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T H E d e s c r i p t i o n of the s t r e s s - s t r a i n c u r v e s and s t r a i n - h a r d e n i n g of m e t a l s by m a t h e m a t i c a l e x p r e s s i o n s is a f r e q u e n t l y used approach. This is b e c a u s e it allows the p l a s t i c p a r t of the c u r v e to be t r e a t e d by c e r t a i n p a r a m e t e r s which can be applied to the study of f o r m a b i l i t y and d e f o r m a t i o n m e c h a n i s m s . The m o s t i m p o r t a n t and widely used a p p l i c a t i o n is the e v a l u a t i o n of s t r e t c h - f o r m a b i l i t y b y the n value, which is the exponent of the Hollomon 1 equation, = Ke n. C a i r n s e t a l . z have also used the n v a l u e in the a s s e s s m e n t o f ' r e s i d u a l d u c t i l i t y of h e a v i l y d e f o r m e d copper. The s t r a i n - h a r d e n i n g exponent, n, can be d e t e r m i n e d b y a s i m p l e t e n s i o n t e s t o r f r o m the m e a s u r e m e n t of s t r a i n in a s p e c i a l s p e c i m e n , s The u n i f o r m s t r a i n , eu, which is equal to n when the Hollomon e q u a tion is valid, has also f r e q u e n t l y b e e n used as a m e a s u r e of f o r m a b i l i t y . However, n is the exponent of a n e m p i r i c a l equation and it is not s u r p r i s i n g that this equation can not a c c u r a t e l y d e s c r i b e the s t r e s s - s t r a i n c u r v e s for all m e t a l s . Thus s e v e r a l e m p i r i c a l r e l a t i o n s without any p h y s i c a l m e a n i n g , but giving a b e t t e r fit to e x p e r i m e n t a l data in some c a s e s , have b e e n developed u s i n g c o m p u t e r s . 4,s In d e f o r m a t i o n m e c h a n i s m s t u d i e s d i f f e r e n t equations have b e e n used to d e s c r i b e d i f f e r e n t s t r a i n r e g i o n s of the u n i f o r m s t r a i n . 6'7 A v e r y c o n v e n i e n t method for f i n d i n g s t a g e s in the s t r e s s - s t r a i n c u r v e s is the C r u s s a r d a - J a o u l 9 (C J) a n a l y s i s w h e r e d a / d e - e - v a l u e s are plotted in l o g - l o g c o o r d i n a t e s . R e c e n t l y H e e d - H i l l e t a l . I~ have p r e s e n t e d a modified C J - m e t h o d for a n a l y z ing the s t a g e s . The a i m of the p r e s e n t work was to study the a p p l i c a b i l i t y of four widely used s t r e s s - s t r a i n r e l a t i o n s for the e s t i m a t i o n of the u n i f o r m s t r a i n ( i . e . , f o r m a b i l i t y ) of m e t a l s . COMPARISON OF THE STRESS-STRAIN RE LATIONS S e v e r a l e m p i r i c a l equations have b e e n used to d e s c r i b e e x p e r i m e n t a l s t r e s s - s t r a i n c u r v e s , but h e r e H. J. KLEEMOLA is Senior Fellow of the Finnish Academy, Department of Mining and Metallurgy, Helsinki University of Technology, Otaniemi, Finland. M. A. NIEMINEN is Research Metallurgist, Metal Laboratory, Pori Works, Outokumpu Oy, Pori, Finland. Manuscript submitted June 8, 1973. METALLURGICAL TRANSACTIONS

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