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Optimum arrangement of coke grain size for electrode graphite as determined by thermal shock tests
CarbonVol. 26,No. 6. pp. 853-866.1988 Printedin GreatBritain.
Copyright0
OOC&6223/88 $3.00 + .OO 1988Pergamon Press plc
OPTIMUM ARRANGEMENT OF COKE GRAIN SIZE FOR ELECTRODE GRAPHITE AS DETERMINED BY THERMAL SHOCK TESTS S.
SATO
Faculty of Engineering, The University of Ibaraki, Hitachi, Ibaraki, 316, Japan
M.
ISHIHARA
and K.
HIRAKAWA
Japan Atomic Energy Research Institute, Tokai, Ibaraki, 319-11, Japan
and M.
and Y.
KIYONO
INOUE
Ohmachi Research Laboratory, Showa Denko K. K., Ohmachi, Nagano, 398, Japan (Received 1 October 1987; accepted in revbed form 20 May 1988) Abstract-This article deals with factors affecting the thermal shock resistance, thermal shock fracture toughness, and other related properties of two kinds of electrode graphite prepared with three different arrangements of grain size of coal and oil cokes respectively. Experimental results on the fracture strength are wholly expressed by the Knudsen type formula; S = &G-“exp
(-np),
where G and P are the mean grain size and porosity, and So, m and n are material constants. Optimum conditions for the coke grain size are obtained to produce a graphite electrode having the maximum thermal shock resistance and the maximum thermal shock fracture toughness. Key Words--Coke
grain size, electrode, thermal shock resistance, fracture toughness.
1. INTRODUCTION
2. EXPERIMENTAL METHODS
Generally, graphite materials are manufactured by carbonizing and then graphitizing heat treatments of molded bodies consisting of granular coke fillers and pitch binder. The arrangement of these coke grains is considered to have significant influence on the mechanical, physical properties of the graphite. Therefore, studies on the coke grains and the arrangement conditions are fundamental for producing better graphite. In this work, six kinds of electrode graphite made with three arrangement conditions for the grain size of the coal and oil cokes are studied in connection with their thermal shock resistance[l] and thermal shock fracture toughness[2] using the disk testing method. Factors, like grain arrangement and some physical properties, which influence the thermal shock characteristics, are discussed. The resistance and fracture toughness for thermal shock are not only related to mechanical properties but also to thermal properties such as thermal conductivity and expansivity of the materials. Therefore, measurements of such properties are useful in deciding the basic conditions of the synthesis of industrial products, especially for electrodes used in steel making arc furnaces. Mechanical properties, such as the diametral compressive strength[3] and fracture toughness[4], for three arrangements of coke grain size are also measured and their influences are discussed.
2.1 Specimens Specimens examined in the study were two kinds of laboratory-made electrode graphite, 100 mm in diameter, produced from coal and oil-cokes. The coke grain sizes are sieved into several groups and arranged to three classes in accordance with the cumulative weight percent. Conventional manufacturing processes by extrusion, carbonization at about 800°C and graphitization at about 3000°C were used to make specimens of electrode graphite. Figure 1 shows the cumulative weight percent of the three classes of graphite as a function of coke grain size. The classes were designated as Gl, G2, and G3 in order of increasing grain coarseness. The two kinds of coke were distinguished by adding the suffixes C for coal coke and 0 for oil coke. The mean grain size representing the three classes of specimen graphite were defined by these, corresponding to 50% cumulative weight. Accordingly, the mean grain sizes G were 381 Frn for Gl-C and -0, 84 p,m for G2-C and -0, and 34 pm for G3-C and -0 specimens. Table 1 shows the common physical and mechanical properties of the coal-coke and oil-coke graphites, respectively. These graphites had anisotropies originating from the extrusion process. The letters L and R in the table show the properties of the logitudinal, or with grain and the radial, or across
853
S. SAT0 et
al.
coke grain size ( pm) Fig. 1. Cumulative weight percent of graphite specimens as a function of coke grain size.
grain, directions
respectively.
Disk specimens
in this
study were cut so as to make the central axis parallel to the extrusion axis of the rod. Therefore, the results obtained with these disk specimens, such as those for thermal shock resistance, reflect the physical properties in the R direction. In these specimens, mean properties were also influenced by changes of grain size G. Porosity P is defined from the apparent density y and the theoretical density y, (=2.26 g/cm3) as follows;
Figure 2 are micrographs of the three classes of grain size of coal-coke and oil-coke graphites, respectively. The grain sizes and the pores or defects are finer in order of Gl > G2 > G3. Specimens were disks with a diameter of 2R = 50 mm and thickness of h = 5 mm for the thermal shock and fracture toughness tests and h = 10 mm for the diametral compressive tests. Square rods 10 x 10 x 20 mm were used for the compressive strength tests. Machining of the edge slit in the disk for the thermal shock fracture toughness tests was carried
out first using a milling cutter (thickness: 0.2 mm), and then sharpened by hand using a serrated thin razor blade, while the slit depth was measured by an optical comparator. The central slit in the disk for the modes I and II fracture toughness measurements was machined first by an ultrasonic processing machine using a razor blade cutter and then finished with a serrated razor blade. 2.2 Outline of the measuring methods Figure 3 is a schematic illustration of the series of disk testing methods employed. 2.2.1 Diametral compressive strength. As shown in Fig. 2(l), measurements of the diametral compressive strength u,,, of the disk were conducted using the method of Awaji and Sato[3] using circular anvils. Considering the contact width 26 of the Hertzian contact due to circular anvils, uH, is determined by the following equation: u H, = [l - 1.15(blR)2
+ 0.22(blR)‘]op,
(2)
where up is the tensil stress PlnRh at the disk for a concentrated loading P.
Table 1. Physical and mechanical properties of graphites of coal coke Graphite
*
Gl-C
G2-C
G3-C
Gl-0
G2-0
G3-0
Apparent density Y (g/cm’) Porosity p Electric resist. p (X 10-Q cm) Young’s modulus, E (GPa) Bending strength ob (MPa) Coef. ther. exp.” o (x lo-bQC-‘)
L R L R L R L R L R
1.376 1.358 0.395 104 170 4.81 1.81 6.77 4.71 1.99 3.30
1.418 1.410 0.373 84 145 6.81 2.55 9.71 6.47 2.02 3.50
1.527 1.516 0.327 67 130 10.73 3.29 14.80 9.90 1.92 4.00
1.404 1.394 0.381 82.5 129 4.12 1.77 7.75 5.10 2.19 3.18
1.513 1.512 0.331 75 131 6.47 2.56 10.8 5.69 2.10 3.60
1.565 1.574 0.306 71 131 8.34 3.14 13.04 6.06 2.00 3.90
*L and R: longitudinal and perpendicular directions for the extrusion axis, respectively.
‘Mean linear coefficient of thermal expansion in 5OO”C-800°C.
Optimum arrangement of coke grain size
855
GZ-0
G3-C
G3-0
(a) Fig.
2.
Microscopic structures of coal- and oil-coke graphite specimens.
2.2.2 Fracture toughness. Fracte toughness tests of the disk with a central slit shown in Fig.2(2) were in two distinct ways, changing the slit angle, whereby modes I and II fracture toughness values K,c and KIIC,as follows[4]: K ICJIC - NIW
6.
PIRh,
(3)
where NIH and NIIH are the stress intensity factors considering the Hertzian contact width, and are determined by H ,H,IIH =
(b)
0.1
NPJIPP
-
(1)
u, and crII are functions of the crack size ratio (c/R) and the contact width ratio (b/R), and NIP and NIIP are the stress intensity factors for concentrated loading (e.g., NIP = 1.136, NIIp = 1.866 for clR = 0.3 in this study). Furthermore, the slit angles 8 for the vertical direction are zero for mode I and 27.2” for mode II, when clR = 0.3. 2.2.3 Deduced uniaxial tensile strength. Uniaxial tensil strength a: is deduced from the fracture criterion using data of uHC, uc and the ratio of Klc and KIIc as follows[5]:
Ul
(4)
(~~R)*lh,~.
(2)
*=Ic.
K K IIC uf,C(l
(31
JP
OirC
KIJC
CU
Fig. 3. Measuring methods for the disk tests.
(4)
aH@C
-
uyh,)
+ (JC’
(5)
S. SATOet al
856
where a;/~;, a ratio of the compressive stress 0; to the tensile stress a, at the center of a disk, is a function of the contact width bJR. cr: will be used later to evaluate the equivalent crack length. 2.2.4 Thermal shock resktance. When the central area of the radius a of a disk is rapidly heated by amount of thermal energy Q ==qRYk(q = WJ~#zh, W, heating power in W), the ma~mum tangential tensile stress uBmanis produced on the disk circumference as illustrated in Fig. 3(3), after a nondimensional thermal diffusion time. If a thermal crack is produced on the disk by a critical amount of heat at a specified nondimensional time T, the stress uomaX is equal to the tensil strength o,. The thermal shock resistance A is determined from the measurement of the critical electric power W using the following equation[ l] : A = tr,klEar
(6)
S*Wp = rh(a/R)2’
(7)
where E, k, and cxare the Young’s modulus, thermal conductivity and expansivity, respectively, and S* denotes the specific nondimensional maximum thermal stress amounting to 1 .lOO x 10v2 for the heating radius aJR = 0.3 at the nondimensional thermal diffusion I = 0.25. 6 is a heating efficiency determined by considering the heating losses due to heating of the upper and lower electrodes, heat convection, and radiation; p % 0.45 under the present expe~mental conditions. 2.2.5 Thermal shock fracture toughness. In the case of rapid heating at the central area of the disk with an edge slit of thickness c, such as in Fig. 3(4), the
thermal shock fracture toughness V is expressed as a function of the critical electric power W to initiate cracking at the edge slit just at the specified time 7 = 0.25, determined by the following equation[2]: V = KIcklEa
(8)
F,GcWp = rrh(a/R)2 ’ where F, is the nondimensional stress intensity factor determined by the tangential thermal stress at the tip of the edge slit and is equal to 1.54 x 10m2 for atR = 0.3 and c/R = 0.3 in this study. 2.3 Experimental apparatus Mechanical properties were investigated by a mechanical testing machine of 5 tons with a constant crosshead speed of 0.5 m~min. The thermal shock tests were conducted by using arc discharge with welders whose current capacities are 350 and 1200 A, 2.4 Empirical formula Many articles so far have deah with the influences of grain size and porosity on the mechanical strengths of polycrystalline ceramics[6-91 and carbons[lO-141. Relationships between material strengths and the grain sizes of most metals and ceramics can be expressed well by Petch’s equation[l5]. However, for porous polycrystalline materials such as graphite, the exponent on the grain size in his expression may be different from the predicated value 0.5. Since the graphite specimens studied here have different porosities (P) through the change in grain size (G), the fracture strengths (S,> in this study were con-
Table 2. Empirical constants involved in Knudsen’s expression for graphites Oil coke
Coal coke Graphite
*
Young’s modulus, E (GPa) Coef. therm. exp., a (x lo-w-‘) Elect. rest., p ( X 10S4fi cm) Bending strength, ub (MPa) Dia. compr. strength, =~@@a)
Compr. strength, oc (MPa) Uniax. tens. strength, a: (MPa) Fract. tough. of mode I, I& (MPam’~) Fract. tough. of mode II, Knc (MPamln) Therm. shock resist., A (W/mm) Therm. shock fract. tough. V (W/mmlR)
so
-m
-n
1.96 x 102 11.09 2.66 16.8 1.77 7.96 197 153
-0.117 - 0.202 0.0367 0.094 0.096 0.098 -0.144 -0.103
-7.63 - 1.54 -1.07 -5.4 3.04 0.43 -6.37 -7.27
18.0
-0.166
- 7.24
34.8
-0.166
-7.24
-m
-n
47.6 18.8 5.00 5.03 5.49 17.7 43.4 8.7
-0.179 -0.087 0.204 -0.087 0.0571 0.0411 -0.145 - 0.05
-3.63 -4.86 -5.35 0.16 0.18 -1.56 -2.27 -0.56
3.43
- 0.020
-1.54
-0.077
-0.18
SLl
16.4
R
7.35
-0.114
-1.24
2.54
-0.042
-0.20
R
1.52
-0.122
-3.87
0.36
- 0.041
-1.06
R
2.35
-0.109
-4.16
0.51
-0.075
- 0.40
R
7.25
- 0.016
5.60
2.77
- 0.052
7.92
0.038
3.19
0.027
3.21
R
61.9
40.6
*L and R; longitudinal and perpendicular directions for the extrusion axis, respectively.
Optimum arrangement of coke grain size 16 -+--o-
coal coke
oil coke
Fig. 4(a). Young’s modulus of graphites as a function of grain size (with grain). ventionally expressed by a generalized equation with G and P as follows: S, = &G-“’ exp (-nP),
3. EXPERIMENTAL RESULTS AND DISCUSSIONS 3.1 Physical properties
Table 2 shows the empirical constants involved in the Knudsen type expression for Young’s modulus E, thermal expansivity IX,electrical resistivity p, and bending stength ub of coal-coke and oil-coke graphites. Figure 4(a) and (b) plot Young’s modulus as a function of G. In this figure, JAERI data[l6] for 11 kinds of reactor-grade graphite, which are arranged
(10)
where S,,, M, and n are material constants. A similar expression has been used for several ceramic materials by Knudsen[S]. A and V for thermal shock were also evaluated by using this Knudsen type expression. 14 --+-o_
caal coke oil coke /
/
H--. --..
.
10 -
JAERI data
. \ q/
I’ \
\
‘\
. . .
E(,)=ll.aG
/
---__~
/
I
-o.20ze-i&P
2-
0..
10
I
I
50
100
I 500
I 1000
5000
Glum)
Fig. 4(b). Young’s modulus of graphites as a function of grain size (across grain).
s. SAT0
858
by the maximum grain sizes, are enclosed in the broken line. Similar data obtained by Inagaki and Noda[l4] on six kinds of oil-coke graphite, which were arranged by the mean grain size, are enclosed in the chain lines, while the data by Kennedy and Kennedy[l3] are in the double chain line. The graphite specimens of Inagaki and Noda were manufactured using three classes of oil-coke grain sizescoarse, medium, and fine-but the mean grain sizes of the specimens were not directly specified. If the size of the fine grain can be assumed to be 100 pm or less, their mean-grain-size coke is deduced as the points in Fig. 4(a). Their data agree fairly well with the present data. On the other hand, Kennedy and Kennedy made their specimens with a constant density by using eleven classes of grain size from 100 to 1000 pm and adjusting the quantities of pitch binder. As the mean grain sizes, they used the mean of the maximum and minimum values for each class. Young’s moduli in this study for both graphites based on coal and oil cokes tendencies increasing with decreasing grain size in proportion to G-(“~os-o~*o~ and also with decreasing porosity in proportion to e-(1.54m7.63)p. Such trends agree well with the data of Inagaki and Noda and Kennedy and Kennedy. JAERI data show a similar trend macroscopically similar to those in the present work, but are widely scattered, since the data were evaluated en masse for different kinds of cokes and manufacturing conditions. It is interesting that the exponents of G in the empirical formulas employed in this study for coal- and oil-coke graphites are nearly equal to the exponent -0.11 given by Kennedy and Kennedy. In our empirical formulas, Young’s moduli deduced for the critical case of P = 0 are (47.6-19.6) GPa in with-grain direction and (11.1-18.8) GPa in across-grain direction. These mean value agrees fairly well with Young’s modulus (E = 23.4 GPa) of polycrystalline graphite presented by Yoda and Fujisaki[l7]. 6.0
--tu
et al.
Figure 5(a) and (b) show influences of grain size and porosity on the thermal expansivities in the withgrain and across-grain directions, respectively. For the sake of comparison, data of JAERI[16] and Inagaki and Noda[l4] are also indicated. Thermal expansivities in the with-grain direction for coal- and oil-coke graphites have a common tendency increasing very slightly with an increase of grain size, in agreement with those found by Inagaki and Noda, but vice versa in the across-grain direction. On the other hand, thermal expansivities as a function of porosity tend to decrease with increasing porosity, except for those of oil-coke graphite in the acrossgrain direction, as is demonstrated by the empirical formulas. JAERI data show the same general trends. Thermal expansivities for zero porosity are 16.8 x 10m6and 2.70 x 10m6K-l for with-grain and acrossgrain directions of coal-coke graphite, while those for oil-coke graphite are 5.0 x 10m6 K-l in both directions. These values are between - 1.5 x 10e6 K-l and 28 x low6Km’ for the u-axis and c-axis directions of a single graphite crystal. Recently, Yoda and Fujisaki[l7] studied the relationship between physical properties of polycrystalline graphite and porosity. They arranged their data in the following form corresponding to a first approximation of our eqn (10); S = So (1 - n P). Values So and n are material constants. Products for Ea in this study obtained from the empirical formulas are found to be influenced only slightly by grain size (G) especially in the with-grain direction, but strongly influenced by porosity (P).Such relationships for Ea and P may be considered to come from the so-called Griineisen relation[20]. Figure 6(a) and (b) show electrical resistivities p in with-grain and across-grain directions of both graphites as a function of grain size. Data by JAERI[16], Inagaki and Noda[l4], and Kennedy and Kennedy[l3] are also shown. In this study, the
coal coke oil coke
-_ C
50
. .
-_-
100
JAERI \ \ _-L--
500
data
\
loo0
3000
G(pm)
Fig. 5(a). Coefficient of thermal expansion of graphites as a function of grain size (with grain).
Optimum arrangement of coke grain size
859
6 v -o_
5-
1
coal coke oi I coke
JAERI data i
100
50
G(bm)
500
1000
Fig. 5(b). Coefficient of thermal expansion of graphites as a function of grain size (across grain).
electrical resistivity p of coal-coke graphite tends to increase with increasing grain size (G) in both directions, but the trend is not clear for oil-coke graphite. Experimental results obtained by Inagaki and Noda are very close to the present data. The influence of porosity on p is not demonstrated as a definite trend in the empirical formulas. In general, the electrical resistivity of graphite may increase with decreasing coke grain size, since the contact resistance at the grain boundary is considered to increase. On the other hand, there are cases showing an increase due to the influence of the pitch binder. Consequently, a simple relationship between p and G covering a wide range of G values cannot be clearly recognized.
d
-c---
Figure 7(a) and (b) show the influences of G and P on the bending strength in the with-grain and acrossgrain directions, respectively. Bending strength increases with decreasing G in proportion to G~~“~05-0~‘45) for both graphites. This coincides with the general trend that the finer the microscopic structures the larger the strength. However, the exponent of G is much smaller than 0.5 in Petch’s relation for metallic materials. This means that porous and polycrystalline materials such as graphite do not always follow Petch’s equation. Regarding the influence of porosity P, the bending strength increases with a decrease of P. This trend is very noticeable for coal-coke graphite, especially in the small grain size.
cd coke oi I coke /.
Kennedy
and Kennedy
I
50
5000 G’?frn
1
1000
3000
Fig. 6(a). Electric resistivity of graphites as a function of grain size (with grain).
8. SAT0 et al.
860 20
18
--+-o-
coal coke oil coke
16
a 6’ IO
I
I
50
100
I 500
I 1000
5000
G(Pm)
Fig. 6(b). Electric resistivity of graphites as a function of grain size (across grain).
3.2 Diametral compressive strength
3.3 Fracture toughnesses
Figure 8 shows the diametral compressive strength of both graphites as a function of G. The trend is quite similar to that of the bending strength. The influence of grain size is more pronounced for coalcoke graphite, especially in the case of small grain size. Figure 9 shows typical fracture appearances in the diametral compression tests. Hairline cracks are produced near the center of the disk and then propagate upward and downward.
Figure 10(a) and (b) show modes I and II fracture toughnesses of coal- and oil-coke graphites as a function of grain size. Coal-coke graphite exhibits a stronger dependence on the grain size than oilcoke graphite does, especially in the small size range. Such a trend is similar to the other mechanical properties. Regarding the influence of porosity, the fracture toughness increases with decreasing porosity. Furthermore, the ratio of the two fracture tough-
30 [ --t_ --+-
25
coal
coke
oil coke
i
-5
IO
50
100 G (urn)
500
1000
3003
Fig. 7(a). Bending strength of graphites as a function of grain size (with grain).
Optimum arrangement of coke grain size 14
861
I + U
12
coal coke oil coke
10
\ -0.05 (&CRj=8.7G
e-o.56P
2
IO
50
100
lax
500
3oco
G (urn) Fig. 7(b). Bending strength of graphites as a function of grain size (across grain).
nesses K,,JKIc is derived from the corresponding formulas as follows; for coal-coke graphite:
K,,,IK,, = 1.55G”.oL3exp (-0.29P),
(15)
and for oil-coke graphite:
Since the exponents on G and P in these expressions are very small, the ratios are almost constant (ie., 1.4-1.5), irrespective of the difference in coke, grain size, and porosity. Similar ratios have been found for several reactor graphites[21]. This implies that the occurrence of crack propagation of the shearing mode is about 1.4 to 1.5 times more difficult than that of the open mode. In other words, the pure
(16)
K,,cIKI, = 1.42G-0.0” exp (-0.66P)
shear strength of graphite is about 1.4 to 1.5 times
4.0
--O---
coal coke oil coke
--o----
t
3.5 -
3.0 -
2.5 : ‘;i 2 -2.0 8 $ b 1.5 -
0.5
1 10
I 50
I
I
I
100
500
loo3
5000
Glum)
Fig. 8. Diametral compressive strength of graphites as a function of grain size (across grain).
S. SAT0 et al.
862
GZ-0
GZ-C
l&&l
Fig. 9. Typical fractures in the diametral compressive
strength test.
greater than the tensile strength. This is supported by Losty’s experiments which shows that measured values of shear strength are of the same order as the ~~es~nding flexural strength[22]. When a rod of graphite is twisted to failure, the crack occurs along a helix. This is typical tensile failure rather than shear. Figure 11(a) and (b) show typical fracture ap pearances of the three classes of grain size for the two graphites in modes I and II fracture-toughness tests, respectively. In these photographs, the loading directions are vertical. In mode II fracture, the cracking initiates at both tips of the central slit at a large angle and then propagates, turning the head vertically, to become like mode I.
0.6 0.5 -
;
+ -@---
coa\ coke oii coke
0‘4 -
-& g 0.3 -
10
100
50
500 .G(pm
1000
3000
1
Fig. 10(a). Mode I fracture toughness of graphites as a function of grain size (across grain).
A
0.6
-c-
coal coke oil coke
Klqfq’
---IO
50
loo
G(m-4
2.356
500
-0.109&&.16P
1000
Fig. 10(b). Mode II fracture toughness of graphites as a function of grain size (across grain).
863
Optimum arrangement of coke grain size
G2-C
nucleated in a heating time of 3 s, with the constant nondimensional thermal diffusion time T = 0.25, was determined using the ratio of heating area alR = 0.5 for 10 disk specimens. Considerable fracture appears during the arc discharge heating, but the mean values are determined as the average area of the power and time on the recording chart. Figure 13 shows typical fracture appearances from thermal shock tests, where thermal cracks are found to occur in the left side of the disk. Some are very minute after cooling to room temperature. Figure 14 shows the thermal shock resistance as a function of grain size. Indicated ranges of the data show that in the upper limits all specimens fracture, but not in the lower limits. Coal-coke graphite clearly shows a larger thermal shock resistance than oilcoke graphite over the range of grain sizes examined. Empirical formulas for the Knudsen type thermal shock resistance were determined by solving thirdorder simultaneous equations for three unknown material constants as follows; for coal-coke graphite:
G2-0
;omm
Fig. 11(a). Typical fractures in the mode I fracture toughness test.
G2-C
G2-0
iomm
Fig. 11(b). Typical fractures in the mode II fracture tough-
A(c) = 7.25G-0.016 exp (5.6P),
ness test.
3.4 Compressive strength Figure 12 shows the compressive strengths of graphites as a function of the coke grain size. For each graphite, an empirical formula is obtained. Similar to other mechanical and fracture toughness properties, coal-coke graphite has stronger dependencies on grain size and porosity than those of oil-coke graphite. In particular, the porosity of coal-coke graphite shows a large effect, as in the diametral compressive strength tests. 3.5 Thermal shock resistance For each of the two kinds of coke graphite, the threshold electric power at which thermal cracks are
and for oil-coke graphite: A(o) = 2.77G-0.52 exp (7.92P). On the other hand, a relationship
+
coal
-o-
oil coke
represent graphite. using the lows; for P(c)
= (-2.42
x 10-6)G2 + (1.20 x 10-3)G + 0.289,
coke
I
‘6t
8-
50
100
between G and
the data by Inagaki and Noda for oil-coke Empirical formulas are given by Lagrange supplementary polynomial equation as folcoal-coke graphite:
18
10
(18)
P for each graphite is shown in Fig. 15. Triangles
22 20
(17)
G(um)
500
1000
5Kxl
Fig. 12. Compressive strength of graphites as a function of grain size (across grain)
(19)
s. SAT0
GZ-C
Both graphites have a slight dependence on grain size, but the dependency on porosity is more definite. On further substituting eqns (19) and (20) into eqns (21) and (22), expressions for thermal shock fracture toughness can be derived as a function of grain size only; for coal-coke graphite:
GZ-0
iomm
et al.
Fig. 13. Typical fractures in the thermal shock resistance test.
V(c) = 61.9G0.038exp [3.19( -2.42
and for oil-coke graphite:
and for oil-coke graphite:
P(o)
V(o) = 40.6G”,m7 exp [3.21( -9.78
= (-9.78
x 10-6)GZ + (6.22 x 10-3)G + 0.286.
(20)
Substituting these relations into eqns (17) and (18), equations for thermal shock resistance expressed only by grain size can be derived. The two curves in Fig. 15 show the results thereby calculated for coal-coke and oil-coke graphites. Each curve indicates the op timum grain size that provides the maximum thermal shock resistance. Optimum grain sizes are about 250 and 300 urn for coal-coke and oil-coke graphites, respectively. Similar investigations have been carried out by Meyer[lO]. He measured the critical electric power for thermal shock fracture of more than 20 types of graphite disks from several sources having grain sizes less than 300 km. He concluded that the optimum grain size was about 80 pm, much smaller than the 250 to 300 pm obtained in this study, probably due to the different type of graphite. 3.6 Thermal shock fracture toughness For the graphite disk with a machined edge slit, the threshold electric power for crack propagation was evaluated under the conditions of alR = 0.3 and clR = 0.3. Figure 16 shows typical fracture appearances in the thermal shock fracture toughness tests. The crack propagates from the tip of the edge slit toward the center of the disk as in mode I fracture. The crack propagation can be clearly seen as high temperatures, but becomes indistinct after cooling. Figure 17 shows the thermal shock fracture toughnesses of the two graphites as a function of grain size. The values for coal-coke graphite are definitely higher than those for oil-coke graphite. Empirical formulas are obtained by solving simultaneous equations for three conditions of coal-coke and oil-coke graphites as follows; for coal-coke graphite:
x 10+GZ+
x lo-‘G*+
1.20 x 10-3G + 0.289)],
6.22 x lo-“G
(23)
+ 0.286)].
(24)
These equations are shown as the solid curves in Fig. 12. The optimum grain sizes, corresponding to the maxima of the curves, are about 250 p.m for coalcoke graphite and about 300 pm for oil-coke graphite. These sizes are the same as those for the maximum thermal shock resistances. 3.7 Parametric considerations of A and V Thermal shock resistance A and thermal shock fracture toughness V are also calculated from combinations of properties given as parameters in eqns (6) and (8), respectively. Unfortunately, the thermal conductivities were not measured in this study, but were estimated using the following relationship with electric resistance at room temperature; k = 1.25 x 10-‘/p
(25)
where dimensions of k and p are [o/crn’C] and [a cm], respectively. Instead of the tensile strength, the deduced uniaxial tensile strength cr: was used. These properties are shown as empirical parameters in Table 2. The calculated thermal shock resistances A in the across grain direction (R) are
120 r 100
I
--W-
--o-
cool coke oil coke
20
V(c) = 61.9GO.O”exp (3.19P),
(21)
and for oil-coke graphite:
50
100
503
11
G(um)
V(o) = 40.6G”,0n exv (3.21P). \ I
t
OL 10
1
\
I
(22) \
I
Fig. 14. Thermal _shock resistance of graphites as a function of grain size (across grain).
Optimum arrangement of coke grain size
865
0.5 + -c-
Coal coke oil coke
P;’ -2.416~10-6)GZ~.199~10-3)G~ 0.2889
P=~-9.78X10’7~G2~(6.219x10-4)G+
c
0.2855
d
-_ 0
100
200
G(am)
300
400
500
Fig. 1.5. Relation between porosity and mean grain size of graphites.
A(c)’ = (a:klEa) = 6.43G-0.1Q exp (5.27P), (W/mm)
(26)
express the qualitative characteristics well, except for the exponent of G for coal-coke graphite.
A(o)’ = (a:klEa)
4. CONCLUSION
= 1.97 G”.091exp (6.06P), for coal-coke
and oil-coke
(W/mm)
graphites,
(27)
respectively.
These expressions for thermal shock resistance do not agree with the empirical formulas, eqns (17) and (18), but represent the qualitative characteristics well. Such a discrepancy comes mainly from the difference in temperature conditions. That is, the temperature of arch discharge heating is close to the sublimation point (3760°C) at the central area, but is about 700 to 800°C on the side surface according to measurements by an optical thermometer. In fact, parameter calculations were made using the properties measured at room temperature, except for the thermal expansivity that was measured between 500°C and 800°C. The thermal shock fracture toughness is calculated in a similar manner as follows, V(c)’ = 42.1G-0.112 exp (2.64P)
(28)
V(0)’ = LL~.~GO.~ exp (5.2P)
(29)
In this study, mechanical properties, especially those related to fracture mechanics, of polycrystalline graphites prepared with different coke grain sizes were investigated, and the grain sizes for coal- and oil-based samples giving the maximum thermal shock resistance and thermal shock fracture toughness were experimentally determined. The results are expressed as empirical formulas of the Knudsen type, and may be summarised as follows: Mechanical strengths, such as bending and/or diametral compressive strengths and Young’s modulus, increase with decreasing grain size and porosity (i.e., the finer the microscopic structure, the higher the strength). Exponents of grain size in the empirical formulas of mechanical strengths were consider-
--t
coal coke
for coal-coke and oil-coke graphites, respectively. Again, the calculated results do not agree with those from the empirical formulas, eqns (21) and (22), but
01
G2-C
lZ-ll
G2-0
Fig. 16. Typical fractures in the thermal shock fracture touehness test.
10
_1
1
50
100
G(um)
500
lcco
Fig. 17. Thermal shock fracture toughness of graphites as a function of grain size (across grain).
866
8. SAT0 et al. tained through combinations properties in A and V.
ably smaller than the exponent 0.5 in the wellknown Petch relation for metals. Probably, fracture in polycrystalline graphite is different
3. 4.
5.
6.
7.
8.
9.
from that expected from a simple model, such as pileup of dislocations at the grain boundary, since the coke grain boundaries consisting of pitch carbon binder are very irregular. No influence of grain size and porosity on thermal expansivity and resistivity was seen. Modes I and II fracture toughness increase with decreasing grain size and porosity, but the ratio K,,cIK,, is almost constant at about 1.4 to 1.5 for many different specimens. The dependence of mechanical and thermal properties on grain size and/or porosity was consistent with those shown by Inagaki and Noda[ 141 and Mayer[ lo]. Empirical formulas for thermal shock resistance were derived for coal-coke and oil-coke graphites and have finally led to a conclusion that the optimum grain sizes are about 250 p,m for coal-coke graphite and about 300 km for oil-coke graphite, respectively. The thermal shock resistance of coal-coke graphite is generally higher than that of oilcoke graphite. Empirical formulas of the thermal shock fracture toughness were also derived for coal-coke and oil-coke graphites and have led to optimum grain sizes nearly the same as those for the thermal shock resistance; the thermal shock fracture toughness of coal-coke graphite was also larger than that of oil-coke graphite. These empirical formulas of thermal shock resistance A and thermal shock fracture toughness V for both graphites were shown to agree qualitatively with the calculated formulae ob-
of individual
REFERENCES
2. 3. 4. 5.
S. Sato, K. Sato, Y. Imamura, and J. Kon, Carbon 13, 309 (1975). S. Sate, fi. Awaii, and H. Akuzawa. Carbon 16. 95 (1978): H. Awaji and S. Sato, J. Eng. Materials and Tech. ASME-H, 101, 139 (1979). H. Awaji and S. Sato, J. Eng. Materials and Tech. ASME-H. 100. 175 (19781. H. Awaji ind s. Sat& J Materials Sci. Japan, 28,295, 336, 349 (1978).
6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
E. Ryshkewitch, J. Am. Cerm. Sot. 36, 65 (1953). W. Duckworth, J. Am. Germ. Sot. 36,68 (1953). E. P. Knudsen, J. Am. Cerm Sot. 40, 376 (1957). S. C. Corniglia, J. Am. Cerm. Sot. 55, 610 (1972). R. A. Mayer, Proc. Continuum Aspects of Graphite Design, Conf. 701105, USAEC, p. 571 (1970). C. .&. Anderson and E. I. SalGowitz, ‘Frackre Mechanics of Ceramics. Vol. 2. D. 509. Plenum Press. New York (1674). ‘I C. A. Anderson and E. I. Salbowitz 11th Biennial Conf. Carbon, p. 95 (1975). E. P. Kennedy and C. R. Kennedy, 13th Biennial Conf. Carbon, p. 445 (1977). M. Inagaki and T. Noda, Tanso (Japanese) No. 40, p. 2 (1964). H. J. Petch, J. Iron and Steel Inst., 174, 25 (1953). JAERI-memo 9641 (1981) p. 45-66. S. Yoda and K. Fuiisaki, Tanso (Jaoanese) No. 110. . p. 81 (1980). ” R. J. Price. Phil. Map. 12.561 (19651. W. N. Reinolds, Piysicbl Priperties of Graphite, p. 81. Elsevier Pub., New York (1968). C. Kettle, Introduction lo Solid State Plysics, Third Ed., p. 183. Wiley, New York (1967). S. Sato, K. Kawamata, H. Awaji, and M. Miyauchi, High Temp.-High
Pres. 12, 23 (1980).
22. R. E. Nightingale, Nuclear Graphite, p. 156. Academic Press, New York (1962).
Copyright0
OOC&6223/88 $3.00 + .OO 1988Pergamon Press plc
OPTIMUM ARRANGEMENT OF COKE GRAIN SIZE FOR ELECTRODE GRAPHITE AS DETERMINED BY THERMAL SHOCK TESTS S.
SATO
Faculty of Engineering, The University of Ibaraki, Hitachi, Ibaraki, 316, Japan
M.
ISHIHARA
and K.
HIRAKAWA
Japan Atomic Energy Research Institute, Tokai, Ibaraki, 319-11, Japan
and M.
and Y.
KIYONO
INOUE
Ohmachi Research Laboratory, Showa Denko K. K., Ohmachi, Nagano, 398, Japan (Received 1 October 1987; accepted in revbed form 20 May 1988) Abstract-This article deals with factors affecting the thermal shock resistance, thermal shock fracture toughness, and other related properties of two kinds of electrode graphite prepared with three different arrangements of grain size of coal and oil cokes respectively. Experimental results on the fracture strength are wholly expressed by the Knudsen type formula; S = &G-“exp
(-np),
where G and P are the mean grain size and porosity, and So, m and n are material constants. Optimum conditions for the coke grain size are obtained to produce a graphite electrode having the maximum thermal shock resistance and the maximum thermal shock fracture toughness. Key Words--Coke
grain size, electrode, thermal shock resistance, fracture toughness.
1. INTRODUCTION
2. EXPERIMENTAL METHODS
Generally, graphite materials are manufactured by carbonizing and then graphitizing heat treatments of molded bodies consisting of granular coke fillers and pitch binder. The arrangement of these coke grains is considered to have significant influence on the mechanical, physical properties of the graphite. Therefore, studies on the coke grains and the arrangement conditions are fundamental for producing better graphite. In this work, six kinds of electrode graphite made with three arrangement conditions for the grain size of the coal and oil cokes are studied in connection with their thermal shock resistance[l] and thermal shock fracture toughness[2] using the disk testing method. Factors, like grain arrangement and some physical properties, which influence the thermal shock characteristics, are discussed. The resistance and fracture toughness for thermal shock are not only related to mechanical properties but also to thermal properties such as thermal conductivity and expansivity of the materials. Therefore, measurements of such properties are useful in deciding the basic conditions of the synthesis of industrial products, especially for electrodes used in steel making arc furnaces. Mechanical properties, such as the diametral compressive strength[3] and fracture toughness[4], for three arrangements of coke grain size are also measured and their influences are discussed.
2.1 Specimens Specimens examined in the study were two kinds of laboratory-made electrode graphite, 100 mm in diameter, produced from coal and oil-cokes. The coke grain sizes are sieved into several groups and arranged to three classes in accordance with the cumulative weight percent. Conventional manufacturing processes by extrusion, carbonization at about 800°C and graphitization at about 3000°C were used to make specimens of electrode graphite. Figure 1 shows the cumulative weight percent of the three classes of graphite as a function of coke grain size. The classes were designated as Gl, G2, and G3 in order of increasing grain coarseness. The two kinds of coke were distinguished by adding the suffixes C for coal coke and 0 for oil coke. The mean grain size representing the three classes of specimen graphite were defined by these, corresponding to 50% cumulative weight. Accordingly, the mean grain sizes G were 381 Frn for Gl-C and -0, 84 p,m for G2-C and -0, and 34 pm for G3-C and -0 specimens. Table 1 shows the common physical and mechanical properties of the coal-coke and oil-coke graphites, respectively. These graphites had anisotropies originating from the extrusion process. The letters L and R in the table show the properties of the logitudinal, or with grain and the radial, or across
853
S. SAT0 et
al.
coke grain size ( pm) Fig. 1. Cumulative weight percent of graphite specimens as a function of coke grain size.
grain, directions
respectively.
Disk specimens
in this
study were cut so as to make the central axis parallel to the extrusion axis of the rod. Therefore, the results obtained with these disk specimens, such as those for thermal shock resistance, reflect the physical properties in the R direction. In these specimens, mean properties were also influenced by changes of grain size G. Porosity P is defined from the apparent density y and the theoretical density y, (=2.26 g/cm3) as follows;
Figure 2 are micrographs of the three classes of grain size of coal-coke and oil-coke graphites, respectively. The grain sizes and the pores or defects are finer in order of Gl > G2 > G3. Specimens were disks with a diameter of 2R = 50 mm and thickness of h = 5 mm for the thermal shock and fracture toughness tests and h = 10 mm for the diametral compressive tests. Square rods 10 x 10 x 20 mm were used for the compressive strength tests. Machining of the edge slit in the disk for the thermal shock fracture toughness tests was carried
out first using a milling cutter (thickness: 0.2 mm), and then sharpened by hand using a serrated thin razor blade, while the slit depth was measured by an optical comparator. The central slit in the disk for the modes I and II fracture toughness measurements was machined first by an ultrasonic processing machine using a razor blade cutter and then finished with a serrated razor blade. 2.2 Outline of the measuring methods Figure 3 is a schematic illustration of the series of disk testing methods employed. 2.2.1 Diametral compressive strength. As shown in Fig. 2(l), measurements of the diametral compressive strength u,,, of the disk were conducted using the method of Awaji and Sato[3] using circular anvils. Considering the contact width 26 of the Hertzian contact due to circular anvils, uH, is determined by the following equation: u H, = [l - 1.15(blR)2
+ 0.22(blR)‘]op,
(2)
where up is the tensil stress PlnRh at the disk for a concentrated loading P.
Table 1. Physical and mechanical properties of graphites of coal coke Graphite
*
Gl-C
G2-C
G3-C
Gl-0
G2-0
G3-0
Apparent density Y (g/cm’) Porosity p Electric resist. p (X 10-Q cm) Young’s modulus, E (GPa) Bending strength ob (MPa) Coef. ther. exp.” o (x lo-bQC-‘)
L R L R L R L R L R
1.376 1.358 0.395 104 170 4.81 1.81 6.77 4.71 1.99 3.30
1.418 1.410 0.373 84 145 6.81 2.55 9.71 6.47 2.02 3.50
1.527 1.516 0.327 67 130 10.73 3.29 14.80 9.90 1.92 4.00
1.404 1.394 0.381 82.5 129 4.12 1.77 7.75 5.10 2.19 3.18
1.513 1.512 0.331 75 131 6.47 2.56 10.8 5.69 2.10 3.60
1.565 1.574 0.306 71 131 8.34 3.14 13.04 6.06 2.00 3.90
*L and R: longitudinal and perpendicular directions for the extrusion axis, respectively.
‘Mean linear coefficient of thermal expansion in 5OO”C-800°C.
Optimum arrangement of coke grain size
855
GZ-0
G3-C
G3-0
(a) Fig.
2.
Microscopic structures of coal- and oil-coke graphite specimens.
2.2.2 Fracture toughness. Fracte toughness tests of the disk with a central slit shown in Fig.2(2) were in two distinct ways, changing the slit angle, whereby modes I and II fracture toughness values K,c and KIIC,as follows[4]: K ICJIC - NIW
6.
PIRh,
(3)
where NIH and NIIH are the stress intensity factors considering the Hertzian contact width, and are determined by H ,H,IIH =
(b)
0.1
NPJIPP
-
(1)
u, and crII are functions of the crack size ratio (c/R) and the contact width ratio (b/R), and NIP and NIIP are the stress intensity factors for concentrated loading (e.g., NIP = 1.136, NIIp = 1.866 for clR = 0.3 in this study). Furthermore, the slit angles 8 for the vertical direction are zero for mode I and 27.2” for mode II, when clR = 0.3. 2.2.3 Deduced uniaxial tensile strength. Uniaxial tensil strength a: is deduced from the fracture criterion using data of uHC, uc and the ratio of Klc and KIIc as follows[5]:
Ul
(4)
(~~R)*lh,~.
(2)
*=Ic.
K K IIC uf,C(l
(31
JP
OirC
KIJC
CU
Fig. 3. Measuring methods for the disk tests.
(4)
aH@C
-
uyh,)
+ (JC’
(5)
S. SATOet al
856
where a;/~;, a ratio of the compressive stress 0; to the tensile stress a, at the center of a disk, is a function of the contact width bJR. cr: will be used later to evaluate the equivalent crack length. 2.2.4 Thermal shock resktance. When the central area of the radius a of a disk is rapidly heated by amount of thermal energy Q ==qRYk(q = WJ~#zh, W, heating power in W), the ma~mum tangential tensile stress uBmanis produced on the disk circumference as illustrated in Fig. 3(3), after a nondimensional thermal diffusion time. If a thermal crack is produced on the disk by a critical amount of heat at a specified nondimensional time T, the stress uomaX is equal to the tensil strength o,. The thermal shock resistance A is determined from the measurement of the critical electric power W using the following equation[ l] : A = tr,klEar
(6)
S*Wp = rh(a/R)2’
(7)
where E, k, and cxare the Young’s modulus, thermal conductivity and expansivity, respectively, and S* denotes the specific nondimensional maximum thermal stress amounting to 1 .lOO x 10v2 for the heating radius aJR = 0.3 at the nondimensional thermal diffusion I = 0.25. 6 is a heating efficiency determined by considering the heating losses due to heating of the upper and lower electrodes, heat convection, and radiation; p % 0.45 under the present expe~mental conditions. 2.2.5 Thermal shock fracture toughness. In the case of rapid heating at the central area of the disk with an edge slit of thickness c, such as in Fig. 3(4), the
thermal shock fracture toughness V is expressed as a function of the critical electric power W to initiate cracking at the edge slit just at the specified time 7 = 0.25, determined by the following equation[2]: V = KIcklEa
(8)
F,GcWp = rrh(a/R)2 ’ where F, is the nondimensional stress intensity factor determined by the tangential thermal stress at the tip of the edge slit and is equal to 1.54 x 10m2 for atR = 0.3 and c/R = 0.3 in this study. 2.3 Experimental apparatus Mechanical properties were investigated by a mechanical testing machine of 5 tons with a constant crosshead speed of 0.5 m~min. The thermal shock tests were conducted by using arc discharge with welders whose current capacities are 350 and 1200 A, 2.4 Empirical formula Many articles so far have deah with the influences of grain size and porosity on the mechanical strengths of polycrystalline ceramics[6-91 and carbons[lO-141. Relationships between material strengths and the grain sizes of most metals and ceramics can be expressed well by Petch’s equation[l5]. However, for porous polycrystalline materials such as graphite, the exponent on the grain size in his expression may be different from the predicated value 0.5. Since the graphite specimens studied here have different porosities (P) through the change in grain size (G), the fracture strengths (S,> in this study were con-
Table 2. Empirical constants involved in Knudsen’s expression for graphites Oil coke
Coal coke Graphite
*
Young’s modulus, E (GPa) Coef. therm. exp., a (x lo-w-‘) Elect. rest., p ( X 10S4fi cm) Bending strength, ub (MPa) Dia. compr. strength, =~@@a)
Compr. strength, oc (MPa) Uniax. tens. strength, a: (MPa) Fract. tough. of mode I, I& (MPam’~) Fract. tough. of mode II, Knc (MPamln) Therm. shock resist., A (W/mm) Therm. shock fract. tough. V (W/mmlR)
so
-m
-n
1.96 x 102 11.09 2.66 16.8 1.77 7.96 197 153
-0.117 - 0.202 0.0367 0.094 0.096 0.098 -0.144 -0.103
-7.63 - 1.54 -1.07 -5.4 3.04 0.43 -6.37 -7.27
18.0
-0.166
- 7.24
34.8
-0.166
-7.24
-m
-n
47.6 18.8 5.00 5.03 5.49 17.7 43.4 8.7
-0.179 -0.087 0.204 -0.087 0.0571 0.0411 -0.145 - 0.05
-3.63 -4.86 -5.35 0.16 0.18 -1.56 -2.27 -0.56
3.43
- 0.020
-1.54
-0.077
-0.18
SLl
16.4
R
7.35
-0.114
-1.24
2.54
-0.042
-0.20
R
1.52
-0.122
-3.87
0.36
- 0.041
-1.06
R
2.35
-0.109
-4.16
0.51
-0.075
- 0.40
R
7.25
- 0.016
5.60
2.77
- 0.052
7.92
0.038
3.19
0.027
3.21
R
61.9
40.6
*L and R; longitudinal and perpendicular directions for the extrusion axis, respectively.
Optimum arrangement of coke grain size 16 -+--o-
coal coke
oil coke
Fig. 4(a). Young’s modulus of graphites as a function of grain size (with grain). ventionally expressed by a generalized equation with G and P as follows: S, = &G-“’ exp (-nP),
3. EXPERIMENTAL RESULTS AND DISCUSSIONS 3.1 Physical properties
Table 2 shows the empirical constants involved in the Knudsen type expression for Young’s modulus E, thermal expansivity IX,electrical resistivity p, and bending stength ub of coal-coke and oil-coke graphites. Figure 4(a) and (b) plot Young’s modulus as a function of G. In this figure, JAERI data[l6] for 11 kinds of reactor-grade graphite, which are arranged
(10)
where S,,, M, and n are material constants. A similar expression has been used for several ceramic materials by Knudsen[S]. A and V for thermal shock were also evaluated by using this Knudsen type expression. 14 --+-o_
caal coke oil coke /
/
H--. --..
.
10 -
JAERI data
. \ q/
I’ \
\
‘\
. . .
E(,)=ll.aG
/
---__~
/
I
-o.20ze-i&P
2-
0..
10
I
I
50
100
I 500
I 1000
5000
Glum)
Fig. 4(b). Young’s modulus of graphites as a function of grain size (across grain).
s. SAT0
858
by the maximum grain sizes, are enclosed in the broken line. Similar data obtained by Inagaki and Noda[l4] on six kinds of oil-coke graphite, which were arranged by the mean grain size, are enclosed in the chain lines, while the data by Kennedy and Kennedy[l3] are in the double chain line. The graphite specimens of Inagaki and Noda were manufactured using three classes of oil-coke grain sizescoarse, medium, and fine-but the mean grain sizes of the specimens were not directly specified. If the size of the fine grain can be assumed to be 100 pm or less, their mean-grain-size coke is deduced as the points in Fig. 4(a). Their data agree fairly well with the present data. On the other hand, Kennedy and Kennedy made their specimens with a constant density by using eleven classes of grain size from 100 to 1000 pm and adjusting the quantities of pitch binder. As the mean grain sizes, they used the mean of the maximum and minimum values for each class. Young’s moduli in this study for both graphites based on coal and oil cokes tendencies increasing with decreasing grain size in proportion to G-(“~os-o~*o~ and also with decreasing porosity in proportion to e-(1.54m7.63)p. Such trends agree well with the data of Inagaki and Noda and Kennedy and Kennedy. JAERI data show a similar trend macroscopically similar to those in the present work, but are widely scattered, since the data were evaluated en masse for different kinds of cokes and manufacturing conditions. It is interesting that the exponents of G in the empirical formulas employed in this study for coal- and oil-coke graphites are nearly equal to the exponent -0.11 given by Kennedy and Kennedy. In our empirical formulas, Young’s moduli deduced for the critical case of P = 0 are (47.6-19.6) GPa in with-grain direction and (11.1-18.8) GPa in across-grain direction. These mean value agrees fairly well with Young’s modulus (E = 23.4 GPa) of polycrystalline graphite presented by Yoda and Fujisaki[l7]. 6.0
--tu
et al.
Figure 5(a) and (b) show influences of grain size and porosity on the thermal expansivities in the withgrain and across-grain directions, respectively. For the sake of comparison, data of JAERI[16] and Inagaki and Noda[l4] are also indicated. Thermal expansivities in the with-grain direction for coal- and oil-coke graphites have a common tendency increasing very slightly with an increase of grain size, in agreement with those found by Inagaki and Noda, but vice versa in the across-grain direction. On the other hand, thermal expansivities as a function of porosity tend to decrease with increasing porosity, except for those of oil-coke graphite in the acrossgrain direction, as is demonstrated by the empirical formulas. JAERI data show the same general trends. Thermal expansivities for zero porosity are 16.8 x 10m6and 2.70 x 10m6K-l for with-grain and acrossgrain directions of coal-coke graphite, while those for oil-coke graphite are 5.0 x 10m6 K-l in both directions. These values are between - 1.5 x 10e6 K-l and 28 x low6Km’ for the u-axis and c-axis directions of a single graphite crystal. Recently, Yoda and Fujisaki[l7] studied the relationship between physical properties of polycrystalline graphite and porosity. They arranged their data in the following form corresponding to a first approximation of our eqn (10); S = So (1 - n P). Values So and n are material constants. Products for Ea in this study obtained from the empirical formulas are found to be influenced only slightly by grain size (G) especially in the with-grain direction, but strongly influenced by porosity (P).Such relationships for Ea and P may be considered to come from the so-called Griineisen relation[20]. Figure 6(a) and (b) show electrical resistivities p in with-grain and across-grain directions of both graphites as a function of grain size. Data by JAERI[16], Inagaki and Noda[l4], and Kennedy and Kennedy[l3] are also shown. In this study, the
coal coke oil coke
-_ C
50
. .
-_-
100
JAERI \ \ _-L--
500
data
\
loo0
3000
G(pm)
Fig. 5(a). Coefficient of thermal expansion of graphites as a function of grain size (with grain).
Optimum arrangement of coke grain size
859
6 v -o_
5-
1
coal coke oi I coke
JAERI data i
100
50
G(bm)
500
1000
Fig. 5(b). Coefficient of thermal expansion of graphites as a function of grain size (across grain).
electrical resistivity p of coal-coke graphite tends to increase with increasing grain size (G) in both directions, but the trend is not clear for oil-coke graphite. Experimental results obtained by Inagaki and Noda are very close to the present data. The influence of porosity on p is not demonstrated as a definite trend in the empirical formulas. In general, the electrical resistivity of graphite may increase with decreasing coke grain size, since the contact resistance at the grain boundary is considered to increase. On the other hand, there are cases showing an increase due to the influence of the pitch binder. Consequently, a simple relationship between p and G covering a wide range of G values cannot be clearly recognized.
d
-c---
Figure 7(a) and (b) show the influences of G and P on the bending strength in the with-grain and acrossgrain directions, respectively. Bending strength increases with decreasing G in proportion to G~~“~05-0~‘45) for both graphites. This coincides with the general trend that the finer the microscopic structures the larger the strength. However, the exponent of G is much smaller than 0.5 in Petch’s relation for metallic materials. This means that porous and polycrystalline materials such as graphite do not always follow Petch’s equation. Regarding the influence of porosity P, the bending strength increases with a decrease of P. This trend is very noticeable for coal-coke graphite, especially in the small grain size.
cd coke oi I coke /.
Kennedy
and Kennedy
I
50
5000 G’?frn
1
1000
3000
Fig. 6(a). Electric resistivity of graphites as a function of grain size (with grain).
8. SAT0 et al.
860 20
18
--+-o-
coal coke oil coke
16
a 6’ IO
I
I
50
100
I 500
I 1000
5000
G(Pm)
Fig. 6(b). Electric resistivity of graphites as a function of grain size (across grain).
3.2 Diametral compressive strength
3.3 Fracture toughnesses
Figure 8 shows the diametral compressive strength of both graphites as a function of G. The trend is quite similar to that of the bending strength. The influence of grain size is more pronounced for coalcoke graphite, especially in the case of small grain size. Figure 9 shows typical fracture appearances in the diametral compression tests. Hairline cracks are produced near the center of the disk and then propagate upward and downward.
Figure 10(a) and (b) show modes I and II fracture toughnesses of coal- and oil-coke graphites as a function of grain size. Coal-coke graphite exhibits a stronger dependence on the grain size than oilcoke graphite does, especially in the small size range. Such a trend is similar to the other mechanical properties. Regarding the influence of porosity, the fracture toughness increases with decreasing porosity. Furthermore, the ratio of the two fracture tough-
30 [ --t_ --+-
25
coal
coke
oil coke
i
-5
IO
50
100 G (urn)
500
1000
3003
Fig. 7(a). Bending strength of graphites as a function of grain size (with grain).
Optimum arrangement of coke grain size 14
861
I + U
12
coal coke oil coke
10
\ -0.05 (&CRj=8.7G
e-o.56P
2
IO
50
100
lax
500
3oco
G (urn) Fig. 7(b). Bending strength of graphites as a function of grain size (across grain).
nesses K,,JKIc is derived from the corresponding formulas as follows; for coal-coke graphite:
K,,,IK,, = 1.55G”.oL3exp (-0.29P),
(15)
and for oil-coke graphite:
Since the exponents on G and P in these expressions are very small, the ratios are almost constant (ie., 1.4-1.5), irrespective of the difference in coke, grain size, and porosity. Similar ratios have been found for several reactor graphites[21]. This implies that the occurrence of crack propagation of the shearing mode is about 1.4 to 1.5 times more difficult than that of the open mode. In other words, the pure
(16)
K,,cIKI, = 1.42G-0.0” exp (-0.66P)
shear strength of graphite is about 1.4 to 1.5 times
4.0
--O---
coal coke oil coke
--o----
t
3.5 -
3.0 -
2.5 : ‘;i 2 -2.0 8 $ b 1.5 -
0.5
1 10
I 50
I
I
I
100
500
loo3
5000
Glum)
Fig. 8. Diametral compressive strength of graphites as a function of grain size (across grain).
S. SAT0 et al.
862
GZ-0
GZ-C
l&&l
Fig. 9. Typical fractures in the diametral compressive
strength test.
greater than the tensile strength. This is supported by Losty’s experiments which shows that measured values of shear strength are of the same order as the ~~es~nding flexural strength[22]. When a rod of graphite is twisted to failure, the crack occurs along a helix. This is typical tensile failure rather than shear. Figure 11(a) and (b) show typical fracture ap pearances of the three classes of grain size for the two graphites in modes I and II fracture-toughness tests, respectively. In these photographs, the loading directions are vertical. In mode II fracture, the cracking initiates at both tips of the central slit at a large angle and then propagates, turning the head vertically, to become like mode I.
0.6 0.5 -
;
+ -@---
coa\ coke oii coke
0‘4 -
-& g 0.3 -
10
100
50
500 .G(pm
1000
3000
1
Fig. 10(a). Mode I fracture toughness of graphites as a function of grain size (across grain).
A
0.6
-c-
coal coke oil coke
Klqfq’
---IO
50
loo
G(m-4
2.356
500
-0.109&&.16P
1000
Fig. 10(b). Mode II fracture toughness of graphites as a function of grain size (across grain).
863
Optimum arrangement of coke grain size
G2-C
nucleated in a heating time of 3 s, with the constant nondimensional thermal diffusion time T = 0.25, was determined using the ratio of heating area alR = 0.5 for 10 disk specimens. Considerable fracture appears during the arc discharge heating, but the mean values are determined as the average area of the power and time on the recording chart. Figure 13 shows typical fracture appearances from thermal shock tests, where thermal cracks are found to occur in the left side of the disk. Some are very minute after cooling to room temperature. Figure 14 shows the thermal shock resistance as a function of grain size. Indicated ranges of the data show that in the upper limits all specimens fracture, but not in the lower limits. Coal-coke graphite clearly shows a larger thermal shock resistance than oilcoke graphite over the range of grain sizes examined. Empirical formulas for the Knudsen type thermal shock resistance were determined by solving thirdorder simultaneous equations for three unknown material constants as follows; for coal-coke graphite:
G2-0
;omm
Fig. 11(a). Typical fractures in the mode I fracture toughness test.
G2-C
G2-0
iomm
Fig. 11(b). Typical fractures in the mode II fracture tough-
A(c) = 7.25G-0.016 exp (5.6P),
ness test.
3.4 Compressive strength Figure 12 shows the compressive strengths of graphites as a function of the coke grain size. For each graphite, an empirical formula is obtained. Similar to other mechanical and fracture toughness properties, coal-coke graphite has stronger dependencies on grain size and porosity than those of oil-coke graphite. In particular, the porosity of coal-coke graphite shows a large effect, as in the diametral compressive strength tests. 3.5 Thermal shock resistance For each of the two kinds of coke graphite, the threshold electric power at which thermal cracks are
and for oil-coke graphite: A(o) = 2.77G-0.52 exp (7.92P). On the other hand, a relationship
+
coal
-o-
oil coke
represent graphite. using the lows; for P(c)
= (-2.42
x 10-6)G2 + (1.20 x 10-3)G + 0.289,
coke
I
‘6t
8-
50
100
between G and
the data by Inagaki and Noda for oil-coke Empirical formulas are given by Lagrange supplementary polynomial equation as folcoal-coke graphite:
18
10
(18)
P for each graphite is shown in Fig. 15. Triangles
22 20
(17)
G(um)
500
1000
5Kxl
Fig. 12. Compressive strength of graphites as a function of grain size (across grain)
(19)
s. SAT0
GZ-C
Both graphites have a slight dependence on grain size, but the dependency on porosity is more definite. On further substituting eqns (19) and (20) into eqns (21) and (22), expressions for thermal shock fracture toughness can be derived as a function of grain size only; for coal-coke graphite:
GZ-0
iomm
et al.
Fig. 13. Typical fractures in the thermal shock resistance test.
V(c) = 61.9G0.038exp [3.19( -2.42
and for oil-coke graphite:
and for oil-coke graphite:
P(o)
V(o) = 40.6G”,m7 exp [3.21( -9.78
= (-9.78
x 10-6)GZ + (6.22 x 10-3)G + 0.286.
(20)
Substituting these relations into eqns (17) and (18), equations for thermal shock resistance expressed only by grain size can be derived. The two curves in Fig. 15 show the results thereby calculated for coal-coke and oil-coke graphites. Each curve indicates the op timum grain size that provides the maximum thermal shock resistance. Optimum grain sizes are about 250 and 300 urn for coal-coke and oil-coke graphites, respectively. Similar investigations have been carried out by Meyer[lO]. He measured the critical electric power for thermal shock fracture of more than 20 types of graphite disks from several sources having grain sizes less than 300 km. He concluded that the optimum grain size was about 80 pm, much smaller than the 250 to 300 pm obtained in this study, probably due to the different type of graphite. 3.6 Thermal shock fracture toughness For the graphite disk with a machined edge slit, the threshold electric power for crack propagation was evaluated under the conditions of alR = 0.3 and clR = 0.3. Figure 16 shows typical fracture appearances in the thermal shock fracture toughness tests. The crack propagates from the tip of the edge slit toward the center of the disk as in mode I fracture. The crack propagation can be clearly seen as high temperatures, but becomes indistinct after cooling. Figure 17 shows the thermal shock fracture toughnesses of the two graphites as a function of grain size. The values for coal-coke graphite are definitely higher than those for oil-coke graphite. Empirical formulas are obtained by solving simultaneous equations for three conditions of coal-coke and oil-coke graphites as follows; for coal-coke graphite:
x 10+GZ+
x lo-‘G*+
1.20 x 10-3G + 0.289)],
6.22 x lo-“G
(23)
+ 0.286)].
(24)
These equations are shown as the solid curves in Fig. 12. The optimum grain sizes, corresponding to the maxima of the curves, are about 250 p.m for coalcoke graphite and about 300 pm for oil-coke graphite. These sizes are the same as those for the maximum thermal shock resistances. 3.7 Parametric considerations of A and V Thermal shock resistance A and thermal shock fracture toughness V are also calculated from combinations of properties given as parameters in eqns (6) and (8), respectively. Unfortunately, the thermal conductivities were not measured in this study, but were estimated using the following relationship with electric resistance at room temperature; k = 1.25 x 10-‘/p
(25)
where dimensions of k and p are [o/crn’C] and [a cm], respectively. Instead of the tensile strength, the deduced uniaxial tensile strength cr: was used. These properties are shown as empirical parameters in Table 2. The calculated thermal shock resistances A in the across grain direction (R) are
120 r 100
I
--W-
--o-
cool coke oil coke
20
V(c) = 61.9GO.O”exp (3.19P),
(21)
and for oil-coke graphite:
50
100
503
11
G(um)
V(o) = 40.6G”,0n exv (3.21P). \ I
t
OL 10
1
\
I
(22) \
I
Fig. 14. Thermal _shock resistance of graphites as a function of grain size (across grain).
Optimum arrangement of coke grain size
865
0.5 + -c-
Coal coke oil coke
P;’ -2.416~10-6)GZ~.199~10-3)G~ 0.2889
P=~-9.78X10’7~G2~(6.219x10-4)G+
c
0.2855
d
-_ 0
100
200
G(am)
300
400
500
Fig. 1.5. Relation between porosity and mean grain size of graphites.
A(c)’ = (a:klEa) = 6.43G-0.1Q exp (5.27P), (W/mm)
(26)
express the qualitative characteristics well, except for the exponent of G for coal-coke graphite.
A(o)’ = (a:klEa)
4. CONCLUSION
= 1.97 G”.091exp (6.06P), for coal-coke
and oil-coke
(W/mm)
graphites,
(27)
respectively.
These expressions for thermal shock resistance do not agree with the empirical formulas, eqns (17) and (18), but represent the qualitative characteristics well. Such a discrepancy comes mainly from the difference in temperature conditions. That is, the temperature of arch discharge heating is close to the sublimation point (3760°C) at the central area, but is about 700 to 800°C on the side surface according to measurements by an optical thermometer. In fact, parameter calculations were made using the properties measured at room temperature, except for the thermal expansivity that was measured between 500°C and 800°C. The thermal shock fracture toughness is calculated in a similar manner as follows, V(c)’ = 42.1G-0.112 exp (2.64P)
(28)
V(0)’ = LL~.~GO.~ exp (5.2P)
(29)
In this study, mechanical properties, especially those related to fracture mechanics, of polycrystalline graphites prepared with different coke grain sizes were investigated, and the grain sizes for coal- and oil-based samples giving the maximum thermal shock resistance and thermal shock fracture toughness were experimentally determined. The results are expressed as empirical formulas of the Knudsen type, and may be summarised as follows: Mechanical strengths, such as bending and/or diametral compressive strengths and Young’s modulus, increase with decreasing grain size and porosity (i.e., the finer the microscopic structure, the higher the strength). Exponents of grain size in the empirical formulas of mechanical strengths were consider-
--t
coal coke
for coal-coke and oil-coke graphites, respectively. Again, the calculated results do not agree with those from the empirical formulas, eqns (21) and (22), but
01
G2-C
lZ-ll
G2-0
Fig. 16. Typical fractures in the thermal shock fracture touehness test.
10
_1
1
50
100
G(um)
500
lcco
Fig. 17. Thermal shock fracture toughness of graphites as a function of grain size (across grain).
866
8. SAT0 et al. tained through combinations properties in A and V.
ably smaller than the exponent 0.5 in the wellknown Petch relation for metals. Probably, fracture in polycrystalline graphite is different
3. 4.
5.
6.
7.
8.
9.
from that expected from a simple model, such as pileup of dislocations at the grain boundary, since the coke grain boundaries consisting of pitch carbon binder are very irregular. No influence of grain size and porosity on thermal expansivity and resistivity was seen. Modes I and II fracture toughness increase with decreasing grain size and porosity, but the ratio K,,cIK,, is almost constant at about 1.4 to 1.5 for many different specimens. The dependence of mechanical and thermal properties on grain size and/or porosity was consistent with those shown by Inagaki and Noda[ 141 and Mayer[ lo]. Empirical formulas for thermal shock resistance were derived for coal-coke and oil-coke graphites and have finally led to a conclusion that the optimum grain sizes are about 250 p,m for coal-coke graphite and about 300 km for oil-coke graphite, respectively. The thermal shock resistance of coal-coke graphite is generally higher than that of oilcoke graphite. Empirical formulas of the thermal shock fracture toughness were also derived for coal-coke and oil-coke graphites and have led to optimum grain sizes nearly the same as those for the thermal shock resistance; the thermal shock fracture toughness of coal-coke graphite was also larger than that of oil-coke graphite. These empirical formulas of thermal shock resistance A and thermal shock fracture toughness V for both graphites were shown to agree qualitatively with the calculated formulae ob-
of individual
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2. 3. 4. 5.
S. Sato, K. Sato, Y. Imamura, and J. Kon, Carbon 13, 309 (1975). S. Sate, fi. Awaii, and H. Akuzawa. Carbon 16. 95 (1978): H. Awaji and S. Sato, J. Eng. Materials and Tech. ASME-H, 101, 139 (1979). H. Awaji and S. Sato, J. Eng. Materials and Tech. ASME-H. 100. 175 (19781. H. Awaji ind s. Sat& J Materials Sci. Japan, 28,295, 336, 349 (1978).
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E. Ryshkewitch, J. Am. Cerm. Sot. 36, 65 (1953). W. Duckworth, J. Am. Germ. Sot. 36,68 (1953). E. P. Knudsen, J. Am. Cerm Sot. 40, 376 (1957). S. C. Corniglia, J. Am. Cerm. Sot. 55, 610 (1972). R. A. Mayer, Proc. Continuum Aspects of Graphite Design, Conf. 701105, USAEC, p. 571 (1970). C. .&. Anderson and E. I. SalGowitz, ‘Frackre Mechanics of Ceramics. Vol. 2. D. 509. Plenum Press. New York (1674). ‘I C. A. Anderson and E. I. Salbowitz 11th Biennial Conf. Carbon, p. 95 (1975). E. P. Kennedy and C. R. Kennedy, 13th Biennial Conf. Carbon, p. 445 (1977). M. Inagaki and T. Noda, Tanso (Japanese) No. 40, p. 2 (1964). H. J. Petch, J. Iron and Steel Inst., 174, 25 (1953). JAERI-memo 9641 (1981) p. 45-66. S. Yoda and K. Fuiisaki, Tanso (Jaoanese) No. 110. . p. 81 (1980). ” R. J. Price. Phil. Map. 12.561 (19651. W. N. Reinolds, Piysicbl Priperties of Graphite, p. 81. Elsevier Pub., New York (1968). C. Kettle, Introduction lo Solid State Plysics, Third Ed., p. 183. Wiley, New York (1967). S. Sato, K. Kawamata, H. Awaji, and M. Miyauchi, High Temp.-High
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22. R. E. Nightingale, Nuclear Graphite, p. 156. Academic Press, New York (1962).