ld
tem
per
atu
re
" 2
00
"C.
Mo
uld
w
all
thic
kn
ess
1"2
8 c
m
Mo
uld
w
all
thic
kn
ess
1.9
2 c
m
Mo
uld
w
all
thic
kes
s 2
.56
cm
Ca
C8
D,
D,
C1
C!
D,
D o
3'8
4
6'3
6
8"8
8
11 "
40
0"0
1
0"0
2
0"0
3
0"0
4
0"0
5
0"0
1
0"0
2
0"0
3
0"0
4
0"0
5
0"0
1
0"0
2
0"0
3
0"0
4
0"0
5
0'0
!
0"P
2
0"0
3
0"0
4
0"0
5
40
,93
29
"01
24
"76
22
"63
21
"!1
63
"24
48
"74
43
"11
40
"22
38
"43
94
-89
78
"92
72
"68
69
-60
67
"33
13
6"1
9
12
3"9
1
11
8-9
3
11
5"4
0
11
3-1
3
30
-51
--
1
9'5
1
1.3"
90
--
23
'06
8"3
7
--
24
"77
5-3
5
--
23
-48
3"7
5
--
16
"84
48
"20
--
1
8"3
1
17
"62
--
1
2"9
9
7"5
4
+ 1
6"6
6
2"5
1
+1
33
"32
--
0-2
4
+2
28
7"5
59
"83
--
1
3"0
2
9"9
5
+ 9
2"0
1
--
6"5
8
+2
62
"03
--
14
.71
+
14
9"6
1
--
19
"44
+
12
7"5
6
65
"26
--
2
"11
--
15
"08
+
16
6"0
9
--
42
"96
+
44
0"2
2
--
56
"82
+
11
4"5
4
--
64
"52
+
10
9"4
2
--
9"7
2
--
10
"23
--
10
'62
--
10
'84
--
10
.60
--
10
"26
--
10
"37
--
10
"56
--
10
"49
--
10
'49
--
10"
71
--
10
"81
--
10
"53
--
10
'32
--
10
"15
--
11"
52
--
11"
65
--
11-5
7
--
11'4
6
--
11"
30
36
"26
3
2"6
4
--
23
-21
--
9
"24
3
6"7
1
30
"17
--
1
7"9
1
--
9'7
27
"26
1
4"0
3
--
23
"61
--
1
0"3
4
26
'50
1
4"2
7
--2
5"2
2
--
10
"14
"~
23
"24
8
"61
--
2
6"
52
--
1
0"3
6
23
"20
8
"60
--
2
6"5
2
--
11
"28
21
"12
5
"84
--
2
8"7
6
--
10
'26
2
1'1
2
5"8
4
--
28
"76
--
1
0"7
8
19
"47
4
"21
--
2
4"7
6
--
8'9
5
19
"59
4
"38
--
1
8"1
8
--
10
"95
~
"
53
"88
4
7"8
1
--
21
"19
--
1
0"0
8
50
"49
4
7"8
1
--
22
"21
--
9
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I I
Local solidification of grey cast iron 49
and the centre of ~aeh casting-from the predicted value using this relationship have also been listed in the tables. Here,
D. ffi To - Tut c~.~t~.) x 100, T°
and D, = T, - T,,tc,u,t,~,~ x 100. T°
From the information provided in the tables it is thus possible to calculate the local solidification times at different locations of each "cast ing" . The calculated values are no doubt approximate in the interior regions but this method provides a generalised treatment for all the "castings " examined despite differences in the shape of solidification time-location curves.
It may be observed from the tables that the deviation eoetficients at the centre of the casting are always negative, implying that the solidification time-location curve " d i p s " at the centre in all cases. On the other hand, the deviation coeffi- cients at the surface of the casting may either be negative or positive depending upon the processing conditions. Physically however, positive deviations are much more significant than negative deviations as observed typically in figure 3.
Farther, the deviation cefficients at the centre of the casting vary over fairly narrow ranges both in the case of plates (abut 2-6 "5~o) and cylinders (about 8.5-14~) as opposed to variation over extremely large ranges of deviation coeffi- cients at the surfac. Very large values of D, are obtained when T-intercept values are small,
4. Application of local solidification time
The application of local solidification time for assessment of such microstmctural features as dendrite-arm spacing is too well-known to be discussed here. It will be shown in this paper that these values may be usefully employed to predict the gross microstructural features at different locations of the "cas t ings" considered in the present work and to estimate the tensile strength of the "cas t ings" at these locations. Chill-free grey iron cast in metallic moulds may have undercooled and/or flake grasphitv associated with ferritic and/or pearlitic matrix in different combinations at different locations. The consequence of this type of microstructure would be differences in mechanical behaviour at different locations. With prior knowledge of the microstructural features however, it would be possible to have a better understanding of the mechanical behaviour of the casting under service coudition~. Knowledge of local solidification times of the casting would be extremely useful in this respect.
In fig'xre 4 is shown the relationship between the solidification time, the dimen- sions of the casting and the m;~crostructural features and in figure 5 the relation- ship b~tw~en the solidifi:ation times and the tensile strength in respect of l~rmaaaent mould chill-free grey iron castings (Rama Prasad et al 1980) where the casting geometry and tlie processing conditions a re similar to those assumed in the present work. It is evident from these figures that it is possible to predict the type of graphite and the matrix to estimate the tensile strength of such castings
~0 Malur N Srinivasan
~ 50
8 us ~5
50
Io}
Predornlnontl V floke - granite /
/Flake and / under coaled
/ gl aphlle
-
/ / under cooled t / grolc~hite
I t I 5 15 25
(b) /
/ °
I I 1 5 i5 25
Volume/surfQce ore• (ram)
Figure 4. Variation in graphite and matrix structure in grey east iron.
40
35
3o
Z 2 s
g 2o
% _ %
_ ' l f¢, ,
Silicon content -- 5 .0% Grey cast iron
o Plates • Cylinders
0 Oe • •
1 0 - -
I ! I I . . . . .
0 60 420 180 240 Solidification time ( w,sec )
Figure 5. Tensile strength versus solidification time.
3o0
from a kaowtedge of the solidification time. Also from a knowledge of local solidification times as computed in this work it should be possible to make a reasonably good prediction of the microstructural features at a given location in such permanent mould grey iron castings and to estimate the tensile strength at that location. For example, the " c a s t i n g " which has the largest total solidi- fication time (about 935 see) among those examined in the present work is a cylinder with 11.40 em diameter. This has been " c a s t " into a mould of 1.28era wall thickness at a pouring temperature of 1350 ° C and initial mould temperature of 250 ° C, the heat transfer coefficient at the casting-mould interface being
Local so/idihca¢iml ~!/,~rey cast iron 51
\ : "..~7~.~ a m . ~ : , y ~ : -
Figure 6-9. 6. Optical i~hotomicrogra)~h showing flake graphite in a matrix predominantly of ferrite (;< 100). 7. Scanning electron microscope showing flake graphite (× 420). 8. Optical photomicrograph showing undercooled graphite Jn a matrix predominantly of ferrite. 9. Scanning electron microscope showing undercooled graphite (× 420).
Local solidification of grey cast iron 53
0"01 C.G.S. units (the value of the latter would be attainable with a thick layer of highly insulating mould coating). The volume-to-surface area ratio of this "ca~t ing" is 2.85 cm. Reference to figure 4 indicates that this " ca s t i ng" could be expected to have coarse flake graphite in a matrix predominantly of ferrite at the centre, a typical microstructure which may correspond to this condition being shown in figure 6. The features of graphite are shown in greater detail in figure 7, which is a scanning electron micrograph of flake graphite. Further, reference to figure 5 shows that the tensile strength of this " c a s t i n g " at the centre may be expected not to exeeeed 10 kg/mm ~.
Also, with reference to table 4 it may be computed that the local solidification time of this " ca s t i ng" at the surface is about 113 seconds. Figures 4 and 5 make it clear that the structure and strength at this location would be similar to those at the centre. Thus a " c a s t i n g , such as this would have the same type of graphite and matrix, and would have uniformly poor tensile strength throughout.
If now the pouring temperature of this " ca s t i ng" is reduced to 1250 ° C, the initial mould temperature to 150 ° C, and the metal is poured into a mould with 2"56 wall thickness coated with a thin layer of mould coating so as to inclease the heat transfer coefficient to 0-05 C.G.S. units, the total solidification time would be reduced to 244 see (table 4). Figures 4 and 5 indicate that the structure in the central region would consist of flake graphite in a matrix of ferrite and that the tensile strength in this region would not exceed 10kg/mm s. However, the local solidification time at the surface would now be only about 4 sec which would mean that the microstructure here will consist of undercooled graphite in a matrix
Table 7. Probable mierostructure and tensile strength at different locations in a 11" 5 cm d i a " casting ".
(refer tensile figure 1) Type of graphite Type of matrix strength
kg/mm 2 (approx.)
6 Und~rcoole~l Ferrite 40-0 (with probably small amount of pearlite)
5 Flake + tmdervooled Ferrite 30"0
4 Flake + undercoeled Ferrite 22" 5
3 Flake Ferrite + pearlite 15- 0
2 Flake Ferrito + pearlite 12" 5
1 Flake Ferrite 10- 0 0 Flake Ferrite 10.0
Pouring temp. 1250°C; initial mould temp. 150°C; mould wall thickness 2.56 cm and h =0"05 CGS units.
54 Malur N Srinivasan
of ferrite (with probably a small amount of pearlite). In figure 8 is shown a typical optical photomicrograph which may correspond to this condition, while in the scanning electron micrograph shown in figure 9 details cf undercooled graphite are clearly visible. Figure 5 indicates that the tensile strength at the surface in this case could be expected to be in the region of 40 kg/mm 2, a four- fold increase over the previous case. The structure and tensile strength at the interior would gradually change according to changes in local solidification time. The expected microstructural features and tensile strength at different locations in this " c a s t i n g " are summarised in table 7.
It is to be appreciated however, that many microscopic events aie involved in solidification and therefore the effectiveness of the present approach in practical situatiorts will be governed by the extent to which the consequences of these eveuts are rettected in the bulk conduction cooling rate of the castings.
Acknowledgement
The author would like to thank the University Grants Commission, Government of India for providing a grant for computational work.
List of symbols
A T
C
c~
C t, C.,.
D
190 D,
h
hc, R
I
K
L
M
ON
r
T
ambient temperature
nodal point at the outer surface of the casting
specific heat (cal/g °C)
slope and intercept in the equation T = Ca / + C2
nodal point at the inner surface of the mould
deviation coefficient at the centre of the casting
deviation coefficient at the surface of the casting
heat transfer coefficient at the casting-mould interface (cal]sec cm~ ° C)
heat transfer coefficient due to convection and radiation (cal/sec cruz o C)
nodal point in the interior of the casting and the mould
thermal conductivity, (cal/sec cm z ° C)
nodal point at the outer surface of the mould
At At modulus a (A-T) ~ or a (A t ) ~
temperature at time t + A t
radius of cylindrical castings (era)
local solidification time in the interior of the casting
T.
T,
Tact
A t
1 t
X
P
0
An', Ar
Local solidification of grey cast iron 55
solidification time at the centre of casting predicted by T -- C1 l + (72
solidifieationtime at the surface of the casting predicted by T = CJ + C2
actual solidification time at a given location
time ineroment (see)
distance of interior nodal point f rom the outer surface of the casting
time (see)
thickness of plate c~t ings (cm)
thermal diffusivity (K/C,p) (cm2/sec)
density (gm/cc)
temperature at time t (°(2)
spatial increment (cm).
References
Angus H T 1960 Physical and engineering properties o f cast iron (British Cast Iron Iron Res. Assoc. Alvechurch)
Dusinbarro G M 1949 Numerical analysis o f heat flow (Now York : McGraw-Hill)
Eyres W R, I-[artree D R., Inghalrt J, Jackson R, Saxjant R J and Wagstaff J B 1946 Philos. Trans. R. Soc. (London) 240A 1
Rama Prasad M S 1976 Solidification structure and strongth of porman~at moulded east iron Ph.D. Thesis, Indian Institute of Sdonco, Bangaloro
