＊2 Analysis of Decarburization Phenomena during Heating and Rolling of Billets Akie Ichihara and Yoshio Nuri Synopsis: This study was carried out to establish an analytical technique for decarburization phenomena during heating and rolling of steel billets, Firstly, for theoretical calculation of the carbon distribution, we applied the Birks's equation based on Fick's second law. The oxidation constants necessary for the calculation were determined by high temperature oxidation experi- ments with steels. As for the carbon distribution in steel, the theoretical calculation was in good agreement with the value analyzed by EPMA. Secondly, theoretical equation was modified in order to apply to practical rolling billets. The modified equation was applied to analysis of the carbon distribution for various size of bars, φ 34, 42, 53, 70, 85mm in outer diameter, respectively. Consequently, the theoretical calculation and the observed value were in good agreement with car- bon concentration profiles and decarburization depth. Key words: Oxidation constant;, Decarburization; Carbon concentration; Bar; Billet; 1 2 2 1 Fig 1 Co Cs X N. Birks¹  ² Fick Fick kc N.Birks² EPMA d t
D 2 1
2 Ch Co-Cs kc 0.01 Cs 0 Cs *** 3 erfc C = 0
3 kc D kc D    R.P.Smith 2 2 N. Birks   4 p m   Fe o
13 kc kc Arrhenius 14
14 kc ko 3
2   3 kc
8 X 9 9 dX kc X dir Xo X ( x o −
10 9 - √8kc · t x = x 0
4 5 6 7 7 Q
92 A 12 13 /T 4 8 x 10 11 6 14 12 3 3 1
70 85mm LSA120 C C 0.8mm 50ms 0.1 μ A 4 μ mass% Table1.  Chemical compositions of steels. 4 4　1 B 1073 1473K Fig 3 10 1473K 1073K Fig. 3. Weight increment as a function of time for various temper- ature of steel B. Fig.3 1473K 1373K 1273K 1173K 1073K 100 5
Fe
Fe Fe 3 O 4  Fe 2 O 3 B 75 84kcal/mol Fe3O4
3 2 Fig 2 1200 Table 1 10mm
3 3 EPMA EPMA1600 Table 2   Fig 4 2 O 2 Ni EPMA 10 μ 10KV EP MA Fig. 2. Experimental apparatus for high temperature oxidation of steel 800 100
D 66.3 exp kc 37.46× 10 5 /RT  m²s ¹  R.P.Smith   3
kc Fig. 5. Result of theoretical calculation of carbon concentration D kc Fig. 6. Carbon concentration profiles analyzed by EPMA mapping method and theoretical calculation for steel B. 4 4 Fig8 φ 167mm φ 34 42 53 70 85mm 95/5/1 Table 3 Fe O 41.1 58.9 0.70 1 FeO Fe 30, FeO Fe 203 0.55 C 0.20 C 5 5　1 Fig 4 Fig.4 0.55 C Fe Fe 2 O 3 0.55 C EPMA Fig3 FeO/Fe 3O 4 /Fe 2 O 3 Table3.  Analysis of scale of 0.55%C steel    mass%
FeO C CO₂ a Fig  7. High temperature oxidation mechanism of metals 7 . 5 2 Fe b FeO　Fe3O 4 0.55 C FeO   Fe 3 O 4 Fig 7    b Fig8 B Table 1 B 0.8mm 0.8mm Fig.8 Fe3O4
FeO FeO Fe 2 100 100 0.5 Co C/Co decarburization depth with various size of steel bars. φ 42mm Fig.8
0.202/0.802 0.252 3 Fig9 C = C
3 3
D T kc D   T 997 φ 42mm kc  τ Arrhenius 1100 50 - 1000
T, t; C 1 15
15 C 1 = C 0 C " tz 21 C 2 C = C 16 FeO kc  τ2 8 Fig 10 Excel C Fe FeO d, d. d.
C" 20
20 20 5 6 C Excel N. Birks and W. Jackson   JISI, 208    1970 81 N. Birks and G. H. Meier Introduction to High Temperature Oxidation of Metals. Translated Japanese in 1988 by K. Nishida and T. Narita 1988 185 R.P.Smith   Trans. Met. Soc. AIME, 230(1964 476 4 3 N.Birks and A.Nicholson  ISI Publication 123 219 1970 Fig8 21 ×
21 1 2 Fig.9
C 1 C 2 kc 2 O 2
cm’s
cm²s ¹
cm²s ¹ 2 Fe 3 4 2 C kc Birks EPMA kc Fick φ 34 42 53 70 85mm C 3 21 C τ =C o 84.1/RT Fe 30, 75 kcal/mol 66 84kcal/mol
74.5/RT
19 t3 21 65.7/RT d 17 6 kc x' = x 19 18 x' 5 P. Kofstad  Nonstoichiometry, Diffusion, and Electrical ConductMty in Binary Metals Oxides, Wiley- Interscience 1972 7 fbid   1982   27 6 1982  23 87