The Bauschinger effect and cyclic hardening in copper
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B A U S C H I N G E R x d i s c o v e r e d in 1886 that the yield s t r e s s for r e v e r s e flow of d e f o r m e d m e t a l s is l o w e r than the flow s t r e s s i n the o r i g i n a l d e f o r m a t i o n d i r e c tion. T h i s " B a u s c h i n g e r E f f e c t " is m o s t c l e a r l y defined in t e r m s of the " B a n s c h i n g e r s t r a i n s " which occur at given s t r e s s l e v e l s as i l l u s t r a t e d in Fig. 1. The B a u s c h i n g e r s t r a i n , / 3 x , is defined as the p l a s t i c s h e a r s t r a i n o c c u r r i n g at a f r a c t i o n x of the p r i o r r e v e r s e s h e a r p r e s t r e s s , ~-p. Sachs and Shoji 2 were the f i r s t i n v e s t i g a t o r s to show that the B a u s c h i n g e r Effect for single c r y s t a l s i s of a c o m p a r a b l e magnitude with that for p o l y c r y s t a l s . Woolley 3 found that the r a t i o of the B a u s c h i n g e r s t r a i n to the p r e s t r e s s , ~x/'Cp, f o r p o l y c r y s t a l l i n e m e t a l s is independent of the p r e s t r e s s l e v e l and i n v e r s e l y p r o p o r t i o n a l to the e l a s t i c m o d u l u s . L a t e r w o r k e r s have r e p o r t e d effects of c r y s t a l o r i e n t a t i o n , 4-7 s t r a i n a m plitude 8- ~1 and t e m p e r a t u r e 7'9-12 on cyclic h a r d e n i n g b e h a v i o r . The d i s l o c a t i o n s t r u c t u r e s p r e s e n t d u r i n g cyclic h a r d e n i n g have been studied u s i n g e l e c t r o n m i c r o s c o p y 9 , 1 1 , 1 3 - 21 and etch pitting. 21 B a s i n k i , et al. 21' found that slip l i n e s f o r m e d d u r i n g c y c l i n g h a r d e n i n g were e x t r e m e l y r e v e r s i b l e except at s m a l l s t r a i n s where new slip l i n e s w e r e o b s e r v e d d u r i n g each h a l f cycle. The p r e s e n t i n v e s t i g a t i o n was u n d e r t a k e n to d e t e r m i n e the cause of the B a u s c h i n g e r Effect d u r i n g the f i r s t few c y c l e s of d e f o r m a t i o n , where slip line r e v e r s i b i l i t y h a s not yet been detected. E x p e r i m e n t a l d e t a i l s of the p r e s e n t i n v e s t i g a t i o n are r e v i e w e d m o r e t h o r oughly e l s e w h e r e . 22
R. C. DANIEL, formerly Graduate Student, Carnegie-MellonUniversity, Pittsburgh, Pa., is now Senior Engineer, Bettis Atomic Power Laboratory, WestinghouseElectric Corp., West Mifflin, Pa. G.T. HORNE, formerly Associate Professor at Carnegie-MellonUniversity, is now Vice President, Industrial Testing Laboratories, Pittsburgh, Pa. This paper is based on a thesis submitted by R. C. DANIEL in partial fulfillment of the requirements ofthe degree of Doctor of Philosophy at Carnegie-MellonUniversity. Manuscript submitted June 25, 1970. METALLURGICALTRANSACTIONS
1) E X P E R I M E N T A L PROCEDURE The ~ in. by -~ in. c r y s t a l s , grown f r o m the m e l t in v a c u u m u s i n g 99.999 pct ASARCO copper stock, had axes a p p r o x i m a t e l y 9 deg off [011] and two s u r f a c e s with
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