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Superplasticity and creep behaviour in pure zirconia Hart, John Laurie 1967

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SUPERPLASTICITY AND CREEP BEHAVIOUR IN PURE ZIRCONIA BY JOHN LAURIE HART B.A.Sc, The U n i v e r s i t y of Toronto, 19^8 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT 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 standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA June, 1967 . 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 o f the 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 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 , 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 t 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 D e p a r t m e n t 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 no t 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 . D e p a r t m e n t o f 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 ABSTRACT An i n v e s t i g a t i o n of creep deformation i n pure z i r c o n i a , using a creep-in-bending method with programmed temperature increase, showed the occurrence of s u p e r p l a s t i c i t y at temperatures near the monoclinic to tetragonal phase transformation. An interesting., phenomenon was observed i n a temporary h a l t to the creep process which occurred with continuing temperature increase beyond the phase transformation. Temperature dependence tests at a maximum f i b r e stress of 314.0 p s i gave o v e r a l l a c t i v a t i o n energies f o r the creep process i n pure z i r c o n i a i n the monoclinic and tetragonal phases of 44 and 103 kcal/mole r e s p e c t i v e l y . TABLE OF CONTENTS Page I. INTRODUCTION 1 I I . SUPERPLASTICITY AND CREEP IN POLYCRYSTALLINE CERAMICS 3 1 . S u p e r p l a s t i c i t y 3 2 . C r e e p 6 I I I . CREEP IN BENDING 10 IV . STRUCTURE OF ZIRCONIUM DIOXIDE 12 V. PREPARATION OF CREEP SPECIMENS 15 1 . Z i r c o n i u m Ox ide Data 15 2 . R e a c t i v e Hot P r e s s i n g 17 3 . Spec imen F i n i s h i n g 20 4 . S p e c i m e n M i c r o s t r u c t u r e 20 V I . EXPERIMENTAL PROCEDURE AND DATA 23 A . Bend C r e e p A p p a r a t u s 23 B. C r e e p T e s t P r o c e d u r e and Data 26 1 . C o n s t a n t L o a d , C o n s t a n t T e m p e r a t u r e 26 2 . C o n s t a n t L o a d , Programmed T e m p e r a t u r e I n c r e a s e 27 3 . C o n s t a n t L o a d , V a r i a b l e T e m p e r a t u r e 27 4 . V a r i a b l e L o a d , C o n s t a n t T e m p e r a t u r e 35 5 . Summary o f E x p e r i m e n t a l C r e e p Data 35 6 . B e n d - i n - C r e e p Spec imens 43 V I I . DISCUSSION OF RESULTS 46 A . S u p e r p l a s t i c i t y 46 B. C r e e p 49 1 . T e m p e r a t u r e Dependence 49 .TABLE OF CONTENTS (Cont.) Page 2. Stress Dependence 54 (a) , Monoclinic Phase 54 (b) .Tetragonal Phase 54 3. Microstructure 55 VIII. SUMMARY AND CONCLUSIONS 57 IX. SUGGESTIONS FOR FUTURE RESEARCH 58 X. APPENDICES 59 APPENDIX I Preparation of Dense Z i r c o n i a P e l l e t s 59 APPENDIX II Summary of Experimental Data 60 APPENDIX III Sources of Errors 61 APPENDIX IV Density and Porosity 62 XI. REFERENCES 63 L I S T OF FIGURES 1 . -' T y p i c a l c r e e p c u r v e ( h i g h - p u r i t y p o l y c r y s t a l l i n e a l u m i n u m ) . . . . 6 2. C r y s t a l s t r u c t u r e o f ( i ) m o n o c l i n i c and ( i i ) t e t r a g o n a l z i r c o n i a . 13 3. P a r t i c l e s o f z i r c o n i u m o x i d e powder as s e e n t h r o u g h t h e e l e c t r o n m i c r o s c o p e 16 4- D i f f e r e n t i a l t h e r m a l a n a l y s i s o f Z r 0 2 powder 18 5 . A t y p i c a l dense p e l l e t 19 6 . S p e c i m e n m i c r o s t r u e t u r e s , 2 , 0 0 0 x 21 7 . S p e c i m e n m i c r o s t r u e t u r e s , 1 0 , 0 0 0 x 22 8 . The c r e e p a p p a r a t u s 23 9 . D i a g r a m o f f u r n a c e and l o a d i n g a s s e m b l y 25 1 0 . C r e e p a t c o n s t a n t l o a d and c o n s t a n t t e m p e r a t u r e , as a f u n c t i o n o f t i m e i n m o n o c l i n i c p h a s e 28 1 1 . C r e e p a t c o n s t a n t l o a d and c o n s t a n t t e m p e r a t u r e , as a f u n c t i o n o f t i m e i n t e t r a g o n a l p h a s e 29 1 2 . Change i n d e f l e c t i o n w i t h programmed t e m p e r a t u r e i n c r e a s e 30 1 3 . Change i n d e f l e c t i o n w i t h programmed t e m p e r a t u r e i n c r e a s e 31 1 4 . Change i n d e f l e c t i o n w i t h programmed t e m p e r a t u r e i n c r e a s e 32 1 5 . Change i n d e f l e c t i o n w i t h programmed t e m p e r a t u r e i n c r e a s e 33 1 6 . Change i n d e f l e c t i o n w i t h programmed t e m p e r a t u r e i n c r e a s e . . . . . 34 1 7 . C r e e p as a f u n c t i o n o f t i m e a t c o n s t a n t l o a d and v a r i a b l e t e m p e r a t u r e 36 1 8 . C r e e p as a f u n c t i o n o f t i m e a t c o n s t a n t l o a d and v a r i a b l e t e m p e r a t u r e 37 1 9 . C r e e p as a f u n c t i o n o f t i m e a t v a r y i n g l o a d and t e m p e r a t u r e . . . 38 2 0 . C r e e p as a f u n c t i o n o f t i m e a t v a r i a b l e l o a d and c o n s t a n t t e m p e r a t u r e 39 2 1 . C r e e p as a f u n c t i o n o f t i m e a t v a r i a b l e l o a d and c o n s t a n t t e m p e r a t u r e 4-0 LIST OF FIGURES (Cont.) No. Page 22. Creep as a f u n c t i o n of time at v a r i a b l e l o a d and constant temperature ,41 23. Creep at v a r i a b l e l o a d and constant temperature . . . . 42 24. Creep specimens a f t e r bending 44-25. Creep specimen ' g ' showing cracks 45 26. T o t a l creep over phase t r a n s i t i o n p e r i o d as a f u n c t i o n of p o r o s i t y 47 27. Arrhenius p l o t showing e f f e c t of temperature on s t r a i n ra te at h i g h s t ress 52 28. Arrhenius p l o t showing e f f e c t of temperature on s t r a i n ra te at low s t ress 53 29. Stress dependence of creep ra te i n t e t r a g o n a l phase 55 30. Specimen micros t ruc ture a f t e r bending 56 LIST OF TABLES No. , Page I . LATTICE PARAMETERS OF ZIRCONIA 12 II . ANALYSIS OF ZIRCONIUM OXIDE POWDER 15 III DEFLECTION IN PHASE TRANSFORMATION PERIOD 47 IV ACTIVATION ENERGIES IN CREEP DEFORMATION OF OXIDES 53 ACKNOWLEDGEMENTS The advice and assistance' of Dr.A.CD. Chaklader i n his direction of the investigation is gratefully) acknowledged. Thanks are also extended to the staff of the Department of Metallurgy for their assistance, particularly to Mr. Alan Causey for his helpful advice, to Mr. Janis Lacis for his assistance with equipment and specimen preparation, and to Mr. Arvid Lacis for his assistance in metallography and photography. Financial assistance was gratefully received from NRC Research Grant No. A -2455. I INTRODUCTION 1 i i — Because of the destructive, reversible phase transformation which occurs in pure zirconium dioxide at approximately 1100°C, i t has not been possible to prepare dense, ceramic bodies of pure zirconia u n t i l the recent development of the reactive hot pressing technique. The success of this technique has been thought to depend on the occurrence of enhanced duc t i l i t y , or superplasticity, at temperatures near that of the phase transformation. As creep-in-bending has been used successfully in the Department of Metallurgy in studies of deformation characteristics of uranium dioxide, i t was decided to use this approach in an attempt to determine whether the phenomenon of superplasticity does actually occur in pure zirconia. There has been considerable discussion in the literature"of the occurrence of superplasticity i n metallic alloy systems. Because of the slow nature of the phase transformations in these systems i t has been possible to carry out these investigations under isothermal conditions. Because of.the rapid athermal nature of the zirconia phase transformation, the study of superplasticity in zirconia by creep deformation was carried out under the condition of programmed, or constant, temperature increase. Creep studies are of importance to the ceramist because they yield data which may be used in determining the mechanism of high temperature deformation processes. This information can be helpful in the development of refractory materials showing high temperature mechanical s t a b i l i t y and strength. Creep data are also important to engineers concerned with the design of_parts and choice of materials in high temperature applications. Because of the lack of standard creep data on pure zirconia in the literature, resulting from the d i f f i c u l t y in preparing pure material of the required structural s t a b i l i t y , a preliminary investigation was carried out to determine creep characteristics of this material in the monoclinic and tetragonal phases, in addition to the investigation of superplasticity. SUPERPLASTICITY AND CREEP IN POLYCRYSTALLINE CERAMICS 1• ' Superplasticity Unusual d u c t i l i t y effects have been observed in studies of mechanical deformation during phase transformations. A review of work on this phenomenon, known as superplasticity, has been given in a paper by E.E. Underwood ^ . Studies on this effect have been mainly on metallic materials but i t should also apply, in principle, to other crystalline structures such as ceramic oxides. Observations on superplastic behaviour (2) in quartz crystals have been reported by A.CD. Chaklader v In his review of superplasticity ^ , Underwood credits discovery of this phenomenon to a Soviet scientist named Bochvar, as reported in 194-5 in an ar t i c l e by Bochvar and Sviderskaya ( 3 ) . Underwood's art i c l e includes an extensive bibliography which indicates that much of the work on superplasticity prior to 1962 was carried out by Soviet workers. Bochvar's work included observations of enhanced creep in a metal alloy system near the s o l u b i l i t y l i m i t . He proposed that precipitation and resolution of an incipient second phase promotes an increase i n atomic mobility, resulting in enhanced creep. Bochvar's observations of enhanced d u c t i l i t y near the s o l u b i l i t y l i m i t have been supported in a more recent .1 t i \ paper by Guy and Pavlick , although their proposed explanation was not completely in agreement with Bochvar's concept of increased atomic mobility. They f e l t along with Bochvar, however, that the enhanced rate of creep could not be accounted for by precipitation alone, but that i t required a cycle of precipitation and resolution. Underwood has summarized a particularly thorough investigation of superplasticity in Al-Zn eutectoidal alloys as carried out by (z) Presnyakov and Chervyakova w ' . This work showed that the occurrence of superplasticity depended on the, existence of a metastable phase in the system under study. This metastability was, achieved.by quenching from above the eutectoid temperature of 275°C. It was indicated that the superplasticity effect was greater when a greater proportion of the alloy was in the metastable state. The superplasticity effect was determined by elongation measurements in tensile tests, with elongations as high ,as 600% being obtained. In later work ^ , Presnyakov and Chervyakova showed the relation between la t t i c e parameter and metastability in an Al-Zn alloy. The alloy with the greatest departure from the equilibrium lattice spacing gave the greatest superplasticity effect. Presnyakov and Chervyakova have reported behaviour in eutectic Al-Cu alloys similar to that observed in eutectoid Al-Zn alloys. This work also led to the observation that elongation was greater as the transformation temperature was approached more closely from either above or below. In a paper dealing with superplasticity in two-phase Pb-Sn alloys, Avery and Backofen explain superplasticity in terms of two (8) competing processes v '„ They developed the following expression: £ = k(J- + B sinh f@a~ where £ is the strain rate, (f is the stress, L is the grain size, and A, B and j3 are constants at a given temperature. The f i r s t term in Equation (l) is associated with the Nabarro-Herring diffusion-controlled creep mechanism and the second with a dislocation climb mechanism,, The former is suggested to predominate at low strain rates with the latter predominating at high strain rates. Packer and Sherby, in a later study on the Pb-Sn eutectic alloy ( 9 ) f agreed with the approach made to the explanation of superplasticity by Avery and Backofen. Packer and Sherby, however, found evidence inconsistent with the Nabarro-Herring model, and proposed a modified expression, as follows: € = k eT 2 + BV" 2 sinh^tf""* 2" 5 L 3 The f i r s t term in Equation (2) is considered to account for a recrystallization or grain boundary migration process. The second term is an expression derived by Weertman and is associated with a process controlled by dislocation climb. Packer and Sherby also presented observations of some microstructural effects in eutectoid Al-Zn which suggest that recrystallization or grain boundary migration takes place during the occurence of superplasticity i n two-phase alloy systems„ - 6 -2 . C r e e p C r e e p has been d e f i n e d as t h e t i m e - d e p e n d e n t p l a s t i c d e f o r m a t i o n o f m a t e r i a l s u n d e r c o n s t a n t s t r e s s . The g r e a t e s t amount o f c r e e p d a t a has been o b t a i n e d on m e t a l l i c m a t e r i a l s . f rom c o n s t a n t l o a d u n i a x i a l t e n s i o n t e s t s . A t y p i c a l c u r v e (11) showing m e t a l l i c c r e e p i n t h r e e s t a g e s i s g i v e n i n F i g u r e 1 . a •H crj U -P CO o •H -P CO CD U -P crj -P O EH 0 . 4 0 . 2 -0 (P r imary - » ! < — S e c o n d a r y > T e r t i a r y • \ S t r e s s = 3000 p s i F j Temp. = 478 K i i i 1 i i i i 0 2 4 6 8 Time u n d e r t e s t , h r . F i g u r e 1 T y p i c a l c r e e p c u r v e ( h i g h - p u r i t y p o l y c r y s t a l l i n e a l u m i n u m ) . C r e e p p r o c e s s e s c a n be v e r y complex and t h e d e t e r m i n a t i o n o f c r e e p mechanisms may be c o m p l i c a t e d by t h e o p e r a t i o n o f more t h a n one mechan ism i n a g i v e n p r o c e s s . These d i f f e r e n t mechanisms may o c c u r s i m u l t a n e o u s l y , o r t h e y may o c c u r s e q u e n t i a l l y as t h e r e s u l t o f i n c r e a s i n g s t r a i n and changes i n t h e s u b s t r u c t u r e o f the m a t e r i a l as c r e e p p r o g r e s s e s . B e c a u s e c r e e p i s t h e r m a l l y a c t i v a t e d , i t i s o f t e n p o s s i b l e t o d e t e r m i n e t h e o v e r a l l a c t i v a t i o n e n e r g y by t e m p e r a t u r e -dependence c r e e p t e s t s i n w h i c h o t h e r f a c t o r s a r e k e p t c o n s t a n t . Some o f the o t h e r f a c t o r s a f f e c t i n g c r e e p i n p o l y c r y s t a l l i n e c e r a m i c s a r e - 7 (12) stress, grain size, crystal structure, porosity, and composition v Although the overall activation energy may be contributed to by more than one mechanism in a given creep process, i t can provide a clue to the type of mechanism which may be predominant and rate determining. This may be deduced by comparing the activation energy of the creep process with values available in the literature for other relevant processes, as for example, self-diffusion of cations or anions i n an oxide crystal l a t t i c e . A considerable amount of data has been reported in the literature from creep studies on polycrystalline specimens of several ceramic oxides. On magnesium oxide, activation energies have been calculated and creep mechanisms postulated by Passmore, Duff, and Vasilos i n a paper published in 1966 ^ 1 2^. These investigators found that activation energies for creep decreased sharply with increasing grain size from 96,000 cal/mole at 2 microns to 54,100 cal/mole at 5.5 microns, but remained constant over the grain size range of 5.5 to 20 microns. Creep in magnesium oxide was attributed in part to a stress-directed diffusional mechanism with extrinsic oxygen ion diffusion as the rate-controlling process in the 5.5 to 20 micron grain sizes. The deformation of sintered uranium dioxide of stoichiometric (13) composition was studied by Armstrong, Irvine, and Martinson v using a creep-in-bending method. The apparent activation energy for the overall flow process was found to be 91,000 - 8,000 cal/mole. - 8 -Observations on the effect of porosity suggested that in the density range covered, only the fraction of total porosity present at grain boundaries influenced the creep behaviour„ In another investigation reported earlier by Scott, Hall and Williams (14-), the activation energy for non-stoichiometric uranium oxides was found to vary with the oxygen/uranium ratio, being about 65,000 cal/mole for UO2 ^ > 72,000 cal/mole for U0 2 < 06 a n d ^ 95,000 cal/mole for U02„00° T h i s latter value compares well with the value of 91,000 + 8,000 cal/mole reported by Armstrong, et. a l . In a later study on non-stoichiometric (ic.) uranium oxides by Armstrong, and.Irvine v J l , activation energies of 55,700 - 5,000 cal/mole for 0/U ratios lower than 2.08 and 63,000 i 8,000 cal/mole for UO2 ]_£ were reported. In a paper published i n 1959, Chang discussed high temperature creep behaviour under tensile testing conditions in beryllium oxide and aluminum oxide .. His observations suggested that the Nabarro Herring creep mechanism predominates in the deformation behaviour of polycrystalline beryllium oxide. Chang was unable to state whether high-temperature creep of Al^O^ follows the same vacancy-diffusion mechanism, because of a lack of self-diffusion data at that time. He reported activation energies for steady-state creep of 120,000 and 200,000 cal/mole for BeO and A I 2 O 3 respectively. These activation energies were unaffected by addition of oxide impurities in the order of one weight per cent. Later work reported by Passmore and Vasilos (19) ? o n fine-grained aluminum oxide, indicated good agreement with the Nabarro-Herring diffusional creep theory for stresses up to about 2,000 psi. I l s c h n e r , R e p p i c h , a n d R i e c k e y ' h a v e m e a s u r e d s t e a d y - s t a t e c r e e p r a t e s i n . c o m p r e s s i o n o n d e n s e p o l y c r y s t a l l i n e i r o n o x i d e , F e - ^ _ x 0 , o v e r a t e m p e r a t u r e r a n g e o f 1 0 0 0 - 1 3 0 0 ° C „ C r e e p w a s f o u n d t o p r o c e e d b y d i s l o c a t i o n m o v e m e n t r a t h e r t h a n b y t h e d i f f u s i o n -c o n t r o l l e d N a b a r r o - H e r r i n g m e c h a n i s m . T h e d i s l o c a t i o n m o v e m e n t , h o w e v e r , i n v o l v e d v a c a n c y d i f f u s i o n b e t w e e n d i s l o c a t i o n s w h i c h m i g h t b e d e s c r i b e d a s l o c a l d i f f u s i o n a l c r e e p . E x p e r i m e n t a l c r e e p r a t e s w e r e p r o p o r t i o n a l t o t h e f o u r t h p o w e r o f t h e a p p l i e d s t r e s s a n d p r o p o r t i o n a l t o e x p ( - Q / R T ) w i t h a n a c t i v a t i o n e n e r g y o f 7 8 , 0 0 0 . c a l / m o l e . - 10 -III CREEP IN BENDING As mentioned i n section I I , the t e n s i l e test, method has been commonly used i n obtaining creep data. Specimen preparation f o r t h i s t e s t , however, can be very d i f f i c u l t when working with hard ceramics of very low d u c t i l i t y at room temperature. For t h i s reason, creep i n bending was chosen as the t e s t method i n t h i s i n v e s t i g a t i o n . This method u t i l i z e s specimens of rectangular cross-section which can r e a d i l y be prepared by c u t t i n g the material with diamond saws, followed by standard p o l i s h i n g procedures. Three-point loading was chosen because of the a v a i l a b i l i t y of t h i s type of apparatus i n the Department of Metallurgy i n materials of construction s u i t a b l e f o r high temperature measurements i n an a i r atmosphere„ When material properties such as porosity, composition, etc., are kept constant, secondary or steady state creep may be represented by the following equations: At constant temperature (^l) ^  £ _ ^ e X p (^^-») (3) At constant stress ( 2 2 ) , 4 = A'exp (-Q/RT) (4.) where C i s the creep s t r a i n r a t e , tTis f i b r e s t r e s s , Q i s a c t i v a t i o n energy, , and A' are material constants, R i s -the gas constant, and T i s absolute temperature. In order to i n t e r p r e t data from creep i n bending t e s t s , several assumptions must be made, as follow:: - 11 -(1) Cross sections remain plane in bending (Bernoulli's hypothesis). (2) Creep properties are alike i n tension and compression. ( 3 ) Conditions of pure bending exist. (A) Arc of bending has constant radius of curvature. In this investigation, stress was calculated as maximum stress of the outermost fibres by the following elastic relationship( 2^) CTmax = 3 p L 2bh 2 (5) where &~max is the elastic stress in the outermost fibres of the beam, P is applied load, L i s distance between support points, and b and h are width and thickness of the beam respectively. Creep strain rates were calculated from deflection rate data using the following relationship : _ 4hd L 2 (6) where i s unit strain, h is specimen thickness, d is deflection in bending, and L is distance between support points. - 1 2 -I V S T R U C T U R E O F Z I R C O N I U M D I O X I D E F r o m r o o m t e m p e r a t u r e t o a p p r o x i m a t e l y 1 1 0 0 ° C . p u r e z i r c o n i a h a s a m o n o c l i n i c c r y s t a l s t r u c t u r e . A t a b o u t 1 1 0 0 ° C . t r a n s f o r m a t i o n t o a t e t r a g o n a l s t r u c t u r e o c c u r s . L a t t i c e p a r a m e t e r s f o r t h e t w o s t r u c t u r e s a r e g i v e n i n T a b l e I a n d ( 2 5 ) u n i t c e l l s a r e s h o w n i n F i g u r e 2 ( i ) a n d 2 ( i i ) T A B L E I L A T T I C E P A R A M E T E R S OF Z I R C O N I A a b c M o n o c l i n i c ^ 5 . 1 4 3 5 . 2 0 4 5 . 3 1 1 8 0 ° 4 5 ' T e t r a g o n a l ^21"> 5 . 0 7 4 - 5.16 I n t h e m o n o c l i n i c p h a s e t h e d e v i a t i o n f r o m a s i m p l e f l u o r i t e s t r u c t u r e i s q u i t e c o n s i d e r a b l e . T h e d i s t a n c e b e t w e e n a z i r c o n i u m a t o m a n d i t s e i g h t s u r r o u n d i n g o x y g e n a t o m s o v a r i e s f r o m a b o u t 1 . 9 5 t o 2 . 6 5 A . I n t h e t e t r a g o n a l p h a s e t h e ' c ' p a r a m e t e r d i f f e r s f r o m ' a ' b y o n l y a b o u t 1 . 5 % , b u t t h e d e v i a t i o n f r o m a f l u o r i t e s t r u c t u r e m a y n o t e x a c t l y f o l l o w t h e s i m p l e d i s t o r t i o n i n d i c a t e d i n F i g u r e 2 ( i i ) . S t u d i e s o n t h e n a t u r e o f t h e m o n o c l i n i c - t e t r a g o n a l t r a n s f o r m a t i o n h a v e b e e n r e p o r t e d i n t h e l i t e r a t u r e . T r a n s m i s s i o n (25} e l e c t r o n m i c r o s c o p y s t u d i e s b y B a i l e y v ; a n d v a c u u m h o t - s t a g e m i c r o s c o p e o b s e r v a t i o n s b y F e h r e n b a c h e r a n d J a c o b s o n h a v e (i) ( i i ) Figure 2- Crystal structure of (i) monoclinic and ( i i ) tetragonal zirconia. Black dots represent zirconium atoms and larger circles oxygen atoms. i H I - H -indicated a martensitic type transformation. In particular, the latter work has indicated an Fe-Ni type of martensitic phase change which exhibits the following features: diffusionless shear mechanism, broad hysteresis, athermal characteristics, platelet morphology, and re v e r s i b i l i t y which can not be prevented by quenching. In a recent note ( 2^), Mazdiyasni, Lynch, and Smith have shown that zirconia can exist in metastable cubic and tetragonal forms, at relatively low temperatures, when prepared as an ultra-high-purity submicron powder by thermal decomposition of alkoxides. At room temperature the oxide was in the metastable cubic form, which in the region of 250 to 300°C. (depending on particle size) transformed into a metastable tetragonal form. Between about 300 to 4-00°C. a gradual change to the stable monoclinic phase took place. - 15 -V. PREPARATION OF CREEP SPECIMENS 1 . Z i r c o n i u m Ox ide Data The z i r c o n i u m o x i d e powder u s e d i n . p r e p a r i n g t h e c r e e p s p e c i m e n s was o b t a i n e d f r o m K o c h - L i g h t L a b o r a t o r i e s L i m i t e d , E n g l a n d , and had a n o m i n a l Z r 0 2 c o n t e n t o f 99.9%. A s p e c t r o g r a p h i c a n a l y s i s , p e r f o r m e d by E l d o r a d o M i n i n g and R e f i n i n g L i m i t e d , P o r t Hope , O n t a r i o , i s g i v e n i n T a b l e I I . C h e m i c a l a s s a y s f o r z i r c o n i u m , h a f n i u m , t i t a n i u m , and u r a n i u m , and w e i g h t l o s s e s a t 110 and 4 0 0 ° C . a r e a l s o g i v e n i n t h i s t a b l e . TABLE IT-ANALYSIS OF ZIRCONIUM OXIDE POWDER S p e c t r o g r a p h i c , ppm Z r b a s i s : A l 15 Mo <10 Ca 45 N i <15 Co < 5 Pb <15 Cr <15 S i 250 Cu <10 Sn <10 Fe 45 V <10 Mg 65 W <75 Mn < 1 Zn <75 C h e m i c a l : Z r 7 3 . 5 % ( T h e o r e t i c a l = 74%) Hf 1 .5% Zr b a s i s T i 0 .087% Z r b a s i s U 2 . 3 ppm Z r b a s i s We igh t l o s s : A t 1 1 0 ° C . <0.1% A t 4 0 0 ° C . 0 . 2 % - 16 -An i n d i c a t i o n of p a r t i c l e s i z e and shape i s given i n the photomicrographs of Figure 3 . These were obtained on the electron microscope using powder s l u r r i e d i n water made s l i g h t l y a c i d i c with HCl. (i) 2,000 x ( i i ) 1,000 x Figure 3 P a r t i c l e s of zirconium oxide powder as seen through the electron microscope. - 17 -A graph showing the results of differential thermal analysis on the zirconium oxide powder is given in Figure ly. The data are based on more than one determination,, Heating rate was 10°C„/min„ and cooling rate was approximately 10°C./min„ 2. Reactive Hot Pressing Dense zirconia pellets were prepared by the reactive hot (30) pressing process s '. Zirconia powder was prepressed at room temperature in a graphite-lined molybdenum die. The pellet was then heated under pressure in the die, using an induction generator. The die assembly was enclosed in Vycor tubing which was continuously purged with helium to prevent oxidation of the molybdenum die and graphite sleeves. The molybdenum die served adequately as susceptor in some pressings but in others a graphite sleeve was used to obtain improved heating performance, depending on the characteristics of the induction generator being used. Pressure was applied to the pellet by use of an hydraulic jack. Densification was achieved by repeated cycling through the temperature range of the reversible phase transformation. The 9% volume expansion which occurs in cooling from the tetragonal to monoclinic phase is thought to enhance the densification process. Although the above method was successful in producing dense materials up to 96% theoretical density, great d i f f i c u l t y was encountered in trying to produce consistently dense, strong and large pellets suitable for preparation of creep specimens. A total of Figure A D i f f e r e n t i a l thermal analysis of ZrO^ powder. - 19 approximately th i r ty - f i ve hot pressings was carried out but only a few pellets were produced from which creep specimens were successfully prepared. Conditions of preparation for pellets from which creep specimens were obtained are given in Appendix I. Photograph of a typical pe l le t , approximately 25.4 mm diameter and 3.6 mm thick, is shown in Figure 5. Figure 5 A typical dense pel let . - 20 -3. Specimen F i n i s h i n g The p e l l e t s of dense z i r c o n i a were mounted on t r a n s i t e with water-glass f o r c u t t i n g i n t o bars. Dimensionally i t was possible to cut four bars, each approximately 3.4mm x 2.2mm cross-section and 0.8$" to 1.0" long, from each p e l l e t . Cutting was c a r r i e d out with diamond abrasive wheels using water as coolant. The as-cut bars were ground to a preliminary f i n i s h on a ca s t - i r o n lapping wheel using an aqueous s l u r r y of s i l i c o n carbide grain, G r i t No. 240-RA. F i n a l f i n i s h was obtained by grinding on a c a s t - i r o n lap using an aqueous s l u r r y of 600 mesh alundum. F i n a l specimen cross-sections were approximately 3.0mm x 2.0mm. U- Specimen Microstructure Using the carbon r e p l i c a technique on specimen surfaces as prepared f o r creep t e s t s , that i s with no further p o l i s h i n g , photomicrographs were obtained on the e l e c t r o n microscope of specimens of d i f f e r i n g p o r o s i t i e s , as shown i n Figures 6 and 7. ( i i ) P o r o s i t y F i g u r e 6 S p e c i m e n m i c r o s t r u e t u r e s , 2 ,000 x . ( i ) Porosity 15% ( i i ) Porosity i.5% Figure 7 Specimen microstructures, 10,000 x. EXPERIMENTAL PROCEDURE AND DATA A Bend Creep Apparatus The equipment assembly used i n obtaining creep data was e s s e n t i a l l y as follows: a furnace f o r heating and housing the specimen-loading device, an e l e c t r i c a l system to con t r o l furnace temperature, and an e l e c t r i c a l recording system to record d e f l e c t i o n rate data. The general arrangement i s shown i n the photograph of Figure 8. Figure 8 The creep apparatus. - 2U -As shown schematically in Figure 9, the furnace consisted of a ve r t i c a l l y mounted mullite tube (A) heated by Globar resistance elements. The elements were surrounded by refractories which were enclosed in a sheet metal container (B). Furnace temperature was controlled by a thermocouple (C) positioned just outside the mullite tube and connected with a Honeywell Versotronic controller. Coarse voltage adjustment was made by use of step-down variable transformers. The control thermocouple (C) was platinum-platinum- + 13% rhodium. Specimen temperature was measured by a platinum-platinum + 10% rhodium thermocouple (D) positioned just below the specimen and connected to a potentiometer to obtain m i l l i v o l t readings. Calibration of this thermocouple was checked against a new thermocouple. Specimen temperature generally did not vary by more than - 2°C. during cycling of the furnace controller. The specimen holding and loading assembly is also shown schematically in Figure 9. A notched alumina tube (E) was used to support the bend specimen (G). The load was applied to the centre of the specimen through a concentric alumina loading tube (F) which was notched at one end to accommodate an alumina wedge. Lead weights (L) were suspended from a loading beam (K) at the top of the loading tube. Specimen deflection was transmitted through a glass deflection rod (i) to a transducer (j) and a d i a l gauge (H). A - Furnace tube B - Furnace C - Control thermocouple D - Specimen thermocouple E - Support tube F - Loading tube G - Bend specimen H - Dial gauge I - Deflection rod J - Transducer K - Loading beam L - Lead weights M - Water cooling Figure 9 Diagram of furnace and loading assembly. - 26 -Beam deflection was recorded continuously by use of a linear d i f f e r e n t i a l transformer. Vertical movement of the core of this transformer, which was equal to specimen deflection, resulted in a voltage change proportional to the movement. This voltage change was transmitted to a direct reading measuring bridge which in turn was connected to a strip-chart recorder. Readings of deflection were also obtained from a d i a l gauge having a sensitivity of 0.0001 inch. Supplemented by the strip chart recorder, these gauge readings were used in plotting the creep curves which represent the experimental data obtained in this investigation. B Creep Test Procedure and Data 1. Constant Load, Constant Temperature In order to avoid lengthy heat-up periods the creep furnace temperature was maintained at approximately 500°C. between creep tests. With the furnace at approximately 500°C, the specimen loading assembly was removed from the furnace and the creep specimen was inserted into the slots provided. The t i p of the loading rod was carefully centred on the specimen beam and the assembly was gently placed back in the creep furnace. During the period of heating from 500°C. to the test temperature, a counterbalance was applied to the loading rod to prevent creep from occurring. This weight was designed to counterbalance most of the assembly load but not to remove the tip from the specimen. This was to ensure that the t i p of the loading rod was not displaced from the centre of the beam. After the test temperature was reached, and following a subsequent temperature equilibration - 27 -p e r i o d , t h e t e s t l o a d was a p p l i e d g e n t l y t o t h e c r e e p s p e c i m e n . The i n i t i a l d i a l gauge r e a d i n g was t a k e n and f u r t h e r gauge r e a d i n g s were t a k e n f r o m t i m e t o t i m e , i n a d d i t i o n t o t h e c o n t i n u o u s s t r i p - c h a r t r e c o r d i n g o f beam d e f l e c t i o n t h r o u g h o u t t h e c r e e p t e s t . C r e e p t e s t s were c a r r i e d o u t by t h e f o r e g o i n g p r o c e d u r e on s p e c i m e n s i n b o t h t h e m o n o c l i n i c and t e t r a g o n a l p h a s e s . C r e e p c u r v e s f o r t h e s e t e s t s , d e r i v e d m o s t l y f r o m d i a l gauge r e a d i n g s b u t s u p p l e m e n t e d w i t h t h e s t r i p - c h a r t r e c o r d e r , a r e g i v e n i n F i g u r e s 10 and 11 t o i l l u s t r a t e t h e c r e e p b e h a v i o u r o f p u r e z i r c o n i a u n d e r c o n d i t i o n s o f c o n s t a n t l o a d and c o n s t a n t t e m p e r a t u r e . The t e s t s were t e r m i n a t e d b e f o r e t e r t i a r y c r e e p was o b s e r v e d . 2 . C o n s t a n t L o a d , Programmed T e m p e r a t u r e I n c r e a s e In t h e s t u d i e s on s u p e r p l a s t i c i t y , the c r e e p s p e c i m e n s . w e r e h e a t e d t h r o u g h t h e phase t r a n s f o r m a t i o n u n d e r c o n s t a n t l o a d . . The h e a t i n g r a t e was m a n u a l l y c o n t r o l l e d a t 5 ° C . / m i n . A r a t e o f 1 0 ° C . / m i n . was a t t e m p t e d but c o u l d n o t be a c h i e v e d i n the e x i s t i n g e x p e r i m e n t a l s e t - u p . The c u r v e s o b t a i n e d d u r i n g t h e programmed h e a t i n g were p l o t t e d s h o w i n g change i n s p e c i m e n d e f l e c t i o n w i t h i n c r e a s i n g t e m p e r a t u r e , as g i v e n i n F i g u r e s 12 t o 1 6 . In F i g u r e 1 5 , t h e t e m p e r a t u r e s c a l e has been s h i f t e d t o t h e r i g h t by t e n d e g r e e s t o c o r r e c t a d i s p l a c e m e n t o f t h e phase t r a n s f o r m a t i o n r e g i o n , w h i c h may have been c a u s e d by s p e c i m e n t h e r m o c o u p l e p o s i t i o n i n g . 3 . C o n s t a n t L o a d , V a r i a b l e T e m p e r a t u r e The e f f e c t o f t e m p e r a t u r e a t a c o n s t a n t l o a d ( max = 314-0 p s i ) was s t u d i e d i n s i m i l a r t e s t s a t p r o g r e s s i v e l y i n c r e a s i n g t e m p e r a t u r e s c o v e r i n g t h e r a n g e o f 980 t o 1 3 0 7 ° C . The h i g h e r l i m i t was d e t e r m i n e d by - 28 -T i m e , h r . F i g u r e 10 C r e e p a t c o n s t a n t l o a d a n d c o n s t a n t t e m p e r a t u r e , as a f u n c t i o n o f t i m e i n m o n o c l i n i c p h a s e . . - 29 -- S p e c i m e n b r o k e 1 0 0 D e n s i t y 8/$ X - s e c t . 2 . 0 x 3 . 3 m m 2 <3~max 1 2 5 0 p s i T e m p . i n c r e a s e 6 ° C . / m i n . 8 0 6 0 4 0 ! — 2 0 L _ 1 1 1 3 0 1 1 4 0 1 1 5 0 1 1 6 0 1 1 9 0 1 1 7 0 1 1 8 0 T e m p e r a t u r e , ° C . F i g u r e 1 2 C h a n g e i n d e f l e c t i o n w i t h p r o g r a m m e d t e m p e r a t u r e i n c r e a s e . 1 2 0 0 1 2 1 0 100 Density 85% X-sect. 1 . 9 x 2 . 6 mm2 o"max 1240 psi Temp, increase 5°C./min. JL 1160 1170 1180 .1220 1190 1200 1210 Temperature, °C. Figure 13 Change in deflection with programmed temperature increase. 1230 124-0 o •H o •H -P O <D H =H 0 Q 6 0 40 20 I— Density 89% 2 X-sect. 2.0 x 3.3 mm C7~max 3140 psi Temp, increase 5°C./min 1130 1140 1150 Specimen broke 1160 117.0 1180 Temperature, °C. 1190 1200 1210 Figure 15 Change i n deflection with programmed temperature increase. 1180 1190 1200 1210' 1220 1230 124-0 1250 1260 Temperature, °C. Figure 16 Change in deflection with programmed temperature increase„ - 35 -d e f o r m a t i o n o f t h e s p e c i m e n t o t h e p o i n t where i t s l i p p e d o u t o f t h e h o l d i n g s l o t s . C r e e p c u r v e s o b t a i n e d u n d e r t h e s e c o n d i t i o n s a r e g i v e n i n F i g u r e s 17 and 1 8 . F u r t h e r c r e e p r a t e d a t a were o b t a i n e d a t a max o f 124-0 p s i o v e r t h e t e m p e r a t u r e r a n g e o f 1255 t o 1 3 4 8 ° C . and a t a &~max o f 3140 p s i o v e r t h e t e m p e r a t u r e r a n g e o f 1257 t o 1 3 1 9 ° C . R e s u l t s a r e shown i n F i g u r e 1 9 i 4 . V a r i a b l e L o a d , C o n s t a n t Tempera tu re The e f f e c t o f l o a d on c r e e p b e h a v i o u r a t c o n s t a n t t e m p e r a t u r e was s t u d i e d b o t h i n t h e m o n o c l i n i c phase and i n t h e t e t r a g o n a l p h a s e . In the m o n o c l i n i c p h a s e , c r e e p r a t e d a t a were o b t a i n e d a t 1 0 7 1 ° C . o v e r a <:7""max r a n g e o f 1260 t o 4590 p s i and a t 1 1 2 2 ° C . o v e r a 0~~max r a n g e o f 1570 t o 3140 p s i . In t h e t e t r a g o n a l p h a s e , c r e e p r a t e d a t a were o b t a i n e d a t 1 2 6 5 ° C o v e r a max r a n g e o f 1240 t o 5350 p s i . R e s u l t s a r e g i v e n i n F i g u r e s 20 t o 2 3 . The t e r m ' b l a n k ' a p p e a r i n g on t h e s e f i g u r e s was u s e d t o d e s i g n a t e t h e l o a d w h i c h r e s u l t e d f r o m t h e combined w e i g h t o f t h e l o a d i n g a s s e m b l y and d i a l gauge s p r i n g t e n s i o n , w i t h the c o n t a i n e r s o f l e a d c h i p s r e m o v e d . 5 . Summary o f E x p e r i m e n t a l C r e e p Data A summary o f t h e e x p e r i m e n t a l c r e e p d a t a i s g i v e n i n t a b u l a r f o r m i n A p p e n d i x I I . Data i n the t a b l e a r e p r e s e n t e d f o r e a c h t e s t i n t h e s e q u e n c e i n w h i c h t h e s e t s o f c o n d i t i o n s were u s e d . S o u r c e s o f e r r o r s a r e d i s c u s s e d i n A p p e n d i x I I I . - 3 6 -C u r v e A 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 C u r v e B 1 2 0 1 2 5 1 3 0 1 3 5 1 4 0 1 4 5 1 5 0 T i m e , h r „ F i g u r e 1 7 C r e e p a s a f u n c t i o n o f t i m e a t c o n s t a n t l o a d a n d v a r i a b l e t e m p e r a t u r e . - 37 -Curve A 10 20 30 40 50 60 Curve B . 45 46 47 . 48 49 50 T i m e , h r . F i g u r e 18 C r e e p as a f u n c t i o n o f t h e t i m e a t c o n s t a n t l o a d and v a r i a b l e t e m p e r a t u r e . - 38 -Curve A 20 4-0 60 80 100 120 Curve B 180 200 220 2^ 0 Time, min. Figure 19 Creep as a function of time at varying load and temperature. 0 20 40 60 80 100 Time, hr. Figure 20 Creep as a function of time at variable load and constant temperature. 0 10 20 30 40 50 60 70 Time, hr„ Figure 21 Creep as a function of time at v a r i a b l e load and constant temperatureo 0 . 0 4 J -0 .03h 0 . 0 2 h o.oil-Tetragonal Phase Temp. 1265°C„ Density 85% « 'Blank' load 124-0 psi 2050 psi-'Blank' load 124-0 psi 314-0 psi Blank' load. " 124-0 psi 3670 psi _L 10 20 30 50 60 70 4-0 Time, min. Figure 22 Creep as a function of time at variable load and constant temperature. 80 90 0.06 Tetragonal Phase 5350 psi 0 20 UO 60 80 100 Time, min. Figure 23 Creep at variable load and constant temperature. - 4 3 6. Bend-in-Creep Specimens A photograph of several creep specimens is shown in Figure 2 4 . Total beam deflections, obtained from di a l gauge readings, are given in order to make comparison with deflections as shown in the photograph. A separate photograph of specimen 'g' is given in Figure 25 to show the cracks which occurred due to volume expansion associated with cooling from the tetragonal to the monoclinic state. Figure 21 Creep specimens after bending. Total Deflection  Specimen from Dial Gauge mm a o 0 . 7 3 c 0.62 d 0 . 9 8 e 1 .86 f 3 . 8 7 g 3 . 8 8 - U5 -Figure 25 Creep specimen 'g' showing cracks. - 46 -VII DISCUSSION OF RESULTS A Superplasticity Strong evidence of the occurrence of enhanced ductility,, or superplasticity, at temperatures near that of the monoclinic to tetragonal phase transformation is given in the deflection curves of Figures 12 to 16. The enhanced d u c t i l i t y is seen in the sharp increase in rate of deflection which occurred in most cases in the temperature range of 1180 to 1210°C. This temperature range agrees with that covered by the endothermic peak on the DTA heating curve shown in Figure 4 . As the monoclinic to tetragonal phase transformation is accompanied by a 9% volume contraction, some of the enhanced du c t i l i t y must be attributable to this dimensional change. Total deflections in the phase transition period, taken in the temperature range of 1170 to 1215°C. but with the upper temperature limit determined by the deflection plateau or by breaking of the specimen, are given in Table III. This table shows that per cent deflection, based on specimen thickness, was always greater than one-third of the percentage volume change, i.e., always greater than 3%. Table III also shows a correlation between material porosity and total creep strain over the phase transition period. A plot of log Ctotal a s a function of porosity, as given in Figure 26, suggests that the relationship between creep and porosity, during the phase transformation, may be expressed as follows: - 47 -£ = C exp (BP) (7) t o t a l where C and B a r e c o n s t a n t s and P i s t h e p o r o s i t y . TABLE I I I DEFLECTION IN PHASE TRANSFORMATION PERIOD D e f l e c t i o n S p e c . T h i c k . % D e f l e c t i o n ^ t o t a l P o r o s i t y F i g . No. i n . mm. mm. i n . / i n . % 0.0030 0 . 0 7 6 1 . 7 4 . 5 0 . 0 0 1 2 5 9 16 0.004-2 0 . 1 0 7 2 . 0 5 . 4 0 . 0 0 2 0 7 11 15 0 . 0 0 5 6 0 . 1 4 2 1 . 9 7 . 5 0 . 0 0 2 6 1 15 13 0 . 0 0 5 9 0 . 1 5 0 2 . 0 7 . 5 0 . 0 0 2 9 0 15 14 0 . 0 1 0 4 0 . 2 6 4 2 . 0 1 3 . 2 0 . 0 0 5 1 2 16 12 P o r o s i t y , % F i g u r e 26 T o t a l c r e e p o v e r phase t r a n s i t i o n p e r i o d as a f u n c t i o n o f p o r o s i t y . - 48 -An interesting feature of the curves in Figures 13, 14 and 16 is the sudden temporary cessation of creep at or near 1200°C. It may be that the beginning of this deflection plateau marks the completion of the phase transformation, or perhaps the completion of a c r i t i c a l proportion of the transformation. In the references to work by Bochvar and Sviderskaya (3) a n d by Presnyakov and Chervyakova ^ ^ w a s n o t e d that superplasticity in their alloy systems depended on the presence of a second phase. In the present investigation, this second phase would be zirconia in the tetragonal state. In studies reported by Kornilov f however, as reviewed by Underwood ^ , a resistance to creep was found in the appearance of a second phase. This contradiction may have been caused by differences in experimental conditions. Possibly a build-up of tetragonal phase in the zirconia deformation under constant temperature increase results in a cessation of creep when a certain proportion is reached. Because of the almost instantaneous nature of the phase transition, slowed in practice by temperature gradients in a given specimen shape, i t seems more probable that the phase transformation is completed at the moment when the deformation process ceases. The occurrence of the deflection plateau and the subsequent reduced slope in the deflection curve suggest that a different mechanism predominates in the creep deformation process in the tetragonal phase than in the monoclinic phase. Because of the very rapid rate of transformation from the monoclinic to tetragonal phase, i t was not feasible to determine the activation energy - 49 -f o r c r e e p d u r i n g . the. .phase t r a n s f o r m a t i o n by i s o t h e r m a l c r e e p a n a l y s i s . S e v e r a l w o r k e r s have r e p o r t e d u s i n g c o n s t a n t h e a t i n g r a t e p l o t s t o (32) d e t e r m i n e a c t i v a t i o n e n e r g i e s f o r t h e r m a l d e c o m p o s i t i o n r e a c t i o n s w ' (33) (34) a n c j f o r o x i d a t i o n o f m e t a l s ( 3 5 ) , An a t t e m p t was made t o use t h i s a p p r o a c h i n t h i s i n v e s t i g a t i o n by t a k i n g a p p r o p r i a t e s l o p e measurements on t h e c u r v e s o f F i g u r e s 12 t o 1 6 . The r e s u l t i n g v a l u e s o f a c t i v a t i o n e n e r g y f o r c r e e p d u r i n g the phase t r a n s f o r m a t i o n were much t o o l a r g e t o be m e a n i n g f u l . In a r e f e r e n c e t o t h e o c c u r r e n c e of . s u p e r p l a s t i c i t y i n a l l o y s as o b s e r v e d by P r e s n y a k o v and C h e r v y a k o v a ( ^ , i t was n o t e d t h a t e l o n g a t i o n became g r e a t e r i n a p p r o a c h i n g t h e t r a n s f o r m a t i o n t e m p e r a t u r e f r o m e i t h e r above o r b e l o w . In w o r k i n g w i t h pure z i r c o n i a , however , i t wou ld be d i f f i c u l t o r i m p o s s i b l e t o o b t a i n d a t a f r o m a programmed t e m p e r a t u r e d e c r e a s e , e q u i v a l e n t t o t h a t shown i n F i g u r e s 12 t o 1 6 , b e c a u s e o f the s t r u c t u r a l i n s t a b i l i t y r e s u l t i n g f r o m the volume e x p a n s i o n a s s o c i a t e d w i t h t h e t e t r a g o n a l t o m o n o c l i n i c phase c h a n g e . B CREEP 1 . T e m p e r a t u r e Dependence As d i s c u s s e d by G a r o f a l o ( 2 2 ) , c r e e p can be e x p r e s s e d as f o l l o w s : S= £ ± Z± ( V , T , S )<q (T , S) exp - A H . ( T , S ) RT (8) where t h e f u n c t i o n i n c l u d e s t h e f r e q u e n c y o f v i b r a t i o n \) , o f t h e f l o w u n i t , t h e e n t r o p y c h a n g e , the t e m p e r a t u r e T , and s t r u c t u r e te rm S ; t h e - 50 -stress function is which may include the temperature and structure terms; and^H^, which may change for different temperatures and structures, is the true activation energy for the i ^ mechanism controlling creep. The value of -^H^ cannot be determined directly without a knowledge of the form of the functions and ^± , but these cannot be determined without knowing the mechanisms controlling creep within certain limits of temperature, stress, and structure. The apparent activation energy, Q, however, can be determined experimentally by maintaining Z^ and <TT reasonably constant. The creep rate expression then becomes € = A exp (-Q/RT), as given earlier in equation (4), chapter I I I . This expression assumes that no significant change in structure occurs over the temperature range employed in determining Q. Temperature dependence of creep i n monoclinic zirconium dioxide is shown in the lower portion of the Arrhenius plot given in Figure 27. The data were obtained from creep tests on specimens having 91% of the theoretical density. These data represent the temperature dependence of creep at a constant stress condition of <-r~max = 314-0 psi. From the slope of the Arrhenius plot, the apparent activation energy, Q, in the monoclinic phase, was found to be 44 kcal/mole. This suggests a creep mechanism in the monoclinic phase dependent upon diffusion of oxygen, based on a diffusion activation energy for oxygen in calcia-stabilized zirconia of 31.2 - 4.3 kcal/mole, as reported by Simpson and Carter . The difference between these activation energies may be attributable to the energy of vacancy formation which would be required in the case of non-stabilized zirconia. - 5 1 -T h e u p p e r p o r t i o n o f F i g u r e 27 s h o w s t h e A r r h e n i u s p l o t f o r z i r c o n i u m d i o x i d e i n t h e t e t r a g o n a l p h a s e . T h e p l o t - i s b a s e d m a i n l y o n d a t a o b t a i n e d f r o m c o n t i n u a t i o n o f t e s t s c a r r i e d o u t u n d e r c o n d i t i o n s o f 91% o f t h e o r e t i c a l d e n s i t y a n d 0~max = 3 1 4 0 p s i . One s e t o f d a t a , h o w e v e r , w a s o b t a i n e d o n a s p e c i m e n h a v i n g 85% o f t h e o r e t i c a l d e n s i t y . T h e c l o s e a g r e e m e n t o f t h e e x p e r i m e n t a l p o i n t s f r o m t e s t s o f s p e c i m e n s a t t h e t w o d e n s i t i e s s u g g e s t s t h a t t h e r e i s n o d e n s i t y e f f e c t o n a p p a r e n t a c t i v a t i o n e n e r g y o v e r t h e d e n s i t y r a n g e c o v e r e d d n t h i s i n v e s t i g a t i o n . F r o m t h e s l o p e o f t h e A r r h e n i u s p l o t , t h e a p p a r e n t a c t i v a t i o n e n e r g y , Q , i n t h e t e t r a g o n a l p h a s e , w a s f o u n d t o b e 1 1 4 k c a l / m o l e . T h i s s u g g e s t s a c r e e p m e c h a n i s m i n t h e t e t r a g o n a l p h a s e d e p e n d e n t u p o n z i r c o n i u m i o n s e l f - d i f f u s i o n , b a s e d o n a d i f f u s i o n a c t i v a t i o n e n e r g y f o r z i r c o n i u m i n c a l c i a - s t a b i l i z e d z i r c o n i a o f 9 2 . 5 - 2 . 4 k c a l / m o l e , a s (37) r e p o r t e d b y R h o d e s a n d C a r t e r . A s i n t h e m o n o c l i n i c p h a s e , t h e h i g h e r a c t i v a t i o n e n e r g y w i t h n o n - s t a b i l i z e d z i r c o n i a m a y b e t h e r e s u l t o f v a c a n c y f o r m a t i o n . S t r e s s d e p e n d e n c e o f a c t i v a t i o n e n e r g y h a s n o t b e e n s t u d i e d e x t e n s i v e l y i n t h i s i n v e s t i g a t i o n , b u t some d a t a w e r e o b t a i n e d a t CF~max = 1 2 4 0 p s i . T h e s e d a t a r e s u l t e d i n a n a c t i v a t i o n e n e r g y o f 5 . 8 k c a l / m o l e a s c a l c u l a t e d f r o m t h e A r r h e n i u s p l o t s h o w n i n F i g u r e 2 8 . T h i s l o w e r a c t i v a t i o n e n e r g y i s c o n t r a r y t o t h e g e n e r a l s t r e s s - d e p e n d e n c e o f a c t i v a t i o n e n e r g y i n m e t a l l i c a n d n o n m e t a l l i c s y s t e m s w h e r e a c t i v a t i o n e n e r g y d e c r e a s e s w i t h i n c r e a s i n g s t r e s s . No c o n c l u s i o n s t h e r e f o r e c a n b e d r a w n f r o m t h e s e d a t a . 9 0 0 0 8 0 0 0 7 0 0 0 6 0 0 0 5 0 0 0 4 0 0 0 3 0 0 0 2 0 0 0 1 0 0 0 9 0 0 m 6 0 0 5 0 0 400 3 0 0 2 0 0 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 7 6 5 4 6 . 0 3 1 4 0 p s i D e n s i t y .% (Tm&x p s i X - s e c t . m m 2 X 8 5 o 9 1 <^ 9 1 3 1 4 0 3 1 4 0 3 1 4 0 2 . 0 x 3 . 1 1 . 9 x 3 . 2 1 . 9 x 2 . 6 C = A ' e x p ( - Q / R T ) O \ T e t r a g o n a l p h a s e (Q=103- k c a l / m o l e ) A o M o n o c l i n i c p h a s e (Q = 44 k c a l / m o l e ) 6 . 5 8 . 0 8 . 5 7 . 0 7 . 5 1 0 , 0 0 0 / T ( T - T e m p e r a t u r e , ° K ) F i g u r e 27 A r r h e n i u s p l o t s h o w i n g e f f e c t o f t e m p e r a t u r e o n s t r a i n -r a t e a t h i g h s t r e s s . . - 5 3 -F o r p u r p o s e s o f c o m p a r i s o n , t h e a c t i v a t i o n e n e r g i e s o b t a i n e d f o r c r e e p d e f o r m a t i o n o f z i r c o n i a i n t h i s i n v e s t i g a t i o n a r e l i s t e d i n T a b l e I V w i t h a c t i v a t i o n e n e r g i e s f o r o t h e r o x i d e s q u o t e d i n t h e d i s c u s s i o n o f t h e l i t e r a t u r e g i v e n i n c h a p t e r I I . " • T A B L E I V A C T I V A T I O N E N E R G I E S I N C R E E P D E F O R M A T I O N O F O X I D E S C o m p o u n d M o n o c l i n i c Z r O ^ T e t r a g o n a l Z r 0 2 U 0 2 . 0 0 U 0 2 . 0 0 U02.06 U 0 < 2 . 0 8 U02.16 U 0 2 . 1 6 M g O , 2>c M g O , 5.5-20./* F e l - x ° BeO A 1 2 0 3 Q s k c a l / m o l e 4 4 • 1 0 3 • 9 1 . 0 ± 8 . 0 > 9 5 . 0 7 2 . 0 5 5 . 7 ± 5 . 0 6 3 . 0 - 8 . 0 6 5 . 0 9 6 . 0 5 4 . 1 7 8 . 0 1 2 0 . 0 2 0 0 . 0 R e f e r e n c e F i g u r e 2 7 F i g u r e 2 7 ( 1 3 ) ( H ) ( 1 4 ) • ( 1 5 ) . ( 1 5 ) ( 1 4 ) ( 1 2 ) ( 1 2 ) ( 2 0 ) ( 1 6 ) • ( 1 6 ) O X 2 0 0 0 1 5 0 0 1 0 0 0 5 . 5 D e n s i t y 85% o~max 1 2 4 0 p s i T e t r a g o n a l p h a s e (Q = 5 . 8 k c a l / m o l e ) ^ 0 575 1 0 , 0 0 0 / T ( T - T e m p e r a t u r e , °K) F i g u r e 28 A r r h e n i u s p l o t s h o w i n g e f f e c t o f t e m p e r a t u r e o n s t r a i n r a t e a t l o w s t r e s s . - 54 -2. Stress Dependence (a) Monoclinic Phase In the monoclinic phase, the creep curves given in Figures 20 and 21 indicate l i t t l e or no stress effect on creep rate under the conditions studied. The conditions may be summarized as follows: 1071°C, 91% density, cTmax 1260-4590 psi. 1122°C, 89% density, CTmax 1570-3140 psi. (b) Tetragonal Phase Various stress-dependence relationships were investigated in an attempt to find an expression which f i t t e d the experimental data obtained at 1265°C. on specimens having 85 and 91% of theoretical density. The expression given in equation (3) € - A exp ($<T~ ) (3) was found to be in reasonable agreement with the experimental data, (21 ) as shown in Figure 29. As discussed by Garofalo K ', this relation has been satisfied at high stress for single crystals and polycrystals of annealed metals and alloys, and A and {3 have been found to depend on temperature. The difference in slope of the lines for 85 and 91% density in Figure 29 indicates that there is a dependence of creep rate in the tetragonal phase on the per cent theoretical density of the creep specimen over the density range covered in this investigation. The overall creep rate expression for zirconia in the tetragonal phase, taking into account both temperature and stress dependence, has the form: *^  = A" exp (-Q/RT) exp ($a-) (9) - 55 -3 . M i c r o s t r u e t u r e The r e s u l t s o f an e x a m i n a t i o n o f the m i c r o s t r u c t u r e o f a c r e e p s p e c i m e n a f t e r b e n d i n g a r e shown i n t h e p h o t o m i c r o g r a p h s o f F i g u r e 3 0 . The g r a i n s t r u c t u r e s were examined i n t h e e l e c t r o n m i c r o s c o p e , u s i n g t h e c a r b o n r e p l i c a t e c h n i q u e on the s p e c i m e n s u r f a c e as i t was a f t e r c o o l i n g f r o m t h e f i n a l c r e e p t e s t t e m p e r a t u r e , i . e . , w i t h no f u r t h e r p o l i s h i n g . As t h i s p a r t i c u l a r s p e c i m e n was t e s t e d i n c r e e p i n b o t h the m o n o c l i n i c and t e t r a g o n a l p h a s e s (see F i g u r e 1 7 ) , t h e o b s e r v e d g r a i n s e p a r a t i o n may have o c c u r r e d as a r e s u l t o f t h e vo lume e x p a n s i o n a s s o c i a t e d w i t h t h e t e t r a g o n a l t o m o n o c l i n i c phase c h a n g e . On the o t h e r h a n d , t h e g r a i n s e p a r a t i o n may v e r y w e l l have been c a u s e d by g r a i n b o u n d a r y s l i d i n g d u r i n g t h e c r e e p d e f o r m a t i o n p r o c e s s , as s u g g e s t e d by (13) A r m s t r o n g e t a l i n t h e i r work on u r a n i u m d i o x i d e O x O I d e n s i t y , 1 2 6 5 ° C I d e n s i t y , 1 2 6 5 ° C . 1000 2000 3000 5000 6000 4-000 cT~max, p s i F i g u r e 29 S t r e s s dependence o f c r e e p r a t e i n t e t r a g o n a l p h a s e . - 5 6 -10,000 x 10,000 x F i g u r e 30 Spec imen m i c r o s t r u c t u r e a f t e r b e n d i n g . (See F i g u r e 17). - 57 -VIII SUMMARY AND CONCLUSIONS 1. Experimental evidence has been obtained from creep deformation tes t s which indicates that s u p e r p l a s t i c i t y occurs i n pure zirconium dioxide at temperatures near the monoclinic to tetragonal phase transformation. T o t a l creep s t r a i n over the phase transformation region, as determined under a condition of constant temperature increase, was indicated to be a function of por o s i t y according to a r e l a t i o n s h i p of the form ^ ^ 0 ^ a ] _ = C exp (BP). 2. A c t i v a t i o n energies f o r creep deformation have been ca l c u l a t e d from creep-in-bendng data obtained under isothermal conditions. The values obtained were UU- kcal/mole i n the monoclinic phase and I 0 3 .kcal/mole i n the tetragonal phase. 3 . There was no evidence of stress dependence of creep i n the monoclinic phase over the range of .stresses investigated ( <3~max = 1260 to 4590 p s i ) . In the tetragonal phase a stress dependence was observed which f i t t e d the expression = A exp {^a~). J+. The o v e r a l l expression f o r creep i n the tetragonal phase was found to be of the form £ = A" exp (-Q/RT) exp {go*). 5. The evidence was not conclusive regarding creep mechanisms but the cal c u l a t e d a c t i v a t i o n energies suggest the p o s s i b i l i t y of a mechanism c o n t r o l l e d by oxygen d i f f u s i o n i n the monoclinic phase and of a mechanism c o n t r o l l e d by zirconium ion s e l f - d i f f u s i o n i n the tetragonal phase. SUGGESTIONS FOR FUTURE RESEARCH Investigations of the effect of stress and of rate of temperature increase would be of interest in developing a better understanding of the superplasticity phenomenon. Attention should be given to development of a reactive hot pressing procedure for zirconia which would give more consistent results in the preparation of specimen shapes for creep testing. Further creep data should be obtained in an investigation of probable creep mechanisms in both the monoclinic and tetragonal states. X APPENDICES - 59 -APPENDIX I PREPARATION OF DENSE ZIRCONIA PELLETS No. H P -P r e s s u r e on p e l l e t p s i No . o f c y c l e s Time p e r c y c l e m i n . A n n e a l i n g C o n d i t i o n s G e o m e t r i c a l d e n s i t y % t h e o r . * Temp. ° C . Time h r . 14 6000 3 16 700 4 89 16 6000 5 15 900 17 85 21 8000 3 14 - 20 700 4 91 34 8000 3 18 - 28 700 15 84 •' * Based on t h e o r e t i c a l o f 5 . 5 6 g/cc ( 3 4 ) . APPENDIX I I SUMMARY OF EXPERIMENTAL DATA d L b h T &~max k P r o g . G e o m e t r i c a l d e n s i t y , % t h e o r e t i c a l b a s e d on 5 .56 g / c c . L e n g t h o f s p e c i m e n between s u p p o r t p o i n t s , i n c h e s . W i d t h o f s p e c i m e n beam, mm. T h i c k n e s s o f s p e c i m e n beam, mm. S p e c i m e n t e s t t e m p e r a t u r e , ° C . E l a s t i c s t r e s s i n o u t e r m o s t f i b r e s o f s p e c i m e n beam, p s i . S t e a d y s t a t e c r e e p r a t e , 1DZ> x hr-1. - Programmed t e m p e r a t u r e i n c r e a s e , ° C / m i n . d L b h T • P r o g . 84 0 .75 3 . 0 2 . 0 1221 1250 300 84 0 . 8 0 3 . 3 2 . 0 P r o g . 1250 - 6 85 0 . 8 0 2 . 6 1 . 9 P r o g . 1240 - 5 1265 1240 1370 -1265 2050 2300 -1265 1240 890 -1265 3140 3640 -1265 1240 570 -1265 3670 4440 -85 0 . 8 0 3 . 1 2 . 0 P r o g . 1240 5 1255 1240 1500 -1285 1240 1740 -1318 1240 1680 -1348 1240 1740 -. 1257 2490 820 -1257 3140 1080 -1287 3140 2040 -1319 3140 4320 — 89 0 . 8 0 3 . 3 2 . 0 1122 1570 3 . 4 -1122 2350 2 . 9 -1122 3140 3 . 5 -P r o g . 3140 _ 5 91 0 . 8 0 3 . 2 1 . 7 1071 1260 NSD 1071 2030 NSD -1071 3140 3 -1071 3670 NSD -1071 4590 2 .5 -P r o g . 2030 - 5 d L b h T ^"max i P r o g . 91 0 . 8 0 3 . 2 1 . 7 1265 2030 1880 _ 1265 2590 1880 -1265 3140 2040 -1265 3690 2200 -1265 4240 2330 -1265 4800 2960 -1265 5350 3860 91 0 . 8 0 3 . 2 2 . 0 1153 3140 15 — 91 0 . 8 0 3 . 2 1 . 9 1026 3140 4 -1074 3140 8 -1123 3140 12 -1153 3140 21 -1181 3140 140 -1201 3140 280 -1221 3140 500 -1240 3140 770 -1249 3140 1020 _ 91 0 . 8 0 2 . 6 1 . 9 1027 3140 4 — 1124 3140 13 — 1170 3140 197 -1181 3140 410 -1188 3140 580 -1202 3140 840 -1219 3140 1000 -1238 3140 1470 — 1268 3140 2850 -1288 3140 4600 -1307 3140 7500 -APPENDIX III SOURCES OF ERRORS (a) Temperature: Temperature variation at the creep test specimen over the control cycle was - 2°C„ After several tests, the thermocouple adjacent to the specimens was found to read 6 and 7°C higher when checked against a new thermocouple at 973 and 1074°C. respectively„ (b) Maximum fibres stress; The calculation of C nax involved three linear measurements and a weight for an estimated overall error of not more than 10%. (c) Creep of apparatus materials: The agreement between di a l gauge readings and measurement of plastic deformation in creep specimens, as in Figure 24, p.44-, indicated that there was no significant effect on deflection data from creep in the reerystallized alumina support tube or loading rod. (d) Friction at support points: Tensile stress caused by f r i c t i o n at the fixed support points, when the specimens were subjected to bending, has been neglected„ It would be present in a l l tests, however, and hence would not greatly affect test comparisons, except possibly where there were large differences in the degree of deflection. APPENDIX IV Density and Porosity A l l material densities reported in this investigation are geometrical densities expressed' as per cent of theoretical density. They were calculated as follows: % theoretical density = W x 100 V x T.D. where W = dry weight in grams V = bulk volume in c c , as determined from micrometer measurements. T.D.= theoretical density of pure Zr02 particles, i.e., 5.56 g/cc. &8K Per cent porosity, as used in this investigation, was taken as 100 - % theoretical density (geometrical). - 63 -R E F E R E N C E S (1) U n d e r w o o d , E . E . , A R e v i e w o f S u p e r p l a s t i c i t y a n d R e l a t e d P h e n o m e n a , J . o f M e t a l s L£ . , 9 1 4 ( 1 9 6 2 ) . ( 2 ) C h a k l a d e r , A . C D . , D e f o r m a t i o n o f Q u a r t z C r y s t a l s a t t h e T r a n s f o r m a t i o n T e m p e r a t u r e , N a t u r e , 1 9 7 , 7 9 1 - 2 , ( 1 9 6 3 ) . ( 3 ) B o c h v a r , A . A . , S v i d e r s k a y a , Z . A . , I z r . A k a d . N a u k . S S S R . , O t d e l . T e k h . N a u k . , ( 9 ) , (1945).. (4) G u y , A . G . , P a r l i c k , J . E . , T r a n s . A I M E . , 2 2 1 , 8 0 2 , (1961). ( 5 ) P r e s n y a k o v , A . A . , C h e r v y a k o v a , V . V . , F i z . M e t . i M e t a l l o v e d e n i e , 8 , ( 1 ) , 1 1 4 ( 1 9 5 9 ) . - ' (6) P r e s n y a k o v , A . A . , C h e r v y a k o v a , V . V . , I z v . A k a d . N a u k . S S S R . , O t d e l . T e k h . N a u k , ( 3 ) , 9 2 , ( i 9 6 0 ) . ( 7 ) i b i d , (3), 1 2 0 ( 1 9 5 8 ) . . . . ( 8 ) A v e r y , D . H . , B a c k o f e n , W . A . , A S t r u c t u r a l B a s i s f o r S u p e r p l a s t i c i t y , A S M T r a n s . Q u a r t . / £8, 5 5 1 (1965). ( 9 ) P a c k e r , C M . , S h e r b y , C D . , A n I n t e r p r e t a t i o n o f t h e S u p e r p l a s t i c i t y P h e n o m e n o n i n T w o - P h a s e A l l o y s , A S M T r a n s . Q u a r t . , 6 0 , ( l ) 2 1 - 2 8 , ( 1 9 6 7 ) . ( 1 0 ) W e e r t m a n , J . , S t e a d y - S t a t e C r e e p t h r o u g h D i s l o c a t i o n C l i m b , J . A p p l . P h y s . , 2 8 , 3 6 2 , ( 1 9 5 7 ) . ( 1 1 ) D o r n , J . 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