The effects of stress, temperature and hydrogen content on hydride-induced crack growth in Zr-2.5 Pct Nb
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T H E a p p e a r a n c e of c r a c k s in s o m e Z r - 2 . 5 pct Nb (Cb) p r e s s u r e tubes of the CANDU* n u c l e a r r e a c t o r s *CANadaDeuteriumUranium. at P i c k e r i n g , O n t a r i o 1 p r o m p t e d an e x t e n s i v e i n v e s t i gation into the d e t a i l s of the c r a c k growth m e c h a n i s m . E a r l y r e s u l t s 2-5 e s t a b l i s h e d the m e c h a n i s m a s one of h y d r o g e n d i s s o l v i n g f r o m h y d r i d e s in r e g i o n s of low s t r e s s and d i f f u s i n g to highly s t r e s s e d r e g i o n s , r e p r e cipitating there as zirconium hydride. This process r e s u l t s in e m b r i t t l e m e n t of the highly s t r e s s e d r e g i o n with consequent n u c l e a t i o n of a c r a c k . The s t r e s s field at the c r a c k - t i p is then capable of r e s t a r t i n g the p r o c e s s giving r i s e to s t e p w i s e c r a c k p r o p a g a t i o n . A t h e o r e t i c a l m o d e l 6 J was d e v e l o p e d to d e s c r i b e this c r a c k growth m e c h a n i s m . In this m o d e l , the flux of h y d r o g e n a t o m s to the s t r e s s e d c r a c k - t i p is d e t e r m i n e d a s a function of s t r e s s i n t e n s i t y , t e m p e r a t u r e and hyd r o g e n c o n c e n t r a t i o n . F o r unit t h i c k n e s s , the n u m b e r of h y d r o g e n a t o m s p e r second, dn/dt, d i f f u s i n g t o w a r d s the c r a c k - t i p r e g i o n is given by:
dn = 2nDHC~{exp(p(L)VhH/RT) -exp(p(l)VhH/RT)} dt f t Z r ~(L,1)
[1]
w h e r e D H = diffusion c o e f f i c i e n t for h y d r o g e n in z i r c o n ium, CH = t e r m i n a l s o l i d s o l u b i l i t y of h y d r o g e n at z e r o s t r e s s (in a t o m f r a c t i o n s ) , p(L) = h y d r o s t a t i c s t r e s s at s o u r c e h y d r i d e s (positive when t e n s i l e ) , L = d i s t a n c e f r o m c r a c k - t i p to s o u r c e h y d r i d e s , V~ = m o l a l v o l u m e of h y d r o g e n in z i r c o n i u m h y d r i d e , p(1) = h y d r o s t a t i c s t r e s s n e a r c r a c k - t i P at s i n k h y d r i d e , l = d i s t a n c e f r o m c r a c k - t i p to c e n t e r of p l a s t i c zone, O(L,l) = function of L and l, u s u a l l y ~ In L/1, and ~2Zr = a t . vol of Z r . The p r i n c i p a l d r i v i n g f o r c e giving r i s e to Eq. [1 ] is the d i f f e r e n c e in l o c a l h y d r o g e n c o n c e n t r a t i o n b e t w e e n h y d r i d e p i a t e l e t s c l o s e to and r e m o t e f r o m the c r a c k t i p . T h i s b o u n d a r y condition is d o m i n a n t due to the l a r g e (14 to 17 pct) v o l u m e e x p a n s i o n a c c o m p a n y i n g the p r e c i p i t a t i o n of h y d r i d e . A n e c e s s a r y condition f o r the o p e r a t i o n of the m e c h a n i s m d e s c r i b e d by Eq. [1] is that the s o l u b i l i t y f o r h y d r o g e n in the m a t e r i a l be e x c e e d e d . At 20~ this is l e s s than 1 t~g/g, r i s i n g L. A. SIMPSON and M. P. PULS are Research Officers, Atomic En
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