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w h e r e GM i s the s h e a r m o d u l u s of the m a t r i x , Vv the v o l u m e f r a c t i o n of p a r t i c l e s of d i a m e t e r d, and yp is the p l a s t i c s h e a r s t r a i n on the p r i m a r y s l i p s y s t e m . Th e co n s t an t , K , is found e x p e r i m e n t a l l y to be n e a r 0.2. Equating the s h e a r s t r e s s d i f f e r e n c e (r - ~-o) to the d i f f e r e n c e in t e n s i l e s t r e s s b e t w e e n f r a c t u r e and y i e l d i n g of p o l y c r y s t a l l i n e , s i n g l e - p h a s e /3 Ti-V~ i . e . , (e - e o ) / m w h e r e the T a y l o r f a c t o r (m) is taken as 2.7 for b cc m e t a l s , or 5.9 kg p e r sq m m , GM to the s h e a r m o d u l u s (c44) of /3 T i 8 o r 0.51 x 104 kg p e r sq m m , Vv to 0.6, and d to an a v e r a g e value of 65~, the p l a s t i c s h e a r s t r a i n r e q u i r e d on the p r i m a r y s y s t e m is e s t i m a t e d to be in the v i c i n i t y of m a c r o s c o p i c y i e l d i n g o r 10 -s. It i s well known that s i g n i f i c a n t d i s l o c a t i o n m o t i o n o c c u r s b e l o w the m a c r o s c o p i c y i e l d s t r e s s . Thus~ the a p p a r e n t b r i t t l e b e h a v i o r of w - c o n t a i n i n g a l l o y s is r e l a t e d to the l a r g e v o l u m e f r a c t i o n and fine p a r t i c l e s i z e of n o n d e f o r m a b l e p r e c i p i t a t e s which inc r e a s e the r a t e of w o r k h a r d e n i n g of the /3 p h a s e . F a i l u r e then o c c u r s by d u c t i l e , i n t e r p a r t i c l e f r a c t u r e on a m i c r o s c o p i c s c a l e . The f o reg o i n g d i s c u s s i o n s u g g e s t s that a t t a i n m e n t of high s t r e n g t h s at r o o m t e m p e r a t u r e with the r e t e n tion of s o m e ductility should be p o s s i b l e by l i m i t i n g the v o l u m e f r a c t i o n of w through a l l o y i n g to slow t r a n s f o r m a t i o n k i n e t i c s and by a p p r o p r i a t e h e a t t r e a t men t . Good t e n s i l e p r o p e r t i e s a r e r e t a i n e d by the p r e s e n c e of ~ d i s p e r s e d throughout the /3 m a t r i x . ot p r e c i p i t a t e s a r e d e f o r m a b l e and have much l a r g e r d i m e n s i o n s in c o m p a r i s o n with the n o n d e f o r m a b l e w p a r t i c l e s . The value of p r i o r w f o r m a t i o n is to d i s t r i b u t e ~ p r e c i p i t a t e s throughout the m a t r i x , r a t h e r 1452-VOLUME 1,MAY 1970

than al o n g g r a i n b o u n d a r i e s . T h u s , it is p o s s i b l e to attain a t t r a c t i v e t e n s i l e p r o p e r t i e s through such duplex heat t r e a t m e n t . T h i s r e s e a r c h was s u p p o r t e d by the A i r F o r c e M a t e r i a l s L a b o r a t o r y , W r i g h t - P a t t e r s o n Air F o r c e B a s e , under c o n t r a c t AF 33(615)-3866. 1. F, R. Brotzen,E. L Harmon,Jr., and A. R. Troiano: A1ME Tran~, 1955, vol. 203, p. 413. 2. E, L. Harmon,J Kozol,and A. R. Troiano Trans ASM, 1958, vol. 50, p. 418. 3. B. S. Hlckma