Internal stresses due to dislocation walls around second phase particles
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RECENT
s t u d i e s of c r e e p a t i n t e r m e d i a t e a n d h i g h temperatures o f o r i e n t e d nickel base superalloy s i n g l e c r y s t a l s , 1,2 h a v e r e v e a l e d t h e f o r m a t i o n o f n e a r edge dislocation w a l l s a r o u n d second p h a s e particles. T h e s e w a l l s s t a r t d e v e l o p i n g d u r i n g t h e i n c u b a t i o n p e r i o d1 a n d t a k e t h e i r full e x t e n s i o n in s e c o n d a r y c r e e p . 2 T h e i r contribution to the internal s t r e s s of the m a t e r i a l can be c l e a r l y e s t a b l i s h e d i f we c o n s i d e r t h e v a r i o u s c o m p o n e n t s of t h e s t r e s s f i e l d t h e y g e n e r a t e . L i3 a n d Marcinkowski 4 s t u d i e d the s h o r t r a n g e and long r a n g e s t r e s s e s a s s o c i a t e d w i t h i n f i n i t e a n d w i t h f i n i t e edge d i s l o c a t i o n w a l l s . I n t h i s p a p e r we c o n s i d e r a d i p o l a r a r r a n g e m e n t of r e g u l a r l y s p a c e d i n f i n i t e a r r a y s of such dislocations. R e s o l v e d c l i m b a n d g l i d e c o m p o n e n t s r e s u l t i n g f r o m t h e c u m u l a t i v e a c t i o n of t w o w a l l s of o p p o s i t e s i g n s l e a d t o a s t r o n g i n t e r n a l s t r e s s b e tween t h e two w a l l s a n d t o a v e r y rapidly d e c r e a s i n g s t r e s s field outside t h e dipolar w a l l . T h i s configurat i o n is probably quite general in two p h a s e alloys and
is m o r e easily identified w h e n the v o l u m e fraction of the hardening p h a s e reaches 50 to 70 pct. It is likely to be found in oriented eutectics submitted to high temperature creep. EXPERIMENTAL
PROCEDURE
T h e n i c k e l b a s e s u p e r a l l o y u s e d h e r e a n d the c r y s tal g r o w i n g a n d orienting p r o c e d u r e s have been des c r i b e d p r e v i o u s l y . 1 T h e v o l u m e f r a c t i o n of t h e V' p h a s e a t t h e c r e e p t e m p e r a t u r e i s a b o u t 60 p c t . A f t e r p r o p e r heat treatments, t h e ~' precipitates a p p e a r a s r o u n d e d c u b o i d s , 3 0 0 0 A i n s i z e a n d l e a v i n g 4 0 0 A wide p a s s a g e s f o r d i s l o c a t i o n s gliding in t h e m a t r i x . T h e ~' p h a s e i s i n p e r f e c t e p i t a x y w i t h t h e m a t r i x but a s l i g h t l a t t i c e m i s m a t c h l e a d s t o a m i s f i t p a r a m e t e r 5 ~- - 4 × 10-3 i n t h i s p a r t i c u l a r a l l o y . Computer simulations o f t h e dipoles a r r a y s were c o n d u c t e d on a D i g i t a l E q u i p m e n t C o r p o r a t i o n 1 1 / 4 5 C. CARRY is Assistant Professor, Ecole Polytechnique, 1007 Lausanne, Switzerland, S. DERMARKAR and J_ L. STRUDEL are Graduate Student and Professor, respectively,Ecole des Mines de Paris Centre des Mat6riaux, 91003 Evry, France, and B. C. WONSIEWICZ is Member, Technical Staff, Bell Laboratories, Murray Hill, N.J. 07940. Manuscript submitted May 2 , 1978. METALLURGICAL
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