Yield strength of overaged alloys containing coherent ordered precipitates
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loops a r o u n d second p h a s e p a r t i c l e s have b e e n o b s e r v e d in s e v e r a l a l l o y s of i r o n , 1,2 n i c k e l 3 and copper 4 with r e l a t i v e l y lower s t a c k i n g f a u l t e n e r g i e s . An e x p r e s s i o n for yield s t r e s s , when the m o v i n g d i s l o c a t i o n s f o r m loops a r o u n d p a r t i c l e s , was o r i g i n a l l y given b y Orowan and this has u n d e r gone s e v e r a l m o d i f i c a t i o n s i n c l u d i n g those by F o r e m a n e t a l s and Ashby. ~ E s s e n t i a l l y , the s t r e s s r e q u i r e d to bow the d i s l o c a t i o n into a c r i t i c a l c o n f i g u r a t i o n is e s t i m a t e d . The e x p r e s s i o n due to Ashby can be w r i t t e n a s : 0.85Gb "r = 7 m
+
4~
~ 0
Rs
In r_~ _ rs
[11
b
Where Tm is the yield s t r e s s of the m a t r i x , 0 is a f u n c t i o n of the angle b e t w e e n the B u r g e r s v e c t o r and the d i s l o c a t i o n line, 2 R s is the p l a n a r i n t e r p a r t i c l e s e p a r a t i o n , and r s is the p l a n a r p a r t i c l e r a d i u s . Although the c a l c u l a t e d v a l u e s f r o m this m o d i f i e d equation a r e quite close to e x p e r i m e n t a l r e s u l t s , ~'6 the m o d e l p r e d i c t s a s h a r p e r d e c r e a s e in yield s t r e s s as a f u n c t i o n of p a r t i c l e size than the e x p e r i m e n t a l o b s e r v a t i o n s . "4, 7 The e x p r e s s i o n for Orowan s t r e s s s u g g e s t s that for a given m a t r i x the y i e l d s t r e s s is only a f u n c t i o n of p a r t i c l e size and v o l u m e f r a c t i o n . The p a r t i c l e s a r e a s s u m e d to be n o n d e f o r m a b l e and i n t r i n s i c p r o p e r t i e s of p a r t i c l e s a r e c o n s i d e r e d to be of no i m p o r t a n c e in d e t e r m i n i n g the l e v e l of s t r e n g t h , a This is not b o r n e out f r o m e x p e r i m e n t a l data. Although Orowan loops f o r m e d in o v e r a g e d condition in both V1682 and Nimonic PE16 a l l o y s , the yield s t r e n g t h of V1682 a l loy in o v e r a g e d state is h i g h e r 2 than that of N i m o n i c PE16 in spite of a s m a l l e r v o l u m e f r a c t i o n of Y' p r e c i p i t a t e s (Table I). The h i g h e r a n t i p h a s e b o u n d a r y e n RAGHURAM is Assistant Foreman, Rourkela Steel Plant, Rourkela, India. L. K. SINGHAL,formerly Manager Research & Development, Alloy Steels Plant, Durgapur is now Chief Metallurgist, Ahmedabad Advance Mills, Metals & Special Alloy Steels Division, Navsari, India. Manuscript submitted June 6, 1974. METALLURGICALTRANSACTIONSA
e r g y of the p r e c i p i t a t e s in V1682 a p p e a r s to i n f l u e n c e the yield s t r e s s of the alloy. F u r t h e r m o r e , in Orowan m o d e l the y i e l d i n g is s u p posed to o c c u r when the f i r s t d i s l o c a t i o n g l i d e s in a slip p l a n e and f o r m s a loop a r o u n d each p a r t i c l e . A n s e l l and Lenel 9 and Keh e t a
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