Flow stress, subgrain size, and subgrain stability at elevated temperature
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T H E f o r m a t i o n of s u b g r a i n s d o m i n a t e s the m i c r o s t r u c t u r a l changes that o c c u r d u r i n g c r e e p flow in m o s t a n n e a l e d p o l y c r y s t a l l i n e m e t a l s at t e m p e r a t u r e s a b o v e about 0.4 T M (Tm is the m e l t i n g t e m p e r a t u r e in d e g r e e s a b s o l u t e ) . - 3 N e v e r t h e l e s s , the s p e c i f i c influence of s u b g r a i n s on the c r e e p r a t e has g e n e r a l l y been ignored; s u b g r a i n f o r m a t i o n is often c o n s i d e r e d to be s i m p l y a p r o d u c t of the c r e e p p r o c e s s and is r e g a r d e d a s n e i t h e r b e n e f i c i a l n o r d e t r i m e n t a l to the c r e e p r e s i s t a n c e of the m a t e r i a l . M o s t c r e e p t h e o r i e s f a i l to include t h i s m i c r o s t r u c t u r a l f e a t u r e a s a v a r i a b l e in the c r e e p p r o c e s s . T h e m a j o r p u r p o s e of t h i s p a p e r i s to e m p h a s i z e that the s u b g r a i n s i z e m a y be v e r y i m p o r t a n t in c r e e p . T h e e x p e r i m e n t a l m e t h o d s e m p l o y e d to quantify the c o r r e l a t i o n w i l l be d e s c r i b e d , with s p e c i f i c a p p l i c a t i o n to p o l y c r y s t a l l i n e a l u m i n u m . The final r e s u l t is a p h e n o m e n o l o g i c a l r e lation which p e r m i t s a q u a n t i t a t i v e p r e d i c t i o n of the c r e e p b e h a v i o r of s u b g r a i n - s t r e n g t h e n e d m a t e r i a l s . T h e a p p l i c a t i o n of s u c h a r e l a t i o n to d i s p e r s i o n s t r e n g t h e n e d m a t e r i a l s w i l l a l s o be d i s c u s s e d .
BASIC
FACTORS INFLUENCING STEADY CREEP AT HIGH TEMPERATURE
STATE
It is well established that atom mobility (diffusion coefficient) and e l a s t i c modulus a r e the two p r i n c i p a l f a c t o r s influencing the c r e e p r a t e (at a given s t r e s s ) of p o l y c r y s t a l l i n e m e t a l s a b o v e 0.4 T m . The fact that c r e e p flow i s c o n t r o l l e d by a t o m m o b i l i t y is convincingly d e m o n s t r a t e d by the e q u a l i t y of the a c t i v a t i o n e n e r g i e s f o r c r e e p , Qc, and l a t t i c e s e l f diffusion, QL, at t e m p e r a t u r e s a b o v e 0.6 T m.1-3 T h i s e q u a l i t y s u g g e s t s that the c r e e p r a t e i s p r o p o r t i o n a l
OLEG D. SHERBY, RODNEY H. KLUNDT, and ALAN K. MILLER are Professor, Research Assistant, and Research Associate, respectively, Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305. This paper is based on a presentation made at a symposium on "Mechanical-Thermal Processing and Dislocation Substructure Strengthening," held at the Annual Meeting in Las Vegas, Nevada, on February 23, 1976, under the sponsorship of the TMS/IMD Heat Treating Committee. METALLURGICAL TRANSACTIONS A
to the l a t t i c e d i f f u s i o n c o e f f i c i e n t . If the diffusion c o e f f i c i e n t is d e c r e a s
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