An empirical analysis of titanium stress-strain curves
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Hollomon z s i m p l i f i e d t h i s equation b y a s s u m i n g cro to be z e r o so that if the s t r e s s - s t r a i n d a t a y i e l d e d a s t r a i g h t line on In (r - In E c o o r d i n a t e s the s l o p e of the line gave tti~ exponent n. H o w e v e r , In cr- In E p l o t s of e x p e r i m e n t a l d a t a often do not give s t r a i g h t l i n e s . The Hollomon p r o c e d u r e is w i d e l y e m p l o y e d , howe v e r , b e c a u s e of a t e n d e n c y to u s e n a s a w o r k h a r d ening index, s-5 A m o r e m e a n i n g f u l w a y to a n a l y z e w o r k h a r d e n i n g is b y p l o t t i n g In d(r/dE a g a i n s t In ~,6-1o for a p o w e r r e l a t i o n b e t w e e n (r and E y i e l d s a s t r a i g h t line r e g a r d l e s s of the e x i s t e n c e of a %. M o r e o v e r , the s l o p e of this line e q u a l s ( n - 1), while i t s i n t e r s e c t i o n with the In e = 0 line g i v e s In (kn), so that both n and k and t h e r e f o r e ao a r e d e t e r m i n a b l e . This method, due to C r u s s a r d Nnd J a o u l , was r e c e n t l y u s e d to i n v e s t i g a t e w o r k h a r d e n i n g in c o m m e r c i a l and high p u r i t y t i t a n i u m a t t e m p e r a t u r e s b e l o w 300 K. ~~ The p r e s e n t i n v e s t i g a t i o n e x t e n d s the p r e v i o u s s t u d y and c o v e r s the b r o a d e r t e m p e r a t u r e r a n g e f r o m 77 to 1026 K. Two g r a d e s of p o l y c r y s t a l l i n e c~-Ti w e r e u s e d ; c o m m e r c i a l p u r i t y and high p u r i t y t r i p l e p a s s zone r e f i n e d i o d i d e t i t a n i u m . The c o m p o s i t i o n s , s p e c i m e n c h a r a c t e r i s t i c s and t e s t i n g p r o c e d u r e w e r e d e s c r i b e d p r e v i o u s l y , u The s t r a i n r a t e was 2.7 • 10 -4 s -~. S t r e s s - s t r a i n d a t a in the m i c r o s t r a i n r e g i o n (to about 0.005 s t r a i n ) and b e y o n d the m a x i m u m l o a d w e r e not c o n s i d e r e d . The r a n g e a n a l y z e d , t h e r e f o r e , i n c l u d e d n e a r l y a l l of the u n i f o r m s t r a i n r a n g e while i g n o r i n g y i e l d p o i n t s and necking. I n s t r o n c h a r t l o a d t i m e d i g i t a l d a t a w e r e f i r s t c o n v e r t e d on a c o m p u t e r to t r u e s t r e s s ( o r ) - t r u e p l a s t i c s t r a i n (Ep). This was then p r o c e s s e d b y L a g r a n g e i n t e r p o l a t i o n of a s e c o n d d e g r e e p a r a b o l a , using t h r e e d a t a p o i n t s at a t i m e , into dcr/dEp, In dcr/dEp, and In ~p d a t a .
RESULTS The
METALLURGICAL TRANSACTIONS
DISCUSSIONS
C r u s s a r d and J a o u l A n a l y s i s : High P u r i t y T i t a n i u m
High p u r i t y t i t a n i u m In da/dEp - In Ep c u r v e s f o r about half the i n v e s t i g a t e d t e m p e r a t u r e s a r e shown in Fig. 1. A r e a s o n a b l e l i n e a r r e l a t i o n s h i p b e t w e e n In da/dEp and In Ep w a s o b t a i n e d at a l l t e m p e
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