UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Superplastic creep in the lead tin eutectic 1969

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1970_A7 S87.pdf
UBC_1970_A7 S87.pdf
UBC_1970_A7 S87.pdf [ 4.74MB ]
Metadata
JSON: 1.0078631.json
JSON-LD: 1.0078631+ld.json
RDF/XML (Pretty): 1.0078631.xml
RDF/JSON: 1.0078631+rdf.json
Turtle: 1.0078631+rdf-turtle.txt
N-Triples: 1.0078631+rdf-ntriples.txt
Citation
1.0078631.ris

Full Text

SUPERPLASTIC CREEP IN THE LEAD TIN EUTECTIC by ALBERT KEITH SURGES B.A. Sc., U n i v e r s i t y of B r i t i s h Columbia, 1967 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 t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r .an a d v a n c e d d e g r e e a t t h e 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 , I a g r e e t h a t t h e 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 f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f M e t a l l u r g y The 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 V a n c o u v e r 8 , Canada Date O c t o b e r 2 7 . 1 9 7 0 i A b s t r a c t An extensive creep study of a s u p e r p l a s t i c m a t e r i a l has not p r e v i o u s l y been made. The present study was c a r r i e d out to determine i f there are any b a s i c d i f f e r e n c e s between the creep of coarse grained m a t e r i a l s and f i n e grained super- p l a s t i c m a t e r i a l s . The r e s u l t s give i n f o r m a t i o n about the mechanical p r o p e r t i e s of s u p e r p l a s t i c a l l o y s and are r e l e v e n t to an understanding of the mechanics of s u p e r p l a s t i c i y . At high s t r a i n r a t e s the s u p e r p l a s t i c l e a d - t i n e u t e c t i c deforms by recovery creep and a 3-stage creep curve i s observed, s i m i l a r to that found f o r coarse grained m a t e r i a l s . As the s t r a i n r a t e i s decreased, the i n i t i a l t r a n s i e n t (primary creep) disappears and the creep curve i s l i n e a r u n t i l necking occurs and t e r t i a r y creep ends i n f a i l u r e . In the p r i n c i p a l s u p e r p l a s t i c range, at medium s t r a i n r a t e s , creep curves are l i n e a r to at l e a s t 50 % s t r a i n . The recovery r a t e i s immediately equal to the s t r a i n hardening r a t e and there i s no primary creep. At low s t r a i n r a t e s the creep curve i s s l i g h t l y convex as the creep r a t e decreases w i t h time. This may be due to the s e l f e x t i n g u i s h i n g nature of d i f f u s i o n a l creep or p o s s i b l y s t r a i n induced g r a i n growth. These r e s u l t s are c o n s i s t e n t w i t h the g r a i n boundary s l i d i n g t h e o r i e s of s u p e r p l a s t i c i t y although d e t a i l s of the accommodation processes are not known. At the lowest s t r a i n r a t e s , d i f f u s i o n a l creep may operate. i i ACKNOWLEDGMENT The author i s g r a t e f u l f o r the advice of and h e l p f u l d i s c u s s i o n w i t h h i s research d i r e c t o r , Dr. T.H. Alden. Thanks are a l s o extended to R.C. Cook and K.C. Donaldson f o r t h e i r d i s c u s s i o n s and suggestions. C.B. S u l l i v a n ' s a s s i s t a n c e w i t h draghting f o r the p r e s e n t a t i o n of t h i s t h e s i s i s a l s o appreciated. I i i TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 Stage II (Superplastic Stage) 3 1.1.1 Review of Experiment 3 1.1.2 Theoretical Discussion 5 1.2 Stage I II 6 1.3 Stage I 6 1.4 Previous Creep Studies on Lead and T i n Systems ... 8 2. EXPERIMENTAL 9 2.1 Material and Specimen Preparation 9 2.2 Creep Tests 10 3. RESULTS 13 3.1 Calculations 13 .3.2 Log Stress versus Log S t r a i n Ra±e Curves 13 3.3 Creep Curves 16 3.3.1 Stage II Creep Curves 16 3.3.2 Stage I Creep Curves 17 3.3.3 Stage II - Stage I II T r a n s i t i o n Creep Curves .... 17 3.3.4 Stage I II Creep Curves 23 3.4 Incremental Loading and Unloading 23 3.5 S t r a i n A f t e r - E f f e c t s 2 9 4. DISCUSSION 30 4.1 Stage I II 30 4.2 Stage I II - Stage II T r a n s i t i o n 35 4.3 Stage I II 37 4.4 Stage I • • 4 0 5. SUMMARY AND CONCLUSIONS 44 6. SUGGESTIONS FOR FUTURE WORK 46 7. APPENDICES 4 7 7.1 Computer Programme 47 7.2 Ad d i t i o n a l Creep Curves 52 i v 7.3 C a l c u l a t i o n of Theoretical Creep Curves f o r Pure Nabarro-Herring Creep and Pure Coble Creep 53 8. BIBLIOGRAPHY 64 V LIST OF FIGURES No. Page 1. C h a r a c t e r i s t i c l o g s t r e s s versus l o g s t r a i n r a t e curve. 1 2. Specimen i n g r i p s . 10 3. Constant s t r e s s creep machine. 12 4. Log s t r e s s versus l o g s t r a i n r a t e curve. (SGS, 2 microns). 14 5. Log s t r e s s versus l o g s t r a i n curve. (LGS, 8 microns). 15 6. Comparison of the S-curve data of the present and previous work. 16 7. Stage I I creep curve (SGS), 429 p s i . 18 8. Stage I I creep curve (SGS), 1716 p s i . , 19 9. Stage I I creep curve (SGS), 715 p s i . 20 10. Stage I I creep curve (LGS), 814 p s i . 21 11. Stage I creep curve (SGS), 97 p s i . 22 12. Creep curve i n stage I I - s t a g e I I t r a n s i t i o n (SGS, 3432 p s i . 24 13. Creep curve i n stage I I - s t a g e I I I t r a n s i t i o n (LGS), 3582 p s i . 25 14.. Stage I I I creep curve (5212 p s i ) . 26 15. Stage I I I creep curve (5535 p s i ) . 26 16. Stage I I I creep curve (6512 p s i ) . 28 17. S t r a i n r e q u i r e d to reach steady s t a t e versus creep s t r e s s . 27 18. Incremental lo a d i n g d u r i n g s u p e r p l a s t i c creep. 18 19. Return of an i n i t i a l t r a n s i e n t w i t h incremental loading i n stage I I I 3 1 20. T r a n s i t i o n to steady s t a t e w i t h unloading i n stage I I I . 31 21. S t r a i n r e l a x a t i o n study i n stage I I 32 22. Reloading a f t e r recovery i n stage I I I 32 23. Log s t r e s s versus l o g 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 Pb-2.45 wt%. v i 24. Log s t r e s s versus l o g 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 Pb-2.45 wt% t h a l l i u m (100 u ) . 25. Experimental, t h e o r e t i c a l N-H and t h e o r e t i c a l Coble creep curves (97 p s i ) . Appendix I I I a. Stage I I (SGS) 572 p s i . b. Stage I I (SGS), 858 p s i . c. Stage I I (SGS), 1144 p s i . d. Stage I I LGS), 407 p s i . e. Stage I I (LGS), 1221 p s i . f. Stage I (SGS), 120 p s i . g. Stage I (SGS), 143 p s i . h. Stage I (SGS), 286 p s i . i . T r a n s i t i o n (SGS), 2574 p s i . j . T r a n s i t i o n (SGS), 2860 P s i . k. T r a n s i t i o n (LGS), 1954 p s i . 1. T r a n s i t i o n (LGS), 2280 p s i . m. T r a n s i t i o n (LGS), 2606 p s i . n. T r a n s i t i o n (LGS), 2932 p s i . o. T r a n s i t i o n (LGS), 32580 p s i . p. T r a n s i t i o n (LGS), 3908 p s i . q. T r a n s i t i o n (LGS), 4234 p s i . r . T r a n s i t i o n (LGS), 4560 p s i . s. T r a n s i t i o n (LGS), 4886 p s i . t . Stage I I I , 2931 p s i . u. Stage I I I , 7326 p s i . v. Stage I I incremental l o a d i n g , w. Stage I I I unloading -1- I. I n t r o d u c t i o n S u p e r p l a s t i c behaviour has been found i n many metal systems. A l l o y s of lead and z i n c have been i n v e s t i g a t e d most f r e q u e n t l y , but systems c o n t a i n i n g n i c k e l , i r o n , aluminium, t i n , cadmium, magnesium, and copper have a l s o e x h i b i t e d s u p e r p l a s t i c p r o p e r t i e s . Studies have a l s o been made to determine deformation mechanisms which are c o n s i s t e n t w i t h experiment. Results of these s t u d i e s may a l s o be important i n the development of new metal-forming techniques. Stress versus s t r a i n r a t e r e s u l t s from t e n s i l e and creep t e s t s have been p l o t t e d as l o g s t r e s s (log a) versus l o g s t r a i n r a t e ( l o g e) to produce a c h a r a c t e r i s t i c three stage S-shaped curve. In the s u p e r p l a s t i c range, stage I I , the s t r a i n r a t e (e) i s i n s e n s i t i v e to the ap p l i e d s t r e s s (C T ) . L O G S T R A I N R A T E Figure 1. C h a r a c t e r i s t i c l o g s t r e s s - l o g s t r a i n r a t e curve. -2- Each stage of the S-curve may be described by the equation a = K e (1) where K i s a constant and m i s c a l l e d the s t r a i n r a t e s e n s i t i v i t y parameter. T y p i c a l values of m vary from l e s s than .1 f o r most metals up to 1.0 f o r hot polymers and glasses. S u p e r p l a s t i c metals have been observed to e x h i b i t m values as high as •SS''", .but are t y p i c a l l y about 0.5. In stage I I , where m i s high, propagation of a neck i s prevented by a l o c a l hardening r e s u l t i n g from an increased s t r a i n r a t e , and thus deformation w i l l proceed i n a s o f t e r p o r t i o n of the m a t e r i a l . A c c o r d i n g l y , a high value of m i s a s s o c i a t e d w i t h l a r g e elonga- 2 t i o n s , r e p o r t e d l y as high as 2000 % . Mathematically, the r e l a t i o n s h i p between m and e l o n g a t i o n can be' shown more e x p l i c i t l y by f i r s t d i f f e r e n t i a t i n g equation (1) to o b t a i n I t can be seen that the l a r g e r the value of m, the more i n s e n s i t i v e s t r a i n r a t e becomes to a change i n s t r e s s . A l s o , over a c e r t a i n s t r a i n r a t e range i n s u p e r p l a s t i c m a t e r i a l s , m increases s l i g h t l y w i t h i n c r e a s i n g s t r a i n r a t e . The p o s i t i v e v a r i a t i o n of m i n s u p e r p l a s t i c m a t e r i a l s w i l l cause the f a c t o r i n brackets i n equation (2) to be reduced, and w i l l f u r t h e r reduce s e n s i t i v i t y to necking. p l a s t i c i t y i s most conveniently done by c o n s i d e r i n g the stages of the logo - loge curve s e p a r a t e l y . Of these, the most important and i n t e n s i v e l y s t u d i e d i s stage I I . (2) Further d e s c r i p t i o n of experimental and t h e o r e t i c a l s t u d i e s on super- -3- 1.1. Stage I I ( S u p e r p l a s t i c Stage) 1.1.1. Review of Experiment A f i n e g r a i n s i z e has been shown to be the most important m i c r o s t r u c t u r - 3-11 a l requirement f o r s u p e r p l a s t i c i t y . P r o v i d i n g the phases are of comparable hardness, the composition and means by which g r a i n refinement i s achieved are 6 9 of secondary importance. ' In two phase systems, a hot or c o l d working step w i l l permit the formation of a f i n e g r a i n s i z e , w h i l e phase boundaries i n h i b i t g r a i n growth. Thus extensive s t u d i e s have been made on the e u t e c t o i d Zn - 22 wt. % A l and the Pb-Sn systems. D i l u t e a l l o y ^ ^ a n d pure metal systems,have als o e x h i b i t e d s u p e r p l a s t i c i t y . The inherent problem w i t h these systems i s to produce and maintain 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 . For a given time and tem- perature, g r a i n s i z e i s l a r g e r i n d i l u t e a l l o y s . Large elongations during stage I I have been c o n s i s t e n t l y reported. The l a r g e s t elongations occur at s t r a i n r a t e s near that associated w i t h peak m 16 18 values ' . Maximum el o n g a t i o n may occur p r e c i s e l y at peak m but the r e s u l t i s obscurred by the decreasing s t r a i n r a t e during a t e n s i l e t e s t on a constant c r o s s - head r a t e machine such as an I n s t r o n . i T e n s i l e t e s t s i n v o l v i n g s e v e r a l g r a i n s i z e s show that the e f f e c t of g r a i n coarsening i s to s h i f t the s t r a i n r a t e at constant s t r e s s to lower v a l u e s . This s h i f t i s expressed by the r e l a t i o n s h i p k ^ 1/L ( f o r constant m) where a 1 3 5 7 8 1 2 1 3 i s u s u a l l y between 2 and A ' ' ' ' ' ' and L i s the spacing between g r a i n or phase boundaries. Temperature a l s o has an e f f e c t on the S-curve. The maximum m f o r each temperature drops w i t h decreasing temperature''". The s t r a i n r a t e correspond- i n g to peak m a l s o decreases w i t h decreasing temperature; An increase i n tempera- _4- ture s h i f t s the curve to higher s t r a i n r a t e s and to s l i g h t l y lower s t r e s s e s . G r a i n boundary s l i d i n g i s observed and i t s c o n t r i b u t i o n to t o t a l s t r a i n increases as the s t r a i n r a t e i s lowered from stage I I I i n t o stage 11^'lL. E x p e r i m e n t a l l y , the c o n t r i b u t i o n of GBS to t o t a l s t r a i n i s determined by measuring the o f f s e t of g r i d l i n e s i n s c r i b e d across g r a i n boundaries p r i o r to deformation. S u p e r p l a s t i c deformation does not cause the b u i l d up of a d i s l o c a t i o n s u b s t r u c t u r e . An Mg-Al alloy''" has been water quenched from 400°C during s u p e r p l a s t i c deformation and transmission e l e c t r o n microscopy showed no d i s l o c a t i o n t r a c e s . D i s l o c a t i o n s are present a f t e r deformation i n stage I I I . The low temperature y i e l d s t r e s s remains unchanged, r e l a t i v e to that of the 13 undeformed m a t e r i a l , a f t e r stage I I deformation . Pb-5% Cd specimens were deformed 2 % at a s e l e c t e d temperature, s t r a i n r a t e and g r a i n s i z e and immedia- t e l y quenched to -90°C. The .2% y i e l d s t r e s s was then determined. Specimens deformed i n the s u p e r p l a s t i c range showed no i n c r e a s e i n y i e l d s t r e s s w h i l e those deformed i n stage I I I showed an increase i n y i e l d s t r e s s . Grain shape remains equiaxed a f t e r as much as 1000- % e l o n g a t i o n ^ . Grain growth o c c u r s ^ ' ^ arid may be important i n the deformation process or may mask other r e l a t i o n s h i p s . 13 Recovery r a t e s are f a s t i n s u p e r p l a s t i c m a t e r i a l s and decrease w i t h i n c r e a s i n g g r a i n s i z e . Pb-5% Cd specimens were deformed 2% at -90°C, annealed f o r various times at 50°C then deformed again at -90°C. The amount of recovery, R, was determined by R = (aH - aR)/(aH - aY) , where aH i s determined a f t e r 2% s t r a i n , oR a f t e r recovery and aY on the annealed m a t e r i a l . There was 40% recovery f o r a 4.1p g r a i n s i z e a f t e r only .2 minutes while i t took 100 minutes to o b t a i n 30 % recovery i n a 15y specimen. -5- Although there i s general agreement i n the experimental observations made on s u p e r p l a s t i c m a t e r i a l s , disagreement on the r e l a t i v e importance or i n t e r p r e t a t i o n of i n d i v i d u a l obeservation has lead to a wide range of suggested mechanisms. 1.1.2. T h e o r e t i c a l D i s c u s s i o n Work on the Al^-33 wt. % Cu e u t e c t i c ^ and the Zn-Al eutectic*"'" lead to s i m i l a r proposals that the high s t r a i n r a t e s e n s i t i v i t y which c h a r a c t e r i z e s s u p e r p l a s t i c i t y i s the r e s u l t of boundary shearing and m i g r a t i o n . G r a i n boundary shear was suggested to be r a t e c o n t r o l l i n g , and mechanical o b s t r u c t - ions to s l i d i n g were removed by s t r a i n r a t e enhanced boundary m i g r a t i o n and r e c r y s t a l l i z a t i o n . At t h i s intermediate s t r a i n r a t e , boundaries become smoother and s t r e s s i s determined by viscous drag along the boundaries. Work 6 5 on the Pb-Sn and Sn-Bi systems a l s o lead to the proposal that g r a i n boundary s l i d i n g was the r a t e c o n t r o l l i n g mechanism. Experimental r e s u l t s showed^ that the g r e a t e s t c o n t r i b u t i o n of g r a i n boundary s l i d i n g occurred when the s t r a i n r a t e s e n s i t i v i t y parameter, m, reached i t s peak value. Another suggested mechanism f o r deformation of Pb-Sn*^ incorporates non-Newtonian g r a i n boundary s l i d i n g and d i f f u s i o n a l (Newtonian) creep a c t i n g together i n p a r a l l e l , and then i n s e r i e s w i t h non-Newtonian s l i p creep. Close reproduction of an ex- perimental loga - l o g ! curve, obtained by using new and p r e v i o u s l y p l o t t e d p o i n t s , could be made using semi-empirical procedures based on the model. Grai n boundary s l i d i n g was proposed to e x p l a i n the s u p e r p l a s t i c be- haviour of the Mg-Al e u t e c t i c by Lee*. GBS i s accompanied by g r a i n deformation and recovery. These cooperative processes are necessary, e s p e c i a l l y i n regions near the boundary, to permit extensive p l a s t i c deformation. No d i s l o c a t i o n s -6- were seen a f t e r 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 i s i s p o s s i b l e b e c a u s e the f i n e g r a i n s i z e p e r m i t s a l l d i s l o c a t i o n s , even i n the b u l k o f a g r a i n , t o be 20 21 a t t r a c t e d t o ' and r e a c h a boundary w h i c h i s s l i d i n g by d i s l o c a t i o n 22 13 2 A movement ' o r d i f f u s i o n a l p r o c e s s e s , and be a n n i h i l a t e d . I t i s s u g g e s t e d t h a t t h i s model might e x p l a i n t h e low amounts o f GBS d u r i n g b i c r y s t a l s l i d i n g 25 26 e x p e r i m e n t s ' where t h e e f f e c t i v e g r a i n s i z e i s more o r l e s s i n f i n i t e , thus l i m i t i n g r e c o v e r y t o r e g i o n s n e a r t h e g r a i n boundary. 3 A n o t h e r model , based on e x p e r i m e n t a l work o n Pb-Sn, i n v o l v e s two competing p r o c e s s e s . These a r e N a b a r r o - H e r r i n g (N-H) c r e e p , and d i s l o c a t i o n m o t i o n . I n t h e h i g h m r e g i o n , the N-H model i s dominant and f l o w i s s t r o n g l y 27 v i s c o u s . A m o d i f i c a t i o n o f t h i s model, i n v o l v i n g the C o b l e v a r i a n t o f t h e N-H a n a l y s i s w h i c h 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 t h a n volume d i f f u s i o n , was s u g g e s t e d t o b e t t e r a c c o u n t f o r the o b s e r v e d s t r a i n r a t e s . 1.2. Stage I I I T h i s r e g i o n a t t h e h i g h s t r a i n r a t e end o f the S-curve i s n o t s u p e r - p l a s t i c . Low m v a l u e s a r e t y p i c a l . There seems to be l i t t l e controversy as t o the mode o f d e f o r m a t i o n p r e s e n t . S l i p i s t h e d e f o r m a t i o n p r o c e s s i n d i c a t e d from p h o t o m i c r o g r a p h s and e l e c t r o n m i c r o g r a p h s w h i c h show s l i p l i n e s and d i s - l o c a t i o n s t r u c t u r e s r e m a i n i n g a f t e r d e f o r m a t i o n . The c o n t r o l l i n g p r o c e s s i s p r o b a b l y r e c o v e r y by d i s l o c a t i o n c l i m b . 1.3. Stage I • ,. . _ , . . 7,28 . . 10 . . j - 29 Stage I shows g r a m e l o n g a t i o n , s t r i a t i o n s o r denuded zones a t t r a n s v e r s e b o u n d a r i e s , and r e d u c e d g r a i n b o u n d a r t y s l i d i n g ^ ' 1 1 . There has been some q u e s t i o n as t o whether t h i s s t a g e i s r e p r e s e n t a t i v e o f a s e p a r a t e -7- mechanism or i s at l e a s t p a r t i a l l y a c o n t i n u a t i o n of stage I I . Further study over a wider range of v a r i a b l e s may e x p l a i n the true r e l a t i o n s h i p . Study of deformation i n t h i s r e g i o n o f t e n r e q u i r e s long term creep t e s t s because of the low s t r a i n r a t e s i n v o l v e d . 30 Chaudhari proposes that i n stage I the d i s l o c a t i o n d e n s i t y i s small and the d i s l o c a t i o n s reaching the g r a i n boundary can be absorbed at the boundary by e i t h e r s l i d i n g or m i g r a t i o n and l o c a l d i s l o c a t i o n climb. As £he s t r e s s i s increa s e d , the f l u x of d i s l o c a t i o n s approaching a g r a i n boundary increases more r a p i d l y than does the a b i l i t y of the g r a i n boundary to absorb them. This r e s u l t s i n a d i s l o c a t i o n b u i l d u p , an i n t e r n a l s t r e s s which increases w i t h s t r a i n r a t e and f i n a l l y stage I I where s t r e s s increases r a p i d l y w i t h s t r a i n r a t e . Deformation of the Mg-Al e u t e c t i c at a low s t r a i n r a t e was st u d i e d by Lee*. He found deformation to be a combined e f f e c t of g r a i n deformation and deformation across transverse g r a i n boundaries. The l a t t e r made up 1/3 of the deformation and occurred by GBS and p o s s i b l y some d i f f u s i o n a l creep. 31 Alden has r e c e n t l y proposed that s l i p at t r i p l e l i n e s i n response to s l i d i n g i s r a t e c o n t r o l l i n g . The model i n v o l v e s the viscous g l i d e of d i s - l o c a t i o n s between a source (the t r i p l e l i n e ) and a p e r f e c t s i n k (the opposite g r a i n boundary) and p r e d i c t s an m value between .33 and .5 and an a c t i v a t i o n energy of bulk d i f f u s i o n . He suggests that s u p e r p l a s t i c creep of Fe-Ni-Cr may be of t h i s type. Fe-Ni-Cr and Zn-Al (40.6 a t . % A l eutectoid) show only 2-stage loga curves. Alden suggests that stage I I i s not e n e r g e t i c a l l y f a v o r - able and only stages I and I I I are seen i n these systems. -8- Constant load creep tests on the 2-stage Zn-Al e u t e c t i c lead 32 Chaudhari to the conclusion that a d i s l o c a t i o n model was involved at temperatures above 200°C. The model involved the motion of d i s l o c a t i o n s i n an i n t e r n a l stress f i e l d generated by neighbouring d i s l o c a t i o n s . Ex- periment showed that above 200°C the s t r a i n rate i s c o n t r o l l e d by a thermally activated process with an a c t i v a t i o n energy of 35.3 k cal./g-atom: below 175°C, by a thermally activated process with an a c t i v a t i o n energy of 21k-calv/ g-atom. These values are close to those associated with bulk d i f f u s i o n i n A l and Zn r e s p e c t i v e l y . Zehr and Backofen^ represent stage I by a non-Newtonian dashpot model. They assign an m value .33 and p l o t a l i n e on the logo - logE curve but state that i t s r a t i o n a l e i s no more than speculative. 1.4 Previous Creep Studies on Lead and T i n Systems The present work was c a r r i e d out on the eutectic Pb-Sn a l l o y of f i n e grain s i z e . Constant stress creep testing was chosen to determine i f this method would show any difference between the creep of superplastic and non-superplastic materials. A l l reported creep work on lead, t i n and 33 l e a d - t i n has involved large grain s i z e materials. In lead s l i p occurred at the i n i t i a t i o n of creep and a time 1/3 law was obeyed u n t i l r e c r y s t a l l i z - 34 35 ation occurred. A three stage creep curve was found. Work on the Pb-Sn eute c t i c , and on pure t i n and lead, always showed a 3-stage creep curve. I t was suggested that primary creep must always occur. 36 Creep studies on large grained t i n at stresses between 629 and 1394 p s i and 22 and 224.5°C always resulted i n 3-stage creep curves. - 9 - I f a m a t e r i a l i s t o t a l l y unloaded a f t e r deformation, i t s shape changes w i t h time beyond an i n i t i a l predominantly e l a s t i c recovery and tends to approach i t s i n i t i a l shape. This i s known as the " a n e l a s t i c a f t e r e f f e c t " . This e f f e c t i s shown by Garofalo f o r l e a d ^ 7 at 25°C where 25 % of the de- formation i s recovered. Most reported s t r e s s versus s t r a i n r a t e data has been obtained using a t e n s i l e t e s t i n g machine. This r e s u l t s i n s t r a i n r a t e decreasing and s t r e s s changing w i t h time. The r e s u l t s of these t e s t s are not u s u a l l y reported w i t h a statement i n d i c a t i n g whether c o r r e c t i o n s were made f o r these e f f e c t s inherent i n the t e n s i l e t e s t i n g machine. I t i s a l s o d i f f i c u l t to determine a "steady sate" w i t h the t e n s i l e machine. A creep t e s t should avoid these d i f f i c u l t i e s . 2. EXPERIMENTAL . i 2.1. M a t e r i a l and Specimen P r e p a r a t i o n Ingots of the Pb-Sn e u t e c t i c (61.9 % Sn) were cast i n graphite molds under argon. M a t e r i a l s of 99.99 % p u r i t y or b e t t e r were used. Ingot dimensions were 5/8 i n c h diameter and 5 inches long. The surface of the cast b i l l e t s was machined and the m a t e r i a l was • extruded at room temperature i n t o rods of.099 and .083 i n c h diameter. The f i r s t and l a s t 18 inches of the e x t r u s i o n s were discarded. The rod was then cut i n t o 3% i n c h lengths. Samples of .099 i n c h diameter rods were roughened at each end w i t h emery paper and epoxied i n t o brass g r i p s (Fig.2) w i t h Epon 828 epoxy r e s i n . The g r i p s were d r i l l e d one i n c h deep w i t h a .113 i n c h d r i l l and the hole was tapped to improve the epoxy bond. These specimens were aged -10- 7 days at room temperature and then stored i n l i q u i d n i t r o g e n . The length of time of t e s t i n g was g e n e r a l l y small compared to the t o t a l time at room temperature so that g r a i n growth during t e s t i n g a t room temperature was minimized. Rods of .083 in c h diameter were sealed i n evacuated glass tubes and were annealed at 165 ± 2°C f o r 30 days'in an o i l bath to produce g r a i n growth. These rods were al s o epoxied i n t o brass g r i p s w i t h a .1015 inch tapped hole. These specimens were stored at room temperature. Comparison of l o g s t r e s s versus log s t r a i n r a t e curves p r e v i o u s l y presented f o r t h i s m a t e r i a l w i t h those r e s u l t i n g from t h i s study shows the small g r a i n s i z e m a t e r i a l (SGS) to have a g r a i n s i z e of 2 microns w h i l e the l a r g e g r a i n s i z e m a t e r i a l (LGS) has a g r a i n s i z e of 8 microns. Figure 2. Specimen i n gips 2.2. Creep Tests Creep t e s t s were performed on a constant s t r e s s machine (Figure 3). The cam design has a mechanical advantage such that the load on the specimen i s twice that i n t h e w e i g h t bucket. The constant s t r e s s cam i s designed f o r a specimen guage length of 25 mm. The a p p l i e d load was transmitted to the -11- specimen by a chromel tape which followed the contour of the cam e x a c t l y r a t h e r than tending to bow as round wires were found to do. The maximum elo n g a t i o n p o s s i b l e w i t h t h i s creep machine corresponded to 50 percent true s t r a i n . Loading and unloading operations were c a r r i e d out by lowering and r a i s i n g a s c i s s o r j a ck under the weight bucket. A l l t e s t s were done at room temperature (22±1°C). Elongation measurements were made w i t h both a t r a v e l l i n g o p t i c a l microscope and an extensometer which was connected to a modified Heathkit recorder and attached to the sample w i t h k n i f e edges. HiElongations could be measured to ± .001 cm with the microscope and to w i t h i n .0002 inches w i t h the extensometer and recorder. The microscope was used to f o l l o w the elo n g a t i o n of specimens deforming under low s t r e s s e s . Measurement was made of the displacement of a s i n g l e mark i n s c r i b e d on the specimen g r i p w i t h a razor blade. Experiment showed that there was no sli p p a g e i n the g r i p s and that i t was not necessary to observe the t r a v e l of two marks on the specimen i t s e l f . .' The extensometer was used at higher s t r e s s e s and s t r a i n r a t e s where automatic continuous recording was e s s e n t i a l . No s i g n i f i c a n t extensometer k n i f e edge i n d e n t a t i o n occurred at theses t r a i n r a t e s . The load was increased or decreased during some t e s t s to determine the e f f e c t of s t r e s s changes on the r e s u l t i n g creep curves. At high s t r e s s e s , i n v o l v i n g the l a r g e g r a i n s i z e m a t e r i a l , changes i n s t r e s s were made during the i n i t i a l t r a n s i e n t of th© creep curves. Specimens were a l s o suddenly un- loaded and the guage length was recorded w i t h the extensometer to determine i f unloading t r a n s i e n t s e x i s t e d over any s t r e s s range. -12- Figure 3. Constant s t r e s s creep machine. 3. RESULTS 3 .1. C a l c u l a t i o n s A l l c a l c u l a t i o n s were done on an IBM 360 computer. The programme i s shown i n Appendix I . Keypunched data i n c l u d e d i n i t i a l guage l e n g t h , and elongations at a s e r i e s of times (hours). A s c a l e f a c t o r was included to convert d e f l e c t i o n s on the Heathkit recorder, used whith the extensometer, to inches. The computer output included a scaled creep curve p l o t of true s t r a i n versus time and s t r a i n rateversus time. A l s o i n c l u d e d was a p r i n t e d t a b l e l i s t i n g each t r u e s t r a i n , s t r a i n r a t e and time p o i n t p l o t t e d . I n i t i a l l y , high s t r a i n r a t e values which f a l l o f f very q u i c k l y may be due to s t r a i g h t e n i n g of the specimen. This e f f e c t should be maximum when a l a r g e quage length i s used as was done w i t h t e s t s using the t r a v e l l i n g microscope. E l a s t i c s t r a i n would a l s o c o n t r i b u t e to t h i s r e s u l t . These e f f e c t s could not be i s o l a t e d and remain i n the computer output. P l o t s of s t r a i n r a t e are determined from the s t r a i n r a t e between two successive p o i n t s . This r e s u l t s i n a jagged s t r a i n r a t e curve. The s t r a i n r a t e s c a l e i s o f t e n expanded and t h i s a l s o tends to make the r e s u l t i n g curve jagged. 3.2. Log Stress versus Log S t r a i n Rate Curves S t r a i n r a t e data obtained from creep t e s t s were used to o b t a i n l o g s t r e s s versus l o g s t r a i n r a t e p l o t s f o r each g r a i n s i z e . These p l o t s are shown i n Figures 4 and 5. S t r a i n r a t e values used were the i n i t i a l s t r a i n r a t e i n stages I and I I and the steady s t a t e creep r a t e i n stage I I I . 4Y Log s t r e s s versus log s t r a i n curve (SGS, 2 microns). Figure 5. Log stress versus l o g s t r a i n rate curve (LGS, 8 microns). - 16 - The p l o t f o r the 2 micron g r a i n s i z e i s s i m i l a r to that determined by Zehr and Backofen*^. The s l o p e , or m v a l u e , i n Stage I i s .33. Stage I I shows a slope of ;5 g e n e r a l l y w i t h a peak value of about .6. The slope decreases a f t e r peak m as s t r a i n r a t e increases and approaches .10 i n stage I I I . The curve determined by Zehr and Backofen, and a l s o using C l i n e and Alden's data, i s shown i n Figure 6. Other p o i n t s are those determined i n the present work. Even i f the two s e t s of data were brought more c l o s e l y i n t o coincidence by moving one set of data to a s l i g h t l y d i f f e r e n t s t r a i n r a t e , the present work shows higher s t r e s s values i n stage I I and lower values i n stage I I I . to 10 1 ' : I I • ; 1 • 1 1 10" 7 10" 6 10"5 1 0 " 4 10~3 10" 2 10"' STRAIN RATE (SEC . - 1 ) Figure 6: Comparison of the S-curve data of the present and previous work. The p l o t f o r the 8 micron g r a i n s i z e shows only stages I I and I I I . Stage I I shows an m value of .5 which f a l l s o f f to a stage I I I value of .10. A stage I I - s t a g e t r a n s i t i o n might be present but lower s t r a i n r a t e data would be, r e q u i r e d before i t could be st a t e d that stage I has been reached. 3.3. Creep Curves 3.3.1. Stage I I Creep Curves For specimens of both g r a i n s i z e s the true s t r a i n versus time curves were s t r a i g h t l i n e s . No primary creep was observed. Steady s t a t e creep was -17- observed from the s t a r t of each t e s t . No necking was present during deforma- tion. For SGS specimens, l i n e a r creep curves were observed from near 300 p s i -2 -1 with a s t r a i n rate of 5 x 10 hr , to 2400 p s i which i s approximately the stress at maximum m. Figures 7 and 8 show curves near the extremes of this stress range. Another curve i s shown i n Figure 9. Above t h i s stress range m decreased as stage III was approached. Below 300 p s i , stage I behaviour was found. More curves t y p i c a l of stage II are shown i n Appendix I I , Figures a to c. Creep tests on LGS specimens did not extend to low enough s t r a i n rates to determine a t r a n s i t i o n stress and s t r a i n rate between stages I and I I . Straight l i n e creep curves were evident up to a stress of 1500 p s i where m began to decrease. Examples are shown i n Figure 10 and Appendix I I , Figures d and e. 3.3.2. Stage I Creep Curves Creep tests c a r r i e d out i n the stress range associated with stage I showed a creep curve with ever decreasing s t r a i n rate. At a stress of 97 p s i , a SGS specimen was extended to a true s t r a i n of .446 a f t e r 696.5 hours. Figure 11 shows this creep curve. LGS creep tests at low stresses were only taken to a few percent elongation and only the creep rate rather than the creep curve shape was determined. Figures f,g, and h i n Appendix II show more SGS creep curves for stage I. 3.3.3. Stage II -Stage III T r a n s i t i o n Creep Curves As s t r a i n rate i s increased above that associated with peak m, the creep curves change from the s t r a i g h t l i n e s of stage I I . Creep curves i n t h i s t r a n s i t i o n range a l l had an i n i t i a l l i n e a r region but the curve increased i n slope, as i n t e r t i a r y creep, a f t e r a s t r a i n of a few percent. A l l specimens,  -19-   o Figure 11. Stage I creep curve (SGS), 97 p s i . -23- i n t h i s region of decreasing m, exhibited neck formation and f a i l u r e occurred at l e s s than .50 true s t r a i n . The t r a n s i t i o n region continued to 5000 p s i , i n the LGS, where m approached a constant value of .10. High s t r a i n rates pre- vented the determination of the end of the stage II - stage I II t r a n s i t i o n . Figures 12 and 13 show creep curves f o r the stage II - stage II t r a n s i t i o n for both grain s i z e s . More plots are shown i n Figures i to s i n Appendix I I . 3.3.4. Stage I II Creep Curves Creep pl o t s i n this stress range showed 3-stage creep curves. There was an i n i t i a l transient. Primary creep was followed by steady state or second- ary creep as s t r a i n increased. Fracture generally occurred at lower and lower s t r a i n s as the creep stress was increased. Creep curves were obtained only for LGS specimens because the very high s t r a i n rates involved to a t t a i n stage III behaviour i n the SGS material made recording of the deformation impossible with the experimental equipment used. Figures 14,15 and 16 demonstrate creep curves, obtained from LGS specimens, over a range of s t r e s s . Two more curves are shown i n Figures t and u i n Appendix I I . Figure 17 i s a p l o t of the s t r a i n at which steady state creep appears versus the testing stress for. the LGS material. The beginning of stage I I I i s thus near 2500 p s i . ii 3.4. Incremental Loading and Unloading Incremental loading and unloading tests were made during creep tests on specimens of both grain sizes i n stage II and I I I . In stage I I , where creep curves are l i n e a r , increasing and decreasing the load r e s u l t s i n an abrupt t r a n s i t i o n to l i n e a r curves of increasing or decreasing slope. Figure 18 i s an example of incremental loading of a SGS specimen. The short s t r a i n rate peak, Figure 12. Creep curve i n stage IT - stage I I t r a n s i t i o n (SGS), 3432 p s i . Figure 13. Creep curve i n stage I I - stage I I I t r a n s i t i o n (LGS), 3582 p s i . -26- T I : T "I 1 — 1 1 1 1 1 Tc 0.0 0.0B 0.16 0.24 0.32 . 0.4 0.48 0.56 0.64 0.72 D.8 TIME HOUR mo - 1 ) Figure 1A. Stage I I I creep curve (5212 p s i ) . - C S ' _ = 6 8 0 3 GM S - 5 5 3 5 P S I O = . 0 B 3 I N . E X T . . i 1 1 1 1 1 1 1 1 1 -|"--; 3.0 O.OB • 0.16 0.24 • 0.32 0.4 0.4B 0.56 0.64 0 72 OS TIME HOUR 1 X 1 0 " 1 ) Figure 15. Stage I I I creep curve (5535 p s i ) S T R A I N T O S T E A D Y S T A T E -28- Figure 18. Incremental loading during superplastic creep. -29- when the s t r e s s reaches 832 p s i , i s due to an e r r o r i n one reading e x a c t l y at t r a n s i t i o n . Another incremental l o a d i n g example i s shown i n F i g u r e v Appendix I I . Curves have the same slope at a l l s t r e s s e s i n stage I I , during incremental l o a d i n g , as when they are i n i t i a l l y loaded to that s t r e s s . S t r a i n r a t e i s independent of p r i o r h i s t o r y i n stage I I . Incremental l o a d i n g during primary creep i n stage I I I r e s u l t s i n a change i n the i n i t i a l t r a n s i e n t . The slope of the curve i s i n s t a n t l y i n - creased and a t r a n s i e n t remains to a higher s t r a i n than would have occurred at the lower s t r e s s . Figure 19 shows the r e s u l t of i n c r e a s i n g the load during steady s t a t e creep i n stage I I I . Here, a t r a n s i e n t reappears. Figure 20 shows the immediate t r a n s i t i o n to steady s t a t e creep when the load i s decreased during primary creep. This r e s u l t i s a l s o shown i n Figure w, Appendix I I . The purpose of these t e s t s was to compare the behaviour of a s u p e r p l a s t i c m a t e r i a l , during l o a d i n g and unloading, to the behaviour of i c n - s u p e r p l a s t i c m a t e r i a l s under s i m i l a r t e s t i n g c o n d i t i o n s . 3.5. S t r a i n A f t e r - E f f e c t s Specimens deforming i n stage I I and stage I I I were unloaded. These specimens were then continuously measured w i t h an extensometer to look f o r s t r a i n r e l a x a t i o n . At no time was there any s i g n of c o n t r a c t i o n during stage I I . An example of t h i s r e s u l t i s shown i n Figure 21. ReusIts of t e s t s on LGS samples i n stage I I I were not con c l u s i v e but always suggested some s t r a i n r e l a x a t i o n . Relaxations of .003 to .004 inches were found on a guage length of .500 inches a f t e r times of 45 minutes to 60 minutes a f t e r s t r a i n s ^ o f .10 ^30- to .30. The return of primary creep a f t e r recovery was looked f o r . Once again the e f f e c t i s small as shown by Figure 22 a f t e r 5 minutes recovery time. I t may be that recovery rates are too slow at room temperature. Recovery at higher temperatures forced the removal of the extensometer and specimen d i s t o r t i o n occurred. These problems once again lead to inconclusive r e s u l t s . . 4. DISCUSSION Creep studies of superplastic materials have seldom been made. Pre- 33-35 vious work on lead, t i n and the l e a d - t i n eutectic has not involved stresses, s t r a i n rates and grain sizes necessary to obtain superplastic be- 38 haviour. Packer, Johnson and Sherby used constant stress creep tests i n the i r study of eutectic Zn-Al and state that they found n e g l i g i b l e s t r a i n hardening during superplastic creep and that the creep rate remained constant under constant stress and temperature. Zehr and Backofen*^ used a creep test 32 to obtain a low s t r a i n rate value on an S-curve for Pb-Sn. Chaudhari has also done some creep work. The present study has been the only one s p e c i f i c a l l y designed to gain more i n s i g h t i n t o the superplastic phenomena through the study of creep curve d e t a i l s over a wide stress range. Discussion w i l l cover mainly the merits of recently suggested mechanisms of s u p e r p l a s t i c i t y , considered i n view of new creep r e s u l t s and other consistently reported observations. 4.1. Stage III Deformation i n stage III i s not superplastic. I t i s s i m i l a r to the creep of coarse grained materials where deformation i s by recovery creep. This conclusion follows from the current observations of primary creep, a -31- Figure 20. T r a n s i t i o n to steady s t a t e w i t h unloading i n stage I I I . -32- Figure 22. Reloading a f t e r recovery i n stage I I I . -33- 3-stage c r e e p c u r v e and a low m v a l u e n e a r .10. A d i s l o c a t i o n s u b s t r u c t u r e i s a l s o p r e s e n t a f t e r s t a g e I I I c r e e p 1>6,7,39^ a g ^ n t ^ e c r e e p Qf c o a r s e 37 g r a i n e d m a t e r i a l s . R e s u l t s ( F i g u r e 21) a l s o seem to show t h e r e t u r n o f an i n i t i a l t r a n s i e n t a f t e r r e c o v e r y . However, s i g n i f i c a n t l y l a r g e r t r a n s i e n t s were n o t seen a t l a r g e r r e c o v e r y t i m e s . A s t r a i n a f t e r - e f f e c t , whereby the specimens s h o r t e n e d s l i g h t l y when the l o a d was removed a f t e r e l o n g a t i o n , has 37 a l s o been o b s e r v e d i n c o a r s e g r a i n e d m a t e r i a l s a f t e r r e c o v e r y c r e e p . P r e s e n t r e s u l t s seem t o show t h a t t h i s d i d o c c u r a f t e r s t a g e I I I d e f o r m a t i o n . N e c k i n g was a s s o c i a t e d w i t h t e r t i a r y c r e e p . R e c o v e r y c r e e p t h e o r i e s i n v o l v e a g e n e r a l e q u a t i o n f o r s t e a d y s t a t e s t r a i n r a t e , E = r / h (3) where r i s t h e r e c o v e r y r a t e , d a / d t , and h i s s t r a i n h a r d e n i n g dh/de. S t r a i n h a r d e n i n g i s a s s o c i a t e d w i t h an i n c r e a s e i n d i s l o c a t i o n d e n s i t y (p) w h i l e r e c o v e r y r e p r e s e n t s a decrease,. P r i m a r y c r e e p r e s u l t s i f the i n i t i a l r e c o v e r y r a t e i s s m a l l e r t h a n t h e h a r d e n i n g r a t e . The v a l u e of r 1 i n an a n n e a l e d specimen i s c l o s e t o z e r o . Steady s t a t e c r e e p r e p r e s e n t s a b a l a n c e between h a r d e n i n g and r e c o v e r y . Such a b a l a n c e i s e x p e c t e d o n l y a f t e r some i n c r e a s e i n d i s l o c a t i o n d e n s i t y , r e l a t i v e t o t h e a n n e a l e d c o n d i t i o n , w h i c h o c c u r s d u r i n g p r i m a r y c r e e p . 40 A modern t h e o r y f o r s t a g e I I I i s t h a t o f McLean . D e f o r m a t i o n a t h i g h t e m p e r a t u r e s i n v o l v e s the b e h a v i o u r o f a t h r e e - d i m e n s i o n a l d i s l o c a t i o n n e t - work. Three i m p o r t a n t a s p e c t s of t h i s b e h a v i o u r a r e t h e t e m p e r a t u r e i n s e n s - i t i v i t y o f the f l o w s t r e s s of a g i v e n n e t w o r k , the n etwork's tendency t o c o a r s e n on h e a t i n g w h i c h c o r r e s p o n d s t o a d e c r e a s e i n p and i t s r e f i n e m e n t -34- on s t r a i n i n g w h i c h corresponds to an i c r e a s e . McLean shows that the recovery r a t e , r , v a r i e s w i t h s t r e s s by 3 r a a (4) The recovery process i n v o l v e s d i f f u s i o n c o n t r o l l e d d i s l o c a t i o n climb and m i g r a t i o n of jogs i n screws. Therefore, i f D i s the d i f f u s i o n c o e f f i c i e n t 3 r a a D (5) P l a s t i c deformation r e f i n e s the d i s l o c a t i o n network. During deformation, moving d i s l o c a t i o n s are h e l d up at p o i n t s where the network i s f i n e and bow out to increase the average d i s l o c a t i o n d e n s i t y . M u l t i p l e s l i p permits network geometry to remain constant as the meshes become smaller . The s t r a i n hardening c o e f f i c i e n t h = 8c/3e i s a measure of the r e f i n i n g a c t i o n . I f -3/2 expression f o r r from eqn.(5) and h from the e m p i r i c a l r e l a t i o n s h i p haa are used i n eqn(3) the r e s u l t i s 4-5 (6) or i f K = ( V B D ) 1 7 4 ' 5 e = BDa .22 , a = Ke (7) which i s the same as equation (1) w i t h m = .22. This value of m i s not q u i t e as low as that found experimentally. Theories of t h i s type are, of c o u r s e / r a t h e r s p e c u l a t i v e and e v i d e n t l y approximate i n nature. I t i s not known to what extent the p h y s i c a l model of McLean corresponds to the de- t a i l e d deformation and recovery processes i n stage I I I . - 35 - 4.2. Stage II-Stage I I I T r a n s i t i o n In the stage I I - s t a g e I I I t r a n s i t i o n , on i n c r e a s i n g s t r a i n r a t e , m f a l l s from a maximum to a sm a l l e s s e n t i a l l y constant value a s s o c i a t e d w i t h stage I I I . The t r a n s i t i o n s t r a i n r a t e 9 -1 -1 range was from 2 x 1 0 - z hr. to 2 hr. f o r the 8 micron g r a i n s i z e and above 2.5 hr 1 f o r the 2 micron g r a i n s i z e . The high s t r a i n r a t e s i n v o l v e d prevented d i f f e r e n t i a t i o n between the end of the t r a n s i t i o n range and the s t a r t of stage I I I i n the sm a l l g r a i n s i z e specimens. Creep curves i n the t r a n s i t i o n r e g ion are convex upward ( t e r t i a r y creep) (Figures 12 and 13). There i s no primary creep. F a i l u r e occurs at s t r a i n s of l e s s than 41 .50 and f a i l u r e occurs at a neck. Chaudhari may have explained t h i s r e s u l t mathematically. D i f f e r e n t i a t i o n of equation (1) leads to dt 1 j-da - l o g ^ dm j ^ ) ^ m a K m The e f f e c t of a la r g e m value i s to decrease the tendency f o r a neck to grow. Conversely, an increase i n the bracketed term increases the s e n s i t i v i t y to necking. I f m i s decreasing w i t h i n c r e a s i n g s t r a i n r a t e , as i t i s i n the t r a n s i t i o n range, dm i s negative and the second term w i l l be added to the f i r s t . The bracketed term becomes l a r g e r and s e n s i t i v i t y to necking i s more pronounced. Observations of neck formation and growth a f t e r only a few percent s t r a i n were made during the present 16 work (Figures 12 and 13). Previous observations of l a r g e s u p e r p l a s t i c elongations using i n i t i a l s t r a i n r a t e s i n t h i s r e g i o n were made w i t h I n s t r o n t e n s i l e machines. These machines have a constant cross head" speed and the s t r a i n r a t e imposed on a specimen i s continuously decreasing. The e f f e c t of a -36- decreasing s t r a i n r a t e i n the t r a n s i t i o n range i s to give a r i s i n g m value as t e s t i n g proceeds. A convex upward creep curve has p r e v i o u s l y been r e p o r t e d , i n the l i t e r - 36 ature but no comment or e x p l a n a t i o n was attempted. Constant s t r e s s creep t e s t s were performed on a number of pure t i n specimens. Four d i f f e r e n t g r a i n s i z e s were used but only the f i n e s t , 37 microns, e x h i b i t e d t h i s behaviour. Others showed primary creep. Figure 23 shows a l o g a r i t h m i c p l o t of s t r e s s versus s t r a i n r a t e using Breen and Weertman's creep r a t e data f o r the s m a l l e s t g r a i n s i z e . This curve i s somewhat comparable to th a t of Alden and d i f f e r e n c e s may be due to g r a i n growth and the f a c t that Alden's curve was obtained using an I n s t r o n t e n s i l e machine, m v a r i e s from .3 to .12. The increase i n ui w i t h decreasing strain.r=te i s due to a slow increase i n sub-grain s i z e v i t h decreasing s t r a i n r a t e ' - . Stage II i s reached when sub-grain 1 13 • s i z e has reached the g r a i n s i z e ' . As t h i s c o n d i t i o n i s approached, accommodation fo r GBS by s l i p becomes e a s i e r and m increases to i t s maximum value. The stage I I I - stage I I t r a n s i t i o n i s a s s o c i a t e d w i t h increased amounts of GBS"\ S u p e r p l a s t i c i t y may a c t u a l l y be p o s s i b l e i n l a r g e r grained m a t e r i a l s i f , at low enough s t r a i n r a t e s , the sub g r a i n s i z e approaches the g r a i n s i z e . Creep 43 t e s t s by G i f k i n s may be i n d i c a t i v e of t h i s . The g r a i n s i z e of extruded Pb-2.45 wt% t h a l l i u m was 100 microns. Stresses of 300,500,1000,1500, and 2000 p s i were used on creep specimens. These creep r e s u l t s are p l o t t e d i n Figure 24. The m value increases from .15 to .45. Micros t r u e t u r a l observations showed that s l i p l i n e s became l e s s r e g u l a r and" more widely spread as the s t r e s s was decreased and at the lowest s t r a i n r a t e s deformation proceeded by "boundary micro-flow" and grains were unde- formed. At 500 p s i e l o n g a t i o n to f a i l u r e was 208 %. S i m i l a r observations weremade -37- by Wood et a l on aluminum w i t h a g r a i n s i z e of 100 to 200 microns. S l i p was prominent during deformation at lower temperatures and higher r a t e s of s t r a i n . As the temperature was increased or the s t r a i n r a t e decreased, s l i p l i n e s g r a d u a l l y vanished and the elements of the ass o c i a t e d substructure showed an increase i n s i z e . This l e f t a coarse s u b s t r u c t u r e which increased i n s i z e w i t h a f u r t h e r i n - crease i n temperature or decrease i n s t r a i n r a t e u n t i l i t was the s i z e of the g r a i n i t s e l f . This c o i n c i d e d w i t h the onset of prominent "boundary micro flow" or GBS. They found that l a t t i c e s t r u c t u r e was unchanged and no s t r a i n hardening occurred during deformation. The observations of Wood et a l and G i f k i n s seem to be very s i m i l a r to the observations made on f i n e grained s u p e r p l a s t i c m a t e r i a l s where GBS becomes 13 more dominant as the s t r a i n r a t e i s decreased from that of stage I I I 4.3. Stage I I The new observations a s s o c i a t e d w i t h stage I I are that the creep curves are l i n e a r and that there are no unloading t r a n s i e n t s . The l i n e a r creep curves are shown i n Figures 8,11. There are no signs of primary or t e r t i a r y creep, only steady s t a t e . The r e s u l t s of unloading t e s t s are shown i n Figure 21. No c o n t r a c t - ions due to recovery has occurred. These r e s u l t s show that recovery t h e o r i e s , which may be v a l i d f o r normal creep, and stage I I I . a r e u n s a t i s f a c t o r y f o r super- 45 p l a s t i c creep. Alden has demonstrated that many proposed models f o r super- p l a s t i c i t y are r e a l l y models based on recovery creep and are thus unacceptable. An 32 i n t e r n a l s t r e s s model which incorporates an accumulation of d i s l o c a t i o n s near the g r a i n boundary seems to be unacceptable because d i s l o c a t i o n s are not seen d u r i n g s u p e r p l a s t i c deformation even when specimens are quenched under l o a d * . Figure 23. Log s t r e s s versus l o g 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 tin,(37u) _1000 _ 10-2 STRAIN RATE 10" I ( D A Y " 1 ) Figure 24. Log s t r e s s versus l o g 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 Pb-2.45 wt.% t h a l l i u m (lOOy). i O J C O I -39- A l s o , the low temperature y i e l d s t r e s s is unchanged a f t e r stage I I deformation I f d i s l o c a t i o n s are accumulated during creep, t h i s y i e l d s t r e s s should i n c r e a s e . Mechanisms and accommodation processes which would show no t r a n s i e n t s are those which do not i n v o l v e a s t r u c t u r a l change Grain boundary s l i d i n g w i t h some s p e c i a l accommodation processes, Nabarro-Herring or Coble creep and g r a i n boundary m i g r a t i o n are examples. Grain boundary m i g r a t i o n , i n a s s o c i a t i o n w i t h GBS, has been observed 46 47 i n s u p e r p l a s t i c m a t e r i a l s ' . Opposition to the idea that m i g r a t i o n i s r a t e - c o n t r o l l i n g i s based on doubt that m i g r a t i o n can be e f f e c t i v e when many phase boundaries are present i n two phase systems. At the same time, i t must be con- si d e r e d that i f there are equal amounts of two phases, each phase might s t i l l be i n contact w i t h 50 % of the l i k e phase. Thus there i s a reasonable chance f o r mi g r a t i o n to be an e f f e c t i v e means of accommodation f o r GBS i n a s u p e r p l a s t i c m a t e r i a l . With only one phase present, d i l u t e a l l o y systems do not, of course, present t h i s problem. Grain e l o n g a t i o n should r e s u l t during d i f f u s i o n a l creep. This i s not observed i n stage 11*^ but Zehr and Bachofen's explanation i s that elongated grains w i l l experience a shape r e l a x a t i o n during s t r a i n i n g through d i r e c t migra- t i o n and r e c r y s t a l l i z a t i o n . They c l a i m that the presence of striated bands on a 2 micron Pb-Sn e u t e c t i c specimen p u l l e d at 3.3 x 10 ^ sec. * supports d i f f u s i o n a l creep. This s t r a i n r a t e i s very near the t r a n s i t i o n to stage I . S i m i l a r s t r i a t i o n s 47 have been oserved i n Cd-5 % Pb over s t r a i n r a t e s a s s o c i a t e d w i t h stages I and I I . 47 Donaldson suggests that s t r i a t i o n s may i n d i c a t e that boundary s l i d i n g occurs on p r e f e r r e d c r y s t a l l o g r a p h i c planes. The t e s t of t h i s i s to c o r r e l a t e g r a i n o r i e n t - a t i o n and the planar o r i e n t a t i o n of the s l i p p e d boundaries w i t h s t r i a t i o n spacing. -40- Narrow s t r i a t i o n spacing would i n d i c a t e l a r g e m i s - o r i e n t a t i o n . The absence of s t r i a t i o n s would i n d i c a t e that the s l i d i n g plane i s a p r e f e r r e d plane. In a Mg-Al a l l o y , the s t r a i n c o n t r i b u t i o n of g r a i n boundary s l i d i n g i n stage I I reached 65 %*. Alden suggests that the g r a i n boundaries may act as " p e r f e c t " s i n k s and that s l i d i n g i s r a t e - c o n t r o l l e d by d i f f u s i o n . This model demands that the absorption r a t e by boundaries of d i s l o c a t i o n s generated at t r i p l e l i n e s be so high that i t i s not r a t e c o n t r o l l i n g . Fast recovery r a t e s i n 13 s u p e r p l a s t i c m a t e r i a l s support t h i s but l i t t l e or no climb can be inv o l v e d or t h i s becomes a recovery creep model. Absorption may be enhanced by GBS by the a t t r a c t i o n f o r c e between s l i d i n g boundaries and d i s l o c a t i o n s * . The r a t e of s l i d i n g i s determined by the e f f e c t i v e v i s c o s i t y of the boundary. The boundaries are rough and the s l i d i n g r a t e i s determined by d i f f u s i o n around these rough areas. The s c a l e of roughness w i l l u s u a l l y i n c r ease w i t h g r a i n s i z e . The model p r e d i c t s the s t r a i n r a t e semi q u a n t i t a t i v e l y i n agreement w i t h observed e f f e c t s of s t r e s s , g r a i n s i z e , and temperature. 4.4. Stage I Stage I , as shown i n Figure 11, i s s i m i l a r to stage I I i n that there are no t r a n s i e n t s s i m i l a r to those found i n stage I I I . The creep curve i s not l i n e a r , however. There i s a d e f i n i t e decrease i n s t r a i n r a t e w i t h time. This decreasing s t r a i n r a t e i s not b e l i e v e d to be i n any way r e p r e s e n t a t i v e of a r e - covery creep model where a decreasing creep r a t e i s found during primary creep. Stage I may represent a change i n the r a t e c o n t r o l l i n g process f o r GBS from d i f f u s i o n around bumps on boundaries to s l i p at t r i p l e l i n e s . I f d i s l o c a - t i o n s are emitted from a source, proceed through a m a t e r i a l without b a r r i e r s and are then absorbed at a " p e r f e c t " s i n k , no s t r a i n hardening w i l l r e s u l t . ' I f the -41- sources of d i s l o c a t i o n s are the edges of s l i d i n g g r a i n s , and the si n k s are g r a i n 30 boundaries, Alden suggests that s t r a i n r a t e w i l l depend on s t r e s s to the power 2 to 3. The slope depends on whether accommodation d i s l o c a t i o n s move on a few s l i p planes or throughout the g r a i n volume. A l i n e a r array i s expected i n a l l o y s w i t h a low s t a c k i n g f a u l t energy such as Fe-Ni-Cr and m should be .5. Motion normal to the s l i p plane i s e a s i e r through cross s l i p i n high s t a c k i n g f a u l t energy ma t e r i a l : and the slope should be .33 as was observed. Lee* found the behaviour i n stage I to be a combined e f f e c t of g r a i n deformation and deformation across transverse g r a i n boundaries, accounting roughly f o r 1/3 and 2/3 of the t o t a l deformation, r e s p e c t i v e l y . The l a t t e r c o n s i s t e d , at l e a s t i n p a r t , of GBS but whether the remaining f r a c t i o n was due to GBS or Coble creep could not be determined. Several experimental observations suggest that d i f f u s i o n a l creep may 7 28 10 co n t r i b u t e to deformation i n stage I . These are g r a i n e l o n g a t i o n ' , s t r i a t i o n s 29 and denunded zones , and creep curves of decreasing slope. Creep curves of decreasing slope could occur by the s e l f - e x t i n g u i s h i n g nature of d i f f u s i o n a l creep. A t h e o r e t i c a l a n a l y s i s of N-H and Coble creep has been made and d e t a i l s are shown i n Appendix I I I . Figure 25 shows the shape of creep curves expected f o r pure N-H and Coble creep. A stage I experimental curve i s a l s o shown and a l l are put on a time s c a l e r e presenting the f r a c t i o n of t o t a l time to leach .40 true s t r a i n . Times in v o l v e d f o r .40 s t r a i n are .87 h r s . f o r Coble creep and 5.39 x 10^ hrs. f o r N-H creep. The experimental curve represents 700 hours and could be p a r t i a l l y r e p r e s e n t a t i v e of some combination of N-H and Coble creep. I t has been reported that there i s no g r a i n e l o n g a t i o n i n the Pb-Sn e u t e c t i c * ^ i n stage I ; There i s g r a i n growth during deformation*^ and a l s o g r a i n 16 s t r a i n . Grain r o t a t i o n has been observed . Lack of g r a i n e l o n g a t i o n might not -42- exclude d i f f u s i o n a l creep as an important p a r t of the deformation mechanism of stage I . A g r a i n may elongate, by d i f f u s i o n , p a r a l l e l to the t e n s i l e a x i s . G r a i n boundary m i g r a t i o n could account f o r the r e t u r n of an equiaxed shape and an increased g r a i n s i z e . Grain r o t a t i o n would change the t e n s i l e a x i s and permit e l o n g a t i o n i n a l l d i r e c t i o n s . I f g r a i n growth does not i n v o l v e d i f f u s i o n a l creep, g r a i n s t r a i n would not be expected.Lee* measured the t r a v e l of two marker wholly w i t h i n a g r a i n . In stage I I I no movement was found. In stage I I t h i s was equal to .21 of the t o t a l s t r a i n and i n stage I t h i s increased to .30. Growth of one g r a i n at the expense of another would not c o n t r i b u t e to an i n t e r n a l t r a v e l of markers but only to the g r a i n volume. Gra i n growth by any means, however, could r e s u l t i n a creep curve of decreasing slope because the s t r a i n r a t e does decrease w i t h i n c r e a s i n g g r a i n s i z e . Stage I deformation i n v o l v e s GBS and probably some combination of N-H and Coble creep. 4> FRACTION OF TIME TO REACH -40 STRAIN Figure 25. Experimental, t h e o r e t i c a l N-H and t h e o r e t i c a l Coble creep curves (97 p s i ) . -4A- 5. SUMMARY AND CONCLUSIONS In the s u p e r p l a s t i c range, m a t e r i a l s d i s p l a y unusual creep p r o p e r t i e s . S t r a i n r a t e i s dependent on g r a i n s i z e and i n s e n s i t i v e to s t r e s s . Creep curves are l i n e a r w i t h no i n i t i a l or f i n a l t r a n s i e n t s . A m a t e r i a l i s considered " s u p e r p l a s t i c " i f s u p e r p l a s t i c p r o p e r t i e s are observed at experimentally reason- able s t r a i n r a t e s . There i s evidence that s u p e r p l a s t i c p r o p e r t i e s may occur at low enough s t r a i n r a t e s i n "normal" m a t e r i a l s . Conversely, a " s u p e r p l a s t i c " m a t e r i a l may d i s p l a y normal creep p r o p e r t i e s at s u f f i c i e n t l y high s t r a i n r a t e s . In stage IT, a l i n e a r creep curve suggests that the deformation mechanism accounting f o r s u p e r p l a s t i c behaviour must be one which i n v o l v e s no s i g n i f i c a n t s t r u c t u r a l change. Creep curves i n stage I I show no t r a n s i e n t s , a f t e r l o a d i n g or unloading and the s t r a i n r a t e , at any s t r e s s i n the s u p e r p l a s t i c range, i s independent of p r i o r s u p e r p l a s t i c deformation h i s t o r y . P r i o r evidence i n d i c a t e s that most of the deformation i n stage I I i s accomplished by g r a i n boundary s l i d i n g . There must be accommodation f o r g r a i n boundary s l i d i n g to operate.Accommodation could i n v o l v e one or more of g r a i n boundary m i g r a t i o n , d i f f u s i o n , or s l i p at t r i p l e p o i n t s . The m value f o r stage I I i n the- l e a d - t i n e u t e c t i c i s near .5 and has a maximum value near .6. At low s t r a i n r a t e s creep curves show an ever decreasing sl o p e , t h i s could be due to d i f f u s i o n or g r a i n growth. GBS occurs i n stage I, but i s not as dominating as i n stage I I . Gra i n s t r a i n increases i n stage I and i s notably i n d i c a t i v e of a d i f f u s i o n a l process. Some combination of N-H and Coble d i f f u s i o n a l creep i s l i k e l y s i n c e the experimental creep r a t e s ; a r e much f a s t e r than those expected f o r N-H creep and much slower than could be -45- a t t r i b u t e d to Coble creep. The r a t e c o n t r o l l i n g process i s not known. Grai n growth, g r a i n r o t a t i o n , g r a i n boundary m i g r a t i o n , and s l i p and t r i p l e l i n e s may a l l have some e f f e c t on deformation and the r e s u l t i n g creep curve. The m value f o r stage I i s .33 and i s constant over the s t r e s s range s t u d i e d . In the stage I I - stage I I t r a n s i t i o n r e g i o n , s u p e r p l a s t i c p r o p e r t i e s depend on the t e s t i n g method. In a constant s t r e s s creep t e s t t e r t i a r y creep begins, as necks propagate and grow, a f t e r only a few percent s t r a i n and f a i l u r e occurs at l e s s than.50 true s t r a i n i n the l e a d - t i n e u t e c t i c . Testing under c o n d i t i o n s where the s t r a i n r a t e decreases as the t e s t proceeds reduces the tendency to neck and e l o n g a t i o n to f a i l u r e i s much greater. -46- SUGGESTIONS FOR FUTURE WORK There are 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 which could extend from the present work. These i n c l u d e : (1) A determination of creep curves and creep r a t e s over a wide s t r e s s range i n stage I f o r s e v e r a l g r a i n s i z e s . (2) A micrographic study of the v a r i a t i o n of the c o n t r i b u t i o n of g r a i n boundary s l i d i n g and g r a i n s t r a i n w i t h s t r e s s over stage I . A study of g r a i n e l o n g a t i o n , g r a i n boundary m i g r a t i o n and g r a i n r o t a t i o n might prove h e l p f u l at low s t r e s s e s . (3) A study of a c t i v a t i o n energy i n stage I over a wide s t r e s s and temperature range and a l s o i n t o stage I I . (4) An e v a l u a t i o n of f a c t o r s , such as time temperature and e l o n g a t i o n , c o n t r i b u t - i n g to g r a i n growth during stage I I deformation. (5) An i n v e s t i g a t i o n of e l o n g a t i o n at v a r i o u s constant s t r e s s e s over the stage I I - stage I I I t r a n s i t i o n to determine i f there i s a r e l a t i o n s h i p between'elongation to f a i l u r e and m. (6) A more c a r e f u l study of the r e l a t i o n s h i p between s t r a i n r a t e and g r a i n s i z e . 1 2 R e l a t i o n s h i p s between /L and 1/4^ 5 have been reported i n the l i t e r a t u r e 1,3,10,13,20^ j-^ggg r e i a t i o n s i p s to be v a l i d , each value taken must be i n stage I I . Some r e l a t i o n s h i p s i n the l i t e r a t u r e have i n v o l v e d a' s t r e s s which i s i n two stages of the S-curve and are t h e r e f o r e i n v a l i d . The present work 1 3 shows a /L dependence although there i s some doubt i n the g r a i n s i z e s . A 13 1 •• 3 p l o t of v a l i d p o i n t s f o r Pb-5 %Cd and e u t e c t i c Pb-Sn shows a /L r e l a t i o n - 1 3 s h i p . The r e l a t i o n s h i p s show s c a t t e r between -2.2 and -3.9 f o r Pb-Sn and -2 and -3 f o r a Mg-Al a l l o y . -47- APPENDIX I Computer Programme •--•i-T!.•/<•; in r, C v n i L ^ r MAIM Q^-17-6<1 1 Ai?lt04 PAGE 0001 r AM/ll.vcjc; n r T H F CRFFP TEST CUPVFS PHB004 P l M c . M s i r i M T [Tl c ( 14) , INOI20.20 ), TIMFf?0,?0),GP.AD(20,?0), PHB005 l S T " A l N(?'.-0), TTMry(200),RATF(200),INI 200),DIAL(20,20),XC(5),YC(5) PH8006 s '»0 0 ? R F A O f , NFxrr.i.! PHB007 /> T i m q FC'P^ATI 15X.I3) PHB008 0 0 4 'IV f-0 1. = 1 , NFXFCU PHB009 ooo^ RFAOfS, DT1TLF PHB010 i FriPM&T('14A4) 000 7 PrAO(5,4) SCAFAC»MSHIFT,ELNOT '.' ? C " 4 riRMATI FI 0.5, 5X.I 3,Fa.3) r.ro / K = 0 PHB014 001 0 f = o .. •'.v..:• •. ' PHB015 001 1 s u « s m = 0 . ., •. -.. PHB016 001 ? OP 10 I = l.NSHIFT PHB017 R F AO(5,5) SHIFT, NMEASW -V'. PHB018 0014 rpRMAT(F10.5,5X, 13) ' " ' PHB0L9 0 015 SUMSHI = SUMSHI • SHIFT • . . . PHB020 001*1 0 T MF NS I ON COMNTSI 9,50,7) , IMPORT (20 ,50 )', T IHEXHt 9i50 )t STRA IH (9 , IMTRANS(O),CRISIS! 20,20,7) 50).PHB021 PHB022 0017 OP 20 J = 1, NMFASU PHB023 coin PFAO (5,ft) TIMF(l , j),GRAD(I , J ) , 0 I A L t t i a i * t l»P0RT ( I , J J , ( C R I S I S < I , J,PHB024 1 I J ) , IJ = 1,7) rt • PHB025 0010 FPRMAT(F9.2,1X,F5.1,3X,F8.5,2X,I2,7A4) , , 00 ?0 K = K + 1 . \ PHB027 00 21 I N ( K ) = K y i^^'i^M^'Vy^:.):['."' :'. PHB028 00?? IF ( OTALtl.J) .GT.O.) GO TO 1? « - PHB029 00? 3 OFITAL = SCAFAC * GRAO(I.J) * SUM'HI r , PHB030 00?4 GH TO 11 PHB031 ^ 0025 12 DFLTAL = 01AL(I,J) " r PHB032 00?f> On TP 11 PHB033 0027 11., TSTRAI = ALOG ( 1. • DEL TAL / ELNOT) * * / , C SFLECTION P.F COMMENTS ' v/Vt'Si'.^'^fey'' ^^i^fi^.^.,;:-^,.' ' PHB035 O0?3 IF ( IMPORT (I , J) . GT.O ) GO TO 13 . ' * _' PHB036 0079 GO TO 14 • " ' - •' " PHB037 00 30 13 M = M + i . / • .. . • . .• .•.'•:v.tv , jv^;^\ :v : i ;K^^ PHB038 , 0031 00 120 IJ = 1,7 PHB039 r 0032 _ 120. . CPMNTS(L,M,I J)..- CRIStS . U , J t I J > PH8040 0033 I»P0RT(L,M) = IMP0RT(1,J) , ' PHB041 0034 TIMEXMIL ,M) : = T I K E ( I . J ) PHB042 0035 STRAIM(L.M) = TSTRAI PHB043 0036 MTRANSID = M , PHB044 0037 14 STRAIN(K) • . = TSTRAI t , PHB045 003S .'. TIMEX <K)....=. TIME! I,.jl . . , . PH8046 003O ?0 CONTINUE , PHB047 . 0040 10 CONTINUE . ^ PHB048 C041 H = K — 1 • . '" • • •' ' ' •S'-'--:.vr:ii-.'':: PHB049 004? DO 30 I = 2, K • PHB050 004 3 IFI I.FO.K1 GO TO 32 PHB051 0044 RATE(I) = (STRA IN(I +1) - STRATN(I-l) ) / ( TIMEXU + l ) - T I HEX ( T -1)IPHB052 0045 GO TO 30 • , i.rv:. . PHB053 004 6 32 RATF(I)=( STRAIN(I)-STRAIN(I-l))/(TIMEX( I ) —TI HEX ( I —11 ) • PHB054 004? 30 CONTINUE ' PH8055 0048 RATE (I ) = RATEI2) . . . PHB056 C TRYING TO GFT A OFCFNT OUTPUT V ; • PHB057 s. 004 0 N U M F R o =o ........ ' ... ., . . <" •. , PHB058 . -48- n r-? T !V T, f p ' - " l l i ' 1 1 '"ATM 0 3 - G 7 - 6 O ]i :4 ' ) : l". fAOF f>002 o r, -i , N S T A R T = 1 P H H 0 5 9 I-. "j r. 1 " F J M 1 S = 4 0 P H B 0 6 0 0 0 «. 7 • I P A C F = K / 4 0 + 1 PHB061 N P A O T F = K - ( . H ' P A G F - 1 ) * t,n P H B .16.2 IT ( N P A O ! F . l - ' O . O ) O P T O 41 P H 3 0 6 3 ,, ; )r,c on T O 4 ? . , PHB064 0 0 ^ 6 . 41 .NPAGP ;=. NPAOF. - 1 PHn065 " 0 ^ 7 42 • ' " D O 40 J = 1,N»AGF . .PH8066 ons a / N U M F R O = ' N I I M C R 0 + 1 • "'• ' ' ' PHfl067 •; WRITFI6,?) NUMFRO , T I T L E '.V PHB068 "060 ? FORMAT(lOX ,33HANA|.YSI .S PF THE C R F F P T F S T CURVES. 1 2/. 5HPAGE ,!?.4X ,PHR069 1 IHS/66X, 1H*/1X, 1 4 A 4 . 2 ! /66X.1H* 1/7H NI.IMRFR , 10X.4HTIME, 10X.6HSTRAIM ,PHB070 . J' : 2 9 X , UHSTRAIN R A T F ,9X , 1H*/16X , 5HH0URS , 2 3 X , 10H H O U R * * - .... I F ( K > L T > N p I N , S ) R ; 0 T O 43^-.'I?I4J.; . V ' 1 . :~;SV' . i , 12 x, i H * i . ; .PHB071 0 0 6 1 '.'..''. ' • " "PH3072" , 0 0 6 2 G O TO 46 .' -.• , ••'':jr;$:ie~'i,•:'• "• PHB07 3 0 0 6 3 4 3 ' ' N F I N I S = 'K '" ;'V;'v«i^;>' ' •'' .-'Or.' •..''•' PHR074 0 0 6 4 46 . , . 00.130 I = NSTART ,NFINI$/: . ' . ••.•.•',..; ;,r^"; •>',..,;,• PHB075 0 0 6 5 V . N S P A = INf-T) - ( !VU »/10n»:-l6 v '= ' ' : . ; ' :^ . :i,V : \ x : PHB076 • . 0 0 6 6 h. IF ( N S P A.EQ.l) GO T O 44' '-'-'^^^C •?> \v ?.' "• \vA;•/,=''.'; •:•' PHB077 0 0 6 7 ' ...... ..... . . ' G O - T O 45 ;:• •' ; ; ' ' - . ^ ^ ^ ^ ^ ^ f ^ ^ ^ Y ^ PHB078 0 0 6 3 • • 44 .• • WRITER,7).M; . ' . ' , . . ' • , •'• ' , ; ; 5 S S 3 ^ .'' .; ':' . ' PH8079' • 0 0 6 9 7 . ••'•• FORMAT { 66X> l.H*')'•'•'• '•'••' "'''>'• PHP080 0 0 7 0 • 0 0 7 1 .•• 4 5 3 •''" .; WRITE!*,3).-IMUt.. TI,MEX! iI ; , lSST ,«A , lfH M , RATE (11 •'• FORMAT ( 3 X , 1 .3 , 6X , F 9 . 3 ,7xV'EiiQ'^3.'»̂ feiE,tO=. 3 ,'.11 X^TH*!-'*!'-if. i 'V PHB081 ' PIIB082 0 0 7 2 . . . . 1 3 0 . .:f ..NSTART .= ",' NSTART ;*-.*Oj;<i!^Ppg ^ S^^^%l , i r -IV f PHB08 3 "•' ~'"-"o07 3 > | " ' i . ' , v • ' . . '• "PHB084" 0 0 7 4 /V'NFINIS = j.NF IN! S' +;j ^ O W ^ 0 l ^ m ^ ^ ^ ^ r < P . '••\")>"}i~'' •'• • i ,PHB08 5 0 0 7 5 ••• W R I T E t6,9 ) -r; 'rtji.v-i '•.''' • PHBC86 0 0 7 6 9 . FORMAT! 1H11 . l V ' ; - 1 i " : ^ ^ l ^ | ^ M f e i ; ^ .-, • PHB 0 (3 7 • v- 0077 . •.'•  V"r;.40̂ '; >:vCONTINUE^,:^f X^^^^S^^^M^^^^^ ; A TR ANSF'E R^/tQi^THEPL'OTT-NGi^'OU^ v̂'X": '.C:'.- " -PHB088 :.l.'i.'.C_.'J CĤ ::y"V'.": J"' '' , 1 .PHB0S9 " •' ooV<i '"' "̂'ot'MENS'lON'ftR̂ ^̂  1V,KTPANS(9) '. PHB090 • 0 0 7 9 ' . • e> no' 70 i ^ K : ^ : * i i a ^ W w € l ^ PHB091 '• 00«0 TiMtt.n .,= T t M F x m l 1 . / . l?:':^'/'' • •1 '• ''-'̂  PHB092 . . 00«l RAT!L,.IK.i»:j..RATEm.;;.'^ )rt,'i/:-;^'v'. . t\- . PHB093 • . 008? • . STOAd.Il = STRAINm?©^«P^ # § S ^ ;.*'~iv̂ .'jv/-''' v}-.̂;; .PHB094 :'±Y 0O83._ , 0 0 / 8 4 •' ,'...•; I.kti/7P4= ; ! i.C.ONTTNllfi^B -v i^ 0O;;,10d'. Xtfyktr-lt-ff&'Wti^ CS-'«'^'-\ . PHB095. .'PHB096 . '.';V- 0 0 8 5 : . . . V T I T (I..T1U: TITLE (,i:)?'\V'<::-'ti;VffMf»?€?^ J'!,- ••'-;'̂ ''7ĵ .V̂  'V.'.'t"''%>i1| ;PHB097 • 00P6 ' • 100 ' CONT INUE.VM" • '•'' '•'•kCij/feSHli&Sv »'-^S'^%te:KiJW'*'J.':-'..'r'-vtV'"' ' ' 5i:''-:< '̂ 'PHB098 . . . . •; 0 0 8 7 KTRANS(L) = K > > , • ' t , , 1 PHB099 ',. 0 0 8 8 ' •• ' " 6 0 ' / ..V.'CONTINUF ,» ' • , i , , ' " , 1 * P H B 1 0 0 0 0 8 9 . .... ... .- .. NA7'A.i^c.,yc. v;5,;;.i!...5,.i.^ ./,..'-.';::•. 5 P H B 1 0 1 . "V"... "c'".' ''^jCiyV* • P H B 1 0 2 •.'•" -'''fit - PLOTTING ROUTINE ^ * ' » 1 r\r-f^V-'.-j'':- "'•'.•''V' ;,PHB103 ',r'"c ''A ;!.;;:-'i: :C.'.>'"..''' •'' P H B 1 0 4 • ; 0090 C A I L PLOTS , > :;i>on- ao L - i,NEXECir ..i;',.-^..j.,-..... PHB105. : . . 0 0 9 1 :-"i:^A"; •" '" - P H B 1 0 6 • i::'̂  0 0 9 ? ' K. = KTP.ANS!L) . P H B 1 0 7 . . ... 0 0 9 3 " ..on'90 I = i , K . . ' - • P H B 1 0 8 • ' : ' : . V . . O 0 9 4 -'.-"i>-7 TIMEX! I ) : = . : T I M ( L ' , 11 ' - .i..v!''-„..; ;/-'''.;c'.'.;rv-.^'''' P H B 1 0 9 • ' • 0 0 9 5 R A T F ( I 1 = RAT 1 1 . , t ) -•".•:V''-.-"':'' ;' -.V •'• - : ^ " ' V ' •• . ' ;.v'"' ' •.. •• P H B 1 1 0 0 0 9 6 ., ..... ... S T P A ! \ ( I) - S T R A ( 1 , I) .., ..• .•;••/< ..... . •PHB112 ' J : 0 0 9 7 9 0 " :•• CONT'TNMF:'-'-.-. > ' - . ' : . : - 'V . ! ' ' : •'' •:''.• '• • ':'.V • ;e .'': "'' :'' -PHB113 • . : 009s ;.. on up. i... f i ' » ' . 4 v. .... . .' ','••. • ' i ' . . ' " ' . • v PHB114 1 -49- 0 W P I I F P MAIN 03-17-C9 18:31: 0 4 PAC.P 0003 pnqn TITLF (1 ) = TIT(Ltl) PHBI lb 0 100 110 CONTIVUF PHB116 0 to 1 CALL 1 IMF (XC.,YC,5,l) PHB117 010? WRITF(ft.lOOO) X C . Y C 0 1 0 ' 1 000 FORMAT(12F6.2) 0 104 CALL PLOT ( l.,0.,-3) PHB118 0 105 CALL SC AL F (TIMFX,K,10.,XMIN, DX , I) PHB119 in of. CALL SCAtE (STRAIN,K,7.,YMIN,DY,1) PHB120 0107 CALL SCALE <RATE,K,7.,ZMIN,07,1> PHB121 CIO" nn 50 I = 1,K PH8122 oioo RATE (I) = RATE(I) f I. PHB123 Oil:) STRAIN! I) = STRAIN!! 1+1. PHB124 0111 l-IR?TF<6,1000) TIMEX( I ), STRAIN (I I.RATFd ) 0112 50 CONTINUE PHB125 0 1 1 1 CALL AXIS (0..I..18H TIME HOUR,-18,10.,0 .,XMIN ,DX) PHB126 0114 CALL AXIS (0..1..12H STRAIN , 1 2, 7. , 90. , YMI N, D Y ) PHB127 0 11 = CALL IINF (TIMEX,STRAIN,K,l) PHB128 011ft XO = TIMFX(K) - .4 , PHB129 -.0117 ..YO =. STRAIN (K) .1. • : .. ;' ' • " • PHB130 CUR CALL SYMBOL (XO,Y0,.07,6HSTRAIN,0.,ft) PHB131 Olio CALL AXIS (10.,1.,25H STRAIN RATE 1/HOUR,-25,7., 90.,7MIN ,DZ)PHB132 0120 CALL LINE ( TTMEX.P.ATE.K, tl • PHB133 0121 ZP = RATF(K) • .5 ...... PHB134 . 0 122 CALL SYMBOL 1X0,Z0, .07, UHSTRATN RATE.O. , 111 ' • PHB135 . "12 3 CALL. SYMROL tl. , 8. , . 1 4, T I TLF , 0. , 80 ), .«.sj •***.> PH8136 "c PHB137 c PRINTING.(IF COMMENTS .. ,•'•',)[ "li /' "?S'0i 'idM :., :• PHB138 . c ' PHB139 012'. M = MTRANS(L) . . ,•,:•;:..:'.-••,..'. PHB140 • 0125 DT MENS T ON TI MM<50),STRAM(501.XFf6),YF(6)i XE(2) ,YE(2) ,C0M1I4) .C0MPHB141 1213),LfAP(50) . PHB142 012ft .. 00 9999 t = l,6 ' • "i. • •', .• ' 0127 XF(1)=0. 1 (' , 012B 9909 YFII) = 0. •> * 0129 XE(1)=O. :v . . . . .-i. : . . . . . . v , - « • . 0130 XE(2)=0. 0131 YE(1)=0. 013? YE(2)=0. 0 133 SPACIN = 0. PHB143 0134 ALTITU - 0. PHB144 0 135 01 STAN = 1. • .. ... .T.-.•.••:. . J ' -'•.>:.. . PHB 150 01.36 KOUNT=0 '. •'''^•^•''^'s'ti'^'V'?" 0137 WRITF(ft,1002) KOUNT 'S^til ••"••Ji". 0138 1002 FORMAT(16) < 1 0139 • on ' 140 J - 1, M I'-; : -V'- v : PHB151 0140 TIMM(J) = (TTMEXM(L.J) - XHIN) / DX ' .,:kV- PHB152 0141 STR AM ( J ) .'= (STRAIM(L.J) - YMIN >/ OY • .1 ̂  • PHB153 014? XF(1) •= TTMM(J) .-.< . PHB154 ... 0143 XF(2) - XF(1) + .0? PHB155 0144 XF(3) = XF( 1 ) PHB156 0145 XF(4) = XF( 1 ) • - .02 PHB157 014ft XF(5) = X F(1) '. PHB158 01 47 XF(6) = XF(1) PHB159 014 8 LOGICAL MIDDLE, PLACE,CLFAR PHB160 014 0 .' .MIDDLE. =. STR AM (J) .GT.5. •• ' PHB161 -50- rp(} T(; ••, rv i ; rr'MM i. "A IN 0 3 - 1 7 - 6 ' ) ' ' 18:31:04 PAGF 0Q04 0 1 so PLAC.F = IMPORTU.J) .LT.? PHB162 0 1 S 1 I F ( J.GT.l) G O Tp 1 V 3 PHB163 0 1 R 7 G O T'l 1 4 4 --> PHB164 < 0 1 5 3 1 4 3 0 1ST AN = TIMM(J) - TIMOUT PHB165 0 1 s 4 I F ( PISTAM . L T . . 2 ) GO TO 1 4 1 ! "' PHB166 0 1 5 R~ 1 4 4 x r n i = T I M « I J I . . V PHB167 0 1 5 6 I F ( X F ( 1 ) .LT. .1) T I M M I J ) = .1 PHB168 0 1 5 7 I F { x t r m . G T . 9.35 i T I M M I J I = 9.85 PHB169 0 15 8 X F ( 2 ) = TTMMU) PH8170 r> i '.T xm = X F ( ? I PHB171 "Iff X 0 2 = X F I ? ) * .1 PHB172 1̂61 1 4 1 IF ( MIPPLF) GO TO 146 PHB173 0 1 6 ? " YF( 1) = 5 . P PHB174 " 1 6 3 YF(?) = 6. PHB175 " 1 6 4 YP1 = YE ( ? ) PHB176 C I 6 5 V F ( T'l = STRAM(J) •' .08 PHB17 7 0 1 6 6 v r ( 6 ) = STRAMI J I + .?5 PH8178 0 1 6 7 K0UNT=K0UNT+1 • 0 1 6 8 W ? I T F ( 6 , 1 9 0 ? ) K O U N T 0 16? GO T O 147 PHB179 0170 1 . 4 6 YF( 1) = 3.7 *' : •• . PHB180 0171 Y F ( 2 ) = 3.5 PHB181 017? Y01 = 2.06 PHB182 0173 YM1) = S T R AM IJ 1 - .08 PHB183 0 1 7 4 Y F ( 6 ) = STBAMUI - . 2 5 . . . . . ' ',' ... , • PHB184 Ot7S 147 Y P 2 = Y01 '•'''',' PHB185 0176 ANGLF = 9 0 . PHB186 0 1 7 7 LFAP ( J ) - 0 PHB187 0175 K O U N T = K C U N T + l 0179 WITE(6,I002) K O U N T 0 1 8 0 I F ( OISTAN .LT. . 2 ... AND. PL AC E ; ) GO TO 142 ' PHB188 0181 G O T O 148 ..... .,.,.''•••.•• :, • ••'.'••' •PHB189 01"? 145 I F I PLACE I G O T O ,141 d ' ' '•' ' PHB190 0183 I F ( TIMMIJ) . G T . .72 ) GO T O 151 PHB191 0184 X01 = .1 ' , '. . ;j PHB192 0185 G O T O 1 5 2 ' • ' • . ' - • • , / ]•'• , " ••: •'' PHB194 0186 • . . 151 .. I F (..TIMMIJ) . G T . 9.27 ). GO.TO 153 ;.'•'"_.-.. . .• '• ,r-.'. •' ' . ''.. . .  PHB195 0187 X01 = TIMMIJ) - .72 .". .• ;•.«;.'» PHB196 0188 G O T O 152 .". . 1 PHB198 0189 153 xm =8.55 ' PHB 199 0190 152 X02 = X01 . •. •• PHB201 0 1 9 1 XE(1) = TIMMIJ) . : "'•"'•;' •..'•''.' ~ • PHB202 019? . XE ( 2 I =. TIMMIJ) .... •.'".'. . ,.1 •• PHB203 0193 ROOM = TIMMIJ) - SPACIN . ' •". .'•''? '• '•" ' ',. PHB204 0194 CLEAR '= ROOM . G T . 1.44 . O R . VCLEAR . G T . .2 . PHB205 0195 VCl.FAR = STRAM(J) - A L T I T U ' PHB206 01O6 SPACIN = TIMMIJ) PHB207 0 1 9 7 ALTITU = STRAMI J) ' . "• PHB208 0198 K O U N T = K O U N T + I . . . ' : . : . . . . . , . ; • ' . ' . ' ' . . • ' • . : • ' . 0199 WRITEI6,10021 KOUNT ' 0?00 I F ( MIOOLF) G O T O 154 PHB209 0 7 0 1 I F ( .NOT. CLEAR ) G O T O 157 PHB210 0?0? 156 I F ( IFAP ( J-l) . F O . 1 ) G O T O 15R PHB211 0 7 0 3 159 Y F(1) = STRAMIJ) + .08 PHB212 . . . 0 7 0 4 LFAPt J 1 = 1 J PHB213 -51- r tf'L'I'-'A' I 1/ [ II c" MAPI 03-17-69 1P:31:04 °*GF 0005 YF(6)'= STRAM(J) + .75 PHB214 0 7 0 (• YF( 1 > - YFIM + .? PHB215 " 7 0 7 Y>-(?) = YC(6I * .4 PHB216 vni = YF(?) + .1 PHB217 vn? = YF(?) PHB218 0 7 1 KPU'NT-KOIINT + 1 C > 1 I WPITF(6,1007) K flUNT 071 ? 00 TO 155 PHB220 o?l < 1 54 IF ( .MOT. CLEAR ) GO TO 156 ; PHB221 0 714 157 IF ( LEAP(J-l) .EQ. ? ) GO T O 159 PHB222 0715 153 YF(l) = STRAM(J) - .OB PHR223 0 ? 1 L cA°(j) = ? PHB224 r? \ i YF ( 6 ) = S TR AM t J I .- .75 PHB225 0 71 1 YF( 1 ) = VF(6) - .2 ••. , PHB226 0 7 I n YE(?) = YF(6) - .4 ' \ .. PHB227 r:7?o YD 1 = YF(7) - .1 PHB228 <~??1 155 ANGI. F = 0. PHB230 07?? YP2 = YEI?) - .? • ' ., , PHB231 i??t KOUNT=KOUNT*l 0 ? 7 /, WRITE (6,100?) KOUNT 0 ? 7 c 149 DO 160 1 = 1,4 PHB232 0??6 160 CPM1(I) = COMNTSIL,J, I) PHB233 0??7 in 170 I = 5,7 PH8234 0 ? 7 o IA = I - 4 -. • . ' . • •• ' , PHB235 0??° 170 CPM?(IA) = COMNTSIL, J, I ) . •.. PHB236 "O?30 CALL LINF ( XE«YE,2,1) ; . , PHB237 o ? 31 WRITF(6,1000) XE,YE 0 71? CALL SYMBOL ( X01 ,Y01 , .07 ,C0M1 , ANGLE, 24) PHB238 r, ? 3 3 CALL SYMpnt (X02,YD2,.07,COM2,ANGLE,18) PHB239 0 7 3/, WPITF(6,1000) X01,X02,YDl,Y02 , V: 0 ? ? r i TTMOUT = TIMM(J) PHB240 n?3f. 14? YF(?) =.YF(1) PHB241 0737 YF(3) = STRAM(J) PHB242 ^7 3? YFI4) = YF ( 11 • • - ' •'• PHB243 0?3i YF(5) = YFf 1) .. ... PHB244 0?40 CALL LINE (XF, Y F , 6,1) PHB245 o?4i WRITEI6.1000) . X F . Y F ; 0?47 1 40 CONTINUE ., PHB251 c THE END O F COMMENTS' PHB252 0?4"< CALL PLOT (12.,0..-3) PH8253 0?',4 no CONTINUE ... , , .. PHB256 P?45 CALL P L O T N O . , > . ' PHB257 0246 .. S T O P _ • PHB258 0 74 7 END •• , '. •. V ' - . ' ... PHB259 -52- APPENDIX I I A d d i t i o n a l Creep Curves Figure a. Stage I I (SGS), 572 p s i . F i g u r e b. Stage I I (SGS), 858 p s i . Figure e. Stage I I (LGS), 1221 p s i Figure f. Stage I (SGS), 120 p s i . Figure i . T r a n s i t i o n (SGS), 2574 p s i . Figure k. T r a n s i t i o n (LGS). 1954 p s i . Figure m. T r a n s i t i o n (LGS),.2606 p s i . Figure 1. T r a n s i t i o n (LGS), 2280 p s i . Figure n. T r a n s i t i o n (LGS,), 2932 p s i . Figure o. T r a n s i t i o n (LGS), 3258 p s i . Figure p. T r a n s i t i o n (LGS), 3908 p s i . Figure r . T r a n s i t i o n (LGS), 4560 p s i . Figure s. T r a n s i t i o n (LGS), 4886 p s i . Figure u. Stage I I I , 7326 p s i Figure v. Stage II incremental loading. -58- Figure w. Stage I I I unloading. -59- APPENDIX I I I C a l c u l a t i o n o f T h e o r e t i c a l Creep Curves f o r P u r e N a b a r r o - H e r r i n g Creep and P u r e C o b l e Creep. N-H. Assume t h a t a g r a i n deforms o n l y by N-H d i f f u s i o n a l c r e e p . I n i t i a l l e n g t h = l o I n i t i a l w i d t h s = w6 I n c r e a s e s i n l e n g t h = A l I n c r e a s e i n w i d t h = Aw F i n a l l e n g t h 1 = l o + o l F i n a l w i d t h w = wo + Aw E n g i n e e r i n g s t r a i n = = E True s t r a i n de = d l / 1 ; e = l n ̂  = I n 1 + ^ = I n (1 4- E) l o l o . F, + 1 = e e o r E = e £ - 1 F o r c o n s t a n t volume e. + + £g = 0 Assume E £ = £ 3 = - Hz\ w i t h a P o i s s o n s r a t i o o f % f o r p l a s t i c d e f o r m a t i o n . l n ( l + f , . - % l „ ( l + | i , 1. ( - i „ ( 1 ( 1 + E T ) = ( 1 + % L ) ~ h Assume i n i t i a l g r a i n d i m e n s i o n s L o , Wo A f t e r e n g i n e e r i n g s t r a i n E -60- L = Lo(1 + E ) = Loe E J_i _ \ , _ G / 9 W = Wo(l + E 2) 2 = Woe ' 2 - E 2 2 2 2 2c Define g r a i n s i z e L where L = ^(L rw ) = %Lo e + ^ Wo e I f the g r a i n i s i n i t i a l l y equiaxed -2 ! 2 j. 2e , _£-, L = %Lo {e + e } From Zehr and B a c k o f e n ^ e " « V D L where a i s a geometrical constant - 10 -23 3 v i s the atomic volume (1.43 x 10 cm f o r Sn) D L i s the c o e f f i c i e n t f o r l a t t i c e d i f f u s i o n — 16 o k i s Boltzman's constant = 1.38 x 10 erg/ K T i s the absolute temperature (°K) Pure N-H creep i s much slower than that found exp e r i m e n t a l l y . Values of D f o r Sn w i l l give the f a s t e s t r a t e . I f the g r a i n s i z e i s 2 microns and T = 26°C. J{ N-H = 2.74 x 1 0 1 7 d y n e S I s e c = 3.96 x 1 0 1 2 l b - s e c / i n 2 crn^ de = dt 71m T2 , f v c raD 1** -f mvD T J • , T 2 a\ L) t = h Lo kT e L d t 2 2e kT o ( e 2 e + e e ) d e - \ Lo {^- + e £ + Jg} t = Z L N ^ { e 2 e _ 2 e - e 4s -61- a = 97 p s i 71 N-H = 3.96 x 1 0 1 2 ^ 5 f £ " x * r = 1.1 x 10 9  v 3600 sec i n ,9 _ 1-1 x 10 • , 2e o -e , * ""4 x 97 { e " 2 e + 1 } t = 2.85 x 1 0 5 { e 2 e - 2e" e + 1} hrs N-H Creep F r a c t i o n of time True S t r a i n Time (hrs) to reach .40 s t r a i n 0 0 0 .01 1.14 x 10 4 2.1 .02 2.28 x 10 4 4.2 .05 5.70 x 10 4 10.6 .10 . 1.16 x 10 5 21.5 .20 2.42 x 10 5 45.0 .30 3.82 x 10 5 71.0 .40 5.39 x 10 5 100.0 Coble The a n a l y s i s i s s i m i l a r to that f o r N-H creep. Grain s i z e i s i d e n t i f i e d as L 3 = h ( L o 3 + Wo3) = h L o 3 e 3 £ + %Wo3e 3 / 2 e f o r equiaxed grains Lo = Wo .3. L J = % L o J ( e " " + e '") 7 3 _ , T_3,_3e , _ - J / 2 E > a rn L 3kT I = 7 l c ° ~~ BvwF u gb -62- where D ^ i s the grain boundary d i f f u s i o n c o e f f i c i e n t i s a constant - 150 ,-7 w i s grain boundary width 10 cm) T i s 26° C L i s 2 microns a i s 97 p s i 77 co = = 3.88 x 1 0 ^ dynes sec/cm 2 since coble creep i s much f a s t e r than the experimental rate and 7 ^ gives a slower rate of creep than7?Sn. L 3de agvwD kT dt T 3 f , 3e . - /2e, , ,aBvwD„>. , Lo (e + e )de = (____££ ) 2 J k T t = L o \ t 3vwDgk v 6 a r 3e . - 3/2 . . 1 e - 2e + 1 J t = Lo kT 3vwD gb f^)Le3e - 2e • 3/2e + l ] , 7 f 3e „ - 3/2e . .1 t = . 271 e - 2e I hrs. - 6 3 - Coble Creep F r a c t i o n of time True S t r a i n Time (hrs) to reach .40 s t r a i n 0 0 0 .01 1.62 x 10~ 2 .0187 •02 3.24'x 10" 2 , .0374 .05 8.4 x 10~ 2 .096 .10 1.7 x 10" 1 .196 .20 ,. 3.6 x 1 0 - 1 .415 .30 5.9 x 10" 1 ' .680 .40 • * 8.7 x IO" 1 1.00 -64- BIBLIOGRAPHY 1. D. Lee, G.E. Res. and Dev. Center Report #69-C-005. 2. C.E. Pearson, J . Inst. Metals, 54 (1934). 3. D.H. Avery and W.A. Backofen, ASM Tran. Quart., 58 (1965) 551. 4. D. Lee and W.A. Backofen, Trans. AIME, 239 (1967) 1034. 5. T.H. Alden, Acta. Met., 15 (1967) 469. 6. H.E. Cl i n e and T.H. Alden, Trans. AIME., 239 (19°?) 710. 7. D.L. Holt and W.A. Backofen, ASM Trans. Quart., 59 (1966) 755. 8. T.H. Alden and H.W. Schadler, Trans. AIME., 242 (1968) 825. 9. P.J. Martin and W.A. Backofen, ASM Trans. Quart., 60(1967) 352. 10. S.W. Zehr and W.A. Backofen, ASM Trans. Quart. , 6(1968) 300. 11. D.L. Holt, Trans. AIME, 242 (1968) 25. 12. H.W. Hayden, R.C. Gibson, H.F. Merrick and J.H. Brophy, ASM Trans. Quart., 60, 3 (1967). 13. T.H. Alden, ASM Trans. Quart., 61 (1968) 559. 14. T.H. Alden, Trans. AIME, 236 (1966) 1633.. 15. R.C. G r i f k i n s , J.. Inst. Metals, 95 (1967) 373.. 16. R.C. Cook, M.A.Sc. Thesis, University of B r i t i s h Columbia. 17. S. Floreen, S c r i p t a M e t . , 1 (1967) 19. 18. W.A. Backofen, I..R. Turner, and D.H. Avery, ASM Trans. Quart., 57 (1964) 980. 19. Private communication with T.H. Alden. 20. A.K. Head, P h i l . Mag., 44, (1953) 92. 21., A.K. Head, Proc. Phys. Soc. (London), 1366 (1953) 793. 22. Y. Ishida and M.H. Brown, Acta Met., 15 (1967) 857. .13. H. G l e i t e r , E. Hornbogen and G. Baro, Acta Met. , 16 (1968) 1053. -65- 24. R.G. Gifkins and K.V. Snowden, Trans. AIME, 239 (1967) 105. 25. S.K. Tung and R. Maddin, Trans. AIME, 109 (1967) 905. 26. P.R. S t r u t t , A.M. Lewis and R.C. G i f k i n s , J . Inst. Metals, 93 (1964) 71. 27. R.B. Jones and R.H. Johnson,Discussion, ASM. Trans. Quart., 59 (1966) 356. 28. W.A. Backofen et a l i n D u c t i l i t y , ASM, Metals Park, (1968) 279. 29. A. Karim, D.L. Holt and W.A. Backofen, Trans AIME, 245 (1969) 1131. 30. P. Chaudhari, IBM Research Report, RC 1946. 31. T.H. Alden, "Interaction of Dislocations and Grain Boundaries During Super- p l a s t i c creep", International Conference, "Interfaces", Melbourne, A u s t r a l i a , August, 1969. 32. P. Chaudhari, Acta Met. , 15 (1967) 1777. 33. E.N. Andrade and K.H. J o l i f f e , Proc. Roy. Soc. (London) A 254 (1960) 291. 34. R.C. G i f k i n s , Trans AIME, 215 (1969) 1015. 35. S. Bhattacharya, W.K.A. Congreve and F.C. Thompson, J . Inst. Metals, 81 (1952) 83. 36. J.E. Breen and J . Weertman, J . Metals, 7 (1955) 1230. 37. F.Garofalo, Fundamentals of Creep and Creep-Rupture i n Metals, N.Y. McMillan (1965). 38. CM. Packer, R.H. Sohnsen and O.D. Sherby, Trans AIME., 242 (1968), 2485. 39. R. Kossowsky and S.H. Bechtold, Trans AIME, 242 (1968) 716. 40. D. McLean, Trans AIME, 242 (1968) 1193. 41. P. Chaudhari, Science and Technology, Sept. 1968, P.42. 42. H.J. McQueen, W.A.. Wong, and J.J.Jones, Can. J . Phys., 45 (1967) 1225. 43. R.C. G i f k i n s , J . Inst. Metals, 79 (1951) 233. 44. W.A. Wood, G.R. Wilms and W.A. RachinRer, J . Inst. Metals, 79 (1951) 159. 45. T.H. Alden, " D i s l o c a t i o n Climb. Theories of Creep and S u p e r p l a s t i c i t y " , (1969). 46. C.M. Parker and O.D. Sherby, ASM Trans. Quart., 60 (1967) 21. 47. Private communication with K.C Donaldson.

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
France 6 0
United States 2 0
China 2 1
India 1 0
City Views Downloads
Unknown 7 0
Beijing 2 1
Redmond 1 0
Ashburn 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}

Share

Share to:

Comment

Related Items