Fluid flow in a propagating crack
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STRESS corrosion cracking, or environmentally-induced, s u b c r i t i c a l c r a c k growth, o c c u r s in a wide r a n g e of m a t e r i a l s and a wide r a n g e of e n v i r o n m e n t s . In t i t a n i u m a l l o y s , f o r e x a m p l e , c r a c k i n g has b e e n o b s e r v e d in a n u m b e r of g a s e o u s , liquid, and s o l i d e n v i r o n m e n t s . H o w e v e r , if one t a k e s a s i n g l e t i t a n i u m a l l o y , in a s i n g l e h e a t t r e a t m e n t condition, and e x a m i n e s c r a c k p r o p a g a z tion a s a function of the m e c h a n i c a l v a r i a b l e , the c r a c k tip s t r e s s i n t e n s i t y , f o r d i f f e r e n t liquid e n v i r o n m e n t s , a c o m m o n p a t t e r n e m e r g e s . ~ That i s , in m a n y e n v i r o n m e n t s the v e l o c i t y (vI) at low v a l u e s of the s t r e s s int e n s i t y is e x p o n e n t i a l l y dependent on the s t r e s s i n t e n s i t y , but b e c o m e s independent (vii) of it at h i g h e r v a l u e s of the s t r e s s i n t e n s i t y . The p r o c e s s which l i m i t s the v e l o c i t y vii is the s u b j e c t of i n t e r e s t in t h i s p a p e r . Although t h e r e is t h i s c o m m o n p a t t e r n which is obs e r v e d in m a n y e n v i r o n m e n t s , the a b s o l u t e magnitude of the v e l o c i t y at a p a r t i c u l a r s t r e s s i n t e n s i t y v a r i e s w i d e l y f o r d i f f e r e n t l i q u i d s , vii is 40 c m / / s in liquid m e r c u r y , 1 c m / s in LiC1-KC1 e u t e c t i c at 375~ 5 • 10 -2 c m / s in 10 M aqueous HC1, 4 • 10 -s c m / s in CC14, and 6 • 10 4 c m / s in m e t h a n o l * . 1 T h e r e f o r e , one h a s the *These data are for titanium-8 pct aluminum-1 pct molybdenum-Ipct vanadium in the mill-annealedcondition at 24~ except as otherwisenoted.
t a s k of e x p l a i n i n g not only the e x i s t e n c e of a p l a t e a u v e l o c i t y f o r e a c h e n v i r o n m e n t , but a l s o why it v a r i e s so much f o r the d i f f e r e n t l i q u i d s . We s h a l l adopt the a s s u m p t i o n f o r the p u r p o s e s of t h i s p a p e r , that a s i m i l a r p r o c e s s i s r e s p o n s i b l e f o r the p l a t e a u v e l o c i t y in e a c h liquid. The fluid flow p h e n o m e n a which should be c o m m o n f o r a l l t h e s e s y s t e m s will be t r e a t e d h e r e . R o s t o k e r , e t a l f i have r e v i e w e d the d a t a on liquid m e t a l e m b r i t t l e m e n t . They have p r o p o s e d a s e m i q u a n t i t a t i v e t h e o r y which a c c o u n t s f o r the l i m i t i n g c r a c k v e l o c i t y by c o n s i d e r i n g fluid flow p r o c e s s e s in the c r a c k . Rhines, e t a l . s i n t e r p r e t t h e i r r e s u l t s a s i n d i c a t i n g that liquid m e t a l e m b r i t t l e m e n t is c o n t r o l l e d b y the flow of the liquid m e t a l to the c r a c k t i p . R o b e r t son 4 h a s d i s c u s s e d the p o s s i b i l i t y of a d i s s o l u t
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