Interrelations between fracture toughness and other mechanical properties in titanium alloys
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F. H. FROES
C r i t i c a l s t r e s s i n t e n s i t y f a c t o r s and g e n e r a l t e n s i l e p r o p e r t i e s w e r e m e a s u r e d for a c l a s s of m e t a s t a b l e beta and a l p h a - b e t a t i t a n i u m alloys with a l i m i t e d n u m b e r of compos i t i o n s but p r o c e s s e d to have a wide v a r i e t y of s t r e n g t h l e v e l s and m i c r o s t r u c t u r e s . T h e s e data w e r e u s e d to t e s t t h i r t e e n t h e o r e t i c a l r e l a t i o n s b e t w e e n the f r a c t u r e toughn e s s and t e n s i l e p a r a m e t e r s . Many of the t h e o r e t i c a l r e l a t i o n s had been proposed p r e viously, but s e v e r a l new f o r m s w e r e d e r i v e d in the p r e s e n t work. The c o r r e l a t i o n showed that for alloys exhibiting a l i m i t e d r a n g e of m i c r o s t r u c t u r e s , the s i m p l e r c o r r e l a t i o n s gave the b e t t e r fits with KIc a Y-~ s p e c i f i c a l l y being the b e s t one. F o r c o r r e l a t i o n s of a l l o y s with a wide r a n g e of m i c r o s t r u c t u r e s , m o r e c o m p l e x c o r r e l a t i o n s which included m i c r o s t r u c t u r a l p a r a m e t e r s w e r e found to be s u p e r i o r .
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have b e e n a n u m b e r of efforts to r e l a t e f r a c t u r e t o u g h n e s s , as m e a s u r e d by the c r i t i c a l p l a n e - s t r a i n s t r e s s i n t e n s i t y factor KIe, to t e n s i l e p r o p e r t i e s for the c a s e of c o n s t r a i n e d - d u c t i l e - f r a c t u r e - b y - h o l e - g r o w t h m e c h a n i s m s . Many of these, b e g i n n i n g with the o r i g i n a l work by Krafft 1 a r e s u m m a r i z e d in p a p e r s by Hahn et al 2'3. A n u m b e r of the c o r r e l a t i o n s a r e b a s e d s o l e l y on m e c h a n i c s a n a l y s e s without c o n s i d e r a t i o n of m i c r o s t r u c t u r e . More r e cent v e r s i o n s , following the p i o n e e r i n g work of R o g e r s 4 and McClintock S on f r a c t u r e by hole growth, include m i c r o s t r u c t u r e i n s o f a r as the d e c o h e r i n g o r c r a c k i n g p a r t i c l e s which lead to hole n u c l e a t i o n a r e treated. In b r o a d t e r m s t h e r e a r e four types of f a c t o r s c o n s i d e r e d in these r e l a t i o n s . F i r s t , f r o m a p u r e l y m e c h a n i c s viewpoint, Kic , s i n c e it is r e l a t e d to the s q u a r e r o o t of the e n e r g y r e l e a s e r a t e , should i n c r e a s e as the p l a s t i c - z o n e s i z e at the c r a c k tip or, e q u i v a l e n t l y , the c r a c k opening d i s p l a c e m e n t , i n c r e a s e s . 6 Second, as s u g g e s t e d by Rice and J o h n s o n v and as i n d i c a t e d i n the work of M c C l i n t o c k et al ~'9 the c r a c k opening d i s p l a c e m e n t should r o u g h l y equal both the s p a c i n g of i n c l u s i o n s or s e c o n d - p h a s e p a r t i c l e s which d e t e r m i n e hole s p a c i n
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