Contribution of grain boundary diffusion and capillarity forces to the diffusional creep of wires or fibers
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AND
G. C. WEATHERLY
H e r r i n g ' s a n a l y s i s of the Newtonian c r e e p of w i r e s with a b a m b o o g r a i n s t r u c t u r e is m o d i fied to include the effects of g r a i n b o u n d a r y diffusion and c a p i l l a r i t y . The g r a i n b o u n d a r y c o n t r i b u t i o n depends on the r a t i o 5 D b / 2 D v R where R is the wire r a d i u s , D b and D v a r e the b o u n d a r y and v o l u m e diffusion coefficients, and 5 is the width of the g r a i n b o u n d a r y . C a p i l l a r i t y is i n t r o d u c e d in a c o n s i s t e n t fashion into the a n a l y s i s and the c l a s s i c a l r e s u l t for e q u i l i b r i u m b e t w e e n the applied load and c a p i l l a r i t y f o r c e s is found. The c r e e p r a t e of s i n g l e c r y s t a l f i b e r s embedded in a p l a s t i c a l l y d e f o r m e d m a t r i x is c o n s i d e r e d for s o m e simple geometries.
T H E diffusional flow or Newtonian v i s c o u s c r e e p of w i r e s is of i n t e r e s t not only in the t r a d i t i o n a l field of s u r f a c e e n e r g y m e a s u r e m e n t s of c r y s t a l l i n e m a t e r i a l s at high t e m p e r a t u r e s , h2 but also in the p o s s i b l e use of fine w i r e s or f i b e r s as a r e i n f o r c i n g phase in a ductile m a t r i x for c r e e p s t r e n g t h . In the l a t t e r application the w i r e s o r f i b e r s will p r o b a b l y be chosen f r o m b r i t t l e m a t e r i a l s that show little d u c t i l i t y by d i s l o c a t i o n m o tion, but diffusional s t r e s s r e l a x a t i o n could l i m i t the e l a s t i c s t r e s s e s that can be t r a n s f e r r e d to the r e i n f o r c i n g phase. A ' % a m b o o " w i r e g r a i n s t r u c t u r e (Fig. 1) is used both for the s u r f a c e e n e r g y m e a s u r e m e n t s and b y H e r r i n g s in his c a l c u l a t i o n of c r e e p r a t e s . The s u r f a c e e n e r g y 7s is found f r o m the e x p r e s s i o n : ~ gR 2
F ~ = 7iR)'s
L
"YGB
[1]
w h e r e R is the w i r e r a d i u s , L is the n o r m a l d i s t a n c e between g r a i n b o u n d a r i e s (Fig. 1), YGB is the g r a i n b o u n d a r y e n e r g y and F o is the load r e q u i r e d for z e r o c r e e p r a t e . F o r loads F < Fo, c a p i l l a r i t y f o r c e s cause the w i r e to s h r i n k . Eq. [1] is d e r i v e d by using the p r i n ciple of v i r t u a l work on the e q u i l i b r i u m s i t u a t i o n , but it should in p r i n c i p l e also be p o s s i b l e to get the s a m e r e s u R b y i n c o r p o r a t i n g c a p i l l a r i t y into H e r r i n g ' s analysis, a Our m a i n c o n c e r n in this paper is the c o n t r i b u t i o n of g r a i n b o u n d a r y diffusion to the c r e e p r a t e . In N a b a r r o - H e r r i n g creep or superplastic deformation of p o l y c r y s t a l l i n e m a t e r i a l s , g r a i n b o u n d a r y diffusion can make s i g n i f i c a n t c o n t r i b u t i o n s to the o v e r a l l r a t
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