Density changes with thermal history for compositions from Cu 1.8 S to Cu 2.0 S
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[I]
where cr is the applied tensile stress, 7 the grainboundary surface energy, G the shear modulus and l the distance over which sliding occurs. If at 2100~ tile sliding distance is on the order of one-eighth of the grain diameter, then a check calculation for Udimet 700 shows that grain-boundary failure is expected. Alternately, it seems reasonable to a s s u m e that at 1950~ the y' particles at grain boundaries limit I to the interparticle spacing along the boundary. For grain size A S T M 3 this represents a decrease m sliding distance of nearly two orders of magnitude. The above criterion then predicts that wedge-type grain-boundary failure would require a m u c h higher stress at 1950~ A n a l t e r n a t e a p p r o a c h is to e x a m i n e the e f f e c t of the g r a i n - b o u n d a r y s t r u c t u r e on g r a i n - b o u n d a r y s l i d i n g , R e c e n t c o n s i d e r a t i o n s 5 h a v e s h o w n that the s l i d i n g r a t e is p r o p o r t i o n a l to s t r e s s and i n v e r s e l y p r o p o r t i o n a l to the s q u a r e o f the g r a i n b o u n d a r y l e d g e height h: ~: ~ / h 2
[2]
S i n c e the l e d g e height at 2100~F is p r o b a b l y on the o r d e r of the g r a i n - b o u n d a r y t h i c k n e s s (-1 • 10 -~ c m ) , t h e g r a i n b o u n d a r y o f f e r s l i t t l e r e s i s t a n c e to s l i d i n g and e x t r e m e l y r a p i d r a t e s a r e p o s s i b l e . A c o n s i d e r a b l y d i f f e r e n t s i t u a t i o n e x i s t s at 1950~ H e r e the l e d g e h e i g h t c o r r e s p o n d s to the d i m e n s i o n of the g r a i n - b o u n d a r y p e r t u r b a t i o n p r o d u c e d by the ),' (~1.5 • 10 -5 c m ) . T h e p r e s e n c e of the g r a i n - b o u n d a r y y ' p a r t i c l e s a c t s to d r a s t i c a l l y r e d u c e the s l i d i n g r a t e for a g i v e n s t r e s s (for c o n s t a n t s t r a i n r a t e the e f f e c t is to " s t r e n g t h e n " the b o u n d a r y ) s u c h that u n i f o r m bulk g r a i n d e f o r m a t i o n is p o s s i b l e . T h e r e s u l t s a r e c o n s i s t e n t w i t h the h y p o t h e s i s that f r a c t u r e o c c u r s d u r i n g w o r k i n g at t e m p e r a t u r e s a b o v e the ).,' s o l v u s b e c a u s e of the r e l a t i v e e a s e of g r a i n METALLURGICALTRANSACTIONS
boundary sliding with a resultant stress concentration and crack initiation at grain-boundary triple lines. In contrast, precipitation of 7' alters the gram-boundary structure and makes it much more resistant to sliding. Therefore, stress concentrations at triple lines are greatly reduced. For this reason nickel-base superalloys such as Udimet 700 are m o r e easily worked h~ the two phase T-,"' condition. To emphasize the importance of the grain boundary structure, a recent experiment was conducted at 1950~ where the size of the 7' particles was held to a minimum so that the precipitate would be a much less effective obstacle to grain-boundary sliding. Under these conditions the fa
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