Uphill diffusion and progressive embrittlement: hydrogen in titanium
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S i n e s , and R o b i n s o n ~ p r e s e n t e d a f o r m u l a t i o n of diffusion due to g r a d i e n t s in a l l o y c o m p o s i t i o n , in s t r e s s , and in t e m p e r a t u r e . F o r t h i s p a p e r , a o n e d i m e n s i o n a l , i s o t r o p i c f o r m of the equation i s u s e d and it c o n t a i n s a l l t h r e e c h e m i c a l p o t e n t i a l g r a d i e n t s a s w e l l a s the g r a d i e n t of the d i f f u s i n g h y d r o g e n .
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I. THE GOVERNING EQUATIONS
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L e t us e x a m i n e the m e t a l l o g r a p h i c s y m p t o m s of a t i t a n i u m - 6 a l u m i n u m - 4 v a n a d i u m (6-4) p r e s s u r e v e s s e l which was f u s i o n w e l d e d with a c o m m e r c i a l l y p u r e (CP} t i t a n i u m r o d and which f a i l e d . F i g u r e 1 i s a p h o t o m i c r o g r a p h of b r i t t l e t i t a n i u m h y d r i d e in the weld m e t a l c l o s e to the f u s i o n l i n e . An i n v e s t i gation ''2 showed that the h y d r o g e n c o n c e n t r a t i o n n e c e s s a r y for h y d r i d e f o r m a t i o n could not have c o m e f r o m c o n t a m i n a t i o n and was not p r e s e n t i n i t i a l l y in the weld. T h i s s e g r e g ' a t i o n m u s t have h a p p e n e d a f t e r welding; h o w e v e r , t h i s i s not p r e d i c t e d by the o r i g i n a l f o r m of F i c k ' s L a w s s T h e f a m i l i a r F i r s t Law f o r a n isotropic material, J :-DVC
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w h e r e D i s the d i f f u s i v i t y and C i s the s o l u t e c o n c e n t r a t i o n , s t a t e s by the u s e of the n e g a t i v e s i g n that c o n c e n t r a t i o n p e a k s d i m i n i s h , not f o r m . H o w e v e r , d i f f u s i o n c a n be d r i v e n by g r a d i e n t s o t h e r than the c o n c e n t r a t i o n g r a d i e n t . T h i s t y p e of d i f f u s i o n was n a m e d " u p h i l l " d i f f u s i o n by D a r k e n . a W a i s m a n , J. L. WAISMANIs at McDonnell Douglas Astronautics Company. Huntington Beach, CA 92647, R. TOOSKY is at Townsend/Textron, Cherry Fasteners, Santa Ana, CA 92707, and GEORGE SINES is at the University of California School of Engmeering, Los Angeles, CA 900249 Manuscript submitted October 11, 1976. METALLURGICAL TRANSACTIONS A
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'.C lOOp i...__ 6-4 BASE----,-. C.P. WELD TRANSITION Fig. 1--Hydride formation in titanium near fusion line of weld. VOLUME 8A, AUGUST ~977-t249
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w h e r e x is d i s t a n c e in the d i r e c t i o n of the diffusion, the s u m of the p r i n c i p a l s t r e s s e s and T i s the a b s o l u t e t e m p e r a t u r e , with K a , K , r and K T b e i n g e x p e r i m e n t a l c o n s t a n t s . If the s u m of the s e c o n d , t h i r d , and f o u r t h t e r m s in the b r a c k e t s i s n e g a t i v e and g r e a t e r than the f i r s t , uphill diffusion will o c c u r .
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