UBC Theses and Dissertations

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UBC Theses and Dissertations

Superplasticity in the zinc-1 per cent aluminum system Turner, David Malcolm 1971

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SUPERPLASTICITY IN THE ZINCTI PERCENT ALUMINUM SYSTEM by DAVID MALCOLM TURNER B . A . S c . U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f METALLURGY We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA December, 1971. In present ing th i s thes i s in p a r t i a l f u l f i l m e n t o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extens ive copying o f th i s thes i s for s cho la r l y purposes may be granted by the Head of my Department or by h i s representat ives . It i s understood that copying or pub l i c a t i on o f th i s thes i s fo r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of Metal lurgy The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date F e b r u a r y 22, 1972 i i ABSTRACT A Zn - 1 wt % A l a l l o y has been s t u d i e d i n an a t tempt to r e -l a t e t e n s i l e d a t a and m e t a l l o g r a p h i c o b s e r v a t i o n s to assumed modes o f s u p e r p l a s t i c d e f o r m a t i o n . T e n s i l e t e s t i n g , was c a r r i e d out a t a c o n -s t a n t c r o s s h e a d speed to d e t e r m i n e the s t r e s s v e r s u s s t r a i n r a t e r e -l a t i o n s h i p s as a f u n c t i o n o f g r a i n s i z e and t e m p e r a t u r e . F u r t h e r a n a l y s i s i n c l u d e d a c t i v a t i o n energy d e t e r m i n a t i o n s , low t e m p e r a t u r e ( - 1 0 0 ° C ) d e f o r m a t i o n b e h a v i o r , d e f o r m a t i o n g r a i n g rowth c h a r a c t e r i s t i c s , , and s u r f a c e and i n t e r n a l m e t a l l o g r a p h y . S t a ge IT d e f o r m a t i o n was c o n s i s t e n t w i t h a p r o c e s s comb in ing boundary s l i d i n g and m i g r a t i o n and boundary d i f f u s i o n . D e f o r m a t i o n i n s t a g e I was c h a r a c t e r i z e d by a low s t r a i n r a t e s e n s i t i v i t y and a v a r i a b l e a c t i v a t i o n ene r gy . Normal s l i p p r o c e s s e s were o p e r a t i v e durxng s t a g e I I I d e f o r m a t i o n . D e f o r m a t i o n g r a i n g rowth and a n i s o t r o p i c g r a i n shape changes were p ronounced and v a r i a b l e i n s t a g e s I and I I . i i i ACKNOWLEDGEMENTS The a u t h o r i s g r a t e f u l f o r and D r . T . A l d e n . S p e c i a l thanks go i n t he b e g i n n i n g and may now w i t n e s s a d v i c e g i v e n by D r . N. R i s e b r o u g h to N. Wa lker who was i n s t r u m e n t a l t h e end - thanks to F . A l p e n . X V TABLE OF CONTENTS Page 1. INTRODUCTION . . 1 2. EXPERIMENTAL . . 7 2 .1 . M a t e r i a l P r e p a r a t i o n 7 2 .2 . Spec imen P r e p a r a t i o n 8 2 .3. T e n s i l e T e s t i n g P r o c e d u r e s 8 2.4. M e t a l l o g r a p h y 10 2 .5 . G r a i n S i z e . . . . 11 3. RESULTS 14 3 .1 . M i c r o s t r u c t u r e 14 3 . 1 . 1 . Homogenei ty o f E x t r u s i o n s - R e p r o d u c i b i l i t y . . . . 14 3 . 1 . 2 . As E x t r u d e d M a t e r i a l 14 3 . 1 . 3 . A n n e a l e d M a t e r i a l 14 3.2. T e n s i l e C h a r a c t e r i s t i c s 24 3 . 2 . 1 . S t r e s s - S t r a i n Ra te R e l a t i o n s h i p s 24 3 . 2 . 2 . G r a i n S i z e E f f e c t 24 3 . 2 . 3 . Tempera tu re E f f e c t 27 3 . 2 . 3 . 1 . G e n e r a l . . 2 ? 3 . 2 . 3 . 2 . A c t i v a t i o n Energy . . 27 V Page 3 .3 . H a l l - P e t c h A n a l y s i s 3 0 3 . 3 . 1 . G e n e r a l 3 0 3 . 3 . 2 . H a l l - P e t c h A n a l y s i s o f Z n - l A l 3 2 3 . 3 . 2 . 1 . T / T = 0.25 3 2 m 35 3 . 3 . 2 . 2 . T / T = 0.42 m 3.4. T r u e S t r e s s - S t r a i n Cu rve and Creep B e h a v i o r 37 3 . 4 . 1 . G e n e r a l 37 3 . 4 . 2 . S t r a i n Rate Dependence o f T r u e S t r e s s - S t r a i n Curves 38 3 . 4 . 3 . T r u e S t r e s s - S t r a i n Curves as a F u n c t i o n o f G r a i n S i z e 38 3 .4 .4 . T r u e S t r e s s - S t r a i n Curves - V a r i a b l e G r a i n S i z e and T e s t Tempera tu re 43 3 . 4 . 5 . Creep B e h a v i o r f o r S tage I and I I D e f o r m a t i o n . . 43 3 .5 . M e t a l l o g r a p h i c O b s e r v a t i o n s o f D e f o r m a t i o n B e h a v i o r and G r a i n Growth 45 3 . 5 . 1 . G e n e r a l 45 3 . 5 . 2 . D e f o r m a t i o n Modes , 45 3 . 5 . 2 . 1 . G r a i n Boundary S l i d i n g 45 3 . 5 . 2 . 2 . D e f o r m a t i o n by S l i p 46 3 . 5 . 2 . 3 . F u r t h e r Boundary O b s e r v a t i o n s 47 3 . 5 . 3 . D e f o r m a t i o n A s s i s t e d G r a i n Growth 47 3 . 5 . 3 . 1 . G e n e r a l 47 3 . 5 . 3 . 2 . D e f o r m a t i o n G r a i n Growth i n Z n - l A l . . . . 53 v i Page 4. DISCUSSION 72 4 . 1 . O v e r a l l 72 4 . 2 . S tage I I I D e f o r m a t i o n 72 4 . 3 . S tages I and I I D e f o r m a t i o n 73 4 . 4 . E m p h i r i c a l R e l a t i o n s h i p s 76 5. CONCLUSIONS 79 v i i L IST OF FIGURES F i g u r e No. Page 2.1 Phase D iagram o f A l u m i n u m - z i n c Sys tem 7 3.1 M i c r o s t r u c t u r e o f E x t r u d e d Z n - l A l . x 4600 . . . . 15 3.2 T h i n F o i l M i c r o s t r u c t u r e o f E x t r u d e d Z n - l A l . x 30500 16 3 .3 . M i c r o s t r u c t u r e o f A n n e a l e d Z n - l A l . x 3600 . . . 17 3.4 T h i n F o i l M i c r o s t r u c t u r e s o f A n n e a l e d Z n - l A l . x 37000 18 3.5 The G r a i n S i z e E f f e c t on the S t r e s s - S t r a i n Ra te R e l a t i o n s h i p o f E x t r u d e d and A n n e a l e d Z n - l A l . . . 19 3.6 The S t r a i n Rate S e n s i t i v i t y , m, o f E x t r u d e d and A n n e a l e d Z n - l A l 20 3.7 The S t r e s s - S t r a i n Ra te R e l a t i o n s h i p f o r Z n - 0 . 2 A l and Z n - l A l . 21 3.8 The Tempera tu re E f f e c t on the S t r e s s - S t r a i n Rate R e l a t i o n s h i p o f E x t r u d e d M a t e r i a l . 22 3.9 The S t r a i n Rate S e n s i t i v i t y as a F u n c t i o n o f T e m p e r a t u r e . ^3 3.10 A c t i v i a t i o n E n e r g y , AH^, f o r s t a g e I and I I 29 D e f o r m a t i o n o f Z n - l A l . 3.11 H a l l - P e t c h R e l a t i o n s h i p f o r Z n - l A l 33 3.12 H a l l - P e t c h s c h e m a t i c f o r Z n - l A l 34 3.13 D e f o r m a t i o n m i c r o s t r u c t u r e s f o l l o w i n g S t r a i n i n g a t - 1 0 0 ° C . a) x 12400, b) x 6308 . . 36 v i i i F i g u r e No. Page 3.14 M-Curves 39 3.15 T r u e S t r e s s V e r s u s S t r a i n a t V a r i o u s S t r a i n -Ra tes f o r L Q = 1.6 m i c r o n s ^ 3.16 T r u e S t r e s s V e r s u s S t r a i n as a F u n c t i o n o f G r a i n S i z e f o r t = 0.01 m i n . 41 3.17 T r u e S t r e s s V e r s u s S t r a i n as a F u n c t i o n o f G r a i n S i z e and Tempera tu re 42 3.18 Creep Cu rve s f o r Z n - l A l . 44 3.19 S u r f a c e M i c r o s t r u c t u r e showing G r a i n Boundary S l i d i n g , G r a i n R o t a t i o n , and Coa r se S l i p . a) x 25400, b) x 4900 48 3.20 I n t e r n a l M i c r o s t r u c t u r e o f Z n - l A l . x 20,000 . . . . 49 3.21 I n t e r n a l M i c r o s t r u c t u r e F o l l o w i n g S tage I I I D e f o r m a t i o n x 20 ,000 . 50 3.22 S u r f a c e M i c r o s t r u c t u r e Showing Boundary S h e a r i n g A) and p e e l i n g B) x 11000 51 3.23 S u r f a c e M i c r o s t r u c t u r e Showing G r a i n Boundary M i g r a t i o n a t (A) x 5600 52 3.24 The G r a i n S i z e , at V a r i o u s S t r a i n R a t e s , F o l l o w i n g 140 P e r Cent S t r a i n . 59 3.25 The G r a i n S i z e L e n g t h 1 Wid th R a t i o , at V a r i o u s S t r a i n - R a t e s , F o l l o w i n g 140 P e r Cent S t r a i n . . . . . 60 3.26 I n t e r n a l M i c r o s t r u c t u r e F o l l o w i n g 600 P e r Cent S t r a i n , x 3800. 61 3.27 S u r f a c e M i c r o s t r u c t u r e s F o l l o w i n g 140 P e r Cent S t r a i n x 3100 6 2 F i g u r e No. P a g e 3.28 I n t e r n a l M i c r o s t r u c t u r e s C o r r e s p o n d i n g t o F i g u r e 3 .27 . x 14000. 64 3.29 The R e l a t i v e G r a i n S i z e Enhancement a t V a r i o u s S t r a i n R a t e s . 66 3.30 The R e l a t i o n G r a i n S i z e Enhancement a t V a r i o u s S t r a i n Rates f o r S n - I B i and Z n - l A l 67 3.31 The R e l a t i v e G r a i n S i z e Enhancement as a F u n c t i o n o f T r u e S t r a i n . . . 68 3.32 The G r a i n S i z e Ver su s T e n s i l e T e s t T ime o f S n - I B i and Z n - l A l . . 69 3.33 The Change i n G r a i n S i z e V e r s u s T e n s i l e T e s t T ime f o r a N i - F e - C r A l l o y and Z n - l A l 70 3.34 The average G r a i n Growth Rate f o r Z n - l A l a t a S t r a i n o f 140 P e r C e n t . 71 4.1 The 0.2 P e r Cent F low S t r e s s V e r s u s G r a i n S i z e . •• 77 4.2 The G r a i n S i z e Ve r su s S t r a i n Rate R e l a t i o n s h i p f o r S tage I I a t a S t r e s s L e v e l o f 8000 p s i . 77 L IST OF TABLES T a b l e No. Page 2 . 1 . D e t a i l s o f Spec imen P r e p a r a t i o n 1 3 3.1 . H a l l - P e t c h and R e l a t e d Da ta 31 3.2. H a l l - P e t c h C o n s t a n t s a t - 100 °C 32 3.3. D e f o r m a t i o n A s s i s t e d G r a i n Growth 54 1 1. INTRODUCTION I n q u i r i e s i n t o the phenomenon o f s u p e r p l a s t i c i t y w i t h a t t e m p t s to q u a l i t a t i v e l y and q u a n t i t a t i v e l y d e s c r i b e a l l a s p e c t s o f s u p e r p l a s t i c (1 2) (3) d e f o r m a t i o n a r e w e l l documented ' . P e a r s o n , l o n g b e f o r e t h e term s u p e r p l a s t i c i t y e n t e r e d the l i t e r a t u r e , o b s e r v e d m e c h a n i c a l d e f o r m a t i o n i n S n - B i a l l o y s w h i c h r e s u l t e d i n e l o n g a t i o n s o f 2000 p e r c e n t . Examples o f systems i n w h i c h e x t e n s i v e d u c t i l i t y has s i n c e been o b s e r v e d i n c l u d e p u r e m e t a l s ^ \ e u t e c t i c and e u t e c t o i d b i n a r y a l l o y s ^ \ and c o n -c e n t r a t e d and d i l u t e b i n a r y and t e r n a r y a l l o y s . The above ment i oned pu re m e t a l s and a l l o y s w i l l de fo rm s u p e r -p l a s t i c a l l y o n l y under c e r t a i n c o n d i t i o n s : a) a h i g h homologous t e m p e r a t u r e , T > 0 . 4 , n b ) r e l a t i v e l y low s t r a i n r a t e s , c ) a f i n e , s t a b i l i z e d m i c r o s t r u c t u r e , d) a h i g h s t r a i n r a t e s e n s i t i v i t y , m, o f the f l o w s t r e s s . A l l m e t a l s , depend ing on t h e i r m i c r o s t r u c t u r e and t h e e x t e r n -a l l y imposed d e f o r m a t i o n c o n d i t i o n s , w i l l have d i f f e r e n t s t r e s s - s t r a i n r a t e r e l a t i o n s h i p s . F o r s u p e r p l a s t i c m a t e r i a l s a r e l a t i o n s h i p r e l a t i n g , , . . . i , ( 2 ,15 -17 ) s t r e s s to s t r a i n r a t e xs g i v e n by : a = k e m (1 .1) where a = f l o w s t r e s s e = s t r a i n r a t e . . . , . d l o g a v m = a p p a r e n t s t r a i n r a t e s e n s i t i v i t y ( i . e . - ^ — z — 2 2 — r ) . d l o g e k = a c o n s t a n t 2 The s i g n i f i c a n c e o f m i n the phenomenal n e c k i n g r e s i s t a n c e o f (2) s u p e r p l a s t i c m e t a l s may be d e m o n s t r a t e d as f o l l o w s : E q u a t i o n (1.1) may be w r i t t e n a s ; a = k im = | (1 .2 ) where P i s the f o r c e t r a n s m i t t e d t h r o u g h t h e c r o s s - s e c t i o n o f area, A . A l s o , the s t r a i n r a t e i s g i v e n a s : L dt A dt U , J ; by r e q u i r i n g the c o n s t a n c y o f vo lume r e l a t i o n s h i p , V = A . L . I n s e r t i n g (1.3) i n t o (1 .2 ) and r e - a r r a n g i n g g i v e s : A m E q u a t i o n (1.4)shows t h a t as m i n c r e a s e s t h e r a t e o f change o f a r e a w i t h t ime becomes l e s s a f f e c t e d by the p r e v a i l i n g a r e a , t h e l i m i t i n g ca se o c c u r r i n g when m = 1, a t wh i ch t i m e , - d A . / ^ i s i n d e p e n d e n t o f a r e a . T h i s means t h a t i n a necked r e g i o n , due to the h i g h h a r d e n i n g r a t e o r s i m i l a r l y the s t r o n g dependence o f f l o w s t r e s s on s t r a i n r a t e , t he a p p a r e n t h a r d e n i n g w i l l cause f u r t h e r d e f o r m a t i o n to o c c u r i n unnecked ' s o f t e r ' r e g i o n s o f the m a t e r i a l . C o n v e n t i o n a l d e f o r m a t i o n o f m e t a l s i s c a r r i e d out w i t h m i n the r e g i o n 0.02 to 0.2 a t t e m p e r a t u r e s , T / T , up to 0 . 9 . F o r s u p e r p l a s t i c d e --m f o r m a t i o n to o c c u r T / T * 0.4 w i t h 0.3 < m $ 1.0. To o b t a i n the c h a r a c t e r i s t i c m 3 s t a g e , S - shaped , s t r e s s - s t r a i n r a t e c u r v e a r e g i o n o f h i g h m must o c c u r i n a c o n v e n i e n t s t r a i n r a t e r a n g e . In g e n e r a l , i n c r e a s i n g the t e m p e r a t u r e a n d / o r d e c r e a s i n g the g r a i n s i z e s h i f t s t he r e g i o n o f h i g h * U4 u * • ( 5 - 7 , 9 , 1 3 , 1 7 , 1 8 ) m to h i g h e r s t r a i n r a t e s ' ' ' ' M i c r o s t r u c t u r a l l y a- f i n e g r a i n s i z e may be o b t a i n e d by t h e (19) a p p r o p r i a t e p r o c e s s i n g o f m e t a l s . In two phase a l l o y s a f i n e m i c r o -s t r u c t u r e may be r e a l i z e d t h r o u g h s o l i d s t a t e t r a n s f o r m a t i o n s d u r i n g ho t and c o l d w o r k i n g . The m e t a l l i c phases may o c c u r i n n e a r l y e q u a l p r o p o r t i o n s , o r as i n t h e c a s e o f d i l u t e a l l o y s , t h e s o l u t e i s i n t he form o f a f i n e d i s p e r s o i d o r i n s o l i d s o l u t i o n . Much e x p e r i m e n t a t i o n has t a k e n p l a c e i n a t t e m p t s t o f u l l y document the p h e n o m e n l o g i c a l a s p e c t s o f s u p e r p l a s t i c i t y . V a r i o u s mechanisms have been sugge s ted w h i c h u s u a l l y i n v o l v e one o r more o f t h e f o l l o w i n g p r o c e s s e s : a) D i f f u s i o n a l P r o c e s s e s I n c l u d e d h e r e a r e N a b a r r o - H e r r i n g (N-H) d i f f u s i o n a l c r e e p (21) i n v o l v i n g l a t t i c e s e l f d i f f u s i o n and the C o b l e v a r i e n t i n v o l v i n g g r a i n (18) boundary d i f f u s i o n . A v e r y and B a c k o f e n s u g g e s t e d t h a t N-H d i f f u s i o n a l c reep was r e s p o n s i b l e f o r t he h i g h s t r a i n r a t e s e n s i t i v i t y o f Pb -Sn s u p e r -p l a s t i c a l l o y s . The C o b l e v a r i e n t was a p p l i e d to t h e i r work by J o n e s and (22) Johnson t o ' - g i v e a more s a t i s f a c t o r y c o r r e l a t i o n between d i f f u s i o n d a t a and e x p e r i m e n t a l r e s u l t s . b ) G r a i n Boundary M o t i o n G r a i n boundary s l i d i n g ( s h e a r i n g ) and boundary m i g r a t i o n were (9) (23) s ugge s ted by H o l t and H o l t and B a c k o f e n as o p e r a t i v e mechanisms i n the s u p e r p l a s t i c d e f o r m a t i o n o f Z n - A l e u t e c t o i d and A l - 3 3 C u e u t e c t i c a l l o y s . A l d e n and A l d e n and C l i n e ^ a l s o a s s o c i a t e d t h e h i g h s t r a i n r a t e s e n s i t i v i t y o f S n - B i and Sn-Pb a l l o y s w i t h g r a i n boundary s l i d i n g . P a r k e r and S h e r b y ^ ^ m o d i f i e d the e x p r e s s i o n o b t a i n e d by A v e r y and (18) B a c k o f e n to d e s c r i b e q u a n t i t a t i v e l y t h e b e h a v i o r o f a Pb - Sn e u t e c t i c a l l o y , and sugges ted t h a t boundary m i g r a t i o n o r r e c r y s t a l l i z a t i o n and n o t N-H d i f f u s i o n a l c r e e p was c o n t r i b u t i n g to s u p e r p l a s t i c i t y . (14) L e e and B a c k o f e n sugge s ted t h a t v i s c o u s boundary s h e a r i n g was t h e r a t e c o n t r o l l i n g p r o c e s s i n T i - a l l o y s . c ) D i s l o c a t i o n M o t i o n D i s l o c a t i o n d e n s i t i e s r e m a i n v e r y low d u r i n g s u p e r p l a s t i c d e -f o r m a t i o n (16,25)^ Mechanisms i n v o l v i n g d i s l o c a t i o n m o t i o n sugges t t h a t d i s l o c a t i o n s by c l i m b and g l i d e , a r e a b l e to r e a c h g r a i n b o u n d a r i e s and be a n n i l i l a t e d . . A r a t e c o n t r o l l i n g d i s l o c a t i o n c l i m b mechanism i s p r o -posed f o r N i - C r - F e a l l o y s and the Z n - A l e u t e c t o i d . A l d e n p r o -(26^ posed a c l i m b - g l i d e d i s l o c a t i o n mechanism f o r Pb-5Cd a l l o y s . Cook o b s e r v e d s u r f a c e s l i p f o l l o w i n g s t a g e I I d e f o r m a t i o n i n Z n - 0 « 2 A 1 . These mechanisms, i n d e p e n d e n t l y o r i n c o m b i n a t i o n , have p r o -v i d e d a b a s i c framework f o r the u n d e r s t a n d i n g o f s u p e r p l a s t i c c r e e p b e h a v i o r . S tage I and I I I o f t h e s t r e s s - s t r a i n r a t e c u r v e have n o t r e c e i v e d t h e same a t t e n t i o n as s t a g e I I . A r a t e c o n t r o l l i n g mode l i n -v o l v i n g t h e " v i s c o u s g l i d e " o f d i s l o c a t i o n s w i t h i n t h e b u l k has been p r o -(27) posed by A l d e n t o e x p l a i n the low s t r a i n r a t e s e n s i t i v i t y i n s t a g e I. The d i s l o c a t i o n mechanisms o f s t a g e I I I a r e assumed to be t h o s e w h i c h a r e o p e r a t i v e i n no rma l c r e e p . A f u r t h e r phenomena w h i c h must be ment i oned i s t h a t i n many 5 s u p e r p l a s t i c a l l o y s an e q u i a x e d s t r u c t u r e has been o b s e r v e d to p r e s i s t a f t e r e x t e n s i v e e l o n g a t i o n s ( 6 > 1 6 , 2 4 , 2 8 ) ^ G r a i n growth and second phase u T u A , ( 10 ,13 ) _ , . (16,29) c o a r s e n i n g have a l s o been r e c o r d e d ' . Brophy e t a l ' made a d e t a i l e d s tudy o f d e f o r m a t i o n a s s i s t e d g r a i n g rowth i n N i - F e - C r a l l o y s . (30) (13) Cook s t u d i e d g r a i n growth as a f u n c t i o n o f s t r a i n i n Zn -0 .2A1 . C l a r k s t u d i e d d e f o r m a t i o n enhanced g r a i n g rowth i n a s u p e r p l a s t i c S n - I B i a l l o y E m p h i r i c a l r e l a t i o n s h i p s have been d e v e l o p e d w h i c h r e l a t e the s t r a i n r a t e , e, to the f l o w s t r e s s , a, g r a i n s i z e , L , and t e m p e r a t u r e , (12 25) T ' . R e l a t i o n s h i p (1.5) i s d e s c r i p t i v e : E - k — exp ( ~ A H / k T ) (1 .5 ) By k e e p i n g c o n s t a n t 2 o f t he 3 v a r i a b l e s i, L , and T the f o l l o w i n g e x p r e s s i o n s may be o b t a i n e d : r ( g j = A exp ( A H / k T ) (1 .6 ) a ( . > T ) = B L n (1 .7) ° ( T , L ) = C " ( 1 ' 8 ) E x p r e s s i o n s ( 1 . 6 ) , (1 .7 ) and (1.8) may be combined to g i v e em-p h i r i c a l r e l a t i o n s h i p s such as ( 1 . 5 ) . V a r i o u s t h e o r e t i c a l mode l s have C25 31) been sugge s ted wh i ch may be compared w i t h such e m p h i r i c a l r e l a t i o n s h i p s ' This work is an extension in many respects of an earlier study (13) by Cook . The system Zn-lAl was chosen because of the existence in this system at +23°C of a relatively stable grain structure and the development of extensive stage I stress-strain rate behavior. Objectives included: 1. A detailed study of stage T£. 2. Studies of grain shape changes during deformation in a l l 3 stages. 3. An activation energy analysis of stages I and II 4. Studies of Hall-Petch behavior. 5. A study of the parameters a, b, and m in expressions 1.5 and 1.8. 7 2. EXPERIMENTAL 2 . 1 . M a t e r i a l P r e p a r a t i o n S t a r t i n g m a t e r i a l s were z i n c and aluminum o f p u r i t y 99.999 p e r c e n t and 99.98 p e r c e n t r e s p e c t i v e l y . The z i n c - a l u m i n u m phase d i ag ram i s shown i n F i g u r e 2 . 1 . "F 1200 I00O 800 600 400 "Al 10 2 0 3 0 4 0 5 0 60 70 8 0 90 Zn Weight Percentage Zinc F i g u r e 2 .1 . Phase d i ag ram o f A l - Z n s y s t e m . (Me ta l s Handbook - 1948) M e l t i n g was c a r r i e d out i n a c r u c i b l e a t 7 0 0 ° C , t he m e l t b e i n g h e l d a t t h i s t e m p e r a t u r e f o r 15 m inu te s p r i o r to c h i l l c a s t i n g i n a copper mo ld to g i v e b i l l e t s o f app rox ima te d i m e n s i o n s 0.9 i n c h e s d i a m e t e r by 4 i n c h e s i n l e n g t h . C h e m i c a l a n a l y s i s showed t h a t t he aluminum c o n t e n t was 0 .91%. P r i o r to e x t r u s i o n , b i l l e t s were homogenized a t 360°C f o r 115 h o u r s f o l l o w e d by a w a t e r quench . The f i n e l y d i s p e r s e d d i s t r i b u t i o n o f aluminum r i c h p r e c i p i t a t e r e s u l t i n g f rom t h i s t r e a t m e n t 8 was n e c e s s a r y as a s i m i l a r d i s p e r s i o n was r e q u i r e d i n t h e f i n a l e x -t r u d e d r o d . The b i l l e t f o r e x t r u s i o n #1 was f u r t h e r t r e a t e d a t 200°C f o r 2 h o u r s f o l l o w e d by a i r c o o l i n g i n o r d e r to s t a b i l i z e the p r e c i p i t a t e d u r i n g subsequent g r a i n growth a n n e a l s . The r e m a i n i n g b i l l e t s d i d n o t r e c e i v e t h i s t r e a t m e n t . A l l b i l l e t s were mach ined to remove t h e s u r f a c e o x i d e l a y e r p r i o r t o e x t r u s i o n . E x t r u s i o n a t a r a t i o o f 25:1 was c a r r i e d out u s i n g Carbowax 1500 as a l u b r i c a n t . The t e m p e r a t u r e was kep t a t a p p r o x i m a t e l y 60°C d u r i n g e x t r u s i o n a t a p r e s s u r e o f 160,000 p s i . As t he r o d e x t r u d e d i t was c u t i n t o 12 i n c h s e c t i o n s , l a b e l l e d , and s t o r e d i m m e d i a t e l y i n l i q u i d n i t r o g e n . The i n i t i a l and f i n a l 6 i n c h e s o f each e x t r u s i o n were d i s c a r d e d . 2 .2. Spec imen P r e p a r a t i o n T e n s i l e spec imens were p r e p a r e d a f t e r a method employed by (13) Cook . T h i s p r o c e d u r e i n v o l v e d the c o l d m a c h i n i n g o f spec imens on a j e w e l e r ' s l a t h e to d i m e n s i o n s 0.100 ± 0.001 i n c h e s d i a m e t e r w i t h a 1 o r 1/2 i n c h gauge l e n g t h . Mach ined spec imens were h e l d i n l i q u i d n i t r o g e n p r i o r t o f u r t h e r t h e r m a l t r ea tmen t a n d / o r t e n s i l e t e s t i n g . To v a r y the g r a i n s i z e o f a s - e x t r u d e d ( A . E . ) mach ined spec imens t h e r m a l t r e a t m e n t s were employed as shown i n T a b l e 2 . 1 . 2 .3 . T e n s i l e T e s t i n g P r o c e d u r e s T e n s i l e t e s t i n g was c a r r i e d out u s i n g a f l o o r mode l I n s t r o n . An i n t r i n s i c f e a t u r e o f a l l t e n s i l e t e s t i n g was a d e c r e a s i n g s t r a i n r a t e w i t h i n c r e a s i n g s t r a i n due to the c o n s t a n t c r o s s - h e a d speed o f t he 9 I n s t r o n m a c h i n e . The c r o s s - h e a d r a t e s ranges i n c r e m e n t a l l y f rom - 4 -1 -1 2.0 x 10 i n c h e s - m i n . to 2.0 i n c h e s - m i n . . I n i t i a l s t r a i n r a t e s f o r spec imens o f one i n c h gauge l e n g t h were t h e r e f o r e i n t he r ange - 4 - 1 - 1 2.0 x 10 m i n . to 2.0 m i n . G r i p p i n g o f t e n s i l e spec imens was a c h i e v e d by p l a c i n g the g r i p s e c t i o n s i n t o s p l i t , i n t e r n a l l y t h r e a d e d , c y l i n d r i c a l s e c t i o n s w h i c h themse l ve s c o u l d be g r i p p e d and s e c u r e l y h e l d i n h o l d i n g b l o c k s . Load c y c l i n g was employed when f a s t e n i n g spec imens i n t h e s e g r i p s . T h i s p r e c a u t i o n was t a k e n t o e n s u r e t h a t spec imens were no t p l a s t i c a l l y d e -formed p r i o r t o a c t u a l t e n s i l e t e s t i n g . Ambient t e s t i n g t e m p e r a t u r e s v a r i e d f rom a low o f - 1 0 0 ° C •' i • (T/T = 0.25) to a h i g h o f + 60°C (T/T = 0 . 4 8 ) . T e m p e r a t u r e c o n t r o l m m o f ± 2°C was o b t a i n e d by emmersing spec imens i n b a t h s o f p e t r o l e u m , e t h e r , e t h y l a c h o h o l ( l i q u i d n i t r o g e n c o o l e d ) , w a t e r and o i l . T e n s i l e t e s t s were o f 3 t y p e s : a) I n c r e m e n t a l s t r a i n r a t e t e s t s t o e s t a b l i s h the homogene i ty o f e x t r u s i o n s . F o r each e x t r u s i o n a spec imen was t aken f rom the i n i t i a l and f i n a l s e c t i o n s o f e x t r u d e d r o d . b) S t r a i n i n g o f spec imens 1 p e r c e n t a t a p a r t i c u l a r b a s e s t r a i n -r a t e , and i n c r e m e n t a l l y i n c r e a s i n g t h i s r a t e t h rough the range o f t h e t e s t i n g mach ine f o r a t o t a l s t r a i n o f a p p r o x i m a t e l y 12 p e r c e n t . These t e s t s were c a r r i e d out t o e v a l u a t e the r e l a t i o n s h i p s e x i s t i n g between f l o w s t r e s s , a , s t r a i n r a t e , e , g r a i n s i z e , L , s t r a i n r a t e s e n s i t i v i t y , m, and t e m p e r a t u r e , T . 10 c) A H a l l - P e t c h a n a l y s i s was c a r r i e d out on d a t a o b t a i n e d by s t r a i n i n g spec imens a t 0.01 m i n . ^ to f a i l u r e a t + 23°C and - 1 0 0 ° C . S i m i l a r t e s t s o v e r a range o f s t r a i n r a t e s p r o v i d e d d a t a f o r t r u e s t r e s s -s t r a i n r e l a t i o n s h i p s . 2.4. M e t a l l o g r a p h y M e t a l l o g r a p h i c o b s e r v a t i o n s were made u s i n g l i g h t and e l e c t r o n m i c r o s c o p y . The pu rpo se o f t h i s m e t a l l o g r a p h y i n c l u d e d : a) D e t e r m i n a t i o n o f g r a i n s i z e and second phase morpho logy and d i s t r i b u t i o n i n a s - e x t r u d e d and a n n e a l e d m a t e r i a l . b) O b s e r v a t i o n o f b u l k and s u r f a c e g r a i n s i z e s f o l l o w i n g d e -f o r m a t i o n . , c) O b s e r v a t i o n o f s t r u c t u r e and second phase i n f o i l s o f a s -e x t r u d e d and a n n e a l e d , deformed s p e c i m e n s . d) O b s e r v a t i o n o f s u r f a c e c h a r a c t e r i s t i c s f o l l o w i n g d e f o r m a t i o n . Specimens were s t r a i n e d 0 , 100 and 200 p e r cen t f o l l o w e d by e l e c t r o p o l i s h i n g and ' s c r a t c h i n g ' w i t h 1 m i c r o n diamond p a s t e p r i o r t o a f i n a l s t r a i n o f 20 p e r c e n t o f t he 'new' gauge l e n g t h . The r e s u l t i n g f i n a l s t r a i n s were 20, 140 and 260 p e r c e n t r e s p e c t i v e l y . V a r i o u s i n i t i a l s t r a i n r a t e s were used f o r t h e s e t e s t s . M e t a l l o g r a p h i c o b s e r v a t i o n s were made on spec imens e l e c t r o -p o l i s h e d i n one o f t h e f o l l o w i n g s o l u t i o n s : a) 25 gm chromium t r i o x i d e 133 ml g l a c i a l a c e t i c a c i d 7 ml d i s t i l l e d w a t e r 11 b) 800 m l e t h y l a l c o h o l 50 m l b u t y l c e l l u s o l v e 60 gm sodium t h l o c y a n a t e 20 m l d i s t i l l e d w a t e r O n l y i n r e l a t i v e l y c o a r s e g r a i n e d m a t e r i a l (> 10 m i c r o n s ) was o b s e r v a t i o n p o s s i b l e d i r e c t l y f o l l o w i n g e l e c t r o p o l i s h i n g . F o r a l l o t h e r spec imens the f i n e g r a i n s i z e was d e l i n e a t e d by s h e a r i n g o f g r a i n b o u n d a r i e s o r by e t c h i n g . The e t c h a n t employed was 0.25 p e r c e n t HNO^ and 0.5 p e r c e n t 1M NaOH (by v o l u m e ) . A 10 t o 15 second e t c h was found t o be s a t i s f a c t o r y . E l e c t r o n m e t a l l o g r a p h y i n v o l v e d the p r e p a r a t i o n o f r e p l i c a s and t h i n f o i l s . Two s t a g e ca rbon -chromium r e p l i c a s p r o v i d e d a v e r y c o n -v e n i e n t means f o r making o b s e r v a t i o n s o f f i n e g r a i n e d , p o l i s h e d and d e -f o rmed , o r p o l i s h e d and e t c h e d s u r f a c e s . T h i n f o i l s were p r e p a r e d by s p a r k - m a c h i n i n g ' s l i c e s ' 0.010 i n c h e s i n t h i c k n e s s f rom deformed spec imens . These s l i c e s were masked a p p r o p r i -a t e l y and f u r t h e r t h i n n e d by e l e c t r o p o l i s h i n g . S o l u t i o n (a) was used f o r i n i t i a l t h i n n i n g f o l l o w e d by f i n a l t h i n n i n g w i t h l e s s r e a c t i v e s o l u t i o n ( b ) . T r a n s p a r e n t s e c t i o n s were t h e n c u t f rom the f o i l and v iewed by the t r a n s m i s s i o n t e c h n i q u e a t 100 KV. 2 .5 . G r a i n S i z e Measurements G r a i n , s i z e d e t e r m i n a t i o n s were c a r r i e d out u s i n g t h e l i n e - i n t e r c e p t method i n v o l v i n g coun t s o f 100 to 300 i n t e r c e p t s . Due to t h e a n i s o t r o p i c shape change o f g r a i n s d u r i n g t e n s i l e t e s t i n g measurements o f g r a i n s i z e were made p a r a l l e l and t r a n s v e r s e t o the t e n s i l e a x i s ( T . A . ) . 12 The number of Intersected g r a i n boundaries, per unit length i s the r e c i p r o c a l of the mean l i n e a l traverse length, L. The g r a i n diameter i s r e l a t e d to L by: G.S. = | L (2.5.1.) Grain s i z e measurements are given as G.S. . G.S., L , and L r e s -° o ' o' p e c t i v e l y . The subscripts denote i n i t i a l g r a in s i z e s otherwise the values given are for grain s i z e following deformation. Grain s i z e measurements appear i n Tables 2.1 and 3.3. 13 TABLE 2 . 1 . D e t a i l s o f Spec imen P r e p a r a t i o n M a t e r i a l P r e p a r a t i o n T h e r m a l T r e a t m e n t L * on (m ic rons ) Specimen B i l l e t #1 1. Homogenized b i l l e t a s - e x t r u d e d ( A . E . ) 1.16 a t 360°C f o r 115 h r s . 125 ) 1.6.5 f o l l o w e d by wa te r 145 . 1.80 quench . 150 ) 1.83 2. A n n e a l 200°C f o r 1 6 5 ) 2 , 0 7 _ • , , 175 ) 2.34 2 h r s . and a i r . . . 200 { 2.57 quenched. ) 225 ) °C f o r 1 h r . 3.86 3. E x t r u d e d a t 60°C O K r . ) r • - , , , , c o 250 . f o l l o w e d by 4.68 , _ n j . . j 300 ) a i r quench 8.60 4. C o l d m a c h i n e d . >. 310 > 11.1 320 ) 25 .0 335 "J 67 .0 ; 1 350 ) 89 .0 B i l l e t #2 As above b u t e x - A . E . (1 to T . A . ) 0.89 t e l u d i n g s t e p #2. A . E . (11 to T . A . ) 0.96 * See 2,5 t mean i n t e r c e p t l e n g t h s J_ and 11 to t e n s i l e a x i s ( T . A . ) 14 3. RESULTS 3 . 1 . M i c r o s t r u c t u r e 3 . 1 . 1 . Homogenei ty o f E x t r u s i o n s - R e p r o d u c i b i l i t y R e p r o d u c i b i l i t y o f e x p e r i m e n t a l d a t a was i n s u r e d by p e r f o r m i n g t e s t s t o e s t a b l i s h t h e homogene i ty o f a l l e x t r u d e d m a t e r i a l . T e n s i l e spec imens were t a k e n f rom the i n i t i a l and f i n a l s e c t i o n s o f each e x t r u s i o n and s u b j e c t e d to s t r e s s - s t r a i n r a t e t e s t i n g a t + 2 3 ° C . A f l o w s t r e s s v a r i a t i o n of 4 5 p e r c e n t was t a k e n as an i n d i c a t i o n o f s t r u c t u r a l homogene i ty o f t h e m a t e r i a l ( i . e . g r a i n s i z e and 2nd phase d i s t r i b u t i o n ) . The r a t i o n a l e f o r such t e s t i n g was t h e v e r y s e n s i t i v e n a t u r e o f t he s t r e s s -s t r a i n r a t e r e l a t i o n s h i p to v a r i a t i o n s i n g r a i n s i z e . G r a i n s i z e measurements t a k e n f rom the i n i t i a l and f i n a l s e c t i o n s o f t h e e x t r u s i o n were c o n s i s t e n t w i t h t h e above r e s u l t s . The mean i n t e r c e p t l e n g t h v a r i e d by l e s s t han 2 p e r c e n t i n the l e n g t h o f t he e x t r u s i o n . 3 . 1 . 2 . A s - e x t r u d e d M a t e r i a l R e p r e s e n t a t i v e m i c r o g r a p h s o f e x t r u d e d m a t e r i a l a r e shown i n F i g u r e 3 . 1 ; e x t r u s i o n 1, t r a n s v e r s e s e c t i o n and e x t r u s i o n 2, l o n g i t u d i n a l s e c t i o n . The f i n e , u n i f o r m d i s t r i b u t i o n o f the 2nd phase A l p r e c i p i t a t e s i s c l e a r l y shown; An e l e c t r o n t r a n s m i s s i o n m i c r o g r a p h o f a s - e x t r u d e d m a t e r i a l i s shown i n F i g u r e 3 .2 . 3.1.3. A n n e a l e d M a t e r i a l The a n n e a l i n g t r e a t m e n t s and r e s u l t i n g g r a i n s i z e s f o r e x -t r u d e d m a t e r i a l appear i n T a b l e 2 . 1 . The g r a i n growth and c o a r s e n i n g and r e d i s t r i b u t i o n o f aluminum p r e c i p i t a t e s a r e shown i n F i g u r e 3 .3 . 15 FIGURE 5 . 1 . M i c r o s t r u c t u r e of extruded Z n - l A l . NaOH - HNOj et c h . a) E x t r u s i o n No. 1 - transverse s e c t i o n . Lo = l „ l 6 microns. xk600 t>) E x t r u s i o n No. 2 - l o n g i t u d i n a l s e c t i o n . Lo = O .89 and O .96 microns perpendicular and p a r a l l e l r e s -p e c t i v e l y t o the wire a x i s which i s v e r t i c a l . x^ 6 0 0 FIGURE 3 . 2 . Thin f o i l microstructtire of extruded Zn-IA.1. Lo = 1 .16 microns. x30 , 5 0 0 17 c) L D = 2 5 . 0 microns FIGURE 3 . 3 . M i c r o s t r u c t u r e of annealed Z n - l A l . X36OO o a) and b) 175*C and 225°C f o r 1 hour. NaOH-HNOj etch. o c) 3 2 0 C f o r 1 hour. Sheared t o d e l i n e a t e g r a i n boundaries „ 18 a) L 0 = 2 . 5 7 microns b ) L D = 1 1 . 1 microns FIGURE 3 A . Thin f o i l microstructures of annealed Z n - l A l . x37,000 o a) 2 0 0 C f o r 1 hour. A i r quench. o b) 3 1 0 C f o r 1 hour. A i r quench. STRAIN R A T E , minr ' FIGURE 3.5. The g r a i n s i z e e f f e c t on the s t r e s s - s t r a i n rate r e l a t i o n s h i p (m-curves) of extruded and annealed Z n - I A l . T = 23 C . m O. I 0.0 FIGURE 3 . 6 . STRAIN R A T E , m i n r l The s t r a i n rate s e n s i t i v i t y , m, of extruded, and annealed Zn-lAl. T = 23°C. Total elongation values are shown for selected grain sizes and st r a i n rates. ho O STRAIN R A T E , min.-i FIGURE 3-7. The s t r e s s - s t r a i n rate r e l a t i o n s h i p f o r Zn-0.2A1 and Zn-IAl. T= 23 °C. STRAIN R A T E , min.-l 3.8. The temperature effect on the stress-strain rate relationship of extruded material. Lo = '0 .89 and O . 9 6 microns perpendicular and p a r a l l e l respectively to the t e n s i l e axis (T.A.). 6 0 ° C 2 3 ° C 8 4 0 ° C JL 1 -L 1 J_ j L 10 -4 10 -3 10 10 10^ STRAIN R A T E , m i n r ' FIGURE 3.9„ The s t r a i n ; r a t e s e n s i t i v i t y as a fu n c t i o n of temperature. ~ 0 as i n F i g . 3.8. 24 In p a r t i c u l a r , w i t h i n c r e a s i n g a n n e a l i n g t e m p e r a t u r e a p r o g r e s s i v e l y g r e a t e r p r o p o r t i o n o f the 2nd phase o c c u r s on g r a i n b o u n d a r i e s . A l s o , above + 2 2 5 ° C , as shown i n F i g u r e 3 .4 (b ) , i t appear s t h a t a v e r y f i n e p r e -c i p i t a t e has n u c l e a t e d an a i r quench i ng f rom t h e a n n e a l i n g t e m p e r a t u r e . T h i s o b s e r v a t i o n wou ld appear r e a s o n a b l e i n terms o f t he Z n - A l phase d i a g r a m . F u r t h e r d i s c u s s i o n o f t h e s i g n i f i c a n c e o f t he p r e c i p i t a t e morpho logy and d i s t r i b u t i o n w i l l appear where n e c e s s a r y . 3 .2 . T e n s i l e C h a r a c t e r i s t i c s 3 . 2 . 1 . S t r e s s - S t r a i n Ra te R e l a t i o n s h i p s In d e s c r i b i n g the s t r e s s - s t r a i n r a t e r e l a t i o n s h i p s o b t a i n e d f o r Z n - l A l a b r i e f d e s c r i p t i o n o f e a r l i e r remarks w i l l be n e c e s s a r y . To r e -p e a t , c o n d i t i o n s n e c e s s a r y f o r s u p e r p l a s t i c d e f o r m a t i o n a r e an a p p r o p r i a t e t e m p e r a t u r e and s t r a i n r a t e t o g e t h e r w i t h a f i n e , s t a b i l i z e d m i c r o s t r u c t u r e . These c o n d i t i o n s may then p r o d u c e a h i g h s t r a i n r a t e s e n s i t i v i t y o f t he f l o w s t r e s s d u r i n g m e c h a n i c a l t e s t i n g . F i g u r e s 3.5 and 3.8 show f a m i l i e s o f f l o w s t r e s s - s t r a i n r a t e c u r v e s f o r Z n - l A l . These " S " shaped o r m - c u r v e s , as they a r e commonly r e f e r r e d t o , w i l l be d i s c u s s e d i n terms o f s t a g e I, I I and I I I b e h a v i o r . Each m-curve was o b t a i n e d u s i n g one spec imen and t h e i n c r e m e n t a l t e c h n i q u e e x p l a i n e d p r e v i o u s l y ( s e c t i o n 2.3) r e s u l t i n g i n a t o t a l spec imen s t r a i n o f a p p r o x i m a t e l y 12 p e r c e n t . The s t r a i n r a t e s e n s i t i v i t y pa ramete r may be c a l c u l a t e d f rom such c u r v e s and i s e x -p r e s s e d as m = d l o g a / , , ° d l o g e 3 . 2 . 2 . G r a i n S i z e e f f e c t F i g u r e 3.5 shows t h e 1 p e r c e n t f l o w s t r e s s as a f u n c t i o n o f s t r a i n r a t e f o r a s - e x t r u d e d m a t e r i a l , (L = 1.16 m i c r o n s ) and a n n e a l e d m a t e r -i a l of v a r i o u s g r a i n s i z e s , The a s - e x t r u d e d m a t e r i a l shows t h e c l a s s i c a l 25 deve lopment o f a 3 - s t a g e c u r v e w i t h i n the range o f a c c e s s i b l e s t r a i n - r a t e s . The f l o w s t r e s s was found to be a p p r o x i m a t e l y i n d e p e n d e n t o f s t r a i n up t o 12% s t r a i n . T h i s f a c t was e s t a b l i s h e d by n o t i n g the nea r c o i n c i d e n c e o f f l o w s t r e s s on the 1.16 m i c r o n c u r v e f o r c o n t r o l spec imens - 2 -1 s t r a i n e d o n l y 1 p e r c e n t a t s t r a i n r a t e s above 5 x 10 m i n . . I n g e n e r a l , a t a c o n s t a n t s t r e s s l e v e l ( F i g u r e 3.5) a d e c r e a s i n g g r a i n s i z e s u p p o r t s an i n c r e a s i n g s t r a i n r a t e . C o n v e r s e l y , a t a c o n s t a n t s t r a i n r a t e d e c r e a s i n g g r a i n s i z e s u p p o r t s a d e c r e a s i n g s t r e s s . S i m i l a r (5-9, b e h a v i o r has. b e e n r e c o r d e d f o r numerous s u p e r p l a s t i c a l l o y s , 13 , 17, 18, 32, 3 3 ) . V a l u e s o f "m" t a k e n f rom F i g u r e 3.5 a r e t y p i c a l l y i n t he r ange 0 , 2 5 , 0 . 4 5 , and 0.15 f o r s t a g e s I, I I and I I I r e s p e c t i v e l y . The com-p l e t e a n a l y s i s o f t he v a r i a t i o n o f "m" w i t h s t r a i n r a t e f o r v a r i o u s g r a i n s i z e s i s p r e s e n t e d i n F i g u r e 3 .6 . In t he c a s e o f an a l l o y where g r a i n g rowth o c c u r s on s t r a i n i n g , t h e r e s u l t i n g m c u r v e w i l l be d i f f e r e n t t h a n the c o r r e s p o n d i n g c u r v e i n (32) t he ab sence o f g r a i n growth . The s i g n i f i c a n e o f an m v a l u e wou ld be a l t e r e d i n t he above sugge s ted c a s e . F i g u r e 3.5 shows t h a t t he 1 p e r c e n t f l o w s t r e s s i s a r e a s o n a b l y s e n s i t i v e f u n c t i o n o f g r a i n s i z e . The f a c t t h a t the 1 p e r c e n t f l o w s t r e s s o f i n d i v i d u a l spec imens t e s t e d a t the v a r i o u s s t r a i n r a t e s was w i t h i n 4 p e r c e n t o f t he 1 p e r c e n t f l o w s t r e s s o f i n c r e m e n t a l l y t e s t e d spec imens ( t o t a l s t r a i n max. t o 12 p e r c e n t ) a t t he a p p r o p r i a t e s t r a i n r a t e would sugges t t h a t g r a i n growth o n l y s l i g h t l y a f f e c t e d the s t r e s s - s t r a i n r a t e r e l a t i o n s h i p s o f F i g u r e 3 .5 . The m v e r s u s s t r a i n r a t e c u r v e s o f F i g u r e 3.6 a r e marked w i t h the maximum e l o n g a t i o n to f a i l u r e o f spec imens s t r a i n e d a t t h e i n i t i a l s t r a i n r a t e s shown. I t i s i n t e r e s t i n g to n o t e t h a t t he maximum e l o n g a t i o n f o r a s - e x t r u d e d m a t e r i a l (L = 1.16 m i c r o n s ) o c c u r r e d i n the low s t r a i n r a t e r e g i o n i n the s t a g e I-II t r a n s i t i o n z o n e . The e l o n g a t i o n i n the maximum m r e g i o n was a p p r o x i m a t e l y 200 p e r c e n t l ower a t 386 p e r c e n t w h i l e t h e -3 -1 e l o n g a t i o n i n s t a g e I was 480 p e r c e n t a t e = 1 x 10 m i n . . I t i s a p p a r e n t f rom t h i s d a t a t h a t t h e s t r a i n r a t e s f o r maximum e l o n g a t i o n and maximum m do no t c o i n c i d e . Cook found a s i m i l a r p a t t e r n w i t h the e x c e p t i o n t h a t v a l u e s f o r maximum e l o n g a t i o n were i n the h i g h s t r a i n r a t e range to (13) the r i g h t o f the ' p e a k ' m v a l u e . The r a t i o n a l e f o r t h i s b e h a v i o r was t h a t maximum e l o n g a t i o n d i d no t o c c u r a t the ' p e a k ' m b u t r a t h e r a t h i g h e r i n i t i a l s t r a i n r a t e s to t he r i g h t r e s u l t i n g i n an i n c r e a s i n g m w i t h d e c r e a s i n g s t r a i n r a t e as s t r a i n i n g p r o c e e d e d . The p r e s e n t r e s u l t s would q u e s t i o n t h i s i n t e r p r e t a t i o n f o r Z n - l A l . Cook d i d no t g i v e v a l u e s o f e l o n g a t i o n f o r spec imens s t r a i n e d i n a comparab le s t r a i n r a t e r e g i o n , to the l e f t o f ' p e a k ' m. F i g u r e 3.6 a l s o shows maximum e l o n g a t i o n s to f a i l u r e f o r m a t e r i a l o f d i f f e r e n t g r a i n s i z e s a t e = 0.01 m i n . ^ . A l t h o u g h the 1.16 m i c r o n and 2.07 m i c r o n m a t e r i a l s have a p p r o x i m a t e l y t he same m, o c c u r r i n g on o p p o s i t e s i d e s o f t he maximum m peak , t he f i n e r g r a i n e d m a t e r i a l i s c o n -s i d e r a b l y more ' s u p e r p l a s t i c ' . The s t r e s s - s t r a i n r a t e b e h a v i o r o f Zn -0 .2A1 and Z n - l A l a r e compared i n F i g u r e 3 .7 . I n i t i a l l y t h e f l o w s t r e s s o f Zn -0 .2A1 (1.6 m i c r o n s ) i s l ower t h a n comparab le s t r a i n r a t e s t r e s s e s f o r Z n - l A l - 3 -1 (1.16 m i c r o n s ) bu t f o r a l l e> 2 x 10 m i n . i t i s g r e a t e r . The r e a s o n f o r t h i s ' c r o s s - o v e r ' o f t he m-curves i s f e l t to be due to more p rominent 27 d e f o r m a t i o n a s s i s t e d g r a i n g rowth o c c u r r i n g i n Z n - 0 . 2 A L . Ha rden ing and s t a b i l i z a t i o n due to the second phase i n Z n - l A l wou ld appear t o be r e s -p o n s i b l e f o r t he i n i t i a l l y h i g h e r f l o w s t r e s s and the r e d u c e d g r a i n g rowth r e s p e c t i v e l y . F o r c o a r s e r g r a i n e d Zn -0 .2A1 (5.0 m i c r o n s ) t h e 1 p e r c e n t f l o w s t r e s s i s c o n s i s t e n t l y l ower t h a n f o r Z n - l A l (4.68 m i c r o n s ) . The Z n - l A l p r e c i p i t a t e would be e x p e c t e d t o i n c r e a s e the f l o w s t r e s s f o r s t a g e I I I d e f o r m a t i o n w h i c h ag rees w i t h the above o b s e r v a t i o n . 3 . 2 . 3 . Tempera tu re E f f e c t 3 . 2 . 3 . 1 . G e n e r a l A s t u d y was made o f t he t e m p e r a t u r e e f f e c t on the f l o w s t r e s s -s t r a i n r a t e r e l a t i o n s h i p . The r e s u l t s a r e shown i n F i g u r e s 3.8 and 3 .9 . Fo r t h i s f a m i l y o f c u r v e s to be m e a n i n g f u l i n terms o f t h e s t r a i n r a t e s e n s i t i v i t y g r a i n growth must no t o c c u r . Fo r T < + 23°C p r e v i o u s r e s u l t s sugges t t h a t l i t t l e g r a i n g rowth o c c u r r e d . To d e t e r m i n e whether g r a i n g rowth was o c c u r r i n g a t + 40°C t h e i n c r e m e n t a l l y s t r a i n e d spec imen - 3 -1 was r e - t e s t e d ( i n c r e m e n t a l l y ) f o r e 2 x 10 m i n . . The f l o w s t r e s s r e s u l t s o f t h i s second s t r a i n i n g were o n l y s l i g h t l y h i g h e r ( i . e . ^ 8 - 2 -1 p e r c e n t a t e = 5 x 10 m i n . ) t han d u r i n g i n i t i a l s t r a i n i n g . T h e r e -f o r e g r a i n c o a r s e n i n g d i d o c c u r b u t was no t e x c e s s i v e . The ; t r e n d shown i n F i g u r e 3.8 i s t h a t w i t h i n c r e a s i n g t e m p e r a t u r e the r e g i o n o f h i g h m i s moved to h i g h e r s t r a i n r a t e s as e x p e c t e d . F i g u r e 3.9 shows the v a r i a t i o n o f m w i t h s t r a i n r a t e f o r t h e c u r v e s o f F i g u r e 3 .8 . The c u r v e s o f F i g u r e 3.8 were a l s o n e c e s s a r y f o r an a c t i -v a t i o n energy a n a l y s i s . 3 . 2 . 3 . 2 . A c t i v a t i o n Energy S u p e r p l a s t i c and n o r m a l c r e e p may be d e s c r i b e d e m p h i r i c a l l y by +u •«-• (32,34) the e q u a t i o n ' & = A e " A H A / R T ( 3 . 2 . 1 . ) where A = a c o n s t a n t A H ^ = a c t i v a t i o n energy o f t h e r a t e c o n t r o l l i n g p r o c e s s R = gas c o n s t a n t = 1.987 c a l / d e g - m o l e T = a b s o l u t e t e m p e r a t u r e I t i s f u r t h e r assumed t h a t t he d e f o r m a t i o n i s c o n t r o l l e d by one r a t e c o n t r o l l i n g p r o c e s s . T h i s does no t n e c e s s a r i l y i m p l y o n l y one mechanism i s o p e r a t i v e b u t r a t h e r t h a t i f t he mechanisms a r e dependent on each o t h e r , the one wh i ch i s the s l o w e s t and r e q u i r e s t h e g r e a t e s t a c t i v a t i o n energy w i l l be the r a t e - c o n t r o l l i n g p r o c e s s . A l t e r n a t e l y i f the v a r i o u s p r o c e s s a r e i n d e p e n d e n t o f each o t h e r t h e one w i t h t h e (34) l owes t a c t i v a t i o n energy w i l l be r a t e - c o n t r o l l i n g . Da t a f o r t he a c t i v a t i o n energy a n a l y s i s was o b t a i n e d by c r o s s -p l o t t i n g a t a c o n s t a n t s t r e s s l e v e l f rom F i g u r e 3 .8 . Ca re was t a k e n to see t h a t t he s t r a i n r a t e s e n s i t i v i t y , m, was a p p r o x i m a t e l y c o n s t a n t (10% v a r i a t i o n ) a t a l l t e m p e r a t u r e s f o r t h i s s t r e s s l e v e l . As ment i oned p r e v i o u s l y t he g r a i n s i z e a t a l l t e m p e r a t u r e s was a p p r o x i m a t e l y c o n s t a n t . F i g u r e 3.10 i s t he A r r h e n i u s p l o t , a t v a r i o u s s t r e s s l e v e l s . A t a c o n -s t a n t s t r e s s l e v e l o f 10,000 p s i ( s t a ge I I ) t he a p p a r e n t a c t i v a t i o n energy was c a l c u l a t e d to be 8.5 k c a l / m o l . These v a l u e s a r e s i m i l a r to (13) those o b t a i n e d by C o o k ( Z n - 0 - 2 A l ) o f 8-10 k c a l / m o l . . Compar i son o f s t a g e I v a l u e s ,-at 3,500 p s i u s i n g the i n s t a n t a n e o u s t e m p e r a t u r e change (32) c r e e p method and the p r e s e n t method a r e 12 k c a l / m o l . and 11.5 k c a l / m o l . r e s p e c t i v e l y . 29 3 . 0 1000 r u . , ) l+.o 5 FIGURE 3 . 1 0 . A c t i v a t i o n energy,A H , f o r s tage I and I I d e f o r m a t i o n o f Zn - I A l . 30 A c t i v a t i o n energy v a l u e s f o r b u l k d i f f u s i o n and g r a i n boundary (35) d i f f u s i o n i n pu re z i n c a r e ^23 and "Vl4 k c a l / m o l . r e s p e c t i v e l y . F o r Z n - l A l t he r a t e c o n t r o l l i n g p r o c e s s e s i n b o t h s t a g e s I and I I has an a c t i v a t i o n energy somewhat l e s s t h a n t h a t f o r g r a i n boundary d i f f u s i o n i n p u r e z i n c . 3 .3 , H a l l - P e t c h A n a l y s i s 3 . 3 . 1 . G e n e r a l A l t h o u g h the pa ramete r s i n v o l v e d i n t h e H-P a n a l y s i s a r e open to v a r i o u s i n t e r p r e t a t i o n s i t was f e l t w o r t h w h i l e to s t u d y t h e y i e l d b e h a v i o r o f Z n - l A l w i t h r e s p e c t t o g r a i n s i z e and t e m p e r a t u r e . The H a l l - P e t c h r e l a t i o n s h i p between f l o w s t r e s s and g r a i n s i z e i s g i v e n b y : a = a Q + k d ~ 1 / 2 ( 3 . 3 . 1 . ) where a = y i e l d s t r e s s d = mean g r a i n d i a m e t e r (d = L ) o OQ = and k = c o n s t a n t s In s i n g l e phase p o l y c r y s t a l l i n e m a t e r i a l s v a r i o u s d i s l o c a t i o n mechanisms a r e assumed to a c t d u r i n g y i e l d i n g g i v i n g r i s e t o E q u a t i o n ( 3 . 3 . 1 . ) . M o d i f i c a t i o n s to t h i s e q u a t i o n have been made by L u n d , Tromans and R i s e b r o u g h i n a t t e m p t i n g to a n a l y s e y i e l d d a t a f o r two phase ( 3 6 3 7 ) m a t e r i a l s ' . The p r e s e n t t r e a t m e n t i s q u a l i t a t i v e i n n a t u r e and shows the y i e l d b e h a v i o r i n Z n - l A l a t low t e m p e r a t u r e s ( - 1 0 0 ° C = 0.25 T ) where the P e t c h r e l a t i o n s h i p i s v a l i d and d e f o r m a t i o n i s s l i p c o n t r o l l e d , and a t " h i g h ' t e m p e r a t u r e s (+ 23°C = 0.42 T ) where g r a i n boundary s l i d i n g and m i g r a t i o n o c c u r and e f f e c t i v e l y r e v e r s e the low t e m p e r a t u r e t r e n d s . TABLE 3.1. H a l l - P e t c h and R e l a t e d D a t a G r a i n s i z e L Q o r d +.23°C -100°C A n n e a l i n g d d " 1 / 2 0.2% Y i e l d T o t a l R e d u c t i o n 0.2% y i e l d T o t a l R e d u c t i o n T rea tment s ( ° C ) (m i c ron s ) S t r e s s S t r a i n i n a r e a * S t r e s s S t r a i n i n a r e a * ( l h r . / a i r ( p s i ) (%•) ( p s i ) (%) c o o l e d ) A . E . 1.16 0.93 3140 584 ^100 57,500 15 25 150 1.83 0.74 5910 338 44.700 24 28 165 2.1 0.69 8430 354 - -175 2.34 0.65 10,000 266 39,000 10 13 200 2.57 0.62 14,150 223 " 36,000 6.5 7 225 3.86 0.51 16,700 90 it 30,700 7.1 7 250 4.68 0.46 20,350 58 97 29,000 4.2 5.4 300 8.6 0.34 18,500 32 79 26,700 4.9 7 310 11.1 0.32 20,600 43 93.7 29,100 4.0 4.2 320 25.0 0.20 22,300 20 25 26,200 3.0 4.1 335 66.6 0.12 16,200 6.8 • - 19,600 < 1 -352 89.0 0.11 13,600 6.4 5 16,400 < 1 -* R e d u c t i o n i n a r e a = A^ - A^ where A^ = A l = i n i t i a l c r o s s - s e c t i o n a l a r e a f i n a l c r o s s - s e c t i o n a l a r e a at p o i n t o f f r a c t u r e . 32 3 . 3 . 2 . H a l l - P e t c h A n a l y s i s o f Z n - l A l 3 . 3 . 2 . 1 . T / T = 0.25 m I n F i g u r e 3.11 a r e shown t h e H a l l - P e t c h p l o t s f o r 0 .2 p e r c e n t y i e l d s t r e s s v e r s u s g r a i n s i z e f o r a s - e x t r u d e d and a n n e a l e d m a t e r i a l . R e l e v a n t d a t a i s g i v e n i n T a b l e 3 . 1 . A t - 1 0 0 ° C t h e g r a i n b o u n d a r i e s a re ' h a r d ' p r e v e n t i n g s l i d i n g and m i g r a t i o n and hence g i v i n g r i s e to s l i p c o n t r o l l e d p l a s t i c d e f o r m a t i o n . The - 1 0 0 ° C cu rve shows t h r e e r a t h e r d i s -- 1 / 2 t i n c t r e g i o n s . The f i r s t r e g i o n (0.1 < d < 0.2) where the 0.2 p e r cent y i e l d s t r e s s i s f a l l i n g r a p i d l y may be the r e s u l t o f a spec imen s i z e - 1 / 2 e f f e c t . F o r d < 0.12 t h e r e a r e fewer than 40 g r a i n s i n the spec imen - 1 / 2 d i a m e t e r . In r e g i o n 2 (0.2 < d < 0.45) t he y i e l d s t r e s s i s r e l a t i v e -l y i n s e n s i t i v e to g r a i n s i z e . The 0.2 p e r c e n t y i e l d s t r e s s i n r e g i o n 3 i s much more s e n s i t i v e to v a r i a t i o n s i n g r a i n s i z e , f a l l i n g r a p i d l y w i t h i n c r e a s i n g . g r a i n s i z e . V a l u e s o f OQ and k f o r r e g i o n s 2 and 3 a re g i v e n i n T a b l e 3 .2 . TABLE 3 .2 . H a l l - P e t c h C o n s t a n t s a t - 1 0 0 ° C Reg i on OQ 1/2 2 24,000 p s i 12,000 p s i (y) ' 3 i - O p s i 62,000 p s i ( y ) 1 / 2 C o o k ' s c o r r e s p o n d i n g r e g i o n 3 v a l u e s o f and k were ^ 0 p s i 1/2 (13) and 45,000 p s i (p) r e s p e c t i v e l y . The p r e s e n t k v a l u e i n r e g i o n 3 i s h i g h as e x p e c t e d f o r h . c . p . m e t a l s w i t h a l i m i t e d number o f s l i p sys tems a v a i l a b l e to s u p p o r t p l a s t i c d e f o r m a t i o n . A s c h e m a t i c r e p r e s e n t a t i o n o f t he low t e m p e r a t u r e b e h a v i o r o f F i g u r e 3.11 i s ' g i v e n i n F i g u r e 3 .12. The c o n s t a n t i n ( 3 . 3 . 1 . ) r e l a t e s to t he s t r e s s n e c e s s a r y to move d i s l o c a t i o n s w i t h i n the g r a i n s . A O"Q v a l u e o f ^ 0 sugge s t s an i n t e r p a r t i c l e s p a c i n g , o f A l - r i c h p r e -c i p i t a t e , o f t he same o r d e r o f magn i tude as t he g r a i n s i z e . The ma jo r o b s t a c l e to d i s l o c a t i o n movement wou ld t h e n be g r a i n b o u n d a r i e s and n o t t h e second p h a s e . T h i s g r a i n boundary f u n c t i o n i s r e f l e c t e d i n t h e h i g h v a l u e o f k. R e g i o n 2 b e h a v i o r s u g g e s t s t h a t a l t h o u g h t h e g r a i n b o u n d a r i e s 1/2 a r e s t i l l e f f e c t i v e b a r r i e r to d i s l o c a t i o n s (k = 12,000 p s i (u) ), t h e second phase morpho logy and d i s t r i b u t i o n i s a l s o e f f e c t i v e l y r e s i s t i n g d i s l o c a t i o n movement w i t h i n the g r a i n s c a u s i n g the f l o w s t r e s s to be r a i s e d by t h e i n c r e m e n t , Ao, r e s u l t i n g i n a o f 24,000 p s i . One i n t e r e s t i n g m e t a l l o g r a p h i c o b s e r v a t i o n was made u s i n g l i g h t m i c r o s c o p y and c o n f i r m e d by t h i n f o i l e l e c t r o n m i c r o s c o p y . T h i s o b s e r v a t i o n was t h a t t h roughou t r e g i o n 2 ( - 1 0 0 ° C ) e x t e n s i v e t w i n n i n g o c c u r r e d d u r i n g d e f o r m a t i o n w h i l e r e g i o n 3 d e f o r m a t i o n was by s l i p a l o n e . F i g u r e 3.13 shows m i c r o s t r u c t u r e s i n t h e s e 2 r e g i o n s f o l l o w i n g d e f o r m a t i o n . S t r a i n i n r e g i o n 2 was between 3 and 5 p e r c e n t as compared to r e g i o n 3 s t r a i n s o f 5 t o 20 p e r c e n t . T a b l e 3.1 shows t o t a l s t r a i n s and r e d u c t i o n s i n a r e a f o r a l l spec imens t e s t e d . 3 . 3 . 2 . 2 . T / T = 0.42 m The + 23°C H a l l - P e t c h p l o t can be c o n v e n i e n t l y d i v i d e d i n t o 3 - 1 / 2 r e g i o n s w i t h d l i m i t s s i m i l a r to t h e s e f o r the - 1 0 0 ° C p l o t . F o r - 1 / 2 d >. 0.5 (concave upwards) d e f o r m a t i o n i s l a r g e l y due to g r a i n boundary s l i d i n g and m i g r a t i o n . The f l o w s t r e s s d e c r e a s e s f o r g r a i n s i z e s < 25 u , and the P e t c h r e l a t i o n s h i p i s t h e r e f o r e i n v a l i d . Wa ldron found t h a t f o r Zn - 0.6 T i p r e p a r e d from powder, and r e s u l t i n g i n o x i d e a) L„ = 11.1 microns. x l2,400 b) L 0 =2.34 microns. x6300 FIGURE 3»13. Deformation m i c r o s t r u c t u r e s f o l l o w i n g s t r a i n i n g at -100°C. a) € = 0.01 min." , € = h percent b) £ = 0.01 min. - 1 , £ = 10 percent 37 (33) s t a b i l i z a t i o n o f g r a i n b o u n d a r i e s , t h a t P e t c h obeyance was o b s e r v e d - 1 / 2 In r e g i o n 2 (0.2 < d < 0.5) d e f o r m a t i o n wou ld be l a r g e l y t h e r e s u l t o f d i s l o c a t o n m o t i o n . A l s o , t h e r e was v e r y l i t t l e s u r f a c e t w i n n i n g o b s e r v e d i n marked c o n t r a s t t o the - 1 0 0 ° C b e h a v i o u r . T h i s i s due to the r e l i e f o f s t r e s s c o n c e n t r a t i o n a t b o u n d a r i e s due to boundary - 1 / 2 m i g r a t i o n . The r a p i d d e c r e a s e i n y i e l d s t r e s s , f o r r e g i o n 3 (d < 0 . 2 ) , w i t h I n c r e a s i n g g r a i n s i z e i s a g a i n (thought to be ) r e l a t e d to a spec imen s i z e e f f e c t . 3.4. T r u e S t r e s s - S t r a i n Cu rve s and Creep B e h a v i o r 3 . 4 . 1 . G e n e r a l One v a l u e o f p l o t t i n g s t r e s s - e n g i n e e r i n g s t r a i n c u r v e s i s to p r o v i d e e v i d e n c e f o r the f a c t t h a t a ' s t e a d y - s t a t e ' f l o w s t r e s s does n o t appear to e x i s t f o r Z n - l A l . T h i s s t a t e m e n t a p p l i e s t h r o u g h o u t the range o f s t r a i n - r a t e s employed i n t e n s i l e t e s t i n g and p a r t i c u l a r l y to s t r a i n s l e s s than 25 p e r c e n t . I t i s e v i d e n t t h e r e f o r e t h a t t he p r e v i o u s a s s u m p t i o n o f a s t e a d y - s t a t e f l o w s t r e s s i s u n w a r r e n t e d . Cook has r a i s e d t h i s p o i n t p r e v i o u s l y w i t h r e s p e c t t o o b s e r v e d b e h a v i o r f o r Zn - 0.2 A l (13) a l l o y s . The a s s u m p t i o n o f a ' s t e a d y - s t a t e ' f l o w s t r e s s was made i n d e t e r m i n i n g the s t r e s s - s t r a i n r a t e c u r v e s u s i n g the i n c r e m e n t a l t e c h n i q u e -F i g u r e s 3. 5 and 3 .8 . As m e n t i o n e d p r e v i o u s l y t e n s i l e t e s t i n g a t c o n s t a n t X -H speeds r e s u l t s i n a d e c r e a s i n g s t r a i n r a t e w i t h i n c r e a s i n g s t r a i n . T h i s c o m p l i c a t i o n w i l l appear i n the t r u e s t r e s s - s t r a i n c u r v e s p u t t i n g the i n i t i a l s t r a i n r a t e and t r u e s t r e s s i n c o r r e s p o n d e n c e o n l y a t 0 i p e r c e n t s t r a i n . Dona ld son n o r m a l i z e d h i s f l o w c u r v e s by a p p l y i n g a (32) c o r r e c t i o n f a c t o r . F i g u r e s 3.15 to 3.17 a r e n o t n o r m a l i z e d bu t a r e n e v e r t h e l e s s u s e f u l f o r q u a l i t a t i v e d i s c u s s i o n . The c u r v e s o f F i g u r e s 3.15 and 3.16 can be r a t i o n a l i z e d i n terms o f v a r i o u s s t r u c t u r a l and m e c h a n i c a l v a r i a t i o n s o c c u r r i n g d u r i n g d e f o r m a t i o n . The s t r e s s w i l l be i n c r e a s e d i n r e s p o n s e to g r a i n g rowth and s t r a i n h a r d e n i n g . A s t r e s s d e c r e a s e w i l l o c c u r due to a d e c r e a s i n g s t r a i n r a t e w i t h i n -c r e a s i n g s t r a i n and as a consequence o f c r e e p r e c o v e r y . 3 . 4 . 2 . S t r a i n Ra te Dependence o f T r u e S t r e s s - S t r a i n Curves F o r r e f e r e n c e , F i g u r e 3.14 shows t h e i n i t i a l s t r a i n r a t e s (upper c a s e l e t t e r s ) f o r t h e t r u e s t r e s s - s t r a i n c u r v e s o f F i g u r e s 3.15 and 3.16. In F i g u r e 3.15 s t r e s s s t r a i n c u r v e s a r e shown f o r a s -e x t r u d e d Z n - l A l o f g r a i n s i z e 1.16 m i c r o n s . Rap id i n i t i a l h a r d e n i n g (e < 20%) i n c r e a s e s w i t h i n c r e a s i n g s t r a i n r a t e . Curves B, C and D ( s t a ge I and I I d e f o r m a t i o n ) show an i n c r e a s e i n t r u e s t r e s s up to a p p r o x i m a t e l y 70 p e r c e n t o f t o t a l spec imen s t r a i n , beyond w h i c h n e c k i n g o c c u r r e d . 3 . 4 . 3 . T r u e S t r e s s - S t r a i n Cu rve s as a F u n c t i o n o f G r a i n S i z e Shown i n F i g u r e 3.16 a r e s t r e s s - s t r a i n c u r v e s as a f u n c t i o n o f i n i t i a l g r a i n s i z e . The c u r v e f o r 1.16 m i c r o n g r a i n s i z e c u r v e H, i s i d e n t i c a l w i t h c u r v e C o f F i g u r e 3 .15. F o r g r a i n s i z e s i n exce s s o f 2,5 m i c r o n s r a p i d h a r d e n i n g o c c u r r e d to a p p r o x i m a t e l y 15% s t r a i n ( s tage I I I d e f o r m a t i o n ) . Curves A and G , . o f F i g u r e s 3.15 and 3.16 r e s p e c t i v e l y , a r e t y p i c a l o f lower r ange s t a g e I I I d e f o r m a t i o n , w h e r e f o r s t r a i n s g r e a t e r t h a n 12 pe r c e n t t h e r e e x i s t s an a p p r o x i m a t e l y l i n e a r r e g i o n o f d e c r e a s i n g s t r e s s w i t h o u t p e r c e p t i b l e n e c k i n g . S tage I I I was no t w e l l d e f i n e d i n t h a t the s t r e s s - s t r a i n c u r v e s d i f f e r e d w i d e l y d e -pend ing on t h e p a r t i c u l a r r e g i o n o f s t a g e I I I d e f o r m a t i o n . 6oo 43 3.4.4. T r u e S t r e s s - S t r a i n Curves f o r V a r i a b l e G r a i n S i z e and Tempera tu re S t r e s s - s t r a i n c u r v e s f o r an e n g i n e e r i n g s t r a i n o f l e s s than 20 p e r c e n t a r e shown i n F i g u r e 3 .17 ; r e l e v a n t d a t a appear s i n T a b l e 3 .1 . F i g u r e 3.17 shows: a) The p e r c e n t e l o n g a t i o n i n c r e a s e s w i t h d e c r e a s i n g g r a i n s i z e a t - 1 0 0 ° C . b) The work h a r d e n i n g r a t e , 0, appear s t o d e c r e a s e w i t h d e -c r e a s i n g g r a i n s i z e . c ) F o r g r a i n s i z e s l e s s than a p p r o x i m a t e l y 2 m i c r o n s t h e r e i s a d i s t i n c t t w o - s t a g e c u r v e at. - 1 0 0 ° C . d) A t - 1 0 0 ° C t h e s t r e s s d e c r e a s e s r a p i d l y w i t h i n c r e a s i n g g r a i n s i z e w h i l e a t + 23°C t h e o p p o s i t e i s t r u e . The o b s e r v a t i o n o f a two s t a g e c u r v e f o r d e f o r m a t i o n o f f i n e g r a i n e d Zn -1% A l a t low t e m p e r a t u r e s has been made p r e v i o u s l y by (32) Dona ld son . However, h i s i n v e s t i g a t i o n s o f low t e m p e r a t u r e d e -f o r m a t i o n were p r i m a r i l y w i t h f i n e g r a i n e d cadmium a l l o y s . The cau se o f n o n - u n i f o r m d e f o r m a t i o n was sugge s ted to be y i e l d i n g by L i i de r s band p r o p a g a t i o n . The p r e s e n t d a t a i s i n s u f f i c i e n t f o r an a n a l y s i s o f low t e m p e r a t u r e d e f o r m a t i o n but does sugges t an a r e a f o r f u t u r e i n v e s t i g a t i o n . A t + 23°C the work h a r d e n i n g r a t e a g a i n d e c r e a s e d w i t h d e -c r e a s i n g g r a i n . s i z e . T h i s i s a r e f l e c t i o n o f a t r a n s i t i o n f rom d e -f o r m a t i o n by s l i p t o d e f o r m a t i o n by g r a i n boundary s l i d i n g and m i g r a t i o n . 3 . 4 . 5 . C reep B e h a v i o u r f o r S tage I and I I D e f o r m a t i o n The c r e e p b e h a v i o r f o r Z n - l A l r e p o r t e d h e r e i s f rom i n v e s t i -15 " 5 . 2h 3 6 TIME (sec.) O a) Stage II deformation. T = 23 C,<r= 5 0 0 0 ps Time unit = 5 sec„ 3 . 2 . C52.4 g l - 6 1-0 . 8 0 I* A B Temp. UOoC 0 C Stress 5 0 0 0 p s i 1500 p s i i r Time Unit 10 2 sec, nr. b) Primary creep i n stage I and II, FIGURE 3 . 1 8 . Creep curves f o r Zn-IAl. g a t i o n s by Dona ld son . The c r e e p spec imens were mach ined f rom e x t r u d e d m a t e r i a l p r e p a r e d f o r t h i s s t u d y . F i g u r e 3.18 shows c r e e p d a t a f o r S tage I and I I d e f o r m a t i o n . A l t h o u g h s t e a d y s t a t e was r e a c h e d f a i r l y q u i c k l y ( s t a ge I I ) t h e r e was a s l i g h t d e c r e a s e i n c r e e p r a t e w i t h i n -c r e a s i n g s t r a i n . T h i s e v i d e n c e , and p r i m a r y c r e e p i n s t a g e s I and I I , was a s s o c i a t e d w i t h t h e p o s s i b i l i t y t h a t g r a i n growth had o c c u r r e d . A r e p r o d u c i b l e and r e c o v e r a b l e p r i m a r y c r e e p was o b s e r v e d i n s t a g e I. 3 .5 . M e t a l l o g r a p h i c O b s e r v a t i o n s o f D e f o r m a t i o n B e h a v i o r and  G r a i n Growth 3 . 5 . 1 . G e n e r a l :. When s t u d y i n g the b u l k d e f o r m a t i o n o f a p o l y c r y s t a l l i n e a g g r e g a t e the c o m p a t a b i l i t y r e q u i r e m e n t s n e c e s s a r y f o r m a i n t a i n i n g a c o n s t a n t vo lume must be c o n s i d e r e d . The "Von M i s e s " c r i t e r i o n s t a t e s t h a t f i v e i n d e p e n d e n t d e f o r m a t i o n modes a r e n e c e s s a r y f o r such d e f o r m a t i o n , I n z i n c , b a s a l . s l i p ({0001} <1120 >) p r o v i d e s two modes and the more d i f f i c u l t p y r a m i d a l s l i p ({1122} < 1123 >) can p r o v i d e f i v e modes. O t h e r modes o f d e f o r m a t i o n must a l s o be c o n s i d e r e d . T w i n n i n g can o c c u r i n z i n c and may p r o v i d e s t r a i n t h e r e b y r e - o r i e n t i n g t h e tw inned r e g i o n making no rma l s l i p modes more f a v o r a b l e . D u r i n g s u p e r p l a s t i c d e -f o r m a t i o n g r a i n boundary s l i d i n g and m i g r a t i o n , v a c a n c y d i f f u s i o n and d i s l o c a t i o n c l i m b may p r o v i d e s t r a i n w i t h o u t t he need f o r s l i p . 3 . 5 . 2 . D e f o r m a t i o n Modes 3 . 5 . 2 . 1 . G r a i n Boundary S l i d i n g G r a i n boundary s l i d i n g b o t h on t r a n s v e r s e b o u n d a r i e s ( s c r a t c h -o f f s e t s ) and l o n g i t u d i n a l g r a i n b o u n d a r i e s ( f r e s h l y exposed s u r f a c e ) was o b s e r v e d . T h i s boundary s l i d i n g o r s h e a r i n g o c c u r r e d t h r o u g h o u t the range o f Imposed s t r a i n r a t e s . Boundary s h e a r i n g i s c l e a r l y shown i n F i g u r e 3 .19(a ) and was o b s e r v e d to be a p p r o x i m a t e l y c o n s t a n t w i t h i n -c r e a s i n g s t r a i n a t a f i x e d i n i t i a l s t r a i n r a t e . T r a n s v e r s e and l o n g i t u d i n a l s c r a t c h marks a r e shown i n F i g u r e 3 . 1 9 ( b ) . F o r l o n g i t u d i n a l s c r a t c h e s s e p a r a t i o n s o c c u r a t s h e a r i n g b o u n d a r i e s b u t a f f e c t s a r e r e d u c e d due to the s i m p l e " s t r e t c h i n g e f f e c t " on the o r i g i n a l s c r a t c h d u r i n g s t r a i n i n g . G r a i n r o t a t i o n i s a l s o e v i d e n t i n F i g u r e 3.19(b) where s c r a t c h segments i n g r a i n s have r o t a t e d . Q u a n t i t a t i v e measurements o f t he c o n t r i b u t i o n to t o t a l s t r a i n o f g r a i n boundary s l i d i n g were no t a t t e m p t e d . 3 . 5 . 2 . 2 . D e f o r m a t i o n by S l i p S u r f a c e o b s e r v a t i o n s were made o f m a s s i v e s l i p f o l l o w i n g s t a g e I I I d e f o r m a t i o n and o f i s o l a t e d s l i p bands f o l l o w i n g s t a g e I I d e f o r m a t i o n . These o b s e r v a t i o n s prompted a s t udy o f i n t e r n a l s t r u c t u r e emp loy ing t h i n f o i l e l e c t r o n m i c r o s c o p y . The p o s s i b i l i t y e x i s t s t h a t a n n e a l i n g o f i m p e r f e c t i o n s may have o c c u r r e d d u r i n g t h i n f o i l p r e -p a r a t i o n . A comparab le i n v e s t i g a t i o n o f t h e Z n - A l e u t e c t o i d by (25) B a l l e t a l , . m a k e s no r e f e r e n c e to t h i s p o s s i b i l i t y . In t he p r e s e n t work s p a r k m a c h i n i n g o f spec imens d i d no t cause g r a i n g r o w t h . The r e m a i n i n g t h i n f o i l p r o c e d u r e s wou ld appear to be l e s s demanding o f t he d e f o r m a t i o n m i c r o s t r u c u t r e . F i g u r e 3.20 shows a s - e x t r u d e d and d e -formed m i c r o s t r u c t u r e s . The deformed m i c r o s t r u c t u r e was o b t a i n e d by s t r a i n i n g 50 p e r c e n t a t a s t r a i n r a t e o f , 0 . 0 5 m i n . ^ ( s t a g e I I ) . V e r y few d i s l o c a t i o n s were o b s e r v e d f o r s t a g e I and I I d e f o r m a t i o n . Whether the s u r f a c e o b s e r v a t i o n o f s l i p , r e s t r i c t e d to a s m a l l p e r c e n t a g e o f t h e 47 g r a i n s , s u g g e s t s comparab le i n t e r n a l b e h a v i o r i s q u e s t i o n a b l e a l t h o u g h t h i s i s t h e p r e s e n t o b s e r v a t i o n . The deformed m i c r o s t r u c t u r e o f F i g u r e 3.20 shows a somewhat random d i s l o c a t i o n s t r u c t u r e i n g r a i n #1 w h i l e g r a i n #2 shows a d i s t i n c t s u b - b o u n d a r y . Such b o u n d a r i e s a r e known to form by (39) a p r o c e s s o f g l i d e - p o l y g o n i z a t i o n ove r a w ide range o f t e s t t e m p e r a t u r e They a r e c l e a r l y shown i n F i g u r e 3.21 i n m a t e r i a l deformed a t - 1 0 0 ° C . 3 . 5 . 2 . 3 . F u r t h e r Boundary O b s e r v a t i o n s Dona ld son has s u g g e s t e d t h a t ' boundary p e e l i n g ' i s a s u r f a c e e f f e c t o c c u r r i n g where s i g n i f i c a n t t e n s i l e s t r e s s e s e x i s t a c r o s s g r a i n (32)' b o u n d a r i e s . A f u r t h e r s u g g e s t i o n i s t h a t p e e l i n g c o u l d r e s u l t by vancancy d i f f u s i o n i n the v i c i n i t y o f t he boundary s u r f a c e t r i p l e l i n e . F i g u r e 3.22 shows boundary s h e a r i n g a t - A , and p e e l i n g a t - B . T h e r e i s a s t r i k i n g r e semb lance between p e e l i n g i n Cd - 3y and t h e p r e s e n t (32) m a t e r i a l . The s t r i a t i o n s o c c u r r i n g a t the p e e l e d boundary i n F i g u r e 3.22 were n o t g e n e r a l l y o b s e r v e d . V e r y s i m i l a r mark ing s a t p e e l e d b o u n d a r i e s i n Cd _ 3y were i n t e r p r e t e d on the b a s i s o f c r y s t a l l o g r a p h i c c o n s i d e r a t i o n s . Boundary m i g r a t i o n was a common o b s e r v a t i o n and i s shown i n F i g u r e 3 .23. Boundary s l i d i n g and m i g r a t i o n a r e common f e a t u r e s o f s u p e r p l a s t i c d e f o r m a t i o n . 3 . 5 . 3 . D e f o r m a t i o n A s s i s t e d G r a i n Growth 3 . 5 . 3 . 1 . G e n e r a l D e f o r m a t i o n a s s i s t e d g r a i n growth has been o b s e r v e d i n b o t h two p h a s e , e u t e c t i c o r e u t e c t o i d t y p e a l l o y s and d e l u t e second phase ( 1 0 , 1 3 , 1 6 , 2 9 , 3 0 , 3 2 ) fc . , f , a l l o y s ' ' ' . The most g e n e r a l o b s e r v a t i o n from the above a) =0.50 min. , x25,400 b) = 0.0'+7 min. , x'+900 FIGURE 3.19. Surface m i c r o s t r u c t u r e showing g r a i n boundary s l i d i n g , g r a i n r o t a t i o n , and coarse s l i p . L D = O.89 and O.96 microns, a) and b) St r a i n e d 1*4-0 and 260 percent r e s p e c t i v e l y as described i n sec. 3 .5°3.2. 49 FIGURE 3„20. I n t e r n a l m i c r o s t r u c t u r e of Z n - l A l . L 0 as i n Fig„ 3.19. x20,000 a) As - extruded,€ = 0 percent b) As - extruded,C = 50 percent at k = 0.05 min.--'-T = +23 °C. 50 FIGURE 3.21. I n t e r n a l microstructure f o l l o w i n g stage I I I deformationo L 0 = 2.3^ microns. S t r a i n of 10 percent at a s t r a i n r a t e of 0.01 m i n . - 1 and -100°C . x20,000 51 3 . 2 2 . Surface mi c r o s t r u c t u r e showing g r a i n boundary shearing (A) and p e e l i n g ( B). T o t a l s t r a i n of 260 percent at a s t r a i n r a t e of 0 . 0 ^ 7 min.""11; T = +23°C. x l l . 0 0 0 FIGURE 3 . 2 3 . Surface m i c r o s t r u c t u r e showing g r a i n boundary mi g r a t i o n at (A). Test c o n d i t i o n s as i n F i g . 3 . 2 2 . x 5 , 6 0 0 53 i n v e s t i g a t i o n s i s t h a t a l t h o u g h g r a i n growth o c c u r s d u r i n g s u p e r p l a s t i c d e f o r m a t i o n the g r a i n s r e m a i n e q u i a x e d . Brophy et a l , i n work w i t h N i - F e - C r a l l o y s , f ound an a n i s o t r o p y o f l o n g i t u d i n a l to t r a n s v e r s e g r a i n ( 2 9 ) s i z e o f o n l y 37 p e r c e n t a f t e r 4 0 0 p e r cen t d e f o r m a t i o n . C l a r k found a c o r r e s p o n d i n g d e v i a t i o n o f o n l y 1 5 p e r ce"nt f o l l o w i n g 3 0 0 p e r c e n t d e -ie Zi (9) f o r m a t i o n i n S n - B i a l l o y s H o l t o b s e r v e d g r a i n e l o n g a t i o n i n the Z n - A l e u t e c t o i d a t h i g h s t r a i n r a t e s where d e f o r m a t i o n was s l i p c o n t r o l l e d G i f k i n s has commented on the a n i s o t r o p i c g rowth ( g r a i n e l o n g a t i o n i n the t e n s i l e a x i s d i r e c t i o n ) t h a t wou ld n e c e s s a r i l y r e s u l t due t o a d e f o r m a t i o n mechanism i n v o l v i n g N-H or C o b l e c reep and s l i p , i n d e p e n d e n t l y o r i n com-b i n a t i o n . The combined mechanisms o f boundary s l i d i n g and g r a i n r o t a t i o n o c c u r r i n g i n c o n j u n c t i o n w i t h s l i p and d i f f u s i o n c o n s t i t u t e a means o f ( 3 8 ) r e t a i n i n g an e q u i a x e d g r a i n shape . G r a i n boundary m i g r a t i o n must a l s o be c o n s i d e r e d as a p o s s i b l e d e f o r m a t i o n o r accommodat ion mechani sm. 3 , 5 , 3 . 2 . D e f o r m a t i o n G r a i n Growth i n Z n - l A l . T a b l e 3 . 3 c o n t a i n s a l l d a t a r e l a t i n g to d e f o r m a t i o n a s s i s t e d g r a i n g rowth . A l l g r a i n s i z e d a t a r e f e r s t o t he b u l k o r i n t e r n a l g r a i n s i z e . Symbols G . S . Q and G.S. r e f e r t o g r a i n s i z e p r i o r t o and f o l l o w i n g d e -f o r m a t i o n r e s p e c t i v e l y . S e c t i o n 2 . 5 d e s c r i b e s t h e i n t e r c e p t method em-p l o y e d f o r mea su r i n g mean l i n e a l t r a v e r s e l e n g t h s and t h e i r c o n v e r s i o n to g r a i n s i z e . D e f o r m a t i o n c o n s i s t e d o f impos ing t o t a l s t r a i n s on i n d i v i d u a l spec imens o f 2 0 , 1 4 0 and 260 p e r c e n t a t v a r i o u s s t r a i n r a t e s . Two g r a i n s i z e d e t e r m i n a t i o n s rcere made: a) F o r s u r f a c e o b s e r v a t i o n and measurement spec imens were e l e c t r o p o l i s h e d a t 0 , 100 and 200 p e r cen t s t r a i n f o l l o w e d by s t r a i n i n g TABLE 3 .3 . D e f o r m a t i o n A s s i s t e d G r a i n Growth* Spec imen No. X -H i n / m i n ? (min. m . (min. "*") e T e n s i l e T e s t Time (min.) G.S. r * * X T . A . (m ic rons ) 11 * * T . A . G.S.—G.S. o (microns ) 0 ( G . S . — G . S . ) I o t ( y - m i n . 1 ) G»S • G • S • ^ 1 — - — 0 0 1.34 1.44 0 — 1.08 2 0 .5 0.9 0.376 1.4 1.55 1.57 1.77 0.33 0.107 1.15 3 0 .2 0.5 0.21 II 2.82 1.8 2.32 0.88 0.157 1.29 4 0.05 0.094 0.039 II 15 1.8 2.63 1.19 0.40 1.46 5 0.02 0.044 0.018 n 32.3 1.96 2.86 1.42 0.022 1.46 6 0.005 0.01 0.004 II 141 1.98 3.03 1.59 0.0056 1.53 7 0.002 0.0046 0.0019 II 308 2.22 3.34 . 1.90 : 0 .0031 1.49 8 0 .0005 0.0009 0.0038 II 1550 2.16 3.51 2.07 0.00067 1.62 9 0.02 0.048 0.04 0.2 4.15 1.53 1.73 0.29 0.035 1.13 10 0.02 0.047 0.013 2.6 55.8 2.28 3.7 2.26 0.0215 1.62 11 0.05 0 .103 0.029 2.6 25.3 2.08 3.15 1.71 0.034 1.52 12 0.05 0.05 0.022 1.4 23.9 2.14 2.88 1,44 0.03 1.34 13 0.05 0.05 0.417 0.2 4.0 1.56 1.8 0.36 0.045 1.11 14 0.0005 0.001 0.0008 0.2 196.0 1.68 1.84 0.40 0.001 1.1 15 0.02 0.48 0.04 0.4 8.3, 1.67 2.13 0.69 0.035 1.29 * G.S. = f i n a l g r a i n s i z e ( c o n c l u s i o n o f t e n s i l e t e s t ) G.S. = i n i t i a l g r a i n s i z e . _ ^ X-H speed E, = i n s t a n t a n e o u s s t r a i n r a t e = c ; — i n i n s t a n t a n e o u s gauge l e n g t h * * J_ and 11 = g r a i n s i z e p e r p e n d i c u l a r and p a r a l l e l t o t e n s i l e a x i s t = G . S . - G . S . o p a r a l l e l t o t e n -s i l e a x i s . •55 an a d d i t i o n a l 20 p e r c e n t o f t he deformed gage l e n g t h r e s u l t i n g i n t o t a l s t r a i n s o f 20, 140 and 260 p e r c e n t . b) F o r b u l k o r i n t e r n a l g r a i n s i z e d e t e r m i n a t i o n s spec imens f rom A w i t h t o t a l s t r a i n s o f 20, 140 o r 260 p e r c e n t were f u r t h e r e l e c t r o -p o l i s h e d to remove t h e s u r f a c e l a y e r and t h e n e t c h e d i n a HNO^ - NaOH s o l u t i o n ( S e c t i o n 2 . 4 ) . F o l l o w i n g e i t h e r a) o r b) r e p l i c a s were t a k e n and g r a i n s i z e measurements made. The t e s t i n g t e m p e r a t u r e was + 2 3 ° C . Specimens h e l d a t t h i s ' t empera tu re f o r t imes up to 15 h o u r s , t h e d u r a t i o n o f minimum s t r a i n r a t e t e s t i n g , d i d n o t show a m e a s u r a b l e i n c r e a s e i n g r a i n s i z e . G r a i n g rowth was t h e r e f o r e the r e s u l t o f d e f o r m a t i o n . In the p r e s e n t s t u d y t h e undeformed g r a i n s i z e d i d show a s l i g h t a n i s o t r o p y w i t h the r a t i o o f g r a i n s i z e i n t he l o n g i t u d i n a l (11 to T . A . ) t o t r a n s v e r s e (1 to T . A . ) d i r e c t i o n s , o r the l e n g t h to w i d t h r a t i o , b e i n g 1.08. D u r i n g d e f o r m a t i o n at a l l s t r a i n r a t e s t h i s r a t i o i n c r e a s e d . In F i g u r e 3.24 the g r a i n s i z e f o l l o w i n g 140 pe r c e n t s t r a i n i s shown p l o t t e d a g a i n s t s t r a i n r a t e . The g r a i n s i z e i n c r e a s e i n the l o n g i t u d i n a l d i r e c t i o n o c c u r s a t a g r e a t e r r a t e t h a n i n t h e t r a n s v e r s e d i r e c t i o n w i t h d e c r e a s i n g s t r a i n r a t e . F o r s t a g e s I and I I d e f o r m a t i o n t h e g r a i n s i z e i n c r e a s e d l i n e a r l y w i t h the d e c r e a s i n g l o g a r i t h m of s t r a i n r a t e . F i g u r e 3.25 shows the g r a i n s i z e l e n g t h to w i d t h r a t i o v e r s u s s t r a i n r a t e f o r 140 p e r c e n t s t r a i n . The o r i g i n a l a n i s o t r o p y and i n c r e a s i n g a n i s o t r o p y - 3 - 1 w i t h d e c r e a s i n g s t r a i n r a t e a r e a p p a r e n t . A t a s t r a i n r a t e o f 10 m i n . the l e n g t h / w i d t h r a t i o has r e a c h e d a v a l u e o f ^ 1.6 o r an a n i s o t r o p y o f 56 g r e a t e r t h a n 50 p e r c e n t . F i g u r e 3.26 i s a m i c r o g r a p h o f i n t e r n a l s t r u c t u r e f o l l o w i n g 600 p e r c e n t s t r a i n a t a s t r a i n r a t e o f 0.01 m i n . The a n i s o t r o p y i n t h i s c a se i s a p p r o x i m a t e l y 80 pe r c e n t . A n i s o t r o p i c g r a i n g rowth f o r Z n - l A l i s t h e r e f o r e g r e a t e r t h a n t h a t r e p o r t e d f o r o t h e r i „. „ -, ( 6 ,24 ,25 ,29 ) _ , . , s u p e r p l a s t i c m e t a l s . S u r f a c e d e f o r m a t i o n o f spec imens s t r a i n e d 140% a t v a r i o u s s t r a i n r a t e s i s shown i n F i g u r e 3 .27 . These m i c r o g r a p h s show v e r y c l e a r l y t he i n c r e a s i n g a n i s o t r o p y w i t h d e c r e a s i n g s t r a i n r a t e . The p o l i s h i n g o f spec imens p r i o r t o f i n a l d e f o r m a t i o n d i d no t r e s u l t i n any g r a i n boundary d e f i n i t i o n . I t i s a p p a r e n t t h e r e f o r e t h a t e x t e n s i v e g r a i n boundary s l i d i n g o c c u r r e d d u r i n g the f i n a l 20 p e r cen t o f d e f o r m a t i o n . T h i s f a c t i s a g a i n emphas ized by t h e s c r a t c h o f f -s e t s . The i n t e r n a l s t r u c t u r e o f F i g u r e 3.28 c o r r e s p o n d to t h e s u r f a c e s t r u c t u r e s o f F i g u r e 3 .27. A d i f f e r e n c e was o b s e r v e d i n t he s u r f a c e and Y i n t e r n a l g r a i n s i z e s . I t was found t h a t t he l a r g e r s u r f a c e g r a i n s were c o n f i n e d to a r e g i o n no t g r e a t e r t han 50 m i c r o n s b e n e a t h t h e s u r f a c e . T h i s f i n d i n g may s i m p l y r e f l e c t the i n a b i l i t y t o count a l l o f t h e s u r -f a c e g r a i n b o u n d a r i e s due to a v a r i a t i o n i n g r a i n houndary s h e a r i n g . I t i s a l s o p o s s i b l e t h a t o n l y t he s u r f a c e g r a i n s were l a r g e r as a r e -s u l t o f t h e i r f r e e s u r f a c e p o s i t i o n . V e r i f i c a t i o n o f t h i s p o s s i b i l i t y was no t a t tempted due t o an i n a b i l i t y t o remove l e s s t han 50 m i c r o n s o f m a t e r i a l w h i l e e l e c t r o - p o l i s h i n g s p e c i m e n s . In f i g u r e 3.29 the r e l a t i v e g r a i n s i z e enhancement a t s t r a i n s o f 20., 140 and 260 pe r cen t i s shown as a f u n c t i o n o f s t r a i n r a t e . A C S . e q u a l s t h e f i n a l deformed g r a i n s i z e minus the i n i t i a l undeformed g r a i n s i z e , G.S. -'G.SQ . A t a l l s t r a i n s t he g r a i n s i z e e n -hancement i n c r e a s e s w i t h d e c r e a s i n g s t r a i n r a t e . F o r a p a r t i c u l a r s t r a i n r a t e the a n i s o t r o p y i n c r e a s e s w i t h i n c r e a s i n g s t r a i n . F i g u r e 3.30 shows the 140 pe r cen t d a t a o f F i g u r e 3.29 and d a t a f o r Sn-1% B i ^ ^ . 57 C l a r k found t h a t f o r a t r u e s t r a i n o f 25 p e r c e n t t h e g r a i n s i z e e n -hancement f i r s t i n c r e a s e d and t h e n d e c r e a s e d w i t h d e c r e a s i n g s t r a i n r a t e . The S n - B i d a t a to t he l e f t o f maximum A G S / G S ^ was o b t a i n e d t h r o u g h c r e e p t e s t i n g w h i l e the h i g h e r s t r a i n r a t e d a t a r e s u l t e d f rom I n s t r o n t e s t i n g . The r e l a t i v e g r a i n s i z e enhancement was a l s o p l o t t e d a g a i n s t t r u e s t r a i n r e s u l t i n g i n t h e l i n e a r r e l a t i o n s h i p s o f F i g u r e 3 .31 . A A G S / G S Q a e r e l a t i o n s h i p was a l s o found by C l a r k f o r Sn-1% B i ^ 3 0 \ The g r a i n s i z e f o r v a r i o u s s t r a i n s may a l s o be p l o t t e d as a f u n c t i o n o f t e n s i l e t e s t t i m e . In F i g u r e 3.32 d a t a has been p l o t t e d i n t h i s f a s h i o n a l o n g w i t h t h e o r e t i c a l c u r v e s o f C l a r k ba sed on a d i f f u s i y i t y enhancement m o d e l . C l a r k ' s e x p e r i m e n t a l d a t a was c o n s i s t e n t w i t h h i s t h e o r e t i c a l c u r v e s f o r t h e s t r a i n r a t e s shown. F o r Z n - l A l d e -formed a t v a r i o u s s t r a i n r a t e s o v e r the same t e n s i l e t ime p e r i o d l a r g e g r a i n s i z e w i l l be a s s o c i a t e d w i t h t h e h i g h e r s t r a i n r a t e s o r e q u i v a l e n t l y the g r e a t e s t s t r a i n . However, f o r a p a r t i c u l a r s t r a i n the change i n g r a i n s i z e i n c r e a s e s w i t h d e c r e a s i n g s t r a i n r a t e o r e q u i v a l e n t l y i n -c r e a s i n g t e n s i l e t e s t t i m e . The change i n g r a i n s i z e , G . S . - G . S . Q , v e r s u s t e n s i l e t e s t t ime i s shown i n F i g u r e 3 .33. A l s o i n c l u d e d i s d a t a o f Bophy e t a l , f o r wh i ch a t a g i v e n e l o n g a t i o n r a t e , t he change i n g r a i n s i z e was found t o be p r o p o r t i o n a l . t o t he -|- power o f d e f o r m a t i o n t i m e . Fo r Z n - l A l a s i m p l e p r o p o r t i o n a l i t y i s no t a p p a r e n t a l t h o u g h t h e p r e s e n t d a t a i s no t s u f f i c i e n t to r u l e ou t such a p o s s i b i l i t y . An ave rage g r a i n growth r a t e , a t 140 p e r cent s t r a i n i s shown p l o t t e d a g a i n s t i n s t a n t e o u s s t r a i n r a t e i n F i g u r e 3.34 ( c a l c u l a t e d f rom X -head speed and the i n s t a n t e o u s gage l e n g t h ) . The growth r a t e i n c r e a s e s 58 w i t h i n c r e a s i n g s t r a i n r a t e i n t o t h e s t a g e I I - I I I t r a n s i t i o n a t w h i c h p o i n t i t b e g i n s to d e c r e a s e . Summar iz ing the d e f o r m a t i o n g r a i n growth b e h a v i o u r f o r Z n - l A l : 1. G r a i n growth o c c u r r e d d u r i n g t e n s i l e t e s t i n g , and r e s u l t e d s o l e l y as a consequence o f such d e f o r m a t i o n . Such g rowth was found to i n c r e a s e c o n s t a n t l y w i t h s t r a i n , o r f o r a f i x e d s t r a i n , c o n s t a n t l y w i t h d e c r e a s i n g s t r a i n r a t e i n s t a g e s I and I I . 2. A n i s o t r o p y i n c r e a s e d , f o r a p a r t i c u l a r s t r a i n , w i t h d e c r e a s i n g s t r a i n r a t e , and f o r a c o n s t a n t i n i t i a l s t r a i n r a t e , w i t h i n -c r e a s i n g s t r a i n . 3. The r e l a t i v e g r a i n s i z e enhancement i n c r e a s e d d u r i n g a l l s t a g e s o f d e f o r m a t i o n f o r a t r u e s t r a i n o f 80 p e r c e n t . 4. A l i n e a r r e l a t i o n s h i p was found between r e l a t i v e g r a i n s i z e i n c r e a s e and t r u e s t r a i n f o r s t a g e I I d e f o r m a t i o n i n b o t h the l o n g i t u d i n a l and t r a n s v e r s e d i r e c t i o n s . 5. The g e n e r a l form o f t h e c u r v e s f o r g r a i n s i z e v e r s u s t e n s i l e t e s t t i m e , f o r s t a g e s I and I I d e f o r m a t i o n , were found t o be s i m i l a r to t h e o r e t i c a l c u r v e s by C l a r k b a s e d on a d i f f u s i v i t y enhancement m o d e l . 6. A s i m p l e power r e l a t i o n s h i p between change i n g r a i n s i z e and the t e n s i l e t e s t t ime was no t f o u n d . 7. F o r a s t r a i n o f 140 p e r c e n t t he ave rage g r a i n growth r a t e was a £ n , f o r s t a g e I and I I d e f o r m a t i o n , w i t h the v a l u e o f n b e i n g a p p r o x i m a t e l y 0 . 7 . i r I r i | r 1 1 j 1 1 1 —r tn c o few o 13. UJ N CO < tr 2.0 G.S. 1 . 0 X 1 1 0 -4 10 STAGES i a n x x x X STAGE'm G.So X X 10 10 10"" STRAIN R A T E , min.-' FIGURE 3 . 2 4 , The g r a i n s i z e , at v a r i o u s s t r a i n r a t e s , f o l l o w i n g iho percent s t r a i n , T = 23°C; I 0 J Cn CO 09 61 FIGURE 3 . 2 6 . I n t e r n a l m i c r o s t r u c t u r e f o l l o w i n g 600 percent s t r a i n at a s t r a i n r a t e of 0 . 0 1 min.--*- Length/width r a t i o equals 1 . 8 . For i n i t i a l g r a i n s i z e see F i g . 3°l(a). T = +23°C, NaOH-HNO e t c h . x 3 , 8 0 0 62 a) € = 0 . 9 min." mifcfc A X I S b) € = 0 . 0 9 4 m i n 0 ~ FIGURE 3 » 2 7 . Surface m i c r o s t r u c t u r e s f o l l o w i n g l 4 0 percent s t r a i n -see s e c t i o n 2 . 4(b). L G = O . 8 9 and O .96 microns perpendicular o and p a r a l l e l t o T.A., T = +23 C. x 3 , 1 0 0 63 d) e = 0 . 0 0 0 9 min." Figure 3 . 2 7 - con't 64 Figure 3.28 - can't i o J + i o - 3 I 0 - 2 I 0 - i I0< STRAIN RATE , min.-" FIGURE 3 „ 2 9 „ The r e l a t i v e grain size enhancement at various s t r a i n rates. T = 23 C. Strain = 2 0 , iko, and 260 percent. 67 TRUE STRAIN (%) 3.31. The r e l a t i v e grain'size enhancement as a function of true s t r a i n . 1 p j r~—~r \ i — — Y — ~ i 1 — ~i r~ T i I 1 1 1 1 1 I i I I i t i i L 0.1 1 10 100 1000 T E N S I L E T E S T T I M E (rninr") FIGURE 3.32. The grain size versus t e n s i l e test time for Sn-IBi and Zn- l A l . ON CO 10 ••'BUM 2 OT c o u i i o cn o I <A 0 . 5 -03 © II TO T.A. G.S A ± TO T.A. 0.016 min.-i DATA Or REF.(29) 0.048 min.-' 0.16 min.-i / / 001 min.-1 ± _L o . i 10 1 0 0 TENSILE T E S T TIME (min.) 1 0 0 0 FIGURE 3 - 3 3 • The change i n grain size versus-tensile test time for a N i - Fe-Or a l l o y and Zn-lAl. T - +23°C. o 4. DISCUSSION 4 . 1 . O v e r a l l (13) In d i s t i n c t i o n to Zn -0 .2A1 , a s o l i d s o l u t i o n a l l o y , Z n - l A l c o n s i s t s o f a z i n c r i c h m a t r i x c o n t a i n i n g a f i n e l y d i s p e r s e d aluminum r i c h p r e c i p i t a t e . T h i s a l l o y was chosen to r e d u c e t h e p r o b l e m s o f g r a i n growth a s s o c i a t e d w i t h the more d i l u t e a l l o y and to o b t a i n a d i s t i n c t 3 - s t a g e s t r e s s - s t r a i n r a t e b e h a v i o r . S u p e r p l a s t i c d e f o r m a t i o n was o b s e r v e d ove r a r ange o f s t r a i n r a t e s and t e m p e r a t u r e s . Z n - l A l s u p e r p l a s t i c p r o p e r t i e s were e s t a b l i s h e d by d e t e r m i n i n g l ° g s t r e s s v e r s u s l o g s t r a i n r a t e c u r v e s as a f u n c t i o n o f g r a i n s i z e and o f t e m p e r a t u r e , F i g u r e s 3 . 5 and 3 .8 . The r e q u i r e m e n t f o r s u p e r p l a s t i c f l o w o f a h i g h s t r a i n r a t e s e n s i t i v i t y ove r an a p p r o p r i a t e s t r a i n r a t e range was f u l f i l l e d . S t r a i n r a t e s e n s i t i v i t y , and hence s u p e r p l a s t i c c r e e p , was dependent upon p a r a m e t e r s such as s t r a i n r a t e , t e m p e r a t u r e , second phase and g r a i n s i z e . The t e m p e r a t u r e - d e p e n d e n c e o f t he c r e e p r a t e was e s t a b l i s h e d o v e r the 3 s t a g e s o f d e f o r m a t i o n . F u r t h e r e v i d e n c e i n s u p p o r t o f p a r t i c u l a r s u p e r p l a s t i c d e f o r m a t i o n mechanisms was o b -t a i n e d through m e t a l l o g r a p h i c o b s e r v a t i o n s . 4 . 2 . S tage I I I D e f o r m a t i o n D e f o r m a t i o n by s l i p i s thought to o c c u r i n s t a g e I I I . M a s s i v e s u r f a c e s l i p and i n t e r n a l s l i p ( t h i n f o i l s ) was o b s e r v e d a t + 23°C and - 1 0 0 ° C r e s p e c t i v e l y i n s u p p o r t o f t h i s v i ew . The s t a g e I I I a c t i v a t i o n energy o f 11 to 13 k c a l / m o l e was g r e a t e r t han the s t a g e I I v a l u e b u t c e r t a i n l y no t comparab le w i t h the b u l k d i f f u s i o n v a l u e o f ^ 23 k c a l / m o l e . (32) Dona ld son f ound comparab le a c t i v a t i o n energy v a l u e s f o r the r a t e 73 c o n t r o l l i n g p r o c e s s f o r s t a g e I I I d e f o r m a t i o n o f Cd-8u and P b - 5 ) J . The p r e s e n t AH^ v a l u e f o r Z n - l A l wou ld sugges t t h a t t he r a t e c o n t r o l l i n g p r o c e s s o c c u r s i n t h e v i c i n i t y o f t h e g r a i n b o u n d a r i e s and n o t i n the b u l k , w h i c h i s r e a s o n a b l e i n terms o f t h e 2nd phase morpho logy and d i s -t r i b u t i o n and the m i c r o n g r a i n s i z e . F o r g r a i n s i z e s < 5 m i c r o n s (d 2 < 0 . 4 5 ) , the H a l l - P e t c h a n a l y s i s a t - 1 0 0 ° C g i v e s f u r t h e r e v i d e n c e o f t he i m p o r t a n c e o f g r a i n b o u n d a r i e s as b a r r i e r s to d i s l o c a t i o n movement. 4 . 3 . Stages I and I I D e f o r m a t i o n V a r i o u s mechanisms may i n d e p e n d e n t l y o r i n c o m b i n a t i o n c o n -t r i b u t e to the t o t a l s t r a i n d u r i n g s u p e r p l a s t i c d e f o r m a t i o n . T h e r e i s s t i l l a c o n s i d e r a b l e c o n t r o v e r s y o v e r w h i c h mechanisms p r e d o m i n a t e d u r i n g such d e f o r m a t i o n . The mechanisms c o n s i d e r e d i n the c o n t e x t o f Z n - l A l a r e d i f f u s i o n a l c r e e p p r o c e s s e s , boundary s l i d i n g and m i g r a t i o n and d i s l o c a t i o n p r o c e s s e s . The r e l a t i o n s h i p between f l o w s t r e s s and g r a i n s i z e (a a L ) has been e s t a b l i s h e d f o r many s u p e r p l a s t i c m e t a l s and g i v e n as e v i d e n c e i n s u p p o r t o f v a r i o u s d e f o r m a t i o n mechanisms. V a l u e s o f ' a ' o f 1, 2 and 3 have been a s s o c i a t e d w i t h boundary s h e a r i n g , N a b a r r o - H e r r i n g (N-H) and (23) C o b l e d i f f u s i o n a l c reep r e s p e c t i v e l y . The v a l u e s o f ' a ' f o r Z n - l A l were found to i n c r e a s e f rom a s t a g e I v a l u e o f 0.9 t o a s t a g e I I (13) v a l u e o f 1.7. Cook >found a c o r r e s p o n d i n g s t a g e I I v a l u e f o r Zn -0 .2A1 o f 1.3. V a l u e s o f ' a ' r a n g i n g from 0.7 to 1.2 have b e e n r e -(9 25) p o r t e d f o r the z i n c - a l u m i n i u m sys tem ' . F o r s t a g e I I I t he g r a i n s i z e dependence was n e g l i g i b l e . The p r e s e n t s t a g e I and I I v a l u e s i n d i c a t e t h a t boundary s h e a r i n g and d i f f u s i o n a l p r o c e s s e s must be c o n s i d e r e d as i s a l s o e v i d e n c e d by m e t a l l o g r a p h i c o b s e r v a t i o n s o f boundary s h e a r i n g and em-p h i r i c a l a c t i v a t i o n e n e r g i e s r e s p e c t i v e l y . The absence o f H a l l - P e t c h 74 b e h a v i o r f o r s u p e r p l a s t i c d e f o r m a t i o n g i v e s f u r t h e r s u p p o r t f o r boundary s h e a r i n g as an i m p o r t a n t d e f o r m a t i o n p r o c e s s i n s t a g e I I . (32) C a l c u l a t i o n s have been made by Dona ld son w i t h e q u a t i o n s d e v e l o p e d to p r e d i c t c reep r a t e s i n terms o f C o b l e and N-H d i f f u s i o n a l p r o c e s s e s . S t r e s s v a l u e s employed c o r r e s p o n d e d t o the s t a g e I I i n -f l e c t i o n p o i n t f o r an m-curve a t + 40° C , F i g u r e 3 .8 . The t h e o r e t i c a l l y p r e d i c t e d C o b l e and N-H c reep r a t e s were r e s p e c t i v e l y 2 and 5 o r d e r s o f magn i tude l e s s than the e x p e r i m e n t a l c r e e p r a t e s . Two f a c t o r s t h a t wou ld make the p r e d i c t e d c reep r a t e s even l ower i n v o l v e r e p l a c i n g the v a l u e s o f L and the f l o w s t r e s s a i n the C o b l e and N-H e q u a t i o n s , w i t h t h e g r a i n s i z e G.S . and the e f f e c t i v e s t r e s s r e s p e c t i v e l y . In p a r t i c u l a r , t h e e f f e c t i v e s t r e s s i n s tages I and I I wou ld be the o b s e r v e d f l o w s t r e s s minus a b a c k s t r e s s . Dona ld son a s s o c i a t e d t h i s b a c k s t r e s s f o r Cd-3u a t + 2 1 ° C w i t h l o n g range d i s l o c a t i o n i n t e r a c t i o n s . Some e v i d e n c e was o b t a i n e d f o r t h e e x i s t e n c e o f a b a c k s t r e s s i n Z n - l A l f o r s t a g e I and to a much l e s s e r deg ree f o r s t a g e I I . The f o r e g o i n g e v i d e n c e i s s u p p o r t e d by o b s e r v a t i o n s o f a d e -c r e a s i n g s t r a i n r a t e s e n s i t i v i t y i n s t a g e I. F u r t h e r e x p e r i m e n t a l work i s r e q u i r e d i n t h i s a r e a . I t must a l s o be m e n t i o n e d t h a t t he C o b l e and N-H mode l s assume a s t r a i n r a t e s e n s i t i v i t y o f u n i t y ( i . e . oae) w h i c h i n f a c t i s u n t r u e f o r most s u p e r p l a s t i c m e t a l s . In p a r t i c u l a r , the s t r a i n r a t e s e n s i t i v i t y f o r Z n - l A l was a p p r o x i m a t e l y 0.25 and 0.4 f o r s t a g e I and I I r e s p e c t i v e l y . D e f o r m a t i o n g r a i n growth d i d o c c u r i n Z n - l A l . The o v e r a l l i n c r e a s e i n g r a i n si?.e was f u r t h e r c h a r a c t e r i z e d by an a n i s o t r o p i c shape change c o n -s i d e r a b l y g r e a t e r than t h a t r e p o r t e d f o r o t h e r s u p e r p l a s t i c m e t a l s . D i f f u s i o n a l c r e e p p r o c e s s e s and s l i p d e f o r m a t i o n can l e a d to g r a i n e l o n g -(38) a t i o n . I s o l a t e d s u r f a c e s l i p bands and i n t e r n a l d i s l o c a t i o n s were 75 o b s e r v e d f o l l o w i n g s u p e r p l a s t i c d e f o r m a t i o n . I n t e r n a l d i s l o c a t i o n d e n s i t i e s were low. The q u e s t i o n as to what e x t e n t d i f f u s i o n a l c r e e p and s l i p i n d i v i d u a l l y c o n t r i b u t e to the a n i s o t r o p i c shape change o f g r a i n s i s u n r e s o l v e d . (38) G i f k i n s c r e e p mode l i n v o l v i n g boundary s l i d i n g p r e d i c t s c r e e p r a t e s o r d e r s o f magn i tude f a s t e r t han the C o b l e m o d e l , w i t h a s u g g e s t i o n t h a t such s l i d i n g wou ld r e s u l t i n no g r a i n e l o n g a t i o n . D e -f o r m a t i o n g r a i n growth w i t h o u t g r a i n e l o n g a t i o n has been o b s e r v e d f o l l o w i n g s u p e r p l a s t i c d e f o r m a t i o n i n many m e t a l s y s t e m s . An ana l ogous m o d e l , (27) by A l d e n , s u gge s t s t h a t due to the f i n e g r a i n s i z e o f s u p e r p l a s t i c m e t a l s b o u n d a r i e s f u n c t i o n as f a s t - a c t i n g s i n k s f o r d i s l o c a t i o n s making s l i p accommodat ion f o r g r a i n o r phase boundary s l i d i n g t h e d o m i n a n t ' d e -f o r m a t i o n p r o c e s s i n s t a g e I I . R e g a r d l e s s o f any mode l r e q u i r e m e n t s , boundary s l i d i n g and g r a i n e l o n g a t i o n p r o c e s s e s o c c u r s i m u l t a n e o u s l y i n Z n - l A l . The a v e r a g e d e f o r m a t i o n g r a i n growth r a t e was found to i n c r e a s e t h r o u g h o u t s t a g e s I and I I . However, the l ower a ve rage growth r a t e s a s s o c i a t e d w i t h s t a g e I r e s u l t e d i n the l a r g e s t g r a i n s i z e s and a n i s o t r o p y o f g r a i n shape f o r a f i x e d s t r a i n , due to the i n c r e a s e d t e n s i l e t e s t t ime f a c t o r . The t empera tu re dependence o f the s t r a i n r a t e , f o r s t a g e I I , was c h a r a c t e r i z e d by an a c t i v a t i o n energy a p p r o x i m a t e l y e q u a l t o t h a t f o r g r a i n boundary d i f f u s i o n . S tage I a c t i v a t i o n e n e r g i e s had i n c r e a s e d t o ^ 11 k c a l / m o l e f rom the s t a g e I I v a l u e o f ^ 8.5 k c a l / m o l e . Creep (32) t e s t c a l c u l a t i o n s on Z n - l A l , by Dona ld son , a t v e r y low s t r e s s e s , showed t h a t AH, had i n c r e a s e d to a v a l u e o f ^ 16 k c a l / m o l e a t a s t r e s s A l e v e l o f 2000 p s i . S tage I a c t i v a t i o n e n e r g i e s a r e t h e r e f o r e v a r i a b l e and g r e a t e r than s t a g e I I v a l u e s . The f o r e g o i n g d i s c u s s i o n has r e v i e w e d the e x p e r i m e n t a l f i n d i n g s f o r Z n - l A l . A s i n g l e mechanism f o r s u p e r p l a s t i c d e f o r m a t i o n was n o t f o u n d . I t i s s u g g e s t e d t h a t s u p e r p l a s t i c d e f o r m a t i o n i n Z n - l A l i s r e -l a t e d to boundary s l i d i n g and m i g r a t i o n , w i t h boundary d i f f u s i o n a l p r o -c e s s e s c o n t r o l l i n g t he r a t e o f s t r a i n i n g . The b e h a v i o r o f d i s l o c a t i o n s and t h e i r r e l a t i o n s h i p to the o v e r a l l d e f o r m a t i o n p r o c e s s r ema in s u n -c e r t a i n . I t i s f e l t however t h a t d i s l o c a t i o n a c t i v i t y must be c o n s i d e r e d i n terms o f g r a i n boundary i n t e r a c t i o n s as r e l a t e d . t o boundary s l i d i n g and m i g r a t i o n . 4 .A . E m p h i r i c a l R e l a t i o n s h i p s D a t a r e l a t i n g the s t r a i n r a t e e , to the f l o w s t r e s s a , g r a i n s i z e L, and t e m p e r a t u r e T , may be combined i n an e m p h i r i c a l r e -l a t i o n s h i p c o n t a i n i n g t h e s e p a r a m e t e r s . Compar i son o f e m p h i r i c a l r e l a t i o n s h i p s w i t h f o r m a l mode l s o f t h e s u p e r p l a s t i c c r e e p p r o c e s s have (25-27) been made i n the l i t e r a t u r e . The g r a i n s i z e dependence o f t h e s t r a i n r a t e i s shown i n F i g u r e 4 . 2 , and y i e l d s t he r e l a t i o n s h i p : T h i s r e l a t i o n s h i p i s v a l i d f o r s t a g e I I d e f o r m a t i o n . F i g u r e 3.5 (L = 1.16 m i c r o n s ) y i e l d s t h e s t a g e I T e m p h i r i c a l s t r e s s dependence o f t h e s t r a i n r a t e : :^ (L ,T) = B a 2 - 4 ( 4 . 4 . 2 ) F i g u r e 3.10 y i e l d s : —AH / A ( 4 . 4 . 3 ) 7 — T — i — I — r O O o 10^ Stage I I Stage I I I _L 1 0 ° 1 0 1 GRAIN SIZE, microns FIGURE k.lc The 0 . 2 fo flow s t r e s s versus g r a i n s i z e at a s t r a i n r a t e of 0 o 0 1 min," 1. T = +23 C i 10 IO"? i o -STRAIN RATE, m i n . - 1 FIGURE 4 „ 2 . The g r a i n s i z e versus s t r a i n r a t e r e l a t i o n s h i p at a constant s t r e s s of 8 0 0 0 p s i (Fig„ 3 . 5 ) „ T = +23 C 78 Combin ing 4.4.1, 4.4.2 and 4.4.3: 2.4 -AH e = K ~ 7 T exp ( - ^ - ) (4.4.4) XJ (25) B a l l and H u t c h i n s o n , i n t h e i r s t u d y o f s u p e r p l a s t i c c r e e p i n t h e Z n - A l e u t e c t o i d s y s t e m , e s t a b l i s h e d a c o r r e s p o n d i n g r e l a t i o n s h i p o f t h e f o r m : 2 -AH e = K ^ exp ( - ~ ) (4.4.5) L The c o n s t a n t K i n equat ion(4.4.4) and (4.4.5) m i gh t be e x p e c t e d to c o n t a i n p a r a m e t e r s r e l a t e d to d i s l o c a t i o n m o t i o n and d i f f u s i o n . Examples (25) (27) would b e the t h e o r e t i c a l mode l s o f B a l l et a l , and A l d e n . 79 5. CONCLUSIONS 1. Zn - 1A1 was found to be s u p e r p l a s t i c o v e r a r ange o f s t r a i n r a t e s d e -pendent on g r a i n s i z e and t e m p e r a t u r e . F o r 1 m i c r o n m a t e r i a l a t + 23°C 3 - s t a ge b e h a v i o r was o b s e r v e d w i t h s t a g e I I s t r a i n r a t e s r a n g i n g f rom -2 -1 - 1 - 1 a p p r o x i m a t e l y 10 min to 10 min . M a x i m u m . e l o n g a t i o n was - 2 -1 a p p r o x i m a t e l y 600 p e r c e n t a t a s t r a i n r a t e o f 10 min . 2. The a c t i v a t i o n energy f o r s t a g e I I was ^ 8 . 5 k c a l / m o l e . S tage I v a l u e s i n c r e a s e d f rom ^ 11.5 k c a l / m o l e (3,500 p s i ) t o A 16 k c a l / m o l e (2,000 p s i -c r e e p t e s t ). S tage I I v a l u e s a r e s l i g h t l y l ower than r e p o r t e d v a l u e s f o r g r a i n boundary d i f f u s i o n b u t a r e n e v e r t h e l e s s f e l t t o be i n d i c a t i v e o f t h a t p r o c e s s . 3. M e t a l l o g r a p h i c o b s e r v a t i o n showed g r a i n boundary s l i d i n g i n a l l 3 s t a g e s o f d e f o r m a t i o n . Cour se s u r f a c e s l i p i n c r e a s e d w i t h i n c r e a s i n g s t r a i n r a t e th roughou t t h e 3 s t a g e s . I n t e r n a l s t r u c t u r e showed v e r y l i t t l e e v i d e n c e o f d i s l o c a t i o n a c t i v i t y i n s t a g e s I and I I . S tage I I I showed a much more d e v e l o p e d d i s l o c a t i o n s u b s t r u c t u r e . 4. D e f o r m a t i o n g r a i n growth d i d o c c u r . The g r a i n s i z e and a n i s o t o p y o f g r a i n shape i n c r e a s e d d u r i n g s t r a i n i n g i n s t a g e s I and I I . F o r a p a c t i c u l a r s t r a i n ( i . e . 140 p e r c e n t ) t h e r e l a t i v e g r a i n s i z e e n -hancement i n c r e a s e d w i t h d e c r e a s i n g s t r a i n r a t e t h roughou t s t a g e s I I and I. The r e l a t i v e g r a i n s i z e enhancement was f o u n d to be p r o p o r t i o n a l t o t r u e s t r a i n f o r s t a g e I I d e f o r m a t i o n a t a s t r a i n r a t e o f 0.048 m in A t 140 p e r cen t s t r a i n the ave rage g rowth r a t e p a r a l l e l t o t he w i r e a x i s 80 increased with increasing s t r a i n rate throughout stages I and I I . 5. Hall-Petch behavior was observed at -100°C. The relationship between grain size and d i s t r i b u t i o n of second phase resulted i n two values of the/Petch constants. 6. Superplastic deformation i n Zn-lAl i s experimentally consistent with a co-operative process involving boundary s l i d i n g and migration, and boundary d i f f u s i o n . . 81 BIBLIOGRAPHY 1. Underwood, E . E . , J . o f M e t a l s , (1962) 914. 2. B a c k o f e n , W.A. e t a l , D u c t i l i t y , ASM, M e t a l s . P a r k , (1968) 279. 3. P e a r s o n , C . E . , J . I n s t . M e t a l s , 54 (1934) 111. 4. F l o r e e n , S., S c r i p t a M e t . , 1 (1967) 19. 5. C l i n e , H .E . and A l d e n , T . H . , T r a n s . AIME, 239 (1967) 710. 6. Z e h r , S.W. and B a c k o f e n , W.A. , ASM T r a n s . Q u a r t . , 6 (1968) 300. 7. S t o w e l l , C . J . e t a l , M e t a l S c i e n c e J o u r n a l , J3 (1969) 41. 8. P a c k e r , C M . e t a l , T r a n s . AIME, 242 (1968) 2485. 9. H o l t , D . L . , T r a n s . AIME, 242 (1968) 25. 10. A l d e n , T . H . and S c h a d l e r , H.W., T r a n s . AIME, 242 (1968) 825. 11. K o s s o w s k i , R. and B e c h t o l d , J . H . , T r a n s . AIME, 242 (1968) 716. 12. Hayden, H.W. et a l , ASM T r a n s . Q u a r t . , 60 (1967) 3. 13. Cook, R . C , M .A . Sc . T h e s i s , U .B .C . (1968). 14. L e e , D. and B a c k o f e n , W.A., T r a n s . AIME, 239 (1967) 1034. 15. P a c k e r , C M . and S h e r b y , O . D . , ASM T r a n s . Q u a r t . , 60 (1967) 21. 16. Hayden, H.W..and B r o d h y , J . H . , ASM T r a n s . Q u a r t . , 61 (1968) 542. 17. C h a u d h a r i , P . , S c i e n c e and T e c h n o l o g y , (1968) 42. 18. A v e r y , D.H. and B a c k o f e n , W.A.,ASM T r a n s . Q u a r t . , 58 (1965) 551. 19. G r a n t , N . J . , The S t r e n g t h e n i n g o f M e t a l s , ( R e i n h o l d , New Y o r k ) , (1964) 163. 20. H e r r i n g , C , J . A p p l . Phys . 21 (1950) 437. 21. C o b l e , R . L . , J . A p p l . P h y s . 34 (1963) 1979. 22. J o n e s , R.B. and J o h n s o n , R .H. , D i s c u s s i o n , ASM T r a n s . Q u a r t . , _59 (.1966) 356. 23. H o l t , D.L. .and B a c k o f e n , Q . A . , ASM T r a n s . Q u a r t . , 59_ (1966) 755. 82 24. Alden, T.H., Acta Met., 15 (1967) 469. 25. B a l l , A., Hutchison, M.M., Metal Science Journal, 3 (1969) 1. 26. Alden, T.H., ASM Trans. Quart., 61 (1968) 559 27. Alden, T.H., J . Aust. Inst., Met. 14 (1969) 207. 28. Chaudhari, P., Acta Met., 15 (1967) 1777. 29. Brodhy, J.H., et a l , ASM Trans. 62_ (1969) 230. 30. Clark, M.A., M.A.Sc. Thesis, U.B.C. (1970). 31. Alden, T.H., Acta Met., 17 (1969) 1435. 32. Donaldson, K.C. Ph.D. Thesis, U.B.C. (1971). 33. Waldron, R.J., Ph.D. Thesis, U.B.C. (1970). 34. Honeycombe, R.W.K., The P l a s t i c Deformation of Metals, (E. Arnold Ltd.),(1968) 365. 35. Wajda, E.S., Acta Met., 2 (1954) 184. 36. Lund, J.A., and Tromans, D,, ASM Trans. Quart., 5_9 (1966) 672. 37. Risebrough, N.R., and Lund, J.A. Trans. ASM 6_1 (1968) 722. 38. G i f k i n s , R.C., J . Inst.. Met. , 95. (1967) 373. 39. Risebrough, N.R. , Ph.D. Thesis, U.B.C, (1965). 

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