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Superplasticity in a dilute zinc aluminum alloy Cook, Richard Charles 1968

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SUPERPLASTICITY IN A DILUTE ZINC ALUMINUM ALLOY by RICHARD CHARLES COOK B.A.Sc, Un i v e r s i t y of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of METALLURGY We accept t h i s thesis as conforming to the r e q u i r e d ^ tandapd THE UNIVERSITY OF BRITISH COLUMBIA September, 1968 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r re fe rence and Study. I f u r t h e r agree that permiss ion fo r e x t e n s i v e copying of t h i s t h e s i s fo r s c h o l a r l y purposes may be granted by the Head of my Department or by h.i>s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s fo r f i n a n c i a l gain s h a l l not be a l lowed wi thout my w r i t t e n p e r m i s s i o n . Department of Metallurgy  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada . ABSTRACT The system Zn-0.2 wt. % Al has been investigated to determine under what conditions of strain rate, grain size and temperature the phenomenon of superplasticity may be observed. The analysis and experimental conditions were based on established procedures which have been applied to known superplastic alloys. However the continually decreasing strain rate and grain growth during testing complicate the normal analysis. Based on this study the requirements for superplastic behavior are a fine-grained microstructure, grain boundaries which are relatively free of obstructions and a homolohous temperature of at least 0.42. A model incorporating grain boundary shear and non- continuous grain growth has been proposed to account for the observed superplastic behavior where grain boundary migration is the rate controlling process. ABSTRACT The system Zn-0.2 wt. % A l has been investigated to determine under what conditions of s t r a i n r ate, grain s i z e and temperature the phenomenon of s u p e r p l a s t i c i t y may be observed. The analysis and experimental conditions were based on established procedures which have been applied to known superplastic a l l o y s . However the continually decreasing s t r a i n rate and grain growth during t e s t i n g complicate the normal an a l y s i s . Based on t h i s study the requirements f o r superplastic behavior are a fine-grained microstructure, grain boundaries which are r e l a t i v e l y f r ee of obstructions and a homolohous temperature of at l e a s t 0.42. A model incorporating g r a i n boundary shear and non- continuous g r a i n growth has been proposed to account f o r the observed s u p e r p l a s t i c behavior where grain boundary migration i s the rate c o n t r o l l i n g process. i i ACKNOWLEDGEMENT The author i s g r a t e f u l f o r the adv ice and encouragement g i v e n by h i s r e s e a r c h d i r e c t o r , Dr . N. R. R isebrough . Thanks are a l s o extended to f e l l o w graduate s tudents f o r t h e i r many h e l p f u l d i s c u s s i o n s . F i n a n c i a l a s s i s t a n c e was r e c e i v e d i n the form of an a s s i s t a n t - s h i p under N a t i o n a l Research C o u n c i l of Canada grant number A - 3 6 7 5 , and i s g r a t e f u l l y acknowledged. i i i TABLE OF CONTENTS Page 1 . INTRODUCTION 1 2 . EXPERIMENTAL 4 2 . 1 . M a t e r i a l P r e p a r a t i o n . . . . . . . . 4 2 . 1 . 1 . Ext ruded C a s t i n g s 5 2 . 1 . 2 . Ext ruded Powders 7 2 . 1 . 3 . R o l l e d M a t e r i a l 7 2 . 2 . Specimen P r e p a r a t i o n 7 2 . 3 . T e n s i l e Procedures . . . . 8 2 . 4 . M e t a l l o g r a p h y 9 3 . RESULTS 11 3 . 1 . Ext ruded C a s t i n g s 11 3 . 1 . 1 . P r e l i m i n a r y I n v e s t i g a t i o n 11 3 . 1 . 2 . G r a i n S i z e E f f e c t 11 3 . 1 . 3 . E f f e c t of Temperature 19 3 . 2 . Ext ruded Powders 25 3 . 2 . 1 . E f f e c t of Temperature 25 3 . 3 . R o l l e d C a s t i n g s 28 3 . 3 . 1 . G r a i n S i z e E f f e c t 31 3 . 4 . H a l l - P e t c h R e l a t i o n s h i p 31 3 . 5 . S t r e s s - S t r a i n Curves 32 3 . 5 . 1 . Nature of the S t r e s s - S t r a i n Curves . . . 32 3 . 5 . 2 . M i c r o s t r u c t u r a l Changes w i t h i n c r e a s i n g S t r a i n 34 3 . 5 . 3 . S t r a i n Rate Dependence of True S t r e s s - S t r a i n Curves 44 3 . 5 . 4 . E f f e c t of G r a i n S i z e . o n S t r e s s Dur ing Deformat ion 47 i v TABLE OF CONTENTS (Cont) Page 4 . DISCUSSION . . 48 4 . 1 . S i g n i f i c a n c e of the S t r a i n Rate S e n s i t i v i t y Parameter 48 4 . 2 . I m p l i c a t i o n s of Mechanism 50 5 . SUMMARY AND CONCLUSIONS 54 6 . SUGGESTIONS FOR FUTURE WORK 56 7 . APPENDICES 57 7 . 1 . E v a l u a t i o n of the S t r a i n Rate S e n s i t i v i t y Parameter 57 7 . 2 . V a r i o u s Specimens Deformed to F a i l u r e at D i f f e r e n t S t r a i n Rates . 59 8 . BIBLIOGRAPHY 61 LIST OF FIGURES M i c r o s t r u c t u r e of Z n - 0 . 2 wt . % A l O r i g i n of S -shaped l o g a - l o g i curve (schematic) The e f f e c t of p r e p a r a t i o n h i s t o r y on 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 f o r ext ruded m a t e r i a l . T = +23°C. The e f f e c t of g r a i n s i z e on 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 f o r ext ruded m a t e r i a l . T = +23°C. The r e l a t i o n s h i p between the r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e . L Q = 3 . 5 m i c r o n s , T = +23°C. The r e l a t i o n s h i p between the r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e . L Q = 1 .6 m i c r o n s , T = +23°C. The e f f e c t of t e s t i n g temperature on 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 . L D= 3 . 7 m i c r o n s . The r e l a t i o n s h i p between the s t r a i n r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e a t d i f f e r e n t t e s t temperatures L = 3 .7 m i c r o n s . A r r h e n i u s p l o t f o r c a s t and ext ruded m a t e r i a l . L = 3 .7 m i c r o n s . The e f f e c t of t e s t i n g temperature 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 f o r pure z i n c . L = 5 microns * 0 . 5 m i c r o n . The e f f e c t of t e s t i n g temperature 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 f o r ext ruded powder a l l o y s . L = 2 m i c r o n s . A r r h e n i u s p l o t f o r ext ruded powders. L = 2 m i c r o n s . The e f f e c t of g r a i n s i z e on the y i e l d 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 . T = +23°C. H a l l - P e t c h p l o t f o r Z n - 0 . 2 wt . % A l . T = +23°C. True s t r e s s - s t r a i n curves f o r specimens of d i f f e r e n t i n i t i a l g r a i n s i z e s . T = +23°C, i = 1 .5 x 1 0 - 2 m i n . - 1 True s t r e s s - s t r a i n curves f o r specimens sub jec ted to d i f f e r e n t s t r a i n s . T = +23°C, i = 7 .8 x 1 0 " 3 m i n . Sur face defo rmat ion c h a r a c t e r i s t i c s at d i f f e r e n t s t r a i n s . T = +23°C, E = 7 .8 x 10 -3 m i n . - 1 , L Q = 1.6 m i c r o n s . v i LIST OF FIGURES (Cont) No. Page 18. S l i p t r a c e s at 43% s t r a i n . T = +23°C, £ = 7 . 8 x l 0 - 3 m i n . - l , L Q = 1 .6 m i c r o n s . 39 19 . G r a i n boundary shear and g r a i n r o t a t i o n a t 43% s t r a i n . T = +23°C, t = 7 .8 x 1 0 " 3 m i n . - 1 , L Q = 1.6 m i c r o n s . 40 20 . As s t r a i n e d s u r f a c e showing s t r i a t e d bands (marked by arrows) i n g r a i n boundary r e g i o n s a t 43% s t r a i n . T = +23°C, i = 7 .8 x 1 0 - 3 m i n . - l , Lo = 1.6 m i c r o n s . 41 2 1 . Dependence of g r a i n s i z e on s t r a i n . T = +23°C, e = 7 .8 x 1 0 " 3 m i n . - 1 43 22 . True s t r e s s - s t r a i n curves f o r c a s t and extruded m a t e r i a l . T = +23°C, L Q = 3 .2 m i c r o n s . 45 2 3 . Dependence of s t r e s s on g r a i n s i z e a t v a r i o u s s t r a i n r a t e s . T = +23°C. 46 1 1 . INTRODUCTION The phenomenon of s u p e r p l a s t i c i t y has been i n v e s t i g a t e d 1-20 27 e x t e n s i v e l y i n the l a s t decade ' . M a t e r i a l from numerous m e t a l systems i n c l u d i n g those of e u t e c t i c , e u t e c t o i d and e s s e n t i a l l y phase pure compos i t ion e x h i b i t the a b i l i t y to w i t h s t a n d l a r g e amounts of n e c k - f r e e d e f o r m a t i o n . I n t e r e s t has been focussed on the search f o r a deformat ion mechanism which i s c o n s i s t e n t w i t h the t e n s i l e 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 . On the o ther hand, the i m p l i c a t i o n s of the p o s s i b l e 3 5 advantages i n a m e t a l - f o r m i n g o p e r a t i o n have not been over looked ' . The b a s i s f o r s u p e r p l a s t i c i t y i s a s t r o n g dependence of the f l o w s t r e s s (a) on the imposed s t r a i n r a t e ( £ ) . These parameters are 3 u s u a l l y r e l a t e d through the r e l a t i o n s h i p : a = Ke where K i s a constant and m i s the s t r a i n r a t e s e n s i t i v i t y parameter . Va lues of m v a r y from l e s s than 0 . 1 f o r most meta ls up to 1 .0 f o r hot polymers and g l a s s e s . At s t r a i n r a t e s where m i s h i g h , the r e g i o n of an i n c i p i e n t neck w i l l be hardened due to the l o c a l i z e d i n c r e a s e i n s t r a i n r a t e and the defo rmat ion proceeds i n the s o f t e r reg ions of the sample. Thus i t i s apparent that f o r a s u f f i c i e n t l y h i g h v a l u e of m (approx imate ly 23 0 . 3 to 0 . 7 ) , l a r g e amounts of deformat ion (up to 2000% e l o n g a t i o n ) can be o b t a i n e d . I t i s known t h a t s u p e r p l a s t i c i t y can be ob ta ined i n a system where a s t r u c t u r a l phase change occurs d u r i n g d e f o r m a t i o n . Thus e a r l i e r s t u d i e s were concerned w i t h two phase a l l o y systems and i t was 2 thought tha t the requi rements were a d i f f u s i o n - c o n t r o l l e d s t r u c t u r a l change concur rent w i t h the deformat ion and a homologous temperature g r e a t e r than 0 . 5 . More recent i n v e s t i g a t i o n has shown t h a t a phase change i s not a necessary requirement and the most important s t r u c t u r a l c o n d i t i o n 4 -12 i s a f i n e l y d i v i d e d m i c r o s t r u c t u r e . T h i s requirement i s e a s i l y 2 s a t i s f i e d i n two phase systems since a s t a b l e , fine-grained micro- structure i s r e a d i l y obtainable. The most extensively studied systems have been the eutectoid Zn-22 wt. % A l and the Sn-Pb a l l o y systems. The eutectic/eutectoid a l l o y systems generally a l l require a hot working step to produce large numbers of i n t e r c r y s t a l l i n e boundaries before the material behaves s u p e r p l a s t i c a l l y and they possess the c h a r a c t e r i s t i c of having two phases which constitute about equal volume f r a c t i o n s of the a l l o y . As opposed to t h i s type of system, extensive work has been c a r r i e d out on e s s e n t i a l l y phase pure 22 7 systems: G i f k i n s on Pb-2-8% Th., C l i n e and Alden on Sn-2wt. % Pb, and pure Sn, Alden on Sn-5wt. % B i ^ , Sn-lwt. % B i ^ , and F l o r e e n 2 ^ on pure N i . Since i t has been generally accepted that a fine-grained microstructure, along with a homologous temperature greater than 0.5, i s e s s e n t i a l to the s u p e r p l a s t i c phenomenon, the inherent problem i n a l l these systems has been to achieve and r e t a i n a f i n e grain s i z e i n the test m a t e r i a l . Thus, the r o l e of the small additions of a second-phase material has been s i m i l a r to the r o l e played by interphase boundaries i n two phase materials, that i s , to r e s t r i c t g r ain growth during material and specimen preparation. Several possible mechanisms have been proposed to account f o r the high rate s e n s i t i v i t i e s and the large amounts of elongation that have been observed i n these systems. 12 a) Holt suggested a model f o r the Zn-Al eutectoid system which was based on grain boundary shear and associated migration of the boundaries to r e l i e v e stress concentrations at t r i p l e points. This suggestion i s g f u r t h e r supported by Holt and Backofen i n the Al-33 wt. % Cu e u t e c t i c system where i t was proposed that grain boundary shear was the rate c o n t r o l l i n g process and that mechanical obstructions to s l i d i n g were removed through s t r a i n r a t e enhanced boundary m i g r a t i o n or r e c r y s t a l l i z a t i o n . G r a i n boundary s l i d i n g was a l s o proposed by A lden^ ^ to be the r a t e c o n  t r o l l i n g p rocess i n S n - B i and Sn-Pb a l l o y s and i t was shown^ tha t the c o n t r i b u t i o n of boundary shear to de fo rmat ion was g r e a t e s t at the maximum v a l u e of the r a t e s e n s i t i v i t y parameter m. At h i g h s t r a i n r a t e s where m v a l u e s are low, i t was found t h a t deformat ion became s l i p c o n t r o l l e d and s u p e r p l a s t i c i t y was not observed . b) The e u t e c t i c system Sn-38 wt . % Pb was examined by Avery and Backofen and they proposed tha t two c o m p e t i t i v e processes c o n t r i b u t e d to the d e f o r m a t i o n . One i n v o l v e s d i s l o c a t i o n mot ion which accounts f o r the low r a t e s e n s i t i v i t y at h i g h s t r a i n r a t e s and the o ther i s v i s c o u s f l o w a s s o c i a t e d w i t h 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 . 26 The Coble v a r i a n t of the N-H a n a l y s i s was suggested by Jones and Johnson i n a d i s c u s s i o n of B a c k o f e n ' s work on the Sn-Pb system^. T h i s model i s based on g r a i n boundary d i f f u s i o n r a t h e r than volume d i f f u s i o n and i t was suggested t h a t i t p r e d i c t e d the deformat ion behav io r more a c c u r a t e l y than the normal N-H a n a l y s i s . c) Zehr and Backof e n ^ suggested tha t g r a i n boundary shear a c t i n g i n p a r a l l e l w i t h d i f f u s i o n a l creep accounts f o r the h i g h r a t e s e n s i t i v i t y 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 observed at low s t r a i n r a t e s i n the Sn-Pb sys tem. E x p e r i m e n t a l 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 s cou ld be reproduced by s e m i - e m p i r i c a l procedures based on t h i s model . 17 4 d) Packer and Sherby proposed a m o d i f i c a t i o n to Avery and B a c k o f e n ' s a n a l y s i s of the data f o r the Sn-Pb e u t e c t i c system. They have suggested t h a t a model based on r e c r y s t a l l i z a t i o n or g r a i n boundary m i g r a t i o n a s s o c i a t e d w i t h a d i s l o c a t i o n - c l i m b - c o n t r o l l e d process r e s u l t s i n b e t t e r agreement w i t h h i g h r a t e s e n s i t i v i t y and m i c r o s t r u c t u r a l e f f e c t s observed. 14 F u r t h e r to t h i s sugges t ion Hayden et a l have proposed that the mechanism 4 of s u p e r p l a s t i c f l o w may be s i m i l a r to the recovery creep mechanism of 28 29 Mott and F r i e d e l based on d i s l o c a t i o n c l i m b . T h e i r r e s u l t s on the two-phase N i - F e - C r system do not support a model based on N-H d i f f u s i o n a l 18 c r e e p . In support of t h i s argument Kossowsky and Bechto ld - have examined the Z n - A l e u t e c t o i d system and have proposed tha t a d i s l o c a t i o n c l imb mechanism i s r a t e c o n t r o l l i n g and p r e d i c t s the c o r r e c t v a l u e s f o r the r a t e s e n s i t i v i t y observed . 20 e) A l d e n , i n a recent p r o p o s a l , has p o s t u l a t e d a c l i m b - g l i d e d i s l o c a t i o n process which would support a model based on g r a i n boundary s l i d i n g . I t i s suggested tha t the g l i d e component c o n t r i b u t e s d i r e c t l y to s l i d i n g but tha t i t i s the c l imb component which i s r a t e d e t e r m i n i n g . Most of the above i n t e r p r e t a t i o n s have been based on an a n a l y s i s of m v a l u e s and c o r r e l a t i o n s between f l o w s t r e s s and g r a i n s i z e . 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 have g e n e r a l l y been r e s t r i c t e d to the s t r u c t u r e s p resent a f t e r r e l a t i v e l y s m a l l amounts of deformat ion (<50% s t r a i n ) . In the p resent work an a l l o y of Z n - 0 . 2 wt . % A l has been prepared by c a s t i n g and f i n a l e x t r u s i o n to ach ieve a f i n e - g r a i n e d , equiaxed m i c r o s t r u c t u r e . T h i s system was chosen so the t e n s i l e behav io r of the Z n - r i c h s o l i d s o l u t i o n of the e u t e c t o i d a l l o y cou ld be s t u d i e d . I t shou ld be noted t h a t p rev ious s t u d i e s on the e u t e c t o i d have been c a r r i e d out at h i g h homologous temperatures (T = 0 . 9 based on the n i n v a r i a n t tempera tu re ) . The t e n s i l e behav io r has been i n v e s t i g a t e d over a range of temperatures to determine the c o n d i t i o n s under which s u p e r - p l a s t i c i t y might be o b t a i n e d . 2 . EXPERIMENTAL 2 . 1 . M a t e r i a l P r e p a r a t i o n A master a l l o y of 5 . 5 wt . % A l was prepared u s i n g s p e c i a l h i g h p u r i t y z i n c (99.999%) and aluminum (99.995%). M a t e r i a l s were prepared e i t h e r by a c a s t i n g or s h o t t i n g procedure f o l l o w i n g the d i l u t i o n to the d e s i r e d a l l o y compos i t ion of Z n - 0 . 2 wt . % A l . M e l t i n g was c a r r i e d out at temperatures of 700-750°C under a f l u x cover of NaCl-50% KC1 to prevent e x c e s s i v e o x i d a t i o n of the z i n c . The melt was h e l d at 700°C f o r 30 minutes p r i o r to c a s t i n g or s h o t t i n g to i n s u r e complete d i s s o l u t i o n of the aluminum i n the z i n c . 2 . 1 . 1 . Ext ruded C a s t i n g s The mel t was c h i l l cas t from 700°C to g i ve b i l l e t s of approximate dimensions 2 .5 i n . by 0 . 9 i n . d iameter . The b i l l e t s were homogenized at 350°C f o r 60 hours i n order to r e d i s s o l v e a l l the A l - r i c h second phase and were then water quenched, to produce a f i n e , randomly d i s t r i b u t e d p r e c i p i t a t e . A f t e r reduc ing the d iameter of the b i l l e t to approx imate ly 0 .75 i n . two d i f f e r e n t e x t r u s i o n procedures were used . In order to ach ieve a f i n e g r a i n s t r u c t u r e the temperature of e x t r u s i o n must be kept as low as p o s s i b l e and to t h i s end a b i l l e t was wrapped i n l e a d f o i l and hot ext ruded i n a s i n g l e o p e r a t i o n at 80°C w i t h a p ressure of 144,000 p s i ( e x t r u s i o n r a t i o 42 :1 ) the g r a i n s i z e obta ined was 3 . 5 m i c r o n s . To ach ieve a f i n e r g r a i n s i z e , a second b i l l e t was extruded a t 30°C and a p r e s s u r e of 144,000 p s i u t i l i z i n g Carbowax 1500 as a d i e l u b r i c a n t . Us ing t h i s procedure the g r a i n s i z e was reduced to 1.6 microns ( F i g . l a ) . The extruded rods of 0 .15 i n . d iameter were s t o r e d i n l i q u i d n i t r o g e n w i t h i n 15 minutes of e x t r u s i o n . To determine the e f f e c t of the s o l u t e a d d i t i o n , pure z i n c (99.999%) was c h i l l c a s t , homogenized under s i m i l a r c o n d i t i o n s and hot ext ruded at room temperature and 144,000 p s i p ressure u s i n g Carbowax 1500 as a l u b r i c a n t . A g a i n , the extruded rods were immediate ly s t o r e d i n l i q u i d n i t r o g e n . 6 b) Cast and r o l l e d m a t e r i a l , L = 16 mic rons . F i g . 1 . M i c r o s t r u c t u r e of Zn - 0 .2 wt . % A l . 7 2.1.2. Extruded Powders The melt of identical composition was held at 700°C for 30 minutes and then was subjected to a powder making procedure as * developed by Waldron et a l . Powders in the size range -200 mesh were compacted hydrostatically into b i l l e t s approximately 3 in. by 0.75 in. diameter. The b i l l e t s were hot extruded to a f i n a l diameter of 0.150 in. u t i l i z i n g 104,000 psi extrusion pressure and a temperature of 270°C. 2.1.3. Rolled Material The melt was cast into 0.5 in. x 1.5 i n . x 5 in. b i l l e t s which were subsequently homogenized in air at 350°C for 25 days and water quenched. The b i l l e t s were cropped and machined to remove surface irregularities prior to hot ro l l i n g . To avoid cracking due to the i n i t i a l l y large grain size, r o l l i n g was carried out at approximately 300°C and reduced the thickness of the b i l l e t to 0.125 in. Grain refine ment was achieved by rolling at room temperature in steps of 0.010 in. to a f i n a l thickness of 0.045 in. Following this procedure a completely recrystallized, equiaxed microstructure was obtained (Fig. lb). 2.2. Specimen Preparation For the extruded material, tensile specimens were machined on a jeweler's lathe to a reduced diameter of 0.075 in. ^  0.0005 in. over a gauge length of 0.65 in. * .01 in. Specimens prepared from extruded castings did not exhibit the grain size s t a b i l i t y of those extruded from compacted powders and hence the heat generated during the machining was apparently sufficient to cause a slight increase i n grain size. For * Procedure given in private communication with R. J. Waldron. t h i s r e a s o n , a c o l d machin ing technique was dev ised whereby dry n i t r o g e n a t a temperature of approx imate ly -50°C was used to c o o l the specimen i n the l a t h e . Us ing t h i s techn ique on a l l samples prepared from extruded c a s t i n g s i t was p o s s i b l e to min imize the apparent problem of g r a i n growth p r i o r to t e s t i n g . For the r o l l e d m a t e r i a l t e n s i l e specimens of 0 .65 i n . gauge l e n g t h and 0 .200 i n . x 0 .045 i n . c r o s s - s e c t i o n were spark -machined from the s t r i p . Damage due to spark machin ing was n e g l i g i b l e . 2 . 3 . T e n s i l e Procedures A l l t e n s i l e t e s t s were conducted on a F l o o r Model I n s t r o n u t i l i z i n g cons tant c r o s s - h e a d speeds which v a r i e d from 2 x 10 ^ i n . / m i n . to 2 i n . / m i n . T e s t i n g media i n c l u d e d coo led e t h y l a l c o h o l (-100°C to 0°C) , heated water (22°C to 100°C), and s i l i c o n e o i l (above 100°C). Temperature c o n t r o l was ± 2°C i n a l l c a s e s . For the r o l l e d specimens g r i p p i n g was ach ieved by a s p l i t jaw g r i p arrangement and f o r the ext ruded specimens by a s p l i t , b u t t o n head g r i p which g r ipped on ly on the shou lder r e g i o n . T e n s i l e t e s t s were of two d i f f e r e n t t y p e s . The f i r s t was a normal t e n s i l e t e s t i n which the specimen was s t r a i n e d to f a i l u r e at a constant crosshead speed. The second , i n which the crosshead speed was changed i n c r e m e n t a l l y from 2 x 10~^ i n . / m i n . to 2 i n . / m i n . , a l lowed an e v a l u a t i o n of the s t r a i n 3 r a t e s e n s i t i v i t y parameter as d e s c r i b e d by Avery and Backofen (see a l s o Appendix I ) . A t any s t r a i n r a t e , when i t appeared tha t a steady s t a t e s t r e s s had been r e a c h e d , the s t r a i n r a t e was i n c r e a s e d by a f a c t o r of 2 or 2 . 5 . The amount of s t r a i n at each s t r a i n r a t e was u s u a l l y of the order of 3 to 4% so tha t the t o t a l amount of s t r a i n per t e s t was approx imate ly 30 to 40%. The v a l u e s f o r t r u e s t r e s s and t r u e s t r a i n r a t e have been c a l c u l a t e d on the b a s i s of ins tantaneous a rea and l e n g t h which were c a l c u l a t e d assuming u n i f o r m deformat ion throughout the e n t i r e gauge l e n g t h of the specimen. 2 . 4 . M e t a l l o g r a p h y E l e c t r o p o l i s h i n g was found to be the most convenient and r e l i a b l e method of p r e p a r i n g a s u r f a c e f o r 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 . P o l i s h i n g t ime was approx imate ly 30 seconds at a c u r r e n t d e n s i t y of 0 . 8 amp/cm which corresponded to the p l a t e a u v o l t a g e . The p o l i s h i n g s o l u t i o n was as f o l l o w s : 800 ml E t h y l A l c o h o l 50 ml B u t y l c e l l u s o l v e 60 g m Sodium t h i o c y a n a t e 20 ml D i s t i l l e d water Most o b s e r v a t i o n s were c a r r i e d out u s i n g p o l a r i z e d l i g h t to r e v e a l the z i n c g r a i n s t r u c t u r e . The second phase aluminum - r i c h p a r t i c l e s were a p p a r e n t l y randomly d i s t r i b u t e d throughout the z i n c m a t r i x . A separa te m e t a l l o g r a p h i c study was made on two -s tage chromium shadowed r e p l i c a s taken from a p r e p o l i s h e d deformed specimen. F i n e s c r a t c h e s imposed on the specimen s u r f a c e p r i o r to deformat ion f a c i l i t a t e d observa t ions on g r a i n boundary shear and g r a i n r o t a t i o n . G r a i n s i z e was determined by the l i n e i n t e r c e p t method u s i n g a t l e a s t two random photomicrographs which e x h i b i t e d approx imate ly one hundred i n t e r c e p t s on a s e r i e s of l i n e s drawn both p e r p e n d i c u l a r and p a r a l l e l to the t e n s i l e a x i s . M i c r o s t r u c t u r a l c o n t r o l was achieved by a n n e a l i n g the samples at e l e v a t e d temperatures f o r p e r i o d s of t ime s u f f i c i e n t to o b t a i n the d e s i r e d g r a i n s i z e . The v a r i o u s thermal and mechan ica l t reatments used to o b t a i n the i n i t i a l g r a i n s i z e s are summarized i n Table I. 10 TABLE I MECHANICAL AND THERMAL TREATMENT APPLIED TO Z n - .2 wt . % A l A l l o y D e s c r i p t i o n Thermal G r a i n S i z e D e s i g n a t i o n Treatment (Microns) A Ext ruded c a s t i n g @ 30°C as extruded 1.6 15 m i n . <§ 100°C 3 . 5 B Ext ruded c a s t i n g @ 80°C as extruded 3 . 5 15 m i n . @ 100° C 3 .7 24 m i n . @ 150°C 4 .7 30 m i n . @ 200°C 7.2 C R o l l e d C a s t i n g as r o l l e d 16 15 m i n . @ 150°C 23 25 m i n . @ 150°C 27 30 m i n . @ 250°C 66 D Ext ruded powders @ 270°C as ext ruded 2 11 3 . RESULTS 3 . 1 . Ex t ruded C a s t i n g s 3 . 1 . 1 . P r e l i m i n a r y I n v e s t i g a t i o n As d e s c r i b e d i n the p r e v i o u s s e c t i o n , the m a t e r i a l s used f o r the p resent i n v e s t i g a t i o n were of s i m i l a r compos i t ion but the r e s u l t i n g s t r u c t u r e v a r i e d due to the d i f f e r e n t methods of p r e p a r i n g the f i n a l t e n s i l e specimen. Data obta ined from the t e n s i l e behav io r of specimens machined from the ext ruded c a s t b i l l e t s w i l l be presented f i r s t f o l l o w e d by data from the ext ruded powder compacts and the r o l l e d s t o c k . 3 . 1 . 2 . G r a i n S i z e E f f e c t A t y p i c a l 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 f o r s u p e r p l a s t i c m a t e r i a l s i s shown i n F i g . 2 . A lden^ has proposed tha t the low r a t e s e n s i t i v i t y at h i g h s t r a i n r a t e s i s due to s l i p c o n t r o l l e d defo rmat ion w h i l e the r e g i o n s of h i g h r a t e s e n s i t i v i t y can be shown to be a s s o c i a t e d w i t h g r a i n boundary s l i d i n g . 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 s found i n Z n - 0 . 2 wt . % A l a t +23°C e x h i b i t the c h a r a c t e r i s t i c S -shaped curve ( F i g . 3 ) . At i n t e r m e d i a t e s t r a i n r a t e s a r e g i o n of h i g h r a t e s e n s i t i v i t y e x i s t s and i s bounded at h i g h and low s t r a i n r a t e s by r e g i o n s of low r a t e s e n s i t i v i t y . The f l ow s t r e s s a t low s t r a i n r a t e s i s d r a s t i c a l l y a f f e c t e d by the p r e p a r a t i o n h i s t o r y of the m a t e r i a l . Curve B i l l u s t r a t e s the h i g h r a t e s e n s i t i v i t y observed when c o l d machin ing i s u t i l i z e d i n specimen p r e p a r a t i o n as opposed to Curve C which i s t y p i c a l f o r a hot machined specimen. By d e c r e a s i n g the temperature of e x t r u s i o n and thus d e c r e a s i n g the g r a i n s i z e i n the ext ruded rod the behav io r i s aga in a f f e c t e d as shown by Curve A. For compar ison , Curve D i s i n c l u d e d to i l l u s t r a t e the low r a t e s e n s i t i v i t y at a l l s t r a i n r a t e s i n the m a t e r i a l ext ruded from a powder compact. The reasons f o r t h i s behav io r w i l l be d i s c u s s e d i n a l a t e r s e c t i o n . F i g . 2. O r i g i n of S-shaped l o g a - l o g i curve ( schemat i c ) . The dominant deformat ion mode at low s t r a i n r a t e s i s g r a i n boundary s l i d i n g , at h igh r a t e s s l i p , ( a f t e r A l d e n ^ ) . • Extruded Casting, L Q Extruded Casting, L 0 Extruded Casting, L £ Extruded powders, L = 1.6 microns. = 3.5 microns. = 3.5 microns, hot machined = 2.0 microns. 10-4 F i g . 3. 10 -3 10 -2 10" 1 0 l S t r a i n r a t e , minutes ^ The e f f e c t of p r e p a r a t i o n h i s t o r y on 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 f o r ext ruded m a t e r i a l . T = + 23°C. For a more d e t a i l e d examination of the r e l a t i o n s h i p between flow stress and grain s i z e , thermal treatments were used to obtain a v a r i e t y of gr a i n sizes (Table I ) . The flow 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 s are shown i n F i g . 4. The e f f e c t of decreasing the grain s i z e i s to s h i f t the curves down and to the r i g h t , that i s , to s h i f t the region of maximum s t r a i n rate seraitivity to a higher s t r a i n rate. At high s t r a i n rates (greater than 1 min ^ ) the flow stress appears to approach a value independent of grain s i z e while at low s t r a i n rates the flow stress i s s i g n i f i c a n t l y lower f o r the f i n e s t grained material. These observations are consistent with those made on known sup e r p l a s t i c materials.** Values of the s t r a i n rate s e n s i t i v i t y parameter m may be obtained from a d i r e c t measurement of the slope of the curve r e l a t i n g flow stress to s t r a i n rate on logarithmic co-ordinates (m = 31n of Sine). A l t e r n a t i v e l y , m can be calculated from the flow stress increment accompanying an i s o l a t e d s t r a i n rate change by a technique described by 3 Avery and Backofen (see Appendix I ) . The l a t t e r method has been used i n t h i s work and the values of m as a function of s t r a i n rate f o r the d i f f e r e n t g rain sizes are shown i n F i g . 5. and F i g . 6. The e f f e c t of decreasing the grain s i z e i s to s h i f t the region of maximum m to higher s t r a i n rates due to the increasing contribution of boundary shear. One should note that the only d i f f e r e n c e between the data i n F i g . 5 and 6 i s the as. extruded grain s i z e . The data of F i g . 5 from the material with the smallest grain s i z e s i l l u s t r a t e that the rate s e n s i t i v i t y r i s e s to a maximum value as s t r a i n rate i s increased. For the larger grained material t h i s peak value was not observed due to the mechanical l i m i t a t i o n s of the te s t i n g procedure. At higher values of s t r a i n rate, the rate s e n s i t i v i t y i s 10 -4 O L • L A L A L 3.5 microns 3.7 microns 4.7 microns 7.2 microns F i g . 5. 10 -3 1 0 " z 1 0 - 1 S t r a i n r a t e , minutes The r e l a t i o n s h i p between the r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e . L = 3 .5 mic rons . 10K T = +23°C r " 1 O L = 1.6 microns • L = 3 . 5 microns S t r a i n r a t e , minutes F i g . 6 . The r e l a t i o n s h i p between the r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e . T = +23°C L = 1.6 mic rons . 18 observed to decrease to a value of approximately 0.1 f o r a l l grain s i z e s . This high s t r a i n rate value of m i s t y p i c a l f o r most metal systems when deformation i s s l i p or twin c o n t r o l l e d . Superimposed on the curve f o r the gr a i n s i z e of 3.5 microns are dotted c i r c l e s to i n d i c a t e the i n i t i a l s t r a i n rates where samples were strained to f a i l u r e r e s u l t i n g i n the elongations in d i c a t e d . The la r g e s t value of elongation obtained -3 -1 for t h i s m a t erial was 460% at an i n i t i a l s t r a i n rate of 1.5 x 10 min. The r e s u l t s presented i n F i g . 6 are f o r material with a smaller i n i t i a l g r a in s i z e (1.6 microns). Only two grain sizes were obtained i n t h i s case but the general trend suggested i n F i g . 5 i s consistent with the data i n F i g . 6 . That i s , f o r an increase i n grain s i z e , the region of maximum rate s e n s i t i v i t y i s s h i f t e d to lower s t r a i n rates -3 -1 -3 -1 (from 3 x 10 min. to 1 x 10 min. )'. There i s reasonable agreement between the curve f o r the annealed material i n F i g . 6 (L = 3.5 micron) and the curve f o r the as extruded material of s i m i l a r g r a i n s i z e i n F i g . 5. Values of t o t a l elongation are again superimposed on the curve f o r the f i n e s t grained: material i n F i g . 6. The maximum value obtained -3 -1 was 590% at an i n i t i a l s t r a i n rate of 7.8 x 10 min. . When a specimen was deformed at a s t r a i n rate corresponding to the maximum value 3 of m the elongation was 350%. I t has been suggested that the s t r a i n rates f o r maximum m and maximum elongation do not coincide due to the decreasing value of true s t r a i n rate as the instantaneous length increases. Thus with an i n i t i a l value of m at i t s maximum, a decrease i n s t r a i n rate r e s u l t s i n a decrease i n m and hence the material would be continually l o s i n g i t s resistance to necking. Correspondingly, with an i n i t i a l value of m at a s t r a i n rate above the point of maximum m, the resistance to necking w i l l be increasing as the specimen elongates. 19 In comparing the v a l u e s of e l o n g a t i o n to f a i l u r e at h i g h s t r a i n r a t e s f o r the two g r a i n s i z e s i t i s i n t e r e s t i n g to note tha t the s t r a i n to f r a c t u r e i s always g r e a t e r f o r the f i n e r g r a i n s t r u c t u r e even a t r e l a t i v e l y h i g h s t r a i n r a t e s . For example, at a s t r a i n r a t e - 2 - 1 of 8 x 10 m i n . , the 1.6 micron m a t e r i a l deforms 360% w h i l e the 3 .5 micron m a t e r i a l f a i l s a f t e r approx imate ly 100-130% d e f o r m a t i o n . 3 . 1 . 3 . E f f e c t of Temperature The t e s t temperature was v a r i e d from +23°C to +100°C so tha t the apparent a c t i v a t i o n energy of the r a t e c o n t r o l l i n g process cou ld be o b t a i n e d . In order to s t a b i l i z e the g r a i n s i z e at these temperatures a l l specimens were h e l d a t 100°C f o r 15 minutes b e f o r e t e s t i n g at any g i v e n temperature . T h i s t reatment produced a s l i g h t i n c r e a s e i n g r a i n s i z e from the as ext ruded v a l u e of 3 . 5 microns to 3 .7 m i c r o n s . Inc rementa l s t r a i n r a t e change t e s t s were done a t f o u r d i f f e r e n t temperatures and the r e s u l t s appear i n F i g . 7. As the temperature of t e s t i n g i n c r e a s e s , the f l o w s t r e s s - s t r a i n r a t e curve i s s h i f t e d to the r i g h t , towards h i g h e r s t r a i n r a t e s , and p o s s i b l y down as w e l l a l though t h i s t rend cannot be comple te l y e s t a b l i s h e d . Thus the r e g i o n of maximum s t r a i n r a t e s a s i t i v i t y i s s h i f t e d to h i g h e r s t r a i n r a t e v a l u e s as the t e s t temperature i n c r e a s e s . T h i s f a c t i s f u r t h e r ev idenced by examining the e f f e c t of temperature on the m - s t r a i n r a t e r e l a t i o n s h i p i n F i g . 8 . A g e n e r a l t rend i s deve lop ing i n t h i s se t of data as seen by the i n c r e a s i n g v a l u e of the peak m as the temperature i n c r e a s e s . Va lues f o r m r i s e from 0.57 at room temperature to g r e a t e r than 0 . 8 at +75°C. Data f o r the +100°C t e s t does not f o l l o w t h i s t rend c o n c l u s i v e l y but there i s a p o s s i b i l i t y that due to the stepped nature of the m d e t e r m i n a t i o n the a c t u a l peak v a l u e may have been s t r a d d l e d . F i g . 8 . The r e l a t i o n s h i p between the s t r a i n r a t e s e n s i t i v i t y parameter m and s t r a i n r a t e , at d i f f e r e n t t e s t temperatures . L = 3 .7 m i c r o n s . 22 T h i s s u g g e s t i o n i s f u r t h e r supported by the i n c r e a s i n g sharpness of the peak as the t e s t temperature i s i n c r e a s e d ( i . e . f o r 100°C. the peak - 2 - 1 m may occur at 10 m i n . and have a v a l u e g r e a t e r than 0 . 8 5 ) . A g a i n , the h i g h s t r a i n r a t e v a l u e f o r m approaches 0 . 1 c o n s i s t e n t w i t h the d a t a on the e f f e c t of g r a i n s i z e ( F i g . 5 ) . An a n a l y s i s has been c a r r i e d out on the data of F i g . 7 so t h a t a v a l u e f o r the apparent a c t i v a t i o n energy can be c a l c u l a t e d . T h i s a n a l y s i s i s based on the assumption tha t the s t r a i n r a t e , at a constant s t r e s s , i s a measure of the r a t e of d e f o r m a t i o n . For t h i s c a l c u l a t i o n the v a l u e s of s t r e s s s e l e c t e d are a l l i n the r e g i o n of 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 and hence the a c t i v a t i o n energy w i l l be a s s o c i a t e d w i t h the mechanism of deformat ion i n t h i s r e g i o n . The v a l u e s of s t r a i n r a t e a t v a r i o u s constant s t r e s s e s are p l o t t e d a g a i n s t r e c i p r o c a l temperature f o l l o w i n g the normal A r r h e n i u s r e l a t i o n s h i p : Rate = A e ^ / R T where A i s a constant and Q, R and T have t h e i r u s u a l meanings. A measure of the s lopes of the l i n e s r e p r e s e n t i n g the data g i v e s the v a l u e of apparent a c t i v a t i o n energy , Q, f o r d i f f e r e n t constant s t r e s s l e v e l s . These v a l u e s are t a b u l a t e d i n F i g . 9 and i n c r e a s e from 8 . 3 K c a l / g . a t o m at 10,000 p s i to 9 .7 K c a l / g . a t o m at 3,000 p s i . The a c t i v a t i o n energy f o r s e l f d i f f u s i o n of z i n c (and d i f f u s i o n of z i n c i n d i l u t e Z n - A l a l l o y s ) i s 20 -25 K c a l / g . a t o m and f o r g r a i n boundary 30 d i f f u s i o n i s 1 4 . 5 K c a l / g . a t o m . The v a l u e obta ined i n the p resent work, 8 -10 K c a l / g . a t o m , i s lower than tha t expected f o r a g r a i n boundary d i f f u s i o n p rocess but the a c t i v a t i o n energy should be decreased s l i g h t l y by the 30 7 a d d i t i o n of aluminum to z i n c . A lden has measured an apparent a c t i v a t i o n energy i n the Sn-Pb system which i n d i c a t e s that the r a t e c o n t r o l l i n g process 23 25 i s one g r a i n boundary d i f f u s i o n . The s i g n i f i c a n c e of the measured a c t i v a t i o n energy values w i l l be discussed i n more d e t a i l i n a l a t e r s e c t i o n . In determining the l i n e of best f i t i n F i g . 9, the rate values at +100°C were e s s e n t i a l l y ignored. I t i s believed that the d i f f e r e n c e between these measured values and the suggested l i n e , p a r t i c u l a r l y at the low stress l e v e l s , i s due to grain growth at the elevated temperature. The e f f e c t of test temperature on the flow 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 was also investigated f o r pure zinc extruded at room temperature (grain s i z e 5 - .5 microns). These r e s u l t s appear i n F i g . 10 and i n d i c a t e that further studies on t h i s material would l i k e l y prove f r u i t l e s s . The major d i f f i c u l t y a r i s e s from not being able to obtain a f i n e enough grain s i z e i n the high p u r i t y z i n c . Although no specimens were strained to f a i l u r e , the equivalent grain s i z e i n the a l l o y Zn-Al res u l t e d i n low values of t o t a l elongation. A p l o t of m versus s t r a i n rate i s not included but the r e s u l t s from that determination ind i c a t e d that at room temperature the values of m decreased r a p i d l y from approximately 0.4 at a s t r a i n rate -4 -1 of 3.1.x 10 min. to a value approaching 0.1 at s t r a i n rates above -3 -1 3 x 10 min. . The maximum value of m obtained decreased with decreasing t e s t temperature to approximately 0.3 at!-40°C. 3.2. Extruded Powders 3.2.1. E f f e c t of Temperature The e f f e c t of temperature on the flow 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 was extensively examined for the extruded powder compacts and the r e s u l t s appear i n F i g . 11. These data are consistent with the S t r a i n r a t e , minutes ^ F i g . 1 1 . The e f f e c t of t e s t i n g temperature on the f l ow 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 f o r extruded powder a l l o y . L Q = 2 m i c r o n s . 27 previously mentioned trend which suggests that as the test temperature i s increased the sigmoidal a - i curve i s s h i f t e d down and to the r i g h t . Results f o r tests above room temperature reveal the en t i r e S- shaped curve while lower temperature tests tend only to ex h i b i t the upper portions of the hig h l y s t r a i n rate s e n s i t i v e region. At low s t r a i n rates and high temperatures the structure i s r e l a t i v e l y s t r a i n rate i n s e n s i t i v e with the stress l e v e l approaching a value of approximately 3,000 p s i . At high s t r a i n rates and low temperatures, the structure i s again s t r a i n - r a t e i n s e n s i t i v e ,with the flow stress approaching a value of approximately 50,000 p s i . A comparison of these data to those f o r the extruded castings shows that the curves f o r the extruded powders may have experienced a general s h i f t to regions of higher st r e s s and lower s t r a i n rate (for castings low asymptote value i s less than 1,000 p s i and the high asymptote i s approximately 40,000 p s i ) . The most s i g n i f i c a n t d i f f e r e n c e between these two sets of data i s the magnitude of the measured value of m. For the extruded powders (grain s i z e 2 microns) at room temperature the peak value f o r m i s approxiinatley 0.2 (by slope -4 -1 estimation) at a s t r a i n rate of 3 x 10- min. while f o r the extruded castings (grain s i z e 1.6 microns) m r i s e s to a value greater than 0.6 - 3 - 1 at a s t r a i n rate of 3 x 10 min. . Associated with the low value of m f o r the powder materials i s a correspondingly low elongation to f a i l u r e (less than 100% as compared to greater than 400%) at s t r a i n rates i n the region of maximum m. I t i s suggested that the presence of a f i n e l y dispersed oxide l a y e r , introduced during the powder making procedure, could account for the low s t r a i n rate s e n s i t i v i t y and much lower elongations to f a i l u r e . The presence of oxide on the grain boundaries would be expected to i n t e r f e r e 28 w i t h a boundary shear process and hence the onset of s l i p would be encouraged and would be 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 parameter and a low v a l u e of t o t a l e l o n g a t i o n . An a n a l y s i s was made of the d a t a i n F i g . 11 to measure a v a l u e f o r the a c t i v a t i o n energy of the r a t e c o n t r o l l i n g process by a procedure d e s c r i b e d e a r l i e r . Four d i f f e r e n t constant s t r e s s l e v e l s were u t i l i z e d and the r e s u l t s appear as t h e . u s u a l A r r h e n i u s p l o t i n F i g . 12 . The v a l u e s f o r Q are a l s o t a b u l a t e d i n F i g . 12 and range from 1 0 . 3 k c a l / g . a t o m at 10,000 p s i to 11 .7 k c a l / g . a t o m at 30,000 p s i . The s l i g h t i n c r e a s e i n Q as the s t r e s s l e v e l i n c r e a s e s r e f l e c t s the f a c t t h a t the r a t e s were measured i n a r e g i o n where the r a t e s e n s i t i v i t y i s beg inn ing to decrease which i n d i c a t e s t h a t deformat ion i s becoming i n c r e a s i n g l y s l i p c o n t r o l l e d . The v a l u e s of apparent a c t i v a t i o n energy measured f o r t h i s m a t e r i a l would imply t h a t a g r a i n boundary d i f f u s i o n a l p rocess i s r a t e c o n t r o l l i n g c o n s i s t e n t w i t h the e a r l i e r r e s u l t s f o r the cas t and ext ruded a l l o y . 3 . 3 . R o l l e d C a s t i n g s The f i n a l r o l l i n g o p e r a t i o n on the c a s t b i l l e t r e s u l t e d i n a g r a i n s i z e of 16 m i c r o n s . When the y i e l d s t r e s s - s t r a i n r a t e b e h a v i o r was s t u d i e d f o r the as r o l l e d m a t e r i a l a d i s t i n c t break was - 3 - 1 n o t i c e d i n the o - e curve a t a s t r a i n r a t e of 5 x 10 m i n . ( F i g . 1 3 ) . A t s t r a i n r a t e s above t h i s v a l u e the s t r e s s was s t r a i n r a t e i n s e n s i t i v e i n d i c a t i v e of a s l i p c o n t r o l l e d process w h i l e at lower s t r a i n r a t e s the s e n s i t i v i t y i n c r e a s e d as i s t y p i c a l f o r a g r a i n boundary p r o c e s s . 29 1/T ° K - 1 x 1 0 3 F i g . 12 . A r r h e n i u s p l o t f o r ext ruded powders. L = 2 m i c r o n s . 30 20 CO I o • H 03 a CO CO CD u 4-1 CO •o <-i 0) • H CN 10 A L = 2 microns (powders) - * L = 3 microns (powders) O L = 16 microns ( r o l l e d c a s t i n g ) • L = 23 microns ( r o l l e d c a s t i n g ) - • L = 27 microns ( r o l l e d c a s t i n g ) • L = 66 microns ( r o l l e d c a s t i n g ) 10 - 5 10 - 4 10 - 3 X 10 - 2 10 - 1 o 10 0 S t r a i n r a t e , minutes F i g . 13 . The e f f e c t of g r a i n s i z e on the y i e l d 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 . 10 T = 23°C. 31 3.3.1. Grain Size E f f e c t Thermal treatments as described i n Table I were used to vary the g r a i n s i z e of the as r o l l e d stock. The e f f e c t of changing the grain s i z e i s shown i n F i g . 13 where a 0.2% o f f s e t y i e l d s t r e s s i s p l o t t e d against s t r a i n rate on logarithmic co-ordinates. Data f or the extruded powders are included f o r comparison. In order to obtain -4 -1 points below a s t r a i n rate of 3 x 10 min. a r o l l e d sample was machined with a gauge length of 10 times that of the normal specimen. This technique allowed values of y i e l d strength to be obtained at a s t r a i n rate of 3.1 x 10 min^ . Notable i n the data presented i n F i g . 13 i s the presence of plateaus at r e l a t i v e l y constant values of stress f o r d i f f e r e n t grain s i z e s . These plateaus d i c t a t e regions where the grain boundaries are hard and hence the deformation would be s l i p c o n t r o l l e d . As the grain s i z e i s increased the plateau i s s h i f t e d to lower stresses and the region of uniform stress extends to lower s t r a i n rates. For the 66 micron material the y i e l d s t r e s s i s i n s e n s i t i v e to s t r a i n rate over the e n t i r e range sutided. 3.4. Hall-Petch Relationship The presence of regions where the deformation i s s l i p c o n t r o l l e d allows a stress to be defined which should be r e l a t e d to the grain s i z e through the Hall-Petch r e l a t i o n s h i p : o Q 2 = a 0 + K d " 1 / 2 where aQ and K are constants dependent on temperature and s t r a i n rate, o n 0 i s the 0.2% o f f s e t flow stress and d i s the mean grain boundary diameter. 32 The Hall-Petch p l o t appears i n F i g . 14 and represents data from material prepared by d i f f e r e n t techniques. The large grain sizes are f o r the r o l l e d and annealed material and the small grain sizes are obtained from both the extruded powders and extruded castings. -1/2 For grain s i z e s greater than 3 microns (d <0.55) a l l the data f i t a l i n e a r Hall-Petch dependence with K approximately equal to 1/2 45,000 p s i (micron) . This high value of K can be a t t r i b u t e d to the r e s t r i c t e d number of s l i p systems on which deformation can occur. At grain s i z e s below t h i s l i m i t , the data f o r the extruded casting diverge from the l i n e a r r e l a t i o n s h i p . At t h i s grain s i z e and s t r a i n rate the y i e l d s t r e s s i s p a r t i a l l y c o n t r o l l e d by grain boundary processes. To obtain the Hall-Petch value, a higher s t r a i n rate would have to be used. The data f o r the f i n e grained extruded powders remains i n agreement with the Hall-Petch r e l a t i o n s h i p due to boundary pinning by the oxide. 21 Tromans and Lund , i n a study of grain boundary e f f e c t s i n Zn-ZnO a l l o y s have measured a K value of approximately 50,000 p s i (micron) 1'' 2 at -100°C and 40,000 p s i ( m i c r o n ) 1 ^ 2 at +20°C. Their room temperature data showed a deviation from l i n e a r i t y below a grain s i z e of 2 microns. I t i s important to note that no stress intercept (O q) was observed i n the present work (Fig. 14). A n e g l i g i b l e aQ would i n d i c a t e that y i e l d i n g i s b a s i c a l l y c o n t r o l l e d by s l i p c ontinuity across grain boundaries and i s athermal at +23°C. 3.5. S t r e s s - S t r a i n Curves 3.5.1. Nature of the S t r e s s - S t r a i n Curves Throughout the l i t e r a t u r e many workers r e f e r to a "steady state flow s t r e s s " which characterizes any study of superplastic materials. The inference has been that as deformation proceeds, the stress reaches 33 CO 0) CO a) u u CO T3 rH Oi 1* >» &•« CN T T A Extruded powders ^ Extruded castings • Rolled castings L 0.2 0.4 0.6 0.8 1.0 (grain size) ^ \ (microns) F i g . 14. Hall-Petch p l o t f o r Zn-0.2 wt.% A l . T = +23°C. 34 a steady s t a t e v a l u e and a t the optimum s t r a i n r a t e e x t e n s i v e amounts of e l o n g a t i o n may be obta ined due to the h i g h r e s i s t a n c e to neck ing n o r m a l l y a s s o c i a t e d w i t h h i g h v a l u e s of m. The "s teady s t a t e f l ow s t r e s s " has a l s o been important i n the Backofen e t a l a n a l y s i s of m v a l u e s which i n v o l v e s i n c r e m e n t a l changes of s t r a i n r a t e a f t e r steady s t a t e 3 c o n d i t i o n s have been reached . Thus the importance of a steady s t a t e s t r e s s has been i m p l i e d and y e t no where i n the l i t e r a t u r e has a p l o t of t r u e s t r e s s - s t r a i n appeared f o r s u p e r p l a s t i c m a t e r i a l s . P l o t s of t r u e s t r e s s - e n g i n e e r i n g s t r a i n are shown i n F i g . 15 where the s t r a i n - 2 - 1 r a t e was 1 .5 x 10 m i n . and the i n i t i a l g r a i n s i z e s were 1.6 microns and 3 . 5 m i c r o n s . Of i n t e r e s t i s the absence of a "s teady s t a t e f l o w s t r e s s " . The curve f o l l o w s e s s e n t i a l l y a p a r a b o l i c r e l a t i o n s h i p up to a maximum v a l u e of s t r e s s and then i s c h a r a c t e r i z e d by a l i n e a r decrease i n s t r e s s w i t h i n c r e a s i n g s t r a i n u n t i l such t ime as a neck forms and f a i l u r e o c c u r s . The e f f e c t of i n c r e a s i n g the g r a i n s i z e i s to s h i f t the peak v a l u e of s t r e s s to lower s t r a i n s and h i g h e r s t r e s s e s . Any a n a l y s i s of s u p e r p l a s t i c i t y i s d i f f i c u l t because of the c o n t i n u a l decrease i n specimen s t r a i n r a t e d u r i n g deformat ion (when a constant crosshead machine i s u s e d ) . For the curves i n F i g . 15 the - 2 - 1 s t r a i n r a t e decreases from an i n i t i a l v a l u e of 1 .5 x 10 m i n . to - 3 - 1 approx imate ly 3 x 10 m i n . at 500% e l o n g a t i o n . Hence, a p o s s i b l e e x p l a n a t i o n f o r the l i n e a r decrease a f t e r the peak s t r e s s cou ld be the decrease i n s t r a i n r a t e . The i m p l i c a t i o n s of the sugges t ion w i l l be d i s c u s s e d l a t e r . 3 . 5 . 2 . M i c r o s t r u c t u r a l Changes w i t h I n c r e a s i n g S t r a i n The appearance of the t r u e s t r e s s - s t r a i n curve i n the r e g i o n up to the maximum s t r e s s was d i f f e r e n t from t h a t i m p l i e d i n the l i t e r a t u r e i n tha t a f t e r i n i t i a l y i e l d i n g o c c u r s , r a p i d hardening i s observed up to F i g . 15. True s t r e s s - s t r a i n curves f o r specimens of d i f f e r e n t i n i t i a l g r a i n s i z e s . T = +23°C t= 1.5 x 1 0 - 2 m i n . - 1 . 36 approx imate ly 100% s t r a i n . S e v e r a l workers have r e p o r t e d t h a t deformat ion appeared to encourage g r a i n growth and A lden^ suggested tha t an i n c r e a s i n g s t r e s s d u r i n g t e s t i n g r e f l e c t e d the i n c r e a s i n g creep r e s i s t a n c e of l a r g e r g r a i n e d m a t e r i a l . The assumption t h a t g r a i n growth would o c c u r , p a r t i c u l a r l y i n a d i l u t e a l l o y system, formed the b a s i s f o r a study on the e f f e c t of s t r a i n on the m i c r o s t r u c t u r e . Specimens were p o l i s h e d and observed under p o l a r i z e d l i g h t to determine the i n i t i a l g r a i n s i z e and then deformed to v a r i o u s s t r a i n s . F o l l o w i n g the d e f o r m a t i o n , two s tage carbon r e p l i c a s were taken from the deformed s u r f a c e and observed on a H i t a c h i 100 KV e l e c t r o n m i c r o s c o p e . The g r a i n s i z e a f t e r deformat ion was determined by r e p b l i s h i n g and o b s e r v a t i o n under p o l a r i z e d l i g h t . The r e s u l t s of the t e n s i l e t e s t s are shown i n F i g . 16 and are r e p r o d u c i b l e to - 6 % . The t a b l e i n F i g . 16 showing the g r a i n growth as a f u n c t i o n of s t r a i n a l s o inc ludes the g r a i n s i z e of a specimen s t r a i n e d to the maximum - 3 - 1 e l o n g a t i o n ob ta ined a t an i n i t i a l s t r a i n r a t e of 7 .8 x 10 m i n . The e f f e c t of i n c r e a s i n g s t r a i n on the m i c r o s t r u c t u r e i s i l l u s t r a t e d i n F i g . 17 . The degree of g r a i n boundary shear i s g r e a t e r a f t e r 43% s t r a i n than a f t e r 11%. S l i p l i n e s are observed on the l a r g e r g r a i n s i n F i g . 17b. O p t i c a l micrographs on the r e p o l i s h e d s u r f a c e s of these specimens i n d i c a t e d tha t the average g r a i n s i z e had i n c r e a s e d from 2.7 microns at 11% s t r a i n to 3 . 3 microns at 43 % s t r a i n . An examinat ion at h i g h e r m a g n i f i c a t i o n ( F i g . 18) showed tha t s l i p t r a c e s comple te l y t r a v e r s e d the o l d shear markings a s s o c i a t e d w i t h the p r i o r g r a i n s i z e and te rminated on ly on boundar ies which were c h a r a c t e r i s t i c of the l a r g e r g r a i n s i z e . T h i s o b s e r v a t i o n i s c o n s i s t e n t w i t h the argument f o r a non -cont inuous g r a i n growth p r o c e s s . I t i s observed t h a t the l a r g e g r a i n i l l u s t r a t e d i n F i g . 18 o r i g i n a l l y c o n s i s t e d of up to e i g h t g r a i n s of s i z e comparable to the i n i t i a l g r a i n s i z e . 38 a) 11% s t r a i n b) 43% s t r a i n F i g . 17. Sur face deformat ion c h a r a c t e r i s t i c s at d i f f e r e n t s t r a i n s . T = +23°C, e = 7.8 x 1 0 ~ 3 m i n . - 1 , L Q = 1.6 m ic rons . 39 40 F i g . 19. G r a i n boundary shear and g r a i n r o t a t i o n at 43% s t r a i n . T = +23°C, i = 7.8 x 10 "3 m i n . - 1 , L = 1.6 m ic rons . 4 1 F i g . 20. As s t r a i n e d s u r f a c e showing s t r i a t e d bands (marked by arrows) i n g r a i n boundary reg ions at 43% s t r a i n . T = +23°C, e = 7.8 x 10 -3 m i n . - 1 L = 1 . 6 mic rons , o 42 The extensive amount of grain boundary shear i s also observed i n F i g . 19 where a l o n g i t u d i n a l scratch has become o f f s e t i n the region of the boundary. Grain r o t a t i o n has also occurred during the deformation as demonstrated by the d i f f e r e n t d i r e c t i o n s that the scratch has assumed with i n each of the three grains i l l u s t r a t e d . The l a s t of the electron micrographs (Fig. 20) i l l u s t r a t e s s t r i a t e d bands along several t e n s i l e loaded boundaries. In t h i s micrograph, the t e n s i l e axis i s shown by the l i n e i n c l i n e d approximately 20° from h o r i z o n t a l . In the Pb-Sn e u t e c t i c system, Zehr and Backofen 1 1 recently observed s t r i a t e d regions s i m i l a r to those i n the present work and they suggested that t h i s banding i s metallographic evidence for the occurrence of a d i f f u s i o n a l creep process. Also v i s i b l e i n F i g . 20 are the networks of old grain boundaries within the larger grained f i n a l structure. The amount of shear on these o r i g i n a l boundaries i s minimal i n comparison to that on the f i n a l boundaries i n d i c a t i n g that the grain s i z e has changed r a p i d l y i n the i n i t i a l stages of deformation r e s u l t i n g i n a larger c o n t r i b u t i o n to t o t a l s t r a i n coming from shear on the boundaries of the la r g e r grains. The grain s i z e dependence on s t r a i n i s shown i n F i g . 21 on logarithmic co-ordinates. The degree of deformation i s p l o t t e d i n terms of both engineering ( s o l i d ) and true s t r a i n (dotted). Lines of best f i t are drawn through the points ignoring the zero percent s t r a i n condition. I t may be argued that data obtained at very low amounts of deformation would not be expected to follow the l i n e a r r e l a t i o n s h i p since a f i n i t e amount of boundary shear i s required to i n i t i a t e the grain growth process. Thus i f one assumes that the grain s i z e would remain stable up to an a r b i t r a r y 44 value of 1 or 2% strain then a l l the data l i e on the illustrated relationships. 3.5.3. Strain Rate Dependence of True Stress-Strain Curves In the present work the effect of strain rate on microstructure was not examined in detail. However the true stress-strain curves at a few different strain rates appear in Fig. 22. The grain size of the cast, homogenized and extruded material was 3.2 microns. The effect of increasing the strain rate i s to shift the peak value of stress to lower strain values (Table II). TABLE II The dependence of strain to maximum stress and i n i t i a l m on imposed strain rate Strain Rate (min. - 1) Strain to Maximum Stress (%) I n i t i a l m .002 100 .72 .008 48 .54 .02 34 .38 .04 22 .30 .08 15 .24 .2 15 .20 It i s not known how the strain rate affects the rate of grain growth during deformation as this study was restricted to a single strain rate. However, the above results suggest that grain growth may be a sensitive function of strain rate and hence be an important parameter in superplasticity as w i l l be discussed later. 46 1 1 - I 1 r — - i — i — T £ (min. ) A 7.8 x 10 (by grain s i z e increase during testing) I , I _ J I _ J I i l i I 1 5 10 Grain s i z e , microns F i g . 23. Dependence of stress on grain s i z e at various s t r a i n rates. T = +23°C. 47 In the absence of d e f o r m a t i o n , no d e t e c t a b l e g r a i n growth occurs i n a p e r i o d of t ime comparable to the t e s t i n g t i m e . 3 . 5 . 4 . E f f e c t of G r a i n S i z e on S t r e s s Dur ing Deformat ion By c ross p l o t t i n g the data from F i g . 4 at v a r i o u s constant s t r a i n r a t e s a g a i n s t g r a i n s i z e on l o g a r i t h m i c c o - o r d i n a t e s , the s t r e s s dependence on i n i t i a l g r a i n s i z e may be determined . Such a p l o t i s shown i n F i g . 2 3 . The d a t a f o r the two lowest s t r a i n r a t e s have been -3 -1 taken from F i g . 4 but the data f o r the h i g h e s t s t r a i n r a t e ( 7 . 8 x 10 min . ) o r i g i n a t e d from F i g . 16 where the g r a i n s i z e was a c t u a l l y measured at v a r i o u s s t r a i n s . The s c a t t e r at the lower s t r a i n r a t e s i s much l a r g e r s i n c e the e f f e c t of s t r a i n has been ignored i n p l o t t i n g the g r a i n s i z e . The s i m i l a r nature of the r e l a t i o n s h i p s shown i n F i g . 23 i n d i c a t e s t h a t the f l o w s t r e s s may be r e l a t e d on ly to ins tantaneous g r a i n s i z e i r r e s p e c t i v e of the o r i g i n of the s t r u c t u r e . I t can then be assumed t h a t the observed harden ing demonstrated by the t r u e s t r e s s - s t r a i n curves ( F i g . 15 and 16) i s due on ly to the i n c r e a s e i n g r a i n s i z e d u r i n g d e f o r m a t i o n . S ince the most r e l i a b l e data p resented here r e l a t e s to the - 3 - 1 a c t u a l measured g r a i n s i z e d u r i n g deformat ion (e = 7 .8 x 10 m i n . ) the g r a i n s i z e dependence on s t r e s s may be represented by the r e l a t i o n s h i p : j 1 .3 a a a In s i m i l a r p l o t s , o ther workers have measured the v a l u e of t h i s exponent to be between 1 and 3 depending on the system under i n v e s t i g a t i o n and the techniques used to e v a l u a t e t h i s dependence. A l l p rev ious techn iques have been r e s t r i c t e d to c ross p l o t t i n g data obta ined from the s t r e s s - s t r a i n r a t e dependence on g r a i n s i z e . Hence, the present technique shou ld be more r e l i a b l e i n determin ing a t r u e e f f e c t of g r a i n s i z e on s t r e s s . 48 4 . DISCUSSION 4 . 1 . S i g n i f i c a n c e of the S t r a i n Rate S e n s i t i v i t y Parameter The phenomenological b a s i s f o r s u p e r p l a s t i c i t y i s the s t r o n g dependence of the observed f l o w s t r e s s on the imposed s t r a i n r a t e . As a r e s u l t the concept of a s t r a i n r a t e s e n s i t i v i t y parameter m has been invoked to d e s c r i b e t h i s b e h a v i o r . The parameters which are known to a f f e c t the i n i t i a l v a l u e of m are s t r a i n r a t e , temperature , amount of second phase present and g r a i n s i z e . Thus any study of s u p e r p l a s t i c i t y has been concerned w i t h the behav io r of m when any one of these parameters are v a r i e d w h i l e the o thers are h e l d c o n s t a n t . However the i d e a l i t y of t h i s s i t u a t i o n i s d i s t u r b e d by s e v e r a l f a c t o r s which are present under many t e s t i n g c o n d i t i o n s . The most obvious i s the v a r i a t i o n of s t r a i n r a t e r e s u l t i n g from the change of specimen l e n g t h d u r i n g an e l o n g a t i o n to f a i l u r e i n v e s t i g a t i o n where the f i n a l l e n g t h may be g r e a t e r by a f a c t o r of ten than the i n i t i a l l e n g t h . Some workers have attempted to a l l e v i a t e t h i s problem by i n c r e a s i n g the crosshead mot ion d u r i n g a long term t e s t to o f f s e t the e f f e c t due to i n c r e a s i n g gauge l e n g t h . However the on ly r e a l s o l u t i o n i s to c a r r y out t e s t i n g on apparatus which a l l o w s a c o n  t inuous v a r i a t i o n of crosshead speed such that a t r u e constant s t r a i n r a t e may be a c h i e v e d . In the p resent s t u d y , o b s e r v a t i o n s of an i n c r e a s i n g g r a i n s i z e d u r i n g t e s t i n g p resent ye t another v a r i a b l e parameter which has normal l y been assumed to be a c o n s t a n t . Thus i n any system where g r a i n growth i s encouraged by deformat ion a d i s c u s s i o n of m must i n c l u d e not on ly the e f f e c t of e s t a b l i s h e d parameters but a l s o the e f f e c t of s t r a i n on the g r a i n s i z e . I t should be noted tha t the v a r i a t i o n of m w i t h s t r a i n r a t e , f o r example F i g . 5 and F i g . 8 , i s v a l i d on ly f o r the i n i t i a l s t r u c t u r e s i n c e the t o t a l s t r a i n i n v o l v e d i s s m a l l w i t h r e s p e c t to the maximum 49 p o s s i b l e e l o n g a t i o n and the amount g r a i n growth i s c o r r e s p o n d i n g l y low. The e f f e c t of i n c r e a s i n g g r a i n s i z e becomes a problem when a d i s c u s s i o n undertakes to e x p l a i n the h i g h degrees of e l o n g a t i o n obta ined on the b a s i s o f . d a t a p e r t a i n i n g to the i n i t i a l s t r u c t u r e . In p a r t i c u l a r , a d e s c r i p t i o n concern ing a s t r a i n r a t e where a maximum v a l u e of m i s observed l o s e s i t s s i g n i f i c a n c e when g r a i n growth i s i n v o l v e d . A l though the e f f e c t of g r a i n s i z e on the m vs s t r a i n r a t e r e l a t i o n s h i p has been f a i r l y w e l l e s t a b l i s h e d the more important f a c t o r of the r a t e of change of g r a i n s i z e (and t h e r e f o r e m) w i t h s t r a i n , s t r a i n r a t e and amount of second phase i s u n r e s o l v e d . T h i s sugges t ion supports the statements 27 of F l o r e e n r e g a r d i n g the ex tent of the e l o n g a t i o n s observed i n pure N i . I t was proposed tha t the h i g h r a t e of change i n g r a i n s i z e d u r i n g t e s t i n g l i m i t e d the t o t a l o b t a i n a b l e e l o n g a t i o n and the amount of s t r a i n which was observed had occur red w h i l e the g r a i n s i z e was s m a l l . Thus to comple te l y e s t a b l i s h the s i g n i f i c a n c e of m an e x p e r i m e n t a l procedure must be f o l l o w e d i n which the v a r i a t i o n of m i s s t u d i e d as a f u n c t i o n of s t r a i n , s t r a i n r a t e and temperature . Th is c o u l d be ach ieved by s t r a i n i n g a m a t e r i a l a t a constant temperature and s t r a i n r a t e and then conduct ing an m d e t e r m i n a t i o n as p r e v i o u s l y d e s c r i b e d at d i f f e r e n t v a l u e s of s t r a i n . An i n v e s t i g a t i o n was c a r r i e d out on the change of m w i t h s t r a i n u t i l i z i n g the s t r e s s - s t r a i n curves i n F i g . 22 . A specimen was deformed - 3 - 1 220% at a s t r a i n r a t e of 2 x 10 m i n . f o l l o w e d by i n c r e m e n t a l s t r a i n r a t e changes to determine a v a l u e of m. T h i s v a l u e was measured to be 0 .39 ( i n i t i a l m was 0 . 7 2 ) . I f one assumes tha t the l i n e a r decrease i n s t r e s s w i t h i n c r e a s i n g s t r a i n ( F i g . 15 and 22) i s e n t i r e l y a response to a d e c r e a s i n g s t r a i n r a t e then a s t r a i n r a t e s e n s i t i v i t y parameter may be c a l c u l a t e d from the observed s l o p e f o l l o w i n g the r e l a t i o n s h i p : 50 91no  m = 91nc T h i s a n a l y s i s a p p l i e d to the d a t a f o r a s t r a i n r a t e of 2 x 10 m i n . r e s u l t e d i n a c a l c u l a t e d v a l u e of 0 .32 f o r the s t r a i n r a t e s e n s i t i v i t y parameter . Th is i s s l i g h t l y lower than the observed v a l u e of 0 .39 . T h i s i s due to the f a c t that i t has been assumed t h a t the f l ow s t r e s s i n t h i s r e g i o n of the curve would no rmal l y be constant i f the s t r a i n r a t e cou ld be h e l d constant i n the specimen. However, i t has been shown that even at these h i g h amounts of s t r a i n the g r a i n s i z e i s s t i l l i n c r e a s i n g s l i g h t l y w i t h s t r a i n . Therefore the t rue s t r e s s shou ld s t i l l be i n c r e a s i n g under c o n d i t i o n s of constant s t r a i n r a t e . There fo re the numerator of the above e x p r e s s i o n has a s l i g h t l y lower v a l u e than under s teady s t a t e . c o n d i t i o n s . However the g e n e r a l i d e a of the decrease i n s t r e s s be ing due on ly to the dec reas ing s t r a i n r a t e i s s t i l l v a l i d . 4 . 2 . I m p l i c a t i o n s of Mechanism As suggested e a r l i e r , any d i s c u s s i o n of mechanism should draw support not o n l y from t e n s i l e behav io r but a l s o from 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 . A c t i v a t i o n energy measurements have r e s u l t e d i n v a l u e s of approx imate ly 10 k c a l / g . a t o m f o r both the extruded powders and extruded c a s t i n g . A l though one m a t e r i a l behaves s u p e r p l a s t i c a l l y w h i l e the other does not the same measured v a l u e of apparent a c t i v a t i o n energy i n no way i m p l i e s an i n c o n s i s t e n c y s i n c e i t i s the r a t e c o n t r o l l i n g process which g i v e s r i s e to the observed a c t i v a t i o n energy. The abso lu te v a l u e of the r a t e at which the r e a c t i o n occurs i s d i f f e r e n t but the r a t e c o n t r o l l i n g process i s the same ( i e . s i m i l a r s l o p e s on an A r r h e n i u s p l o t ) . 51 P r e v i o u s work on s u p e r p l a s t i c systems has proposed that assuming the s t r e s s - g r a i n s i z e dependence f o l l o w s the r e l a t i o n s h i p cr a L , a measured v a l u e of a = 1 would imply a process of g r a i n boundary s h e a r , w h i l e v a l u e s of 2 or 3 would be i n d i c a t i v e of N a b a r r o - H e r r i n g creep g or the Coble v a r i a n t f o r g r a i n boundary d i f f u s i o n a l creep . The v a l u e of a = 1 .3 from F i g . 23 i s c o n s i s t e n t w i t h a g r a i n boundary shear p rocess but the q u e s t i o n of the v a l i d i t y of t h i s type of a n a l y s i s i s u n r e s o l v e d . Observat ions of g r a i n growth d u r i n g deformat ion have been made 6 , 7 , 9 , 1 1 , 1 8 , 2 7 , „ , , i n many systems ' but have g e n e r a l l y been ignored i n an e n s u i n g m e c h a n i s t i c d i s c u s s i o n . The nature of g r a i n growth i n the p resent work has r e s u l t e d i n the f o l l o w i n g c h a r a c t e r i s t i c s : a) G r a i n growth i s g r e a t l y enhanced by deformat ion ( t a b l e i n F i g . 16 and F i g . 1 7 ) . b) G r a i n growth i s a d i s c o n t i n u o u s p r o c e s s . A g r a d u a l i n c r e a s e i n g r a i n d iameter would r e s u l t i n ledges forming due to consecut i ve s h e a r i n g and m i g r a t i o n p r o c e s s e s , w h i l e a sudden i n c r e a s e i n g r a i n s i z e would be expected to r e s u l t i n a s u r f a c e s t r u c t u r e s i m i l a r to F i g . 18 or F i g . 2 0 , where the shear markings d e l i n e a t i n g the o r i g i n a l s t r u c t u r e resemble a network of subboundar ies . c) G r a i n growth i s r a p i d d u r i n g the i n i t i a l s tages of deformat ion but tends to decrease as s t r a i n i n c r e a s e s ( F i g . 2 1 ) . Based on these o b s e r v a t i o n s , a model i n c o r p o r a t i n g g r a i n boundary shear and " e x p l o s i v e g r a i n growth" i s proposed to account f o r the s u p e r p l a s t i c behav io r of t h i s a l l o y . Shear on the o r i g i n a l boundar ies i s assumed to occur i n i t i a l l y and s i n c e t h i s process i s e s s e n t i a l l y one c o n t r i b u t i n g to hardening, a d r i v i n g f o r c e f o r g r a i n boundary m i g r a t i o n i s c r e a t e d due to d i f f e r e n c e s i n d i s l o c a t i o n d e n s i t y on e i t h e r s i d e of 52 a s h e a r i n g boundary. T h i s d i f f e r e n c e i n d e n s i t y cou ld r e s u l t from sources f i r s t becoming o p e r a t i v e i n the l a r g e r g r a i n s of the m a t r i x (from s l i p p lane l e n g t h c o n s i d e r a t i o n s ) l e a d i n g to a g r e a t e r d e n s i t y of d i s l o c a t i o n s b e i n g s u p p l i e d to a boundary from w i t h i n a l a r g e r g r a i n . Hence, f o l l o w i n g shear by a c l i m b - g l i d e or s i m i l a r mechanism, the boundary moves r a p i d l y to e l i m i n a t e the areas of h i g h e s t d i s l o c a t i o n d e n s i t y . T h e r e f o r e , the l a r g e r g r a i n s tend to decrease i n s i z e as the s m a l l e r g r a i n s grow - a s u g g e s t i o n c o n s i s t e n t w i t h o b s e r v a t i o n s of an equiaxed s t r u c t u r e a f t e r l a r g e amounts of s u p e r p l a s t i c d e f o r m a t i o n . The o b s e r v a t i o n of a l i n e a r l o g a r i t h m i c dependence of g r a i n s i z e on s t r a i n ( F i g . 21) i s not complete ly unders tood . The problem i s compl i ca ted by a c o n t i n u a l l y d e c r e a s i n g s t r a i n r a t e which may or may not a f f e c t the r a t e of g r a i n growth. At p resent i t i s thought that a decrease i n the e x p l o s i v e nature of the proposed boundary m i g r a t i o n may r e s u l t i n the f l u c t u a t i o n of boundar ies back and f o r t h to e l i m i n a t e a l t e r n a t e l a y e r s of excess d i s l o c a t i o n s . A l though no c o n c l u s i v e ev idence f o r t h i s type of behav io r has been observed , a s m a l l degree of support i s found on numerous e l e c t r o n micrographs of r e p l i c a s taken from the deformed specimen s u r f a c e . In p a r t i c u l a r , some boundary r e g i o n s are b r o a d , wavy and d i f f u s e i n nature which may i n d i c a t e t h a t t h e i r o r i g i n was from some process o ther than a s imple s h e a r i n g . The p o s s i b i l i t y a l s o e x i s t s that the s t r i a t e d reg ions observed by Zehr and Backofen"*""*" as w e l l as i n F i g . 20 may w e l l be i n d i c a t i v e of a boundary f l u c t u a t i o n process r a t h e r than one of d i f f u s i o n a l c reep . A f i n a l o b s e r v a t i o n of the deformed s u r f a c e m i c r o s t r u c t u r e i s tha t some g r a i n e l o n g a t i o n had occur red at a s t r a i n r a t e where l a r g e 53 elongations are obtained. This could come as a r e s u l t of the e f f e c t of a l i m i t e d amount of s l i p combined with Nabarro-Herring creep. I t may therefore be proper to think i n terms of grain boundary migration as the rate c o n t r o l l i n g process i n s u p e r p l a s t i c i t y instead of the s p e c i f i c deformation modes associated with boundary shear. Although migration cannot by i t s e l f contribute to s t r a i n i t can be rate c o n t r o l l i n g i f i t does determine the rate at which shear can occur. Any boundary motion w i l l d e f i n i t e l y a f f e c t the d i s l o c a t i o n structure i n the region of the boundary and hence w i l l determine 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 s . The observed a c t i v a t i o n energy of 10 kcal/g.atom i s approximately that expected f o r d i f f u s i o n i n the region of a grain boundary and hence f o r the process of boundary migration. This value 20 would also be expected f o r d i s l o c a t i o n climb (associated with shear) i n the region of a boundary. Therefore any a c t i v a t i o n energy determination by i t s e l f cannot d i s t i n g u i s h between these two known features associated with s u p e r p l a s t i c i t y . However the continuity of the shear mode of deformation i s dependent on the migration process. Therefore i t i s f e l t that migration i t s e l f must be rate c o n t r o l l i n g . 34 5 . SUMMARY AND CONCLUSIONS The i n t e r p r e t a t i o n of the m e t a l l o g r a p h i c and t e n s i l e behav io r o b s e r v a t i o n s made on the z i n c - r i c h s o l i d s o l u t i o n of the Z n - A l e u t e c t o i d a l l o y may be summarized as f o l l o w s : 1) The e x t e n s i v e e l o n g a t i o n s and h i g h s t r a i n r a t e sensi t iv i ty g e n e r a l l y a s s o c i a t e d w i t h s u p e r p l a s t i c m a t e r i a l s have been observed i n a f i n e - g r a i n e d Z n - 0 . 2 wt . % A l a l l o y at T „ = 0 . 4 2 . T h i s i s the lowest homologous temperature at which s u p e r p l a s t i c i t y has been observed i n any system to d a t e . 2) The r e g i o n of s u p e r p l a s t i c behav io r i s observed at h i g h e r s t r a i n r a t e s as the g r a i n s i z e i s r e f i n e d . The most important requi rements are a g r a i n s i z e i n the micron range and g r a i n boundar ies tha t are r e l a t i v e l y f r e e of o b s t r u c t i o n s . E x c e s s i v e amounts of ox ide i n the a l l o y tend to i n t e r f e r e w i t h g r a i n boundary shear and m i g r a t i o n , and thus r e s t r i c t s u p e r p l a s t i c d e f o r m a t i o n . 3) C o n s i d e r a t i o n s of the s t r a i n r a t e s e n s i t i v i t y d e t e r m i n a t i o n s at l a r g e amounts of s t r a i n suggest tha t the dec reas ing v a l u e s of t r u e s t r e s s r e f l e c t the dec reas ing s t r a i n r a t e a s s o c i a t e d w i t h the i n c r e a s e i n specimen l e n g t h . The degree of decrease i n s t r e s s i s masked s l i g h t l y by the i n c r e a s i n g g r a i n s i z e . 4) G r a i n growth i s encouraged d u r i n g d e f o r m a t i o n . A l though the e f f e c t of the r a t e of g r a i n growth was unreso lved i t i s expected to be an important parameter i n s u p e r p l a s t i c deformat ion i n tha t the ins tantaneous g r a i n s i z e a f f e c t s the s t r a i n r a t e s e n s i t i v i t y parameter m. The g r a i n growth was shown to f o l l o w a l i n e a r l o g a r i t h m i c dependence w i t h s t r a i n . 55 5) The apparent a c t i v a t i o n energy of the r a t e c o n t r o l l i n g process i s approx imate ly 10 k c a l / g . a t o m . A model i n c o r p o r a t i n g g r a i n boundary shear and " e x p l o s i v e g r a i n growth" i s proposed to account f o r the s u p e r p l a s t i c behav io r i n t h i s system. A l though a c t i v a t i o n energy c o n s i d e r a t i o n s cannot d i s t i n g u i s h between g r a i n boundary m i g r a t i o n and d i s l o c a t i o n c l imb i t i s f e l t tha t the former i s the r a t e c o n t r o l l i n g p rocess as i t w i l l determine the r a t e at which g r a i n boundary shear can o c c u r . 6) In r e g i o n s where the deformat ion i s s l i p c o n t r o l l e d the y i e l d s t r e s s dependence on g r a i n s i z e obeyed the H a l l - P e t c h r e l a t i o n s h i p : - 1 / 2 C?Q £ = a D + Kd where K was measured to be approx imate ly 45,000 p s i 1/2 (micron) and a was n e g l i g i b l e . 56 6 . SUGGESTIONS FOR FUTURE WORK S e v e r a l l i n e s of i n v e s t i g a t i o n are suggested from the d i s c u s s i o n of the p resent work. These i n c l u d e : 1) An i n v e s t i g a t i o n of s u p e r p l a s t i c deformat ion u t i l i z i n g constant s t r a i n r a t e t e s t i n g c o n d i t i o n s . S ince the r a t e s e n s i t i v i t y parameter i s s t r o n g f u n c t i o n of s t r a i n r a t e , any a n a l y s i s i s compl i ca ted when the s t r a i n r a t e i s c o n t i n u a l l y d e c r e a s i n g d u r i n g t e s t i n g . 2) An e x t e n s i v e study on how the r a t e of g r a i n growth i s a f f e c t e d by s t r a i n r a t e , temperature and amount of second- phase p r e s e n t . 3) A study i n v o l v i n g the v a r i a t i o n of amount and nature of second phase i n the a l l o y i n an attempt to ach ieve a f i n e r , more s t a b l e g r a i n s i z e . APPENDIX I E v a l u a t i o n of the S t ra in Rate S e n s i t i v i t y Parameter The s t r a i n r a t e sensi t iv i ty parameter m as d e s c r i b e d by the r e l a t i o n s h i p a = Ktm i s the s l o p e of the l o g s t r e s s - l o g s t r a i n r a t e c u r v e , or more e x p l i c i t l y , m = 91na/9 In e . Th is Va lue may be obta ined g r a p h i c a l l y by measuring the s l o p e of the o-k curve or by u t i l i z i n g a techn ique d e s c r i b e d by Backofen et a l (Trans. ASM 57 (1964) 980) . The procedure i n v o l v e s making i n c r e m e n t a l changes i n crosshead speed. The accompanying schemat ic diagram r e p r e s e n t s a change of crosshead speed from v to v ' at a t ime t ^ . The loads are measured at t imes A and B, the l a t t e r be ing the t ime at which the e x t r a p o l a t e d curve at speed v would reach an i d e n t i c a l amount of s t r a i n as at speed v ' and t ime A . The v a l u e of m can then be c a l c u l a t e d f rom: l o g P A / P B m = — — f l o g / v and i s a s s o c i a t e d w i t h the lower s t r a i n r a t e of e = V / & B where £ g i s the specimen l e n g t h at t ime B. i V _ i t L t, A B Time 58 The crosshead speed was v a r i e d from 2 .0 x 1 0 - ^ i n . / m i n . up to 1 i n . / m i n . i n s teps i n which the r a t i o A)was e i t h e r 2 or 2 . 5 . 59 APPENDIX I I Var ious Specimens Deformed to F a i l u r e at D i f f e r e n t S t r a i n Rates The e x t e n s i v e amounts of e s s e n t i a l l y n e c k - f r e e deformat ion that occur i n s u p e r p l a s t i c m a t e r i a l s are worthy of p r e s e n t a t i o n i n p i c t o r i a l form as w e l l as g r a p h i c a l . Inc luded i n the f o l l o w i n g photograph are t e n s i l e specimens i n the as s t r a i n e d c o n d i t i o n both f o r the ext ruded c a s t i n g and r o l l e d s t o c k . S e v e r a l of the specimens shown e x h i b i t more than one neck along the gauge l e n g t h which would i n d i c a t e tha t a neck may develop dur ing the t e s t but due to the l o c a l i n c r e a s e i n s t r a i n r a t e , and a h i g h v a l u e of m, the r e g i o n of an i n c i p e n t neck work hardens and f a i l u r e does not occur at the i n i t i a l c r o s s - s e c t i o n a l i r r e g u l a r i t y . 60 D e s c r i p t i o n I n i t i a l S t r a i n I n i t i a l m T o t a l S t r a i n (%) Rate ( m i n . - 1 ) 1 . C o n d i t i o n A (Table I ) 0 2 . " 0.077 0 . 2 365 3 . " 0.0077 0 . 5 590 4. " 0 .0031 0 .6 (maximum) 350 5 . C o n d i t i o n B 0.0154 0 . 2 157 6 . 11 0.00154 0 .6 457 7. C o n d i t i o n C 0.00031 0 .15 216 61 BIBLIOGRAPHY 1) A . A . Bochvar and Z. A . S v i d e r s k a i a , I z v . Akad. Nauk . , SSSR, O t d e l , Tekh N a u k . , 9 (1945) 821. 2) E. E. Underwood, J . M e t a l s , 14 (1962) 914. 3) W. A . B a c k o f e n , I. R. T u r n e r , and D. H. A v e r y , ASM Trans . Q u a r t . , 57 (1964) 980. 4) D. H. Avery and W. A . B a c k o f e n , ASM Trans . Q u a r t . , 58 (1965) 551. 5) D. Lee and W. A . B a c k o f e n , T rans . AIME, 239 (1967) 1034. - 6) T. H. A l d e n , A c t a . M e t . , 15 (1967) 469. • 7) H. E. C l i n e and T. H. A l d e n , T rans . A I M E . , 239 (1967) 710. 8) D. L. H o l t and W. A . B a c k o f e n , ASM Trans . Q u a r t . , 59 (1966) 755. - 9 ) T. H. A lden and H. W. S c h a d l e r , T rans . A I M E . , 242 (1968) 825. 10) P . J . M a r t i n and W. A . B a c k o f e n , ASM Trans . Q u a r t . , 60 (1967) 352. 11) S . W. Zehr and W. A . B a c k o f e n , ASM Trans . Q u a r t . , 61 (1968) 300. 12) D. L . H o l t , T rans . AIME, 242 (1968) 2 5 . 13) E. W. H a r t , A c t a . M e t . , 15 (1967) 1545. 14) H. w. Hayden, R. C. G i b s o n , H. F. M e r r i c k and J . H. Brophy, ASM T rans . Q u a r t . , 60 (1967) 3 . 15) D. O e l o c h l a g e l and V. W e i s s , ASM T rans . Q u a r t . , 59 (1966) 143. 16) D. L. H o l t , T rans . AIME, 242 (1968) 740. 17) C. M. Packer and 0 . D. Sherby , ASM Trans . Q u a r t . , 60 (1967) 2 1 . 18) R. Kossowsky and J . H. B e c h t o l d , T rans . AIME, 242 (1968) 716. 19) T. H. A l d e n , T rans . AIME, 236 (1966) 1633. 20) T. H. A l d e n , to be p u b l i s h e d , ASM T rans . Quar t . 21) D. Tromans and J . A . Lund , ASM T rans . Q u a r t . , 59 (1966) 672. 22) R. C. G i f k i n s , J . I n s t . M e t a l s , 95 (1967) 373. 23) C. E. P e a r s o n , J . I n s t . M e t a l s , 54 (1934) 111. 24) W. Schu lze and F. Sauerwald , Z. M e t a l l k u n d e , 53 (1962) 660. 25) T. H. A l d e n , D i s c u s s i o n , ASM Trans . Q u a r t . , 60 ( 1 9 6 7 ) , 2 7 4 . 26) R. B. Jones and R. H. Johnson , D i s c u s s i o n , ASM Trans . Q u a r t . , 59 (1966) 356. 27) S . F l o r e e n , S c r i p t a Met . , 1 (1967) 19. 28a) N. F. M o t t , P h i l . Mag. 44 (1953) 742. b) N. F. M o t t , P r o c . Phys . S o c , B64 (1951) 729. 29a) J . F r i e d e l , "Les D i s l o c a t i o n s " , G a u t h i e r - V i l l a r s , P a r i s (1956) 1 7 6 - 1 7 9 , 1 9 8 - 2 0 1 . b) J . F r i e d e l , " D i s l o c a t i o n s " , A d d i s i o n - W e s l e y (1964) , Read ing , M a s s . , F i r s t E n g l i s h E d i t i o n pp. 299 and 315. 30) C. J . S m i t h e l l s , " M e t a l s Reference Book" , v o l . 2 , B u t t e r w o r t h ' s London (1962) . 

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