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Uniaxial tension and compression and cyclic stress-strain behavior of β brass
Scripta M E T A L L U R G I C A
Vol. 14, pp. 631-636, 1980 ,Printed in the U.S.A.
UNIAXIAL TENSION AND COMPRESSION OF ~
Pergamon Press Ltd. All rights reserved
AND CYCLIC STRESS-STRAIN BEHAVIOR BRASS by
Hiroshi Yaguchi and Harold Margolin D e p a r t m e n t of P h y s i c a l a n d E n g i n e e r i n g M e t a l l u r g y Polytechnic I n s t i t u t e of New Y o r k B r o o k l y n , New Y o r k 11201 (Received March ii, 1980) (Revised Harch 28, 1980)
Evidence for different initial resolved shear stresses in compression and tension, corresponding to testing in the twinning and anti-twinning directions, have been reported for a number of bcc metals and alloys, Ta, Nb, Mo(1), Si-Fe(2), W(3) and ~ - Ti(4). The critical resolved shear stress is lower in the twinning direction than in the anti-twinning direction, and this difference has been attributed to the difference in Peierls stress for motion of the dissociated screw dislocation core in the twinning and anti-twinning directions (2). In general the strains used to study the differences in tension and compression behavior have been small. B o w e n , C h r i s t i a n a n d T a y l o r ( 5 ) c o n d u c t e d a n e x t e n s i v e s t u d y of t h e d e f o r m a t i o n of Nb single crystals and reported, f o r s t a g e I, s t r a i n h a r d e n i n g in c o m p r e s s i o n a n d , in some c a s e s , s o f t e n i n g in t e n s i o n . In s t a g e II s t r a i n h a r d e n i n g was f o u n d to b e h i g h e r in c o m p r e s sion t h a n in t e n s i o n . In some i n s t a n c e s s t r a i n h a r d e n i n g r a t e s in c o m p r e s s i o n w e r e two to t h r e e t i m e s as h i g h a s t h o s e in t e n s i o n . A t low t e m p e r a t u r e s , 77-175K, 13 - b r a s s s h o w e d d e f o r m a t i o n a l b e h a v i o r s i m i l a r to t h e m e t a l s ( 6 ) , b u t a t room t e m p e r a t u r e t h e r e is l i t t l e d i f f e r e n c e in t h e y i e l d s t r e s s b e t w e e n flow in t h e t w i n n i n g a n d a n t i - t w i n n i n g d i r e c t i o n s ( 6 ) . A t 423K y i e l d i n g in t h e t w i n n i n g d i r e c t i o n s r e q u i r e s a h i g h e r s t r e s s t h a n in t h e a n t i - t w i n n i n g d i r e c t i o n ( 7 ) .
bcc
T h e r e s u l t s p r e s e n t e d h e r e c o m p a r e u n i a x i a l flow s t r e s s in t e n s i o n a n d c o m p r e s s i o n w i t h t h e b e h a v i o r in r e v e r s e d l o a d i n g . T h e w o r k is p a r t of a s t u d y to d e t e r m i n e t h e g r a i n b o u n d a r y c o n t r i b u t i o n to t h e B a u s c h i n g e r e f f e c t in B - b r a s s b i c r y s t a l s . Experimental Procedure 13 - b r a s s s i n g l e c r y s t a l s of 4 8 . 5 w t . % Z n w e r e g r o w n b y t h e B r i d g m a n t e c h n i q u e . O n l y t h o s e p o r t i o n s of t h e c r y s t a l s w e r e u s e d w h i c h h a d y i e l d s t r e s s e s w i t h i n 2 . 1 Mpa of o n e another. F o r t h e c y c l i c l o a d i n g t e s t s t h e s i n g l e c r y s t a l was d i f f u s i o n b o n d e d to two ~ b r a s s pole p i e c e s t h r o u g h w h i c h t e n s i o n a n d c o m p r e s s i o n w e r e a p p l i e d w i t h s e l f - a l i g n i n g g r i p s . T h e d i m e n s i o n s a n d s t r a i n r a t e s a p p l i e d to e a c h c r y s t a l a r e a s follows: Tension:
£ = 6.35 mm, w = 4 . 8 3 mm, t = 0.71 mm
= 1.33 x 1 0 - 4 / s e c C o m p r e s s i o n : ~ = 1 2 . 9 rnm, w = 8 . 4 mm, t = 4 . 9 5 mm Cyclic:
= 1.65 x 10-4/sec £ = 1 2 . 7 ram, w = 4 . 0 5 ram, t = 5.1 ram = 0.77 x
lO-4/sec
T h e t e n s i o n a n d c o m p r e s s i o n t e s t s w e r e c a r r i e d o u t in a n I n s t r o n m a c h i n e , w h i l e t h e c y c l i c s t r e s s s t r a i n t e s t s w e r e c o n d u c t e d w i t h a n MTS m a c h i n e . T h e c y c l i c t e s t s w e r e b e g u n in compression. Slip line o b s e r v a t i o n s w e r e m a d e w i t h t h e u s e of a s i n g l e s t a g e r e p l i c a t e c h n i q u e . R e p l i c a t e c h n i q u e s w e r e u s e d b e c a u s e of t h e p o s s i b i l i t y t h a t r e c o v e r y w o u l d t a k e p l a c e d u r i n g u n l o a d i n g a n d r e l o a d i n g a n d to a v o i d t h e a l i g n m e n t p r o b l e m s a t t e n d a n t w i t h r e p e a t e d d i s a s s e m b l y of t h e g r i p s u s e d i n c y c l i c t e s t i n g .
631 0036-9748/80/060631-06502.00/0 Copyright (c) 1980 Pergamon Press Ltd.
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Fig. 1 s h o w s t h e r e s u l t s o b t a i n e d f o r u n i a x i a l c o m p r e s s i o n a n d t e n s i o n . Also s h o w n , o n a cumulative shear strain basis, are the results for cyclic testing. T h e o r i e n t a t i o n of t h e s i n g l e c r y s t a l is also g i v e n . T e n s i o n a n d c o m p r e s s i o n a r e p l o t t e d in t h e same d i r e c t i o n . T h e p o i n t s o n t h e s t r e s s s t r a i n c u r v e s c o r r e s p o n d to t h e p o s i t i o n s a t w h i c h s t r a i n i n g was h a l t e d , w i t h o u t u n l o a d i n g , to t a k e r e p l i c a s . T h e cyclic c u r v e s , a p p e a r i n g as d a s h e d l i n e s , s h o w t h r e e p o i n t s . The l o w e s t p o i n t c o r r e s p o n d s to a d e v i a t i o n of 0.01% f r o m e l a s t i c b e h a v i o r . The second point c o r r e s p o n d s to t h e s t r e s s w h i c h is t h e same as t h a t o b t a i n e d b y t h e i n t e r s e c t i o n of t h e e l a s t i c p o r t i o n s w i t h t h e b a c k w a r d e x t e n s i o n of t h e i n i t i a l p o r t i o n s of t h e p l a s t i c r e g i o n . T h e t h i r d p o i n t c o r r e s p o n d s to t h e h i g h e s t s t r e s s o b t a i n e d d u r i n g l o a d i n g i n a g i v e n d i r e c tion. Replicas were taken after each half-cycle. Up to a r e s o l v e d s h e a r s t r a i n of a b o u t 2% t h e u n i a x i a l s t r e s s - s t r a i n c u r v e s f o r t e n s i o n a n d c o m p r e s s i o n c o i n c i d e . A b o v e t h i s s t r a i n t h e r e is i n c r e a s i n g d i v e r g e n c e , w i t h t h e comp r e s s i o n c u r v e s l y i n g a t t h e h i g h e r l e v e l s . B e c a u s e of t h e c h a n g e i n c r o s s s e c t i o n a l a r e a t h e t r u e s t r e s s e s will b e d i f f e r e n t f r o m t h e n o r m a l s t r e s s e s . T h e t r u e s t r e s s in c o m p r e s s i o n a t a r e s o l v e d s h e a r s t r a i n 20.5% is m a r k e d 4 a n d t h e t r u e s t r e s s i n t e n s i o n a t a r e s o l v e d s h e a r s t r a i n of a b o u t 24% is m a r k e d 5. On i n i t i a l l o a d i n g in t h e c o m p r e s s i o n h a l f - c y c l e t h e f i r s t cyclic c u r v e r e v e a l s t h a t t h e y i e l d s t r e s s is q u i t e close to t h e y i e l d s t r e s s e s o b t a i n e d f o r t h e u n i a x i a l t e s t s . However, c o m p r e s s i n g to a s t r a i n a b o v e t h a t c o r r e s p o n d i n g to t h e y i e l d s t r e s s , r e s u l t s i n m u c h h i g h e r s t r a i n h a r d e n i n g t h a n was n o t e d f o r t h e s i n g l e c r y s t a l w i t h o u t t h e pole p i e c e s . Similarly, t h e t e n s i o n h a l f - c y c l e , following t h e f i r s t c o m p r e s s i o n p r o d u c e s s t r e s s e s a b o v e t h e u n i a x i a l tension curve. H o w e v e r , in s u b s e q u e n t c y c l e s , t h e maximum c o m p r e s s i o n s t r e s s falls below t h e c o r r e s p o n d i n g u n i a x i a l s t r e s s a t t h e same s t r a i n , w h i l e t h e s t r e s s f o r t h e t e n s i o n h a l f c y c l e c o n t i n u e s a b o v e t h e s t r e s s f o r t h e c o r r e s p o n d i n g s t r a i n in t h e u n i a x i a l t e n s i o n c u r v e . T h e i n c r e a s e in s t r e s s l e v e l of t h e t e n s i o n h a l f - c y c l e is c o n s i d e r a b l y h i g h e r t h a n t h e d e c r e a s e in s t r e s s d u r i n g t h e c o m p r e s s i o n h a l f - c y c l e . If t h e c y c l e m a r k e d A, B a n d C, Fig. 1, a r e e x a m i n e d , i t c a n b e s e e n t h a t t h e s t r e s s e s in t h e B , o r t e n s i o n , c y c l e a r e close to t h e c o r r e s p o n d i n g s t r e s s e s i n t h e p r e c e d i n g comp r e s s i o n c y c l e , A. H o w e v e r , o n g o i n g to t h e s u c c e e d i n g c o m p r e s s i o n h a l f c y c l e , C, t h e r e is a d i s c o n t i n u o u s i n c r e a s e in t h e s t r e s s e s c o r r e s p o n d i n g to t h e s t r a i n s a t c o m p a r a b l e p o s i t i o n s of t h e t e n s i o n h a l f - c y c l e . C o m p a r e p o i n t s 1' a n d 1, 2' a n d 2, 3' a n d 3. 2. Slip B e h a v i o r Slip c h a r a c t e r i s t i c s i n u n i a x i a l c o m p r e s s i o n a n d t e n s i o n a r e d i s t i n c t l y d i f f e r e n t , F i g s . 2-5. B a n d i n g a n d c o a r s e slip in c o m p r e s s i o n a r e c l e a r l y e v i d e n t a t 4 . 2 4 r e s o l v e d s h e a r s t r a i n , y, in Fig. 2, w h i l e slip a p p e a r s s h a r p e r in t e n s i o n a t t h e same y, F i g . 3. I n b o t h t e n s i o n a n d c o m p r e s s i o n s i n g l e slip o n t h e {110} <111> p r i m a r y slip s y s t e m , P, w a s f o u n d . A t $ = 20.5% i n d i v i d u a l p r i m a r y slip b a n d s w e r e n o t r e a d i l y d i s t i n g u i s h a b l e i n c o m p r e s s i o n , Fig. 4. I n a d d i t i o n some e v i d e n c e of c o n j u g a t e , C J , a n d c r i t i c a l , C, slip b a n d s w e r e d i s t i n g u i s h a b l e . I n t e n s i o n a t t h e same s t r a i n , Fig. 5, i n d i v i d u a l p r i m a r y slip b a n d s w e r e r e a d i l y detectable. F i g s . 6 a n d 7 r e v e a l t h e s t r u c t u r e s o b t a i n e d a f t e r i n i t i a l c o m p r e s s i v e ¥ of 20.5% a n d t e n s i l e y of 43%, r e s p e c t i v e l y , followed b y p o l i s h i n g a n d r e s t r a i n i n g a n a d d i t i o n a l 14. Fig. 6 s h o w s c o a r s e slip i n t e r m i n g l e d w i t h c r o s s slip f o r c o m p r e s s i o n , w h i l e Fig. 7 r e v e a l s t h e f i n e s t r a i g h t slip c h a r a c t e r i s t i c of t e n s i o n . F i g s . 8-10 s h o w t h e same a r e a a f t e r c y c l i c s t r a i n s c o r r e s p o n d i n g to p e a k s t r e s s e s a t s u c c e s s i v e h a l f - c y c l e s a t p o s i t i o n 6 ( c o m p r e s s i o n ) , 7 ( t e n s i o n ) a n d 8 ( c o m p r e s s i o n ) i n Fig. 1. E x a m i n a t i o n of t h e s e f i g u r e s i n d i c a t e s t h a t t h e d i f f e r e n c e s i n slip b e h a v i o r n o t e d e a r l i e r f o r t h e u n i a x i a l t e s t s a r e n o t e v i d e n t h e r e . T h i s o c c u r s
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b e c a u s e slip w h i c h h a s b e e n a c t i v a t e d , f o r e x a m p l e , in t h e c o m p r e s s i o n c y c l e , p o s i t i o n 6, Fig. 8, also o p e r a t e s in t h e s u c c e e d i n g c y c l e , p o s i t i o n 7, Fig. 9. I n a d d i t i o n , n e w slip t a k e s p l a c e in t h e t e n s i o n c y c l e . C o m p a r e t h e a r e a s m a r k e d A a n d B of Fig. 8, w h i c h s h o w l i t t l e slip w i t h t h e same a r e a s of Fig. 9, w h i c h do s h o w n e w s l i p . I n Fig. 10, c o r r e s p o n d i n g to t h e n e x t c y c l e , n e w slip a p p e a r s a l s o . A r e a A r e v e a l s more slip a n d a r e a B h a s b e c o m e s m a l l e r b e c a u s e of s l i p a t t h e l o w e r b o u n d a r y of a r e a B m o v i n g i n t o a r e a B. Note c r o s s slip in a r e a D, Fig. 10. With i n c r e a s e d c u m u l a t i v e s h e a r s t r a i n , X,/, t h e l a c k of d i s t i n c t i o n b e t w e e n slip in t e n s i o n a n d c o m p r e s s i o n c o n t i n u e s u p to Ey = 37.5%, t h e limit u s e d h e r e . The slip b a n d a p p e a r a n c e a f t e r a c u m u l a t i v e cyclic s h e a r s t r a i n of 21% is s h o w n in Fig. 11, w h i c h s h o u l d b e c o m p a r e d w i t h F i g s . 4 a n d 5. Slip b a n d s of Fig. 11 a r e q u i t e c o a r s e a n d more n e a r l y like t h e slip h a n d s of Fig. 5 t h a n Fig. 4. Discussion Slip in c o m p r e s s i o n o n {110} <111> f o r t h e o r i e n t a t i o n s h o w n in Fig. 1 c a n b e c o n s i d e r e d to b e in t h e t w i n n i n g d i r e c t i o n a n d slip in t e n s i o n o n t h e same slip s y s t e m to b e in the chit-twinning direction. T h e d a t a of Fig. 1 s h o w t h a t flow in t h e t w i n n i n g d i r e c t i o n r e q u i r e s a h i g h e r s t r e s s t h a n flow in t h e a n t i - t w i n n i n g d i r e c t i o n . Thus the transition from n o r m a l b e h a v i o r r e c o r d e d p r e v i o u s l y a t 4 2 3 K ( 7 ) n o w a p p e a r s to o c c u r a t room t e m p e r a t u r e . I n t h e e a r l i e r w o r k t h e d i f f e r e n c e b e t w e e n t e n s i o n a n d c o m p r e s s i o n was e v i d e n t a t t h e y i e l d s t r e s s , w h i l e in Fig. 1 t h e d i f f e r e n c e d e v e l o p e o n l y a f t e r a s h e a r s t r a i n of a b o u t 2%. As F i g s . 6 a n d 7 i l l u s t r a t e w a v y slip is m u c h more p r e d o m i n a n t w h e n s t r e s s i n g in t h e t w i n n i n g ( c o m p r e s s i o n ) t h a n in t h e a n t i - t w i n n i n g ( t e n s i o n ) d i r e c t i o n . U m a k o s h i a n d Yamag u c h i ( 8 ) h a v e s h o w n t h a t t h e r e is a t e n d e n c y f o r c r o s s slip f r e q u e n c y _ t o i n c r e a s e f o r o r i e n t a t i o n s w h o s e s t r e s s a x e s , p r o j e c t e d o n t o t h e ( 1 1 1 ) p l a n e , a p p r o a c h [211] o n t h e " t w i n n i n g " s i d e of t h e [ i 0 1 ] - [211] r e g i o n of t h e ( 1 1 1 ) p l a n e a n d a d e c r e a s e d f r e q u e n c y as t h e s t r e s s a x e s m o v e s a w a y f r o m [211] . If t h i s b e h a v i o r c a n b e a p p l i e d to w a v y slip in g e n e r a l , t h e n o n e w o u l d e x p e c t m u c h l e s s w a v y slip in t h e a n t i - t w i n n i n g t e n s i o n s t r a i n i n g , a s o b s e r v e d . T h e i n c r e a s e d s t r a i n h a r d e n i n g n o t e d in t h e i n i t i a l c o m p r e s s i o n h a l f - c y c l e , p o s i t i o n 6 in Fig. 1, is p r o b a b l y r e l a t e d to t h e c o n s t r a i n t s i m p o s e d b y t h e b o n d e d g r i p s . Similar b e h a v i o r was also o b s e r v e d in b i c r y s t a l s b u t t h e m a g n i t u d e was s m a l l e r , p r e s u m a b l y b e c a u s e of t h e p r e s e n c e of t h e b i c r y s t a l b o u n d a r y . The difference between the uniaxial tension and compression single crystal stress-strain c u r v e s m u s t b e a c c e p t e d as a n i n t r i n s i c d i f f e r e n c e , because the cyclic behavior shows similar behavior. T h i s is e v i d e n t f r o m Fig. 1, w h e r e it c a n b e s e e n t h e l o c u s of t h e p e a k s t r e s s e s in t e n s i o n lie b e l o w t h e c o r r e s p o n d i n g l o c u s in compression. I t s h o u l d b e n o t e d t h a t t h e l o c u s of t h e t e n s i l e p e a k s t r e s s e s is m u c h c l o s e r to t h e c o m p r e s s i o n u n i a x i a l c u r v e t h a n to t h e t e n s i o n c u r v e . I t s e e m s e v i d e n t t h a t p r i o r slip in c o m p r e s s i o n m a r k e d l y r a i s e s t h e s t r e s s r e q u i r e d f o r flow a t c o r r e s p o n d i n g s t r a i n s in t h e s u c c e e d i n g t e n s i o n c y c l e , w i t h o u t r a i s i n g t h e s e s t r e s s e s a b o v e t h o s e in c o m p r e s s i o n . T h e d i s c o n t i n u o u s i n c r e a s e s in s t r e s s f o r c o r r e s p o n d i n g s t r a i n s in t h e f o l l o w i n g c o m p r e s s i o n c y c l e n e v e r r e a c h t h e v a l u e of t h e u n i a x i a l c u r v e a f t e r t h e t h i r d cycle. T h u s p r i o r c y c l i n g in t e n s i o n limits t h e s t r a i n h a r d e n i n g in c o m p r e s s i o n . T h e r e is no TEM d a t a a v a i l a b l e a t t h i s p o i n t to p e r m i t a n e x p l a n a t i o n b a s e d o n o b s e r v a t i o n . ACKNOWLEDGMENT T h e a u t h o r s w i s h to e x p r e s s t h e i r a p p r e c i a t i o n to t h e N a t i o n a l S c i e n c e F o u n d a t i o n w h i c h h a s s u p p o r t e d t h i s w o r k on G r a n t #DMR-7704118. REFERENCES 1. 2. 3. 4.
P. J . S h e r w o d , F. G u i u , H. C. Kim, a n d P. L. P r a t t : C a n a d i a n J . P h y s . 45, 1075 (1967). T . T a o k a , S. T a k e u c h i a n d E. F u r u b a y a s h i : J . P h y s . Soc. J a p a n 19, 701 (1964) A . S . A r g o n a n d S. R. Maloof: A c t a Met 14, 1445, ( 1 9 6 5 ) . D. A. Koss a n d J . C. C h e s s n u t t : T i t a n i u m S c i e n c e a n d T e c h n o l o g y , P l e n u m P r e s s _2, 1097 ( 1 9 7 3 ) .
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W. Christian and G. Taylor: Canadian J. Phys. 45, 903, (1967). Yoshida and Y. Fukuzawa: T r a n s . JIM 1__77,393 (1976). Yamaguchi, Y. Namba and K. Murakami: Acta Met. 2 j , 89 (1976). M. Yamaguchi: Scripta Metallurgica 1_!1, 909 (1977).
I00
I00
90
90
80
8O 0
l
11. =E
!
70
! ! !
¢~ 7(; or) LU nI-(/3 60
4
60 I
0
W
#
Unoxiol Compression --o-- Cyclic Compression Uniaxial Tension - - - e - - Cyclic Tension
I !
W ._1 4 0 0 if) uJ 3O
6
20
I
0
40
30
7
20
Q. 50 3~
0.05
I
]
0.10
0.15
CUMULATIVE Fig. 1
I
020 PLASTIC
]
0.25 RESOLVED
I
0.30 SHEAR
]
I
035
040
STRAIN
Resolved shear stress-resolved shear strain curves.
~Jo 1-o 0~5
Vol.
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6
CYCLIC S T R E S S - S T R A I N
BEHAVIOR
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Fig. 2
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 1.2%.
Fig. 3
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s h e a r s t r a i n of 4.2%
Fig. 4
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 20.5%
Fig. 5
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s h e a r s t r a i n of 20.5%
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 20.5%, repolishing and straining an addit i o n a l 1%.
Fig. 7
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s t e a r s t r a i n 43%, r e p o l i s h i n g a n d a n a d d i t i o n a l s t r a i n of 1%.
Fig. 6
636
CYCLIC
Fig. 8
STRESS-STRAIN
Slip b a n d s t r u c t u r e of s i n g l e c r y s t a l b o n d e d to pole p i e c e s a f t e r a n i n i t i a l half-cycle compression shear strain
BEHAVIOR
Vol.
14, No.
6
Fig. 9
Same s p e c i m e n same a r e a a s Fig. 8 p l u s a n a d d i t i o n a l t e n s i l e s h e a r s t r a i n of 0.9%. ~.¥ = 1.8%
Fig. 11
Same s p e c i m e n a n d same a r e a s a s F i g s . 8 10 of a c o m p r e s s i v e s h e a r s t r a i n ~y = 20.5%.
of O. 9%.
s
Fig. 10
Same s p e c i m e n a n d same a r e a a s F i g . 9 p l u s a n a d d i t i o n a l c o m p r e s s i o n s h e a r s t r a i n of
1.2%. ~y= 3.0%.
Vol. 14, pp. 631-636, 1980 ,Printed in the U.S.A.
UNIAXIAL TENSION AND COMPRESSION OF ~
Pergamon Press Ltd. All rights reserved
AND CYCLIC STRESS-STRAIN BEHAVIOR BRASS by
Hiroshi Yaguchi and Harold Margolin D e p a r t m e n t of P h y s i c a l a n d E n g i n e e r i n g M e t a l l u r g y Polytechnic I n s t i t u t e of New Y o r k B r o o k l y n , New Y o r k 11201 (Received March ii, 1980) (Revised Harch 28, 1980)
Evidence for different initial resolved shear stresses in compression and tension, corresponding to testing in the twinning and anti-twinning directions, have been reported for a number of bcc metals and alloys, Ta, Nb, Mo(1), Si-Fe(2), W(3) and ~ - Ti(4). The critical resolved shear stress is lower in the twinning direction than in the anti-twinning direction, and this difference has been attributed to the difference in Peierls stress for motion of the dissociated screw dislocation core in the twinning and anti-twinning directions (2). In general the strains used to study the differences in tension and compression behavior have been small. B o w e n , C h r i s t i a n a n d T a y l o r ( 5 ) c o n d u c t e d a n e x t e n s i v e s t u d y of t h e d e f o r m a t i o n of Nb single crystals and reported, f o r s t a g e I, s t r a i n h a r d e n i n g in c o m p r e s s i o n a n d , in some c a s e s , s o f t e n i n g in t e n s i o n . In s t a g e II s t r a i n h a r d e n i n g was f o u n d to b e h i g h e r in c o m p r e s sion t h a n in t e n s i o n . In some i n s t a n c e s s t r a i n h a r d e n i n g r a t e s in c o m p r e s s i o n w e r e two to t h r e e t i m e s as h i g h a s t h o s e in t e n s i o n . A t low t e m p e r a t u r e s , 77-175K, 13 - b r a s s s h o w e d d e f o r m a t i o n a l b e h a v i o r s i m i l a r to t h e m e t a l s ( 6 ) , b u t a t room t e m p e r a t u r e t h e r e is l i t t l e d i f f e r e n c e in t h e y i e l d s t r e s s b e t w e e n flow in t h e t w i n n i n g a n d a n t i - t w i n n i n g d i r e c t i o n s ( 6 ) . A t 423K y i e l d i n g in t h e t w i n n i n g d i r e c t i o n s r e q u i r e s a h i g h e r s t r e s s t h a n in t h e a n t i - t w i n n i n g d i r e c t i o n ( 7 ) .
bcc
T h e r e s u l t s p r e s e n t e d h e r e c o m p a r e u n i a x i a l flow s t r e s s in t e n s i o n a n d c o m p r e s s i o n w i t h t h e b e h a v i o r in r e v e r s e d l o a d i n g . T h e w o r k is p a r t of a s t u d y to d e t e r m i n e t h e g r a i n b o u n d a r y c o n t r i b u t i o n to t h e B a u s c h i n g e r e f f e c t in B - b r a s s b i c r y s t a l s . Experimental Procedure 13 - b r a s s s i n g l e c r y s t a l s of 4 8 . 5 w t . % Z n w e r e g r o w n b y t h e B r i d g m a n t e c h n i q u e . O n l y t h o s e p o r t i o n s of t h e c r y s t a l s w e r e u s e d w h i c h h a d y i e l d s t r e s s e s w i t h i n 2 . 1 Mpa of o n e another. F o r t h e c y c l i c l o a d i n g t e s t s t h e s i n g l e c r y s t a l was d i f f u s i o n b o n d e d to two ~ b r a s s pole p i e c e s t h r o u g h w h i c h t e n s i o n a n d c o m p r e s s i o n w e r e a p p l i e d w i t h s e l f - a l i g n i n g g r i p s . T h e d i m e n s i o n s a n d s t r a i n r a t e s a p p l i e d to e a c h c r y s t a l a r e a s follows: Tension:
£ = 6.35 mm, w = 4 . 8 3 mm, t = 0.71 mm
= 1.33 x 1 0 - 4 / s e c C o m p r e s s i o n : ~ = 1 2 . 9 rnm, w = 8 . 4 mm, t = 4 . 9 5 mm Cyclic:
= 1.65 x 10-4/sec £ = 1 2 . 7 ram, w = 4 . 0 5 ram, t = 5.1 ram = 0.77 x
lO-4/sec
T h e t e n s i o n a n d c o m p r e s s i o n t e s t s w e r e c a r r i e d o u t in a n I n s t r o n m a c h i n e , w h i l e t h e c y c l i c s t r e s s s t r a i n t e s t s w e r e c o n d u c t e d w i t h a n MTS m a c h i n e . T h e c y c l i c t e s t s w e r e b e g u n in compression. Slip line o b s e r v a t i o n s w e r e m a d e w i t h t h e u s e of a s i n g l e s t a g e r e p l i c a t e c h n i q u e . R e p l i c a t e c h n i q u e s w e r e u s e d b e c a u s e of t h e p o s s i b i l i t y t h a t r e c o v e r y w o u l d t a k e p l a c e d u r i n g u n l o a d i n g a n d r e l o a d i n g a n d to a v o i d t h e a l i g n m e n t p r o b l e m s a t t e n d a n t w i t h r e p e a t e d d i s a s s e m b l y of t h e g r i p s u s e d i n c y c l i c t e s t i n g .
631 0036-9748/80/060631-06502.00/0 Copyright (c) 1980 Pergamon Press Ltd.
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Vol.
14, No.
Results 1.
Stress-Strain
Behavior
Fig. 1 s h o w s t h e r e s u l t s o b t a i n e d f o r u n i a x i a l c o m p r e s s i o n a n d t e n s i o n . Also s h o w n , o n a cumulative shear strain basis, are the results for cyclic testing. T h e o r i e n t a t i o n of t h e s i n g l e c r y s t a l is also g i v e n . T e n s i o n a n d c o m p r e s s i o n a r e p l o t t e d in t h e same d i r e c t i o n . T h e p o i n t s o n t h e s t r e s s s t r a i n c u r v e s c o r r e s p o n d to t h e p o s i t i o n s a t w h i c h s t r a i n i n g was h a l t e d , w i t h o u t u n l o a d i n g , to t a k e r e p l i c a s . T h e cyclic c u r v e s , a p p e a r i n g as d a s h e d l i n e s , s h o w t h r e e p o i n t s . The l o w e s t p o i n t c o r r e s p o n d s to a d e v i a t i o n of 0.01% f r o m e l a s t i c b e h a v i o r . The second point c o r r e s p o n d s to t h e s t r e s s w h i c h is t h e same as t h a t o b t a i n e d b y t h e i n t e r s e c t i o n of t h e e l a s t i c p o r t i o n s w i t h t h e b a c k w a r d e x t e n s i o n of t h e i n i t i a l p o r t i o n s of t h e p l a s t i c r e g i o n . T h e t h i r d p o i n t c o r r e s p o n d s to t h e h i g h e s t s t r e s s o b t a i n e d d u r i n g l o a d i n g i n a g i v e n d i r e c tion. Replicas were taken after each half-cycle. Up to a r e s o l v e d s h e a r s t r a i n of a b o u t 2% t h e u n i a x i a l s t r e s s - s t r a i n c u r v e s f o r t e n s i o n a n d c o m p r e s s i o n c o i n c i d e . A b o v e t h i s s t r a i n t h e r e is i n c r e a s i n g d i v e r g e n c e , w i t h t h e comp r e s s i o n c u r v e s l y i n g a t t h e h i g h e r l e v e l s . B e c a u s e of t h e c h a n g e i n c r o s s s e c t i o n a l a r e a t h e t r u e s t r e s s e s will b e d i f f e r e n t f r o m t h e n o r m a l s t r e s s e s . T h e t r u e s t r e s s in c o m p r e s s i o n a t a r e s o l v e d s h e a r s t r a i n 20.5% is m a r k e d 4 a n d t h e t r u e s t r e s s i n t e n s i o n a t a r e s o l v e d s h e a r s t r a i n of a b o u t 24% is m a r k e d 5. On i n i t i a l l o a d i n g in t h e c o m p r e s s i o n h a l f - c y c l e t h e f i r s t cyclic c u r v e r e v e a l s t h a t t h e y i e l d s t r e s s is q u i t e close to t h e y i e l d s t r e s s e s o b t a i n e d f o r t h e u n i a x i a l t e s t s . However, c o m p r e s s i n g to a s t r a i n a b o v e t h a t c o r r e s p o n d i n g to t h e y i e l d s t r e s s , r e s u l t s i n m u c h h i g h e r s t r a i n h a r d e n i n g t h a n was n o t e d f o r t h e s i n g l e c r y s t a l w i t h o u t t h e pole p i e c e s . Similarly, t h e t e n s i o n h a l f - c y c l e , following t h e f i r s t c o m p r e s s i o n p r o d u c e s s t r e s s e s a b o v e t h e u n i a x i a l tension curve. H o w e v e r , in s u b s e q u e n t c y c l e s , t h e maximum c o m p r e s s i o n s t r e s s falls below t h e c o r r e s p o n d i n g u n i a x i a l s t r e s s a t t h e same s t r a i n , w h i l e t h e s t r e s s f o r t h e t e n s i o n h a l f c y c l e c o n t i n u e s a b o v e t h e s t r e s s f o r t h e c o r r e s p o n d i n g s t r a i n in t h e u n i a x i a l t e n s i o n c u r v e . T h e i n c r e a s e in s t r e s s l e v e l of t h e t e n s i o n h a l f - c y c l e is c o n s i d e r a b l y h i g h e r t h a n t h e d e c r e a s e in s t r e s s d u r i n g t h e c o m p r e s s i o n h a l f - c y c l e . If t h e c y c l e m a r k e d A, B a n d C, Fig. 1, a r e e x a m i n e d , i t c a n b e s e e n t h a t t h e s t r e s s e s in t h e B , o r t e n s i o n , c y c l e a r e close to t h e c o r r e s p o n d i n g s t r e s s e s i n t h e p r e c e d i n g comp r e s s i o n c y c l e , A. H o w e v e r , o n g o i n g to t h e s u c c e e d i n g c o m p r e s s i o n h a l f c y c l e , C, t h e r e is a d i s c o n t i n u o u s i n c r e a s e in t h e s t r e s s e s c o r r e s p o n d i n g to t h e s t r a i n s a t c o m p a r a b l e p o s i t i o n s of t h e t e n s i o n h a l f - c y c l e . C o m p a r e p o i n t s 1' a n d 1, 2' a n d 2, 3' a n d 3. 2. Slip B e h a v i o r Slip c h a r a c t e r i s t i c s i n u n i a x i a l c o m p r e s s i o n a n d t e n s i o n a r e d i s t i n c t l y d i f f e r e n t , F i g s . 2-5. B a n d i n g a n d c o a r s e slip in c o m p r e s s i o n a r e c l e a r l y e v i d e n t a t 4 . 2 4 r e s o l v e d s h e a r s t r a i n , y, in Fig. 2, w h i l e slip a p p e a r s s h a r p e r in t e n s i o n a t t h e same y, F i g . 3. I n b o t h t e n s i o n a n d c o m p r e s s i o n s i n g l e slip o n t h e {110} <111> p r i m a r y slip s y s t e m , P, w a s f o u n d . A t $ = 20.5% i n d i v i d u a l p r i m a r y slip b a n d s w e r e n o t r e a d i l y d i s t i n g u i s h a b l e i n c o m p r e s s i o n , Fig. 4. I n a d d i t i o n some e v i d e n c e of c o n j u g a t e , C J , a n d c r i t i c a l , C, slip b a n d s w e r e d i s t i n g u i s h a b l e . I n t e n s i o n a t t h e same s t r a i n , Fig. 5, i n d i v i d u a l p r i m a r y slip b a n d s w e r e r e a d i l y detectable. F i g s . 6 a n d 7 r e v e a l t h e s t r u c t u r e s o b t a i n e d a f t e r i n i t i a l c o m p r e s s i v e ¥ of 20.5% a n d t e n s i l e y of 43%, r e s p e c t i v e l y , followed b y p o l i s h i n g a n d r e s t r a i n i n g a n a d d i t i o n a l 14. Fig. 6 s h o w s c o a r s e slip i n t e r m i n g l e d w i t h c r o s s slip f o r c o m p r e s s i o n , w h i l e Fig. 7 r e v e a l s t h e f i n e s t r a i g h t slip c h a r a c t e r i s t i c of t e n s i o n . F i g s . 8-10 s h o w t h e same a r e a a f t e r c y c l i c s t r a i n s c o r r e s p o n d i n g to p e a k s t r e s s e s a t s u c c e s s i v e h a l f - c y c l e s a t p o s i t i o n 6 ( c o m p r e s s i o n ) , 7 ( t e n s i o n ) a n d 8 ( c o m p r e s s i o n ) i n Fig. 1. E x a m i n a t i o n of t h e s e f i g u r e s i n d i c a t e s t h a t t h e d i f f e r e n c e s i n slip b e h a v i o r n o t e d e a r l i e r f o r t h e u n i a x i a l t e s t s a r e n o t e v i d e n t h e r e . T h i s o c c u r s
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6
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b e c a u s e slip w h i c h h a s b e e n a c t i v a t e d , f o r e x a m p l e , in t h e c o m p r e s s i o n c y c l e , p o s i t i o n 6, Fig. 8, also o p e r a t e s in t h e s u c c e e d i n g c y c l e , p o s i t i o n 7, Fig. 9. I n a d d i t i o n , n e w slip t a k e s p l a c e in t h e t e n s i o n c y c l e . C o m p a r e t h e a r e a s m a r k e d A a n d B of Fig. 8, w h i c h s h o w l i t t l e slip w i t h t h e same a r e a s of Fig. 9, w h i c h do s h o w n e w s l i p . I n Fig. 10, c o r r e s p o n d i n g to t h e n e x t c y c l e , n e w slip a p p e a r s a l s o . A r e a A r e v e a l s more slip a n d a r e a B h a s b e c o m e s m a l l e r b e c a u s e of s l i p a t t h e l o w e r b o u n d a r y of a r e a B m o v i n g i n t o a r e a B. Note c r o s s slip in a r e a D, Fig. 10. With i n c r e a s e d c u m u l a t i v e s h e a r s t r a i n , X,/, t h e l a c k of d i s t i n c t i o n b e t w e e n slip in t e n s i o n a n d c o m p r e s s i o n c o n t i n u e s u p to Ey = 37.5%, t h e limit u s e d h e r e . The slip b a n d a p p e a r a n c e a f t e r a c u m u l a t i v e cyclic s h e a r s t r a i n of 21% is s h o w n in Fig. 11, w h i c h s h o u l d b e c o m p a r e d w i t h F i g s . 4 a n d 5. Slip b a n d s of Fig. 11 a r e q u i t e c o a r s e a n d more n e a r l y like t h e slip h a n d s of Fig. 5 t h a n Fig. 4. Discussion Slip in c o m p r e s s i o n o n {110} <111> f o r t h e o r i e n t a t i o n s h o w n in Fig. 1 c a n b e c o n s i d e r e d to b e in t h e t w i n n i n g d i r e c t i o n a n d slip in t e n s i o n o n t h e same slip s y s t e m to b e in the chit-twinning direction. T h e d a t a of Fig. 1 s h o w t h a t flow in t h e t w i n n i n g d i r e c t i o n r e q u i r e s a h i g h e r s t r e s s t h a n flow in t h e a n t i - t w i n n i n g d i r e c t i o n . Thus the transition from n o r m a l b e h a v i o r r e c o r d e d p r e v i o u s l y a t 4 2 3 K ( 7 ) n o w a p p e a r s to o c c u r a t room t e m p e r a t u r e . I n t h e e a r l i e r w o r k t h e d i f f e r e n c e b e t w e e n t e n s i o n a n d c o m p r e s s i o n was e v i d e n t a t t h e y i e l d s t r e s s , w h i l e in Fig. 1 t h e d i f f e r e n c e d e v e l o p e o n l y a f t e r a s h e a r s t r a i n of a b o u t 2%. As F i g s . 6 a n d 7 i l l u s t r a t e w a v y slip is m u c h more p r e d o m i n a n t w h e n s t r e s s i n g in t h e t w i n n i n g ( c o m p r e s s i o n ) t h a n in t h e a n t i - t w i n n i n g ( t e n s i o n ) d i r e c t i o n . U m a k o s h i a n d Yamag u c h i ( 8 ) h a v e s h o w n t h a t t h e r e is a t e n d e n c y f o r c r o s s slip f r e q u e n c y _ t o i n c r e a s e f o r o r i e n t a t i o n s w h o s e s t r e s s a x e s , p r o j e c t e d o n t o t h e ( 1 1 1 ) p l a n e , a p p r o a c h [211] o n t h e " t w i n n i n g " s i d e of t h e [ i 0 1 ] - [211] r e g i o n of t h e ( 1 1 1 ) p l a n e a n d a d e c r e a s e d f r e q u e n c y as t h e s t r e s s a x e s m o v e s a w a y f r o m [211] . If t h i s b e h a v i o r c a n b e a p p l i e d to w a v y slip in g e n e r a l , t h e n o n e w o u l d e x p e c t m u c h l e s s w a v y slip in t h e a n t i - t w i n n i n g t e n s i o n s t r a i n i n g , a s o b s e r v e d . T h e i n c r e a s e d s t r a i n h a r d e n i n g n o t e d in t h e i n i t i a l c o m p r e s s i o n h a l f - c y c l e , p o s i t i o n 6 in Fig. 1, is p r o b a b l y r e l a t e d to t h e c o n s t r a i n t s i m p o s e d b y t h e b o n d e d g r i p s . Similar b e h a v i o r was also o b s e r v e d in b i c r y s t a l s b u t t h e m a g n i t u d e was s m a l l e r , p r e s u m a b l y b e c a u s e of t h e p r e s e n c e of t h e b i c r y s t a l b o u n d a r y . The difference between the uniaxial tension and compression single crystal stress-strain c u r v e s m u s t b e a c c e p t e d as a n i n t r i n s i c d i f f e r e n c e , because the cyclic behavior shows similar behavior. T h i s is e v i d e n t f r o m Fig. 1, w h e r e it c a n b e s e e n t h e l o c u s of t h e p e a k s t r e s s e s in t e n s i o n lie b e l o w t h e c o r r e s p o n d i n g l o c u s in compression. I t s h o u l d b e n o t e d t h a t t h e l o c u s of t h e t e n s i l e p e a k s t r e s s e s is m u c h c l o s e r to t h e c o m p r e s s i o n u n i a x i a l c u r v e t h a n to t h e t e n s i o n c u r v e . I t s e e m s e v i d e n t t h a t p r i o r slip in c o m p r e s s i o n m a r k e d l y r a i s e s t h e s t r e s s r e q u i r e d f o r flow a t c o r r e s p o n d i n g s t r a i n s in t h e s u c c e e d i n g t e n s i o n c y c l e , w i t h o u t r a i s i n g t h e s e s t r e s s e s a b o v e t h o s e in c o m p r e s s i o n . T h e d i s c o n t i n u o u s i n c r e a s e s in s t r e s s f o r c o r r e s p o n d i n g s t r a i n s in t h e f o l l o w i n g c o m p r e s s i o n c y c l e n e v e r r e a c h t h e v a l u e of t h e u n i a x i a l c u r v e a f t e r t h e t h i r d cycle. T h u s p r i o r c y c l i n g in t e n s i o n limits t h e s t r a i n h a r d e n i n g in c o m p r e s s i o n . T h e r e is no TEM d a t a a v a i l a b l e a t t h i s p o i n t to p e r m i t a n e x p l a n a t i o n b a s e d o n o b s e r v a t i o n . ACKNOWLEDGMENT T h e a u t h o r s w i s h to e x p r e s s t h e i r a p p r e c i a t i o n to t h e N a t i o n a l S c i e n c e F o u n d a t i o n w h i c h h a s s u p p o r t e d t h i s w o r k on G r a n t #DMR-7704118. REFERENCES 1. 2. 3. 4.
P. J . S h e r w o d , F. G u i u , H. C. Kim, a n d P. L. P r a t t : C a n a d i a n J . P h y s . 45, 1075 (1967). T . T a o k a , S. T a k e u c h i a n d E. F u r u b a y a s h i : J . P h y s . Soc. J a p a n 19, 701 (1964) A . S . A r g o n a n d S. R. Maloof: A c t a Met 14, 1445, ( 1 9 6 5 ) . D. A. Koss a n d J . C. C h e s s n u t t : T i t a n i u m S c i e n c e a n d T e c h n o l o g y , P l e n u m P r e s s _2, 1097 ( 1 9 7 3 ) .
634
CYCLIC
5. 6. 7. 8.
D . K . Bowen, J. T. Yamagata, H. Y. Umakoshi, M. Y. Umakoshi and
STRESS-STRAIN
BEHAVIOR
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14,
No.
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W. Christian and G. Taylor: Canadian J. Phys. 45, 903, (1967). Yoshida and Y. Fukuzawa: T r a n s . JIM 1__77,393 (1976). Yamaguchi, Y. Namba and K. Murakami: Acta Met. 2 j , 89 (1976). M. Yamaguchi: Scripta Metallurgica 1_!1, 909 (1977).
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6
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0.30 SHEAR
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040
STRAIN
Resolved shear stress-resolved shear strain curves.
~Jo 1-o 0~5
Vol.
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6
CYCLIC S T R E S S - S T R A I N
BEHAVIOR
635
Fig. 2
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 1.2%.
Fig. 3
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s h e a r s t r a i n of 4.2%
Fig. 4
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 20.5%
Fig. 5
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s h e a r s t r a i n of 20.5%
Slip b a n d s t r u c t u r e a f t e r a c o m p r e s s i v e s h e a r s t r a i n of 20.5%, repolishing and straining an addit i o n a l 1%.
Fig. 7
Slip b a n d s t r u c t u r e a f t e r a t e n s i l e s t e a r s t r a i n 43%, r e p o l i s h i n g a n d a n a d d i t i o n a l s t r a i n of 1%.
Fig. 6
636
CYCLIC
Fig. 8
STRESS-STRAIN
Slip b a n d s t r u c t u r e of s i n g l e c r y s t a l b o n d e d to pole p i e c e s a f t e r a n i n i t i a l half-cycle compression shear strain
BEHAVIOR
Vol.
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6
Fig. 9
Same s p e c i m e n same a r e a a s Fig. 8 p l u s a n a d d i t i o n a l t e n s i l e s h e a r s t r a i n of 0.9%. ~.¥ = 1.8%
Fig. 11
Same s p e c i m e n a n d same a r e a s a s F i g s . 8 10 of a c o m p r e s s i v e s h e a r s t r a i n ~y = 20.5%.
of O. 9%.
s
Fig. 10
Same s p e c i m e n a n d same a r e a a s F i g . 9 p l u s a n a d d i t i o n a l c o m p r e s s i o n s h e a r s t r a i n of
1.2%. ~y= 3.0%.