Diffusion modeling of the carburization process
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C A R B U R I Z A T I O N is one of the o l d e s t i n d u s t r i a l p r o c e s s e s in which m a s s t r a n s p o r t - d i f f u s i o n p l a y s a m a j o r r o l e . A s o u r c e of c a r b o n is p r o v i d e d at the s u r f a c e of a low c a r b o n s t e e l . The c a r b o n d i f f u s e s into the s t e e l at high t e m p e r a t u r e s u s u a l l y 1600 to 1800~ (871 to 982~ for t i m e p e r i o d s g e n e r a l l y f r o m a few h o u r s to a d a y . A c a r b o n g r a d i e n t is p r o d u c e d in which the c a r b o n content d e c r e a s e s f r o m the s u r f a c e into the s t e e l . In the p a c k o r gas c a r b u r i z i n g p r o c e s s the c a r b o n c o n c e n t r a t i o n at the s u r f a c e of the s t e e l is c o n t r o l l e d by the CO/CO2 r a t i o in the gas a t m o s p h e r e , the t e m p e r a t u r e and the s o l u b i l i t y of c a r b o n in the s t e e l . G u r r y 1 has c o n s i d e r e d the t h e r m o d y n a m i c a s p e c t s of the h e a t t r e a t m e n t of p l a i n c a r b o n s t e e l s in CO/CO2 g a s m i x t u r e s p r o d u c e d in e n d o t h e r m i c o r e x o t h e r m i c g e n e r a t o r s . U s i n g the a n a l y s i s of G u r r y the c o m p o s i tion of the gas m i x t u r e in e q u i l i b r i u m with a s p e c i f i e d s u r f a c e c a r b o n content can be c a l c u l a t e d . R e c e n t l y H a r v e y 2 has d e s c r i b e d a s i m i l a r c a l c u l a t i o n s c h e m e f o r the h e a t t r e a t m e n t of a l l o y e d s t e e l s . The s i m p l e s t c a r b u r i z a t i o n p r o c e s s , w h e r e b y c a r bon d i f f u s e s into a p l a i n c a r b o n s t e e l at one t e m p e r a t u r e can be d e s c r i b e d b y the V a n - O s t r a n d D e w e y s o l u t i o n to the diffusion equation:
C s = s u r f a c e c o n c e n t r a t i o n of carbon, C O = i n i t i a l c a r b o n l e v e l in F e ,
D = diffusion coefficient for C in the y p h a s e , D~, which is a s s u m e d to be independent of concent r a t i o n , and C C = c a r b o n c o n c e n t r a t i o n a s a function of d i s t a n c e X and t i m e t f r o m the s u r f a c e at X = 0. It is a s s u m e d that no v o l u m e changes o c c u r in the l a t t i c e d u r i n g diffusion. T h i s is a v a l i d a s s u m p t i o n for i n t e r s t i t i a l diffusion p r o c e s s e s . F i g u r e 1 shows c a r bon p r o f i l e s f o r v a r y i n g t i m e s at 1700~ and F i g . 2 shows c a r b o n p r o f i l e s at 1600, 1700 and 1800~ f o r 8 h c a r b u r i z a t i o n t r e a t m e n t s a l l c a l c u l a t e d u s i n g Eq. 0
40 I
DISTANCE { . O O t " ) 80 120 I i
160 L
1700~ D = CONST z 1.6 uJ ~9 fig
1.2 z o
:t=2hrs
Cc
-
CS
CO - CS = e r r (X/2 vrDt)
[1]
z 0.8
z o C9 Z 0
where
t.) 0.4
J. I. GOLDSTEINis Professor of Metallurgy and Materials Engineering, Lehigh University, Bethlehem, PA 18015, and A. E. MOREN, formerly Graduate Assistant, Metallurgy and Materials EngineeringDepartment, Lehig
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