Stress-strain relationship during transformation enhanced plasticity
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AND
R. J. DE
ANGELIS
The effects of a deformation induced reaction kinetics upon the stress-strain curve of materials which transform during deformation is theoretically discussed. It is shown that the observed work hardening rate, d(%*/d E~ depends on both the occurrence of a transformation and on the instantaneous rate of the reaction.
VARIATIONS in the r a t e of work h a r d e n i n g d u r i n g i s o t h e r m a l and c o n s t a n t s t r a i n r a t e p l a s t i c d e f o r m a t i o n of a m a t e r i a l i n d i c a t e s that c h a n g e s a r e o c c u r r i n g in e i t h e r the b a s i c d i s l o c a t i o n d e f o r m a t i o n m e c h a n i s m or in the s t r u c t u r e of the m a t e r i a l . However, the c o r r e c t i n t e r p r e t a t i o n of t h e s e o b s e r v a tion r e q u i r e s that all f a c t o r s involved in the p r o c e s s be taken into c o n s i d e r a t i o n . This concept is v e r y i m p o r tant in the c a s e of m a t e r i a l s which t r a n s f o r m d u r i n g d e f o r m a t i o n . P a r t i c u l a r l y when the t r a n s f o r m a t i o n exhibits a shape change, such as a m a r t e n s i t i c t r a n s f o r m a t i o n o r m e c h a n i c a l twinning, which c o n t r i b u t e s to the total o b s e r v e d d e f o r m a t i o n . This c o m m u n i c a t i o n deals with the c o r r e c t i o n s which m u s t be applied to the well known e x p r e s s i o n s I,~ for: t) T r u e - s t r e s s , (%*, a* = s(1 + e) [1] where s and e a r e the v a l u e s of the e n g i n e e r i n g s t r e s s and s t r a i n and, ii) T r u e - s t r a i n , E*, 9 *=ln (l+e)
[2]
F u r t h e r m o r e , it will be shown that, independent of c h a n g e s in the i n t r i n s i c d e f o r m a t i o n m e c h a n i s m of the m a t e r i a l , v a r i a t i o n s in the r a t e of t r a n s f o r m a t i o n d u r ing d e f o r m a t i o n will c a u s e changes in the o b s e r v e d work h a r d e n i n g r a t e d(%*/dE~ where e~ is the t r u e p l a s tic s t r a i n , defined by the r e l a t i o n / (%* =
--
[3]
W
where E is the Young's m o d u l u s of the m a t e r i a l . THEORY C o n s i d e r a t i o n of Strain Let a b a r of a m a t e r i a l which t r a n s f o r m s d u r i n g d e f o r m a t i o n be s u b j e c t e d to a t e n s i l e d e f o r m a t i o n . If at a given point along the d e f o r m a t i o n path the body length is L, the c r o s s - s e c t i o n a r e a A, the applied load P, and the t r u e s t r e s s a then, by definition: P =a • A
[4]
If this b a r is f u r t h e r elongated a d i s p l a c e m e n t i n c r e ment d L , J. R. C. GUIMARAESis Professor of Materials Science, Instituto Militar de Engenharia, P~a. Gen. Tibflrcio s/n-ZC 82- Urca, 20.000Rio de Janeiro-Brazil. R.J. DE ANGELIS is Visiting Professor at the Instituto Militar Engenharia, while on leave from the Department of Metallurgical Engineeringand Materials Science, University of Kentucky, Lexington, Ky. 40506. Manuscript submitted December 8, 1972.
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