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Deformation of polycrystalline cobalt 1972

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DEFORMATION OP POLYCRYSTALLINE COBALT by C. C. Sanderson B.A.Sc., University of B r i t i s h Columbia, 196 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of METALLURGY We accept t h i s thesis as conforming to the standard required from candidates for the degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF BRITISH COLUMBIA July, 1972 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 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 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 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 t h e 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 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 . D e p a r t m e n t o f Metallurgy 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 August 11, 1972 ABSTRACT The deformation of p o l y c r y s t a l l i n e cobalt has been investigated over the temperature range where the hep phase i s stable (0 to 0.39 T ). m The structure of cobalt following various annealing procedures has been detailed. Following heat treatment, cobalt i s a two phase aggregate of fee and hep phases, A maximum of 50-60% retained fee occurs i n small grained specimens (6 - 10 microns) decreasing to less than 15% retained fee for 60 micron material. The amount of retained fee phase also decreases with increasing purity. The variety of substructures a r i s i n g from the r u l t i v a r i a n t transformation are discussed. The y i e l d stress for cobalt exhibits d i f f e r i n g temperature dependence above and below 0.25 T . Below 0.25 T , the 0.2% y i e l d stress i s almost temperature independent, whereas above 0.25 T the y i e l d stress m decreases rapidly. The behaviour belov; 0.25 T i s related * m to the bulk transformation of retained fee phase while the decreasing stress l e v e l s observed above 0.2 5 T are explained m i n terms of decreasing P e i e r l s stress on the {1122} s l i p planes. The y i e l d stress increases rapidly as the grain size i s reduced. This e f f e c t i s compared to similar behaviour in other hep metals that exhibit a limited number of s l i p systems. i i i The d u c t i l i t y of cobalt i s related to the retained fee phase by equations of the form e = A (10) ° , A larger f r a c t i o n of retained fee phase gives r i s e to increased d u c t i l i t y . The elongation to fracture decreases as t e s t temperature increases, r e f l e c t i n g obeyance of Considere's C r i t e r i o n . The observed work hardening rates are high, as are the measured values for flow stress. The values are compared to data obtained for other metals that transform m a r t e n s i t i c a l l y while undergoing deformation. Metallographic evidence i s presented to substantiate the occurence of non-basal s l i p i n cobalt above 0.25 T . m Twins having high and low shear values occur at a l l temperatures where the hep phase i s stable. The intense surface shear r e s u l t i n g from transformation and continuing; d i s l o c a t i o n production on variously oriented basal planes i s discussed. i v TABLE OF CONTENTS PAGE 1. INTRODUCTION , 1 1.1 Cobalt and the Common Hexagonal- Close-Packed Metals 1 1.2 Cobalt Single Crystals 8 1.3 The A l l o t r o p i c Transformation and Structure of Cobalt 12 1.3.1 History of the Transformation..... 12 1.3.2 Mechanisms for the Martensitic Transformation 14 1.3.3 Multivariant Transformation 17 1.3.4 Retained FCC Phase 19 1.3.5 Thermodynamics of the Transformation * 20 1.3.6 The Hysteresis of the Transformation . 21 1.4 Scope of Present Work... 21 2. EXPERIMENTAL PROCEDURE , 23 2.1 Materials 23 2.2 Preparation of Tensile Specimens 25 2.2.1 Machining 2 5 2.2.2 Annealing Procedures.... 27 2.2.3 X-Ray Analysis 27 2.3 Tensile and Hardness Tests 32 2 . 4 Metallography . 34 2.4.1 Optical Metallography 34 2 . 4 . 2 Electron Microscopy Repligas. 36 EXPERIMENTAL PROGRAM AND RESULTS 37 3 . 1 The Structure of P o l y c r y s t a l l i n e Cobalt.. 37 3 . 1 . 1 As Received Material 37 3 . 1 . 1 . 1 Preferred Orientation.... 38 3 . 1 . 1 . 2 Stacking Fault Energy and Fault Analysis....... 39 3 . 1 . 2 Recovery, R e c r y s t a l l i z a t i o n and Grain Growth 40 3 . 1 . 2 . 1 Recovery... 43 3 . 1 . 2 . 2 R e c r y s t a l l i z a t i o n and Grain Growth. . 43 3 . 1 . 3 Completeness of Transformation.... 47 3 . 1 . 4 Discussion and Summary 55 3.2 Tensile Behaviour of Cobalt Polycrystals 67 3 . 2 . 1 Tensile Results 67 3 . 2 . 1 . 1 True Stress - True Strain Curves 67 3 . 2 . 1 . 2 Y i e l d Stress and Ultimate Tensile Stress 79 3 . 2 . 1 . 3 D u c t i l i t y and Fracture... 107 3 . 2 . 1 . 4 Work Hardening Behaviour 113 3 . 2 . 1 . 5 Discussion and Summary... 119 3 . 2 . 2 Deformation and the A l l o t r o p i c Transformation . 130 3 . 2 . 2 . 1 Purity 13 6 3 . 2 . 2 . 2 Grain Size..., 139 3 . 2 . 2 . 3 Temperature 140 VI. PAGE 3 . 2 . 2 . 4 Von Mises C r i t e r i o n 146 3 . 2 . 2 . 5 M e t a l l o g r a p h i c O b s e r v a t i o n , 153 3 . 2 . 2 . 5 . 1 P u r i t y and G r a i n S i z e . . . . 155 3 . 2 . 2 . 5 . 2 O p t i c a l Metallography. 156 3 . 2 . 2 . 5 . 3 R e p l i c a O b s e r v a t i o n s . . 162 3 . 2 . 2 . 5 . 4 Summary 168 3 . 2 . 2 . 6 D i s c u s s i o n and Summary , . 171 3 . 2 . 2 . 6 . 1 The Y i e l d S t r e s s 171 3 . 2 . 2 . 6 . 2 Flow S t r e s s . . . 176 3 . 2 . 2 . 6 . 3 E l o n g a t i o n i to F a i l u r e . . . . 176 3 . 2 . 2 . 6 . 4 Work Hardening Behaviour 178 4. CONCLUSIONS 180 5. SUGGESTIONS FOR FUTURE WORK 182 6. APPENDICES 183 6 . 1 X-Ray A n a l y s i s 183 6.2 Measurment of T e n s i l e Parameters by an I n t e r s e c t Method 187 7. REFERENCES 193 v i i TABLES PAGE TABLE I Data Sheet for the Hexagonal- Close-Packed Metals .... 2,3 TAELE II C r i t i c a l l y Resolved Shear Stress for Various Metals 11 TABLE III Martensitic Transformation .Studies.... 13 TABLE IV Spectrographs Analysis of Cobalt Matrix 24 TABLE V Summary of Retained FCC Data 50 TABLE VI Martensite- Transformations i n Hon-Ferrous Materials 78 TABLE VII Polyc r y s t a l Cobalt 0.2% Y i e l d Stress Data 85 TABLE VIII Temperature Dependence of Flow Stress (Aa/G for 100 PC temperature change)... 94 TABLE IX Ultimate Strength Data for Cobalt Polycrystals 95 TABLE X Parameters From an Equation of the Form a . . , = cr. + KD ' 100 y i e l d l TABLE XI Summary of True Strain Data for Polycrystal Cobalt 10 8 TABLE XII The Two Stage Behaviour of Flow Stress and Work Hardening Rate as a Function of Temperature... 120 TABLE XIII Behaviour of the Strain Induced Transformation i n Cobalt Expressed f | c c an Equation of the Form: e = A (10) '* " 137 TABLE XIV Summary of Experimental Results 172 TABLE XV Typical Data From a Step-Pull Tensile Test. 190 v i i i FIGURES PAGE FIG. 1 Tensile specimens and important dimensions 26 FIG. 2 Typical record of vacuum annealing treatment 26 FIG. 3 Raw x-ray data for 99.7% cobalt 30 FIG. 4 Diamond Pyramid Hardness data for cobalt 42 FIG. 5 Variation i n grain size for 1 hour anneals at indicated temperatures 45 FIG. 6 Annealing spectrum i n 99.9% cobalt 340X.... 48 FIG. 7 99.7% cobalt, annealed at 600°C (a) and 80'0°C (b) 1 hr 49 FIG. 8 99.9% cobalt, annealed at 900°C for 1 hr. 39 y 49 FIG. 9 99.998% cobalt, annealed at 600°C (a) and 800°C (b) 1 hr . 49 FIG. 10(a) % retained fee vs grain size 51 (b) % retained fee vs l / / g r a i n size 51 FIG. 11 99.998% Cobalt under polarized l i g h t 900X 54 FIG. 12 Annealing Parameters • 56 FIG. 13 Volume changes during the martensitic transformation i n cobalt .. 58 FIG. 14 Etching of grain boundaries and martensite plates. 99.7% cobalt. 920X.. 60 FIG. 15(a) 99.9% cobalt. 4000X 60 (b) 99.9% cobalt. 10,OOOX 60 (c) 99.9% cobalt. 10,000X 60 FIG. 16 99.9% cobalt, 6.5 micron grain s i z e 4000X 62 i x PAGE FIG. 17 Shear markings f o l l o w i n g heat treatment. 6500X 62 FIG. 18 Annealing twin boundaries i n 99.9% c o b a l t . 5000X 62 FIG. 19 Banded s t r u c t u r e a r i s i n g from coplaner m u l t i v a r i a n c e i n c o b a l t . (a) 4,000X 64 (b) 10,O00X 64 (c) 10,000X 64 FIG. 20 99.998% c o b a l t , 47 micron crrain s i z e 2000X 64 FIG. 21 True s t r e s s - t r u e s t r a i n curves a t s e l e c t e d temperatures, 99.998% c o b a l t . . 68 FIG. 22 I n i t i a l p o r t i o n of t r u e s t r e s s - t r u e s t r a i n curves, 99.9% c o b a l t , 6.5 micron g r a i n s i z e 69 FIG. 23 True s t r e s s - s t r a i n curves a t s e l e c t e d temperatures, 99.7% c o b a l t 70 FIG. 24 True s t r e s s - s t r a i n curves a t 20°C. c o b a l t 70 FIG. 25(a) Nominal s t r e s s - s t r a i n curves f o r Co, Mg, Zn, and T i 71 (b) Nominal s t r e s s - s t r a i n curves f o r Co, Ag, Cu, and A l 74 FIG. 26 True s t r e s s - t r u e s t r a i n curves f o r m a t e r i a l s undergoing s t r a i n induced m a r t e n s i t i c t r a n s f o r m a t i o n 7 6 FIG. 27 Y i e l d s t r e s s versus t e s t temperature f o r two p u r i t y grades of c o b a l t 80 FIG. 28 Y i e l d s t r e s s data f o r p o l y c r y s t a l c o b a l t 82 FIG. 29 Comparison of y i e l d s t r e s s data o b t a i n e d by i n d i v i d u a l t e s t s and i n t e r u p t e d s i n g l e specimen t e s t i n g . 99.9% c o b a l t , G.5 micron g r a i n s i z e 83 FIG. 30 Y i e l d s t r e s s versus t e s t temperature f o r c o b a l t and magnesium 87 PAGF Y i e l d s t r e s s versus temperature f o r c o b a l t s i n g l e c r y s t a l s and p o l y c r y s t a l s 89 Y i e l d s t r e s s and u l t i m a t e s t r e n g t h data f o r 99.9% c o b a l t , 6 .5 micron g r a i n s i z e 91 T y p i c a l data f o r determing the temperature dependence of flow s t r e s s . 99.7% c o b a l t , 7.0 micron g r a i n s i z e 92 Y i e l d s t r e s s v ersus r e c i p r o c a l square r o o t of g r a i n s i z e 98 Y i e l d s t r e s s versus r e c i p r o c a l square r o o t of g r a i n s i z e 102 F r a c t u r e s u r f a c e , 99.9% c o b a l t t e s t e d a t 20°C. 6 .5 micron g r a i n s i z e . 7500X. . 112 F r a c t u r e s u r f a c e , 99.998% c o b a l t t e s t e d a t 20°C. 47 micron q r a i n s i z e . 5000X . . . . 112 V a r i a t i o n of work hardening r a t e w i t h s t r a i n f o r 99.9% c o b a l t 114 The .work hardening behaviour of c o b a l t as a f u n c t i o n of temperature 117 V a r i a t i o n i n work hardening behaviour w i t h i n c r e a s i n g s t r a i n . 99.9% c o b a l t , 6 .5 micron g r a i n s i z e 118 Temperature change t e s t s , 99.9% c o b a l t . 6 .5 micron g r a i n s i z e 122 Temperature change t e s t , 99.9% c o b a l t . 6 .5 micron g r a i n s i z e 123 T e n s i l e s t r a i n induced t r a n s f o r m a t i o n of c o b a l t a t room temperature 131 Room temperature t e n s i l e s t r a i n induced t r a n s f o r m a t i o n f o r c o b a l t of v a r i o u s g r a i n s i z e s . . 132 Room temperature t e n s i l e s t r a i n induced t r a n s f o r m a t i o n f o r c o b a l t of v a r i o u s g r a i n s i z e s (semilog) 133 T e n s i l e s t r a i n induced t r a n s f o r m a t i o n of c o b a l t a t room temperature ( s e m i l o g ) . . . 134 x i PAGE F I G . 47 T e n s i l e s t r a i n induced t r ans fo rma t ion fo r c o b a l t a t v a r i o u s temperatures , (semilog) 135 FIG. 48 X - r a y data fo r 99.9% c o b a l t , s t ep - p u l l e d a t 20°C and 250°C, 6.5 micron g r a i n s i z e . . . , , 142 F I G . 49 X - r a y da ta fo r 99.7% c o b a l t , s t ep - p u l l e d a t 20°C and 250°C, 7 micron g r a i n s i z e . . . , 143 FIG. 50 Volume % s t r a i n induced mar tens i t e present i n 99,9% c o b a l t as a f u n c t i o n of s t r a i n . . . . , 145 FIG. 51 M a r t e n s i t e shear markings in t roduced bv a sur face s c r a t c h i n 99.9% c o b a l t 1900X , 153 FIG. 52 Deformation of 99.998% c o b a l t , 850X 157 F I G . 53 Deformation markings i n 99.998% c o b a l t a t f a i l u r e . 1000X 158 F I G . 54 G r a i n shape change i n 99.9% c o b a l t 1000X 158 F I G . 55 Twinning i n c o b a l t a t - 1 9 6 ° C . 850X 160 F I G . 56 Twinning i n c o b a l t a t 350°C. 850X 160 F I G . 57 Deformation of 99.7% c o b a l t a t 250°C. 3000X 163 FIG. 58 S t r e s s r e l i e f a t a boundary between two reg ions where shear has taken p lace on d i f f e r e n t systems. 6500X 164 FIG. 59 T y p i c a l sur face shear markings i n c o b a l t -196°C t e s t . 6500X \ 164 F I G . 60 Twinning i n c o b a l t a t - 1 9 6 ° C . 3 7 0 0 X . . . . 166 FIG. 61 Twinning i n c o b a l t a t 250°C. 370OX 166 x i i PAGE FIG. 62 Non-basal s l i p i n p o l y c r y s t a l cobalt tested at 250°C. 7500X 167 FIG. 63 Shear markings i n 99.9% cobalt tested at 20°C. 7500X 169 FIG. 64 Shear Markings i n 99.9% cobalt tested at 250°C. 7500X 169 FIG. 65 Mechanisms c o n t r o l l i n g y i e l d i n pol y c r y s t a l cobalt 175 FIG. 66 Step-pull t e n s i l e t e s t . 99.9% cobalt, 6.5 micron grain size 188 FIG. 67 Determination of the int e r s e c t y i e l d strength from step-pull data 189 ACKNOWLEDGEMENTS The author acknowledges the advice and assistance given '. his research d i r e c t o r , Dr. N. R. Risebrough. Thanks are also extended to other members of the faculty and the graduate students for hel p f u l discussions. F i n a n c i a l assistance provided by the National Research Council i s g r a t e f u l l y acknowledged. 1. I n t r o d u c t i o n C o b a l t i s a high m e l t i n g p o i n t t r a n s i t i o n metal l y i n g between n i c k e l and i r o n i n the p e r i o d i c t a b l e 1 1 2 . Upon c o o l i n g , c o b a l t undergoes an a l l o t r o p i c phase t r a n s f o r m a t i o n from f a c e - c e n t r e d - c u b i c (fee) to hexagonal-close-packed (hep) at approximately 417°C 3. T h i s m a r t e n s i t i c t r a n s f o r m a t i o n proceeds to completion o n l y under very s p e c i a l circumstances, such as a s i n g l e i n t e r f a c e t r a n s f o r m a t i o n i n a s i n g l e c r y s t a l 4 ' 5 . C o b a l t i s ferromagnetic and has a C u r i e P o i n t of 1 1 1 5 ° C 2 ' 6 . The incomplete m a r t e n s i t i c t r a n s f o r m a t i o n from one close-packed phase to another y i e l d s many i n t e r e s t i n g p o s s i b i l i t i e s f o r i n v e s t i g a t i o n . In the p r e s e n t work, an attempt has been made to o b t a i n a d e t a i l e d understanding of the s t r u c t u r e and t e n s i l e p r o p e r t i e s of c o b a l t p o l y c r y s t a l s at temperatures where the hexagonal-close-packed phase i s s t a b l e . A summary of p e r t i n e n t i n f o r m a t i o n a v a i l a b l e i n the l i t e r a t u r e i s presented i n t h i s i n t r o d u c t i o n . 1.1 C o b a l t and the Common Hexagonal-Close-Packed Metals C o b a l t i s unique among the common hep metals i n many . r e s p e c t s (Table I ) . The observed s l i p systems and twinning modes f o r the common hexagonal metals as w e l l as other r e l e v a n t i n f o r m a t i o n are shown i n t h i s t a b l e . The data are drawn from many sources; the most important being P a r t r i d g e 7 , Chalmers 1, the A.S.M. Handbook 8 and R e e d - H i l l 9 . The hep metals may be d i v i d e d i n t o two c a t e g o r i e s . Zirconium, t i t a n i u m and b e r y l l i u m are high m e l t i n g p o i n t TABLE I Data Sheet f o r the Common Hexagonal-Close-Packed Metals Metal Cd Zn Mg Co Zr T i Be c/a R a t i o 1.886 1.856 1.623 1.623 1.592 1.587 1.568 M e l t i n g P o i n t °C 321 420 650 14 9 5 1852 1668 1277 A l l o t r o p i c T r ansformation and Temp. °C - - - fee hcp4- 417 bcc hcp4- 862 bcc hep 4- 882 bcc hcp + 1260 S l i p Modes Bas a l {0001} <1120> * * * * 1 2 i 1 3 Obs. Obs. * Prism {1010} <1120> — - Obs. - * * Obs. Pvramidal {1011} <1120> Obs. - Obs. - 2nd 2nd Obs. Corrugated {1122} <1123 > 2nd 2nd Obs. Obs. 1 h Obs. - Obs. TABLE I (Con't) Twinning Modes {1012} {10ll} {101n} {1121} {1122} {112n} Obs, Obs, Obs. Obs. {1013} Obs. 4 Obs. * Obs. 1 1 I if Obs, Obs, Obs, Obs, Obs. Obs. {1124} {1123} Obs. Obs. { H 2 4 } 5 Estimated S t a c k i n g F a u l t 2 Energy ergs/cm 150 300 300 20 1 9 ~ 2 1 300 180 * -- Predominant s l i p mode 2nd -- Secondary s l i p mode Obs. — Observed metals w i t h c / a r a t i o s l e s s than i d e a l w h i l e z i n c and cadmium, v/ i th h igh c / a r a t i o s , and magnesium w i t h an almost i d e a l c / a r a t i o are low m e l t i n g p o i n t me ta l s . Coba l t s t r a d d l e s both groups w i t h a h igh m e l t i n g p o i n t and a c / a r a t i o s i m i l a r to magnesium. Attempts have been made to e x p l a i n the observed d e f o r - mation modes of the hep metals based on geometric c o n s i d e r a t i o n s of t h e i r c / a r a t i o s 7 ' 1 0 . Th i s approach appears to e x p l a i n the predominant deformat ion mode i n most cases but does not account fo r the i n d i v i d u a l d i v e r s i t y of secondary deformat ion processes . For c / a r a t i o s equal to or g rea te r than i d e a l (/8/3) the predominant deformat ion process f o r e c a s t i s s l i p on the ba sa l plane i n a c lose -packed d i r e c t i o n . Indeed, ba sa l s l i p i s the most important deformat ion mode i n the metals z i n c , cadmium, magnesium and c o b a l t . Over a range of c / a r a t i o s l e s s than i d e a l , f i r s t order pr i sm s l i p becomes the p r e f e r r ed mode. Z i r con ium, and t i t an i t im w i t h c / a r a t i o s of 1.592 and 1.587 r e s p e c t i v e l y , s l i p predominat ly on the {1010} <1120> pr i sm system. B e r y l l i u m w i t h c / a equal to 1.568 deforms main ly v i a {0001} <112~0> basa l s l i p which i s not the expected mode. Al though the pr imary deformat ion mode appears to be a s t rong f u n c t i o n of the c / a r a t i o , the secondary deformat ion processes are more complex and are i n f l uenced s t r o n g l y by v a r i a b l e s such as temperature, s t a c k i n g f a u l t energy and p u r i t y . Although prism s l i p i s the primary s l i p mode i n z i r c o n i u m and t i t a n i u m , both the pyramidal and b a s a l s l i p systems have been o b s e r v e d 7 . B a s a l s l i p predominates i n h i g h p u r i t y b e r y l l i u m y e t prism s l i p and pyramidal s l i p a l s o occur. In c o b a l t the o n l y s l i p mode commonly observed i s b a s a l s l i p n , 5 , 1 1 i i 2 , i 3 _ N o n b a s a l s l i p {H22> <1123), has been observed by S e e g e r 1 4 but t h i s o b s e r v a t i o n has not been d u p l i c a t e d elsewhere. H o l t 4 was unable to i n i t i a t e non b a s a l s l i p although s i n g l e c r y s t a l specimens were s t r e s s e d i n o r i e n t a t i o n s s p e c i f i c a l l y f o r t h i s purpose. Kink boundary formation, e s p e c i a l l y a t h i g h temperatures, i s an important deformation mode. In zirconium, R e e d - H i l l 9 p o s t u l a t e s t h a t kink boundaries ease c o n s t r a i n t and thus reduce the need f o r twinning a t high temperature. Kink boundary formation has been observed i n z i n c 1 6 , magnesium 7, c o b a l t 2 ' 1 , z i r c o n i u m 9 , and t i t a n i u m 1 5 . The bend plane i s o f t e n a simple { 1 1 2 0 } t i l t boundary made up of d i s l o c a t i o n s having the same Burgers v e c t o r . Other more complex kink boundaries, or accomodation k i n k s , are o f t e n observed near twins. A l l the hexagonal metals twin i n the {1012}plane. T h i s mode of twinning i n v o l v e s the lowest shear and r e q u i r e s o n l y simple s h u f f l e s i n the plane of shear. The observed shape of deformation twins i s i n f l u e n c e d by the twinning s h e a r 7 ' 9 . When the twinning shear i s small as f o r {1012} the twin becomes l e n t i c u l a r as i t grows because the twin i n t e r f a c e can d e v i a t e c o n s i d e r a b l y from the twinning plane without a l a r g e i n c r e a s e i n twin i n t e r f a c e energy'. When the shear 6 i s large the twins formed are narrow and have e s s e n t i a l l y p a r a l l e l boundaries. In zirconium and titanium both {1121} and {1122} twins have been observed. Twins of t h i s form have a much higher shear value than those i n the {1012} plane. For titanium, the r a t i o of shear values are 1.7/2.3/6.4 for {10l2}/ {1122}/ (1121) type twins respectively. Thus the {1122} and {ll"2l} twins are observed as narrow and straight while {1012} twins are commonly very wide and l e n t i c u l a r i n shape. Magnesium with a c/a r a t i o similar to cobalt, twins on the {1011} and {1013} pla nes as well as on the {1012} plane. Twinning has also been observed on higher order planes of the form {101n}. The complexity a r i s i n g i n {1013} and higher order twinning has led investigators to propose that a double- twinning mechanism involving retwinning of a primary twin i s required to form these twins. {1012} twins have been observed i n cobalt by a number of investigators 4 ' 5 1 ,l 2 . Davis 1 1 observed { 1121} zig-zag twinning i n cobalt, similar to those observed i n titanium by Rosi 1 5 . Seeger observed both { 1122} and { 1124} twinning i n single c r y s t a l cobalt k ; these twin planes have also been observed i n titanium. Holt1* i n a comprehensive single c r y s t a l study observed { 1011} twins which have also been observed i n magnesium. The preceding should not be construed as a complete compilation of the s l i p and twinning modes noted i n the l i t e r a t u r e for the hexagonal metals. The data has been presented to allow a comparison to be made between cobalt and the other common hexagonal metals with respect to t h e i r 7 normal deformation p r o c e s s e s . The important o b s e r v a t i o n i s th a t no prominent secondary s l i p system has been observed f o r c o b a l t but a m u l t i p l i c i t y of twinning modes e x i s t . For the other common hexagonal metals s e v e r a l s l i p systems are observed. The l a c k of obvious secondary s l i p systems i n c o b a l t may a r i s e from two sources. F i r s t , c o b a l t i s the onl y common hexagonal metal t h a t has a low s t a c k i n g f a u l t energy. As noted i n Table I, the s t a c k i n g f a u l t energy on the b a s a l plane i n c o b a l t i s a t l e a s t a f a c t o r of f i v e l e s s than f o r any of the other common hexagonal metals. The s t a c k i n g f a u l t energy has been measured by s e v e r a l techniques and although there are small d i f f e r e n c e s i n the v a l u e s o b t a i n e d , 2 i t i s unanimous t h a t the v a l u e i s below 30 erg/cm 19 .20 .21 ^ 2 The v a l u e u s u a l l y quoted i s 20 ergs/cm compared to 150 to 2 300 ergs/cm f o r the other common hexagonal metals. The low s t a c k i n g f a u l t energy i n c o b a l t ensures t h a t the m a j o r i t y of d i s l o c a t i o n s i n the b a s a l plane are e x t e n d e d 2 2 ' 2 3 1 2 4 . For d i s l o c a t i o n s to move from the b a s a l plane to other planes by a c r o s s - s l i p process the p a r t i a l d i s l o c a t i o n s must c o n s t r i c t . T h e r e f o r e , the p r o b a b i l i t y of many d i s l o c a t i o n s a r r i v i n g on secondary planes to p r o v i d e s l i p on these planes i s s m a l l . To o b t a i n a p p r e c i a b l e d i s l o c a t i o n s on the secondary planes, they must e i t h e r n u c l e a t e or be grown i n , on these p l a n e s . T h i s i n t r o d u c e s the second problem r e g a r d i n g secondary s l i p i n c o b a l t . Upon c o o l i n g from h i g h temperature, fee c o b a l t transforms m a r t e n s i t i c a l l y to hep c o b a l t . One of the close-packed {111} planes i n the f a c e - c e n t r e d phase becomes the b a s a l plane i n the hexagonal l a t t i c e . T h i s i s the o n l y plane t h a t remains r e l a t i v e l y unchanged d u r i n g t r a n s f o r m a t i o n . The disappearance or a b s o r p t i o n of d i s l o c a t i o n s on other - C l l l > planes or any other plane i n the f a c e - c e n t r e d - c u b i c phase i s not understood a t p r e s e n t . I t has been observed by s e v e r a l authors, t h a t the d i s l o c a t i o n s observed i n c o b a l t are p r i m a r i l y b a s a l 2 2 ' 2 3 ' 2 1 * . S u f f i c i e n t non-basal d i s - l o c a t i o n s to y i e l d f i n i t e amounts of deformation by s l i p have not been observed i n t h i n f i l m s . 1.2 C o b a l t S i n g l e C r y s t a l s S e v e r a l i n v e s t i g a t i o n s of c o b a l t and c o b a l t - n i c k e l a l l o y s i n g l e c r y s t a l s are a v a i l a b l e i n the l i t e r a t u r e . Researchers such as D a v i s 1 1 ' 1 2 ' 1 3 , Holt'*, and a group of workers a t the Max Planck I n s t i t u t e have l i m i t e d t h e i r i n v e s t i g a t i o n s predominantly to the deformation behaviour of c o b a l t s i n g l e c r y s t a l s 5' 1*' 2 4 ' 2 5 ' 2 6 . C h r i s t i a n 2 7 , A l s t e t t e r and co-workers 2 8 ' 2 9 ' 3 0 1 3 1 , have t e s t e d c r y s t a l s to d i s c o v e r the d e t a i l e d mechanism of the t r a n s f o r m a t i o n . The work by the l a t t e r group w i l l be d i s c u s s e d i n the next s e c t i o n where a complete review of the t r a n s f o r m a t i o n and r e l a t e d t o p i c s w i l l be o u t l i n e d . Hexagonal c o b a l t s i n g l e c r y s t a l s e x h i b i t t e n s i l e curves s i m i l a r to other hexagonal metals. In c o b a l t c r y s t a l s , Stage A and Stage B are observed but a t h i r d stage i s not. The c r i t i c a l ! ' r e s o l v e d shear s t r e s s of c o b a l t v a r i e s s i g n i f i c a n t l y with p u r i t y 1 2 ' 1 ' 2 k' 1 5 f r i s i n g from 1400 p s i f o r 99.998% p u r i t y 2 4 to 2800 p s i f o r 99.1% m a t e r i a l 1 \ Thi s parameter i s a l s o temperature dependent r i s i n g from 1400 p s i a t room temperature to 2400 p s i a t -196°C S e e g e r 1 4 p o s t u l a t e d tha t the h igh shear s t r e s s was due to e i t h e r r e t a i n e d cub ic phase or a very h igh b a s a l d i s l o c a t i o n d e n s i t y . Hep c o b a l t e x h i b i t s a long i n i t i a l r e g i o n (Stage A) which may extend to s e v e r a l hundred percent s t r a i n . The work hardening r a t e i n Stage A (0 ) i s temperature dependent, r i s i n g from 2000 p s i to 2500 p s i as the temperature i s reduced from room temperature to -196°C 1 2 1 1 k ' 5 . 0 a l s o inc reases w i t h i n c r e a s i n g i m p u r i t y con ten t . Dur ing t e s t s of hexagonal c o b a l t c r y s t a l s , the s l i p l i n e spacing decreases w i t h i n c r e a s i n g deformat ion up to 20% s t r a i n . Throughout the remainder of Stage A , the step he igh t inc reases w h i l e s l i p l i n e spacing remains constant I i* i 2 4 i 2 5 _ T h i e r i n g e r determined tha t the d i s l o c a t i o n d e n s i t y i n 99.998% c o b a l t l i e s between 0.4 and 1.2 X 1 0 9 2 4 per cm w i t h a s t a c k i n g f a u l t d e n s i t y of 2 to 6 X 10 per cm. He observed tha t the d i s l o c a t i o n d e n s i t y inc reases approximate l i n e a r l y w i t h s t r e s s and s t r a i n i n Stage A . B o s e r 5 and T h i e r i n g e r 2 4 1 2 5 both repor ted tha t no inc rease i n non-basal d i s l o c a t i o n s occured du r ing deformat ion . The number of a c t i v e s l i p l i n e s and the work hardening r a t e inc rease upon en t e r ing Stage B. T h i e r i n g e r 2 , 4 1 2 5 found tha t the s t r e s s at which Stage B begins i s independent of p u r i t y and occurs a t 2300 p s i at room temperature. The onset of Stage B i n hexagonal c o b a l t has been exp l a ined by: the ope ra t i on of a second s l i p s y s t e m 1 2 , a s t rong inc rease i n the frequency of t w i n n i n g 2 1 * ' 2 5 , the agglomerat ion of i m p u r i t i e s 5 , and the p roduc t i on of excess vacancies '* . The c r i t i c a l l y r e s o l v e d shear s t r e s s and work hardening r a t e s are much h igher fo r fee c o b a l t c r y s t a l s than fo r hep c r y s t a l s ' * . Stage I of the f ace -cen t e r ed -cub ic t e n s i l e curve i s not de tec ted due to the h igh t e s t temperatures r e q u i r e d to a t t a i n the cub ic phase w h i l e Stage I I and Stage I I I p o r t i o n of the curve are observed. The shape of the t e n s i l e curves are s i m i l a r to those fo r other fee me ta l s . H o l t t e s t ed specimens w h i l e c y c l i n g through the t r a n s - format ion temperature range. The temperature was changed i n steps i n some cases and c o n t i n u o u s l y i n o t h e r s . These t e s t s showed tha t the f low s t r e s s i s not a s t rong f u n c t i o n of the c r y s t a l s t r u c t u r e but depends on ly upon the e x i s t i n g defec t s t r u c t u r e . The work hardening r a t e , on the other hand, i s s t r o n g l y dependent upon the c r y s t a l s t r u c t u r e , being much h igher i n the fee phase. A comparison of c r i t i c a l l y r e s o l v e d shear s t r e s s f o r a number of c r y s t a l s i s presented i n Table I I . The s t r e s s fo r c o b a l t i s c o n s i d e r a b l y h igher than fo r metals w i t h s i m i l a r s t r u c t u r e . The hep m o d i f i c a t i o n has a c / a r a t i o s i m i l a r to magnesium and deforms predominant ly on the b a s a l plane as does magnesium, ye t i t has a c r i t i c a l l y r e s o l v e d shear s t r e s s more r e p r e s e n t a t i v e of the metals t i t a n i u m and z i r con ium which deform on the pr i sm system. In f a c t , the c r i t i c a l l y r e so lved shear s t r e s s fo r c o b a l t on the ba sa l plane i s l a r g e r than the va lue r e q u i r e d to y i e l d pr i sm s l i p TABLE I I C r i t i c a l l y Resolved Shear S t r e s s f o r V a r i o u s Meta l s METAL SLIP SYSTEM C . R . S . S . (psi) TEST T / M . P t . PURITY Cd hep Basa l 82 0.51 99.996 Zn hep Basa l 26 0.43 99.999 Mg hep Basa l 63 0.33 99.996 Co hep Basa l 1400 0.17 99.998 Zr hep Pr i sm 900 0.14 - T i hep Pr i sm Basa l 1980 16000 0.16 0.16 99.99 Be hep Basa l 5700 0.19 - Co fee <111><110> 2680 0.40 99.998 A l fee (111><110> 14 8 0. 32 99. 93 Ag fee {111><110> 54 0. 24 99.99 Au fee <111><110> 132 0.23 - Cu fee <111><110> 92 0.22 99.999 N i fee <111><110> 820 0.17 - Fe bcc {110} <110> {112} {123} 4000 0.17 99.6 Mo bcc 7000 0.10 - Data drawn from: H o l t 4 A h k t a r 3 2 D e i t e r 3 3 , 3 4 R e e d - H i l l 3 5 i n z irconium. T h i s data i m p l i e s t h a t the low s t a c k i n g f a u l t energy and the m a r t e n s i t i c t r a n s f o r m a t i o n i n c o b a l t produce a unique s i t u a t i o n t h a t a t p r e s e n t i s not w e l l understood. 1.3 The A l l o t r o p i c T r a n s f o r m a t i o n and S t r u c t u r e of C o b a l t The r e l a t i o n s h i p between s i n g l e and p o l y c r y s t a l c o b a l t i s complicated due to the m a r t e n s i t i c t r a n s f o r m a t i o n t h a t occurs a t a low homologous temperature. The l i t e r a t u r e shows t h a t p o l y c r y s t a l c o b a l t cjoes not t r a n s f o r m completely to the hep phase upon c o o l i n g 3 6 ' 3 7 . Thus, p o l y c r y s t a l c o b a l t , a t temperatures below the t r a n s f o r m a t i o n temperature, c o n t a i n s two a l l o t r o p i c m o d i f i c a t i o n s . The f o l l o w i n g s e c t i o n w i l l o u t l i n e the a v a i l a b l e data on the t r a n s f o r m a t i o n and the r e s u l t i n g s t r u c t u r e s i n c o b a l t . 1 . 3 . 1 H i s t o r y of the T r a n s f o r m a t i o n The o r i g i n a l d i s c o v e r y t h a t c o b a l t e x i s t e d i n two a l l o t r o p i c m o d i f i c a t i o n s i s c r e d i t e d to H u l l 3 8 i n 1921. The e a r l y c o b a l t s t u d i e s d e a l t with the d e t e r m i n a t i o n of l a t t i c e parameters and the t r a n s f o r m a t i o n temperatures. T h i s e a r l y work i s summarized i n Table I I I . U n t i l 1942, there was c o n t r o v e r s y r e g a r d i n g a second high temperature a l l o t r o p i c t r a n s f o r m a t i o n 3 9 ' k 9 . The d e t a i l e d high temperature x-ray work by Edwards 5 5 and o t h e r s 5 6 ' 5 7 , showed c o n c l u s i v e l y t h a t a second t r a n s f o r m a t i o n d i d not occur. More r e c e n t i n v e s t i g a t o r s a t t r i b u t e the h i g h temperature t r a n s f o r m a t i o n observed to the chancre from the ferromagnetic to the paramagnetic s t a t e , i . e . the C u r i e P o i n t 6 . 13 1.3.2 Mechanisms fo r the M a r t e n s i t i c Transformat ion The mechanism whereby the h igh temperature fee l a t t i c e transformed i n t o the low temperature hep phase was o r i g i n a l l y env i s ioned by v a r i o u s r e s e a r c h e r s 5 8 ' 5 9 as be ing accomplished by the passage of Schockley p a r t i a l d i s l o c a t i o n s over every second plane i n the fee l a t t i c e to y i e l d the hep l a t t i c e . A l l t h e o r i e s r ega rd ing the t r ans fo rma t ion have assumed t h i s type of d i s l o c a t i o n mot ion , they d i f f e r on ly i n p roposa l s as to how the p a r t i a l d i s l o c a t i o n s a r i s e and how they operate to t ransform a bulk of m a t e r i a l from one phase to the o the r . C h r i s t i a n 5 9 f i r s t advanced a hypothes i s i n v o l v i n g r e f l e c t i o n of p a r t i a l d i s l o c a t i o n s at a f ree surface to g i v e r i s e to a hep l a t t i c e . Th i s mechanism was thought by l a t e r workers to be improbable . The po le mechanism p o s t u l a t e d by S e e g e r 6 0 ' 6 1 i s a more s u c c e s s f u l attempt a t e x p l a n a t i o n . He assumes tha t p e r f e c t d i s l o c a t i o n s of the form a/2 [101] d i s s o c i a t e i n the (111) p l ane . I f the d i s l o c a t i o n i s pinned by a s e s s i l e "pole" d i s l o c a t i o n w i t h a screw component equal to twice the (111) i n t e r p l a n e r spacing the hep l a t t i c e w i l l be generated from the fee l a t t i c e . F o l l o w i n g i n v e s t i g a t o r s found problems w i t h t h i s mechanism 3 1 1 6 2 - 7 1 r e l a t e d to the number of these h igh energy pole d i s l o c a t i o n s r e q u i r e d to g ive r i s e to bu lk t r a n s f o r m a t i o n . Th i s i s c r i t i c a l when s i n g l e c r y s t a l whiskers are c o n s i d e r e d 6 2 . B o l l m a n 2 2 , i n 1961, pos tu l a t ed tha t the t r ans fo rma t ion proceded by a n u c l e a t i o n mechanism based on the i n t e r s e c t i o n of s t a c k i n g f a u l t s on v a r i o u s {111} p l anes . To accomodate 15 s t r e s s v/hen one s t a c k i n g f a u l t impinged on a n o t h e r , a new s t a c k i n g f a u l t was n u c l e a t e d . Due t o f r e e energy c o n s i d e r a t i o n s i t grew and t h e mechanism r e p e a t e d . The problem w i t h t h i s t h e o r y i s t h a t i t does n o t a l l o w f o r m a t i o n o f a s i n g l e c r y s t a l . T r a n s f o r m a t i o n on more th a n one o f t h e {111} p l a n e s i n t h e p a r e n t c r y s t a l , ( i . e . m u l t i v a r i a n t t r a n s f o r m a t i o n ) must be under way b e f o r e s u i t a b l e c o n d i t i o n s a r e a v a i l a b l e t o a l l o w f u r t h e r t r a n s f o r m a t i o n . A l t s t e t t e r and c o w o r k e r s 2 6 - 3 1 s t u d i e d c o b a l t s i n g l e c r y s t a l s and p o l y c r y s t a l s . T h e i r f o r m u l a t i o n o f t h e t r a n s f o r m a t i o n appears p r o m i s i n g i n t h a t t h e mechanism t h e y propose e x p l a i n s many o b s e r v a t i o n s made by o t h e r s 2 " 1 2 5 1 3 6 * 3 7 ' 6 5 ~ 7 X . Delamotte and A l t s t e t t e r 3 1 p r e s e n t a n u c l e a t i o n t h e o r y based on work by V e n a b l e s 7 2 and o t h e r w o r k e r s 7 3 ' 7 1 * . They propose t h a t p a r t i a l d i s l o c a t i o n l o o p s a r e n u c l e a t e d on e v e r y second (111) p l a n e and c o n s i d e r t h e f r e e energy f o r f o r m a t i o n o f a l o o p o f r a d i u s r as f o l l o w s : AF = 2Trr (Gb2/4Tr) l n ( 2 r / r ) - i r r 2 ( T b ) - ^ r 2 c A g .....1) *— y 9_> » y 1 \ y t, i i i i i i G = shear modulus o = shear s t r e s s c = t w i c e t h e ^ a y e r ^ s p a c i n g A g t = energy per cm f o r t r a n s f o r m a t i o n b = B u r g e r s v e c t o r Where: i ) i s t h e e l a s t i c energy ( d i s l o c a t i o n l o o p l i n e energy) r e q u i r e d f o r d i s l o c a t i o n f o r m a t i o n w i t h B u r g e r s v e c t o r b. F o r r e a l i s t i c n u c l e a t i o n r a t e s t h e shear modulus, G, a t t h e i n t e r f a c e between phases must have an a n o m a l o u s l y low v a l u e . T h i s problem has been t r e a t e d by o t h e r w o r k e r s 7 5 . i i ) i s the reduction i n free energy due to p a r t i a l d i slocations sweeping over the fcc-hcp interface under the influence of stress T . T can a r i s e from both i n t e r n a l constraints as well as from externally applied shear stress. i i i ) i s the free energy available due to transformation of a volume of material from one phase to the more stable phase, c i s equal to twice the layer spacing. g t i s the free energy per cubic centimeter for transforming one phase into the other. This mechanism operates for the i n i t i a l fee to hep transformation when nuclei of Shockley p a r t i a l d i s l o c a t i o n s form from perfect a/2[l01] type di s l o c a t i o n s that have been drawn from sub-boundaries at low stress, or produced by deformation. It may be expressed as: 1/2 a[101]* 1/6 a [112] + 1/6 a [211] 2) As the temperature i s decreased the d r i v i n g force increases u n t i l further stacking f a u l t s (loops of p a r t i a l dislocation) can be nucleated. As c e r t a i n numbers of a given 1/6 a <121> loop are nucleated on successive planes, the constraints due to transformation w i l l cause a d i f f e r e n t coplanar variant 1/6 a <121> loop to nucleate. In other words, once an i n t r i n s i c stacking f a u l t e x i s t s , formation of subsequent p a r t i a l d i slocations w i l l be controlled by the l o c a l value of shear stress. 1 . 3 . 3 M u l t i v a r i a n t Transformation A m u l t i v a r i a n t t r a n s f o r m a t i o n i s one t h a t takes p l a c e on more than one of the planes a v a i l a b l e f o r t r a n s f o r m a t i o n ; i n t h i s case, more than one (111) type plane. I f t r a n s - formation proceeds i n more than one d i r e c t i o n on a g i v e n (111) type plane, t h i s i s termed coplanar m u l t i v a r i a n c e . The mechanism o u t l i n e d above g i v e s r i s e to coplanar m u l t i v a r i a n c e i . e . o p e r a t i o n of d i f f e r e n t 1/6 a [121] type d i s l o c a t i o n s i n a g i v e n -(111) plane. The a n a l y s i s i s e q u a l l y v a l i d f o r a l l {111} planes i n the high temperature fee phase and t h e r e f o r e t r a n s f o r m a t i o n can occur on a l l {111} planes i f s u f f i c i e n t n u c l e i are present and no e x t e r n a l c o n s t r a i n t s are imposed. The absence of strong s u r f a c e shear markings has been poin t e d out i n the l i t e r a t u r e 7 6 . Bulk t r a n s f o r m a t i o n by coplanar m u l t i v a r i a n c e i s p o s s i b l e with l i t t l e average shear s t r a i n i f the o p e r a t i v e shear d i r e c t i o n of the tran s f o r m i n g {111}- plane changes o f t e n . Thus, i t i s not s u r p r i s i n g t h a t shear markings were overlooked by some authors. I f high e x t e r n a l a p p l i e d s t r e s s e s are i n v o l v e d d u r i n g t r a n s f o r m a t i o n , the n u c l e a t i o n of p a r t i a l d i s l o c a t i o n loops w i l l occur f o r 1/6 a [112] shear d i r e c t i o n s t h a t w i l l minimize the e f f e c t of the e x t e r n a l s t r e s s . By t h i s technique, D e l a m o t t e 3 1 observed s u r f a c e shear c l o s e to the t h e o r e t i c a l maximum c a l c u l a t e d f o r t h i s t r a n s f o r m a t i o n 2 8 . In p o l y c r y s t a l m a t e r i a l , the o p e r a t i v e p a r t i a l s n u c l e a t e d are i n f l u e n c e d by the c o n s t r a i n t s a r i s i n g out of thermal an i so t ropy and volume changes due to the t r a n s - fo rmat ion . Thus, fo r p o l y c r y s t a l l i n e m a t e r i a l v a r i o u s shear va lues are observed depending on g r a i n s i z e and other f a c t o r s . U u l t i v a r i a n t t r ans format ions i n c o b a l t p o l y c r y s t a l s have been observed by numerous i n v e s t i g a t o r s 2 8 1 7 1 1 7 6 1 7 7 . Th i s phenomenon! has a l s o been observed i n a l l o y systems where a s i m i l a r phase t r ans fo rma t ion o c c u r s 7 8 ' 7 9 . The absence of a m u l t i v a r i a n t t r ans fo rma t ion i n the p roduc t ion of c o b a l t s i n g l e c r y s t a l s has been exp l a ined i n v a r i o u s ways. S e e g e r 6 0 ' 6 1 p o s t u l a t e d tha t the {111} plane having the g r ea t e s t area i n the s i n g l e c r v s t a l i s the one tha t operates du r ing the t r ans fo rma t ion ; l a t e r i n v e s t i g a t o r s found t h i s was not the case . The e x p l a n a t i o n put forward by A l t s t e t t e r and Adams 3 0 and v e r i f i e d by them for s i n g l e c r y s t a l s , i s tha t the u n i d i r e c t i o n a l c o o l i n g dur ing c r y s t a l s o l i d i f i c a t i o n i s the d e c i d i n g f a c t o r . The {111} plane tha t has the g r ea t e s t area normal to the c o o l i n g d i r e c t i o n i n v a r i a b l e g ive s r i s e to the t r a n s f o r m a t i o n . They a l s o d i s cove red tha t upon r ehea t ing the s i n g l e c r y s t a l through the t r ans fo rma t ion two p o s s i b i l e o r i e n t a t i o n s may o c c u r . These are e i t h e r the o r i g i n a l fee o r i e n t a t i o n or i t s tw in as has been v e r i f i e d by Adams 3 0 and observed by Holt 1* . A f t e r the i n i t i a l c o o l i n g t r ans fo rma t ion fo r a s i n g l e c r y s t a l or a p o l y c r y s t a l , the next annea l ing c y c l e has an important e f f e c t on the t r ans fo rma t ion tha t w i l l then occur upon c o o l i n g . I f the annea l ing treatment i s c a r r i e d out below 600°C, the ope ra t i ve h a b i t p lanes d u r i n a the hea t ing t r a n s f o r m a t i o n are the same h a b i t planes t h a t operate d u r i n g c o o l i n g 7 1 ' 3 0 . Thus, a s i n g l e c r y s t a l remains a s i n g l e c r y s t a l and a polycrysta}. maintains the same degree of m u l t i v a r i a n c e . I f a specimen i s annealed a t higher temperatures, or a t 600°C f o r very long p e r i o d s of time, each r e g i o n of c r y s t a l t h a t was of one o r i e n t a t i o n b e f o r e a n n e a l i n g w i l l e x h i b i t a m u l t i v a r i a n t t r a n s f o r m a t i o n upon c o o l i n g . F u r t h e r a n n e a l i n g treatments of t h i s type w i l l f u r t h e r r e f i n e the s t r u c t u r e w i t h i n a gi v e n fee g r a i n . The above o b s e r v a t i o n s are due to the p r o d u c t i o n and m o b i l i t y of d i s l o c a t i o n s as r e l a t e d to temperature and the t r a n s f o r m a t i o n . 1.3.4 Retained FCC Phase Except i n the s p e c i a l case of s i n g l e c r y s t a l s (or very f i n e p a r t i c l e s ) 8 0 c o b a l t a t room temperature i s a mixture of fee and hep phases. The r e t e n t i o n of fee i n p a r t i c l e s l a r g e r than 1 micron or i n bulk specimens a r i s e s from the m u l t i v a r i a n c e of the t r a n s f o r m a t i o n and the smal l thermodynamic d r i v i n g f o r c e tending to complete the t r a n s f o r m a t i o n . Other f a c t o r s t h a t a f f e c t the amount of r e t a i n e d fee are the d e f e c t s t r u c t u r e , p u r i t y and g r a i n s i z e of the specimens i n v o l v e d . The t r a n s f o r m a t i o n takes p l a c e a t a r e l a t i v e l y low temperature (0.39T m) where some d i s l o c a t i o n rearrangement and a n n i h i l a t i o n may occur, but major r e d i s t r i b u t i o n cannot take p l a c e 7 6 . As the untransformed areas decrease i n s i z e they w i l l remain fee e i t h e r because of a l a c k of s u i t a b l e d i s l o c a t i o n sources or because the surroundi.ng transformed; material cannot accommodate further volume changes. During research on p o w d e r s 5 5 - 5 7 , thin f i l m s 3 6 ' 3 7 , w h i s k e r s 6 2 - 6 k and p o l y c r y s t a l l i n e c o b a l t 8 1 " 8 3 , measured values for retained fee phase vary from zero to over 50%. I t has also been observed that any type of deformation forces the transformation towards c o m p l e t i o n 8 3 - 8 6 . ; 1.3.5 Thermodynamics of the Transformation The thermodynamics of the transformation have been s t u d i e d 3 0 and the enthalpy for the transformation i s approximately 100 c a l o r i e s per mole. Adams 3 0 determined that about 15% of the enthalpy change i s associated with defect production. This i s s u f f i c i e n t energy to produce stacking f a u l t s on every 10th plane, a d i s l o c a t i o n density 1 1 2 of 10 /cm , or an increase i n vacancy concentration of 0.04%. Therefore, as cobalt i s transformed, the defect structure may increase perceptibly. As pointed out by Y e g o l a y e v 8 5 ' 8 6 and Houska 7 6 the f i n a l defect structure depends upon the temperature to which the cobalt specimen i s cycled. Defects are produced during each transformation cycle but a n n i h i l a t i o n also takes place at the high temperature. As the number of cycles increases, either a balance i s reached where a large proportion of the defects produced by one cycle i s annihilated at the high temperature or r e c r y s t a l l i z a t i o n begins. The r e s u l t s of any given set of c y c l i n g experiments depend upon the specimens used and the temperatures involved. 1.3.6 The H y s t e r e s i s of the Transformat ion Data fo r the t r a n s f o r m a t i o n 2 8 , i n d i c a t e s tha t the h y s t e r e s i s i s sma l l e r fo r s i n g l e c r y s t a l s than fo r p o l y c r y s t a l s 3 0 . For both types of m a t e r i a l the h y s t e r e s i s inc reases w i t h c y c l i n g through the t r a n s f o r m a t i o n , but e v e n t u a l l y reaches a s t a b l e v a l u e . Adams 3 0 determined M -A to be 13°C for s i n g l e c r y s t a l s , and 30°C fo r s s p o l y c r y s t a l s . Other authors 3 6 ' 8 5 1 8 6 have found va lues c o n s i d e r a b l y l a r g e r fo r other forms of c o b a l t . P a r r 6 3 , working w i t h c o b a l t w h i s k e r s , observed a h y s t e r e s i s of l e s s than 5°C. The h y s t e r e s i s i s ve ry l a rge fo r sma l l p a r t i c l e s and t h i n f i l m s . P e t r o v 8 0 found tha t 500 Angstrom a e r s o l p a r t i c l e s of c o b a l t d i d not t ransform to hep a t any temperature i n the absence of deformat ion . However, upon h e a t i n g , the t r ans fo rma t ion to fee occured a t about 500°C. V o t a v a 3 6 ' 3 7 working w i t h t h i n f i l m s i n the e l e c t r o n microscope found tha t the h y s t e r e s i s was inc reased r a d i c a l l y by one c y c l e through the t r a n s f o r m a t i o n . He pos tu l a t ed tha t the observed h y s t e r e s i s of 450°C (M equals 100°C, A g equals 550°C) was due to l o s s of n u c l e i fo r t r ans fo rma t ion and l a c k of c o n s t r a i n t i n the t h i n f i l m s . 1.4 Scope of Present Work The ob jec t of the present study i s to p rov ide a d e t a i l e d p r o f i l e of the t e n s i l e p r o p e r t i e s of c o b a l t p o l y c r y s t a l s over the temperature range where the hexagonal phase i s s t a b l e . A major p o r t i o n of the work i s r e l a t e d to the e f f e c t of the incomplete a l l o t r o p i c phase t r a n s f o r m a t i o n on the deformat ion behaviour of c o b a l t . I t i s proposed t h a t by m o n i t o r i n g the completeness of the t r a n s f o r m a t i o n at a l l s tages of d e f o r m a t i o n , c l a r i f i c a t i o n of much anomalous data present i n the l i t e r a t u r e may r e s u l t . The deformat ion of c o b a l t i s examined w h i l e v a r y i n g p u r i t y , annea l ing p rocedures , completness of t r a n s f o r m a t i o n and t e s t temperature . The exper imenta l program begins w i t h e v a l u a t i o n of the s t r u c t u r e of specimens befo re t e s t i n g . A l l f u r t h e r exper imenta l r e s u l s are r e l a t e d to the s t r u c t u r e s observed i n t h i s prepared m a t e r i a l . 23 2. Experimental Procedure 2.1 M a t e r i a l s The l a c k of agreement between r e s u l t s gathered from the l i t e r a t u r e has o f t e n been a t t r i b u t e d to d i f f e r e n c e s i n p u r i t y of the c o b a l t t e s t e d 8 7 ' 8 8 . The method of c o b a l t p r o d u c t i o n has a l s o been shown to have important e f f e c t s on p r o p e r t i e s 8 1 . The m a j o r i t y of the data i n the l i t e r a t u r e d e a l s w i t h e l e c t r o l y t i c c o b a l t , e i t h e r as d e p o s i t e d or i n remelted form. In r e c e n t y e a r s , c o b a l t powders have a l s o become an important source of m a t e r i a l . The p r o p e r t i e s of the bulk m a t e r i a l produced by powder m e t a l l u r g y d i f f e r somewhat from the r e f i n e d e l e c t r o l y t i c m a t e r i a l s Three l e v e l s of p u r i t y have been i n v e s t i g a t e d i n t h i s study. The nominal p u r i t y v a l u e s are 99 .7%, 99.9%, and 99.998% c o b a l t ; a d e t a i l e d r e p o r t on the i m p u r i t i e s p r e s e n t i s presented i n Table IV. C o b a l t analyses were obtained from Koch L i g h t L a b o r a t o r i e s , Colnbrook, England and S h e r r i t t Gordon Mines L i m i t e d , F o r t Saskatchewan, A l b e r t a . The major d i f f e r e n c e between the three grades of c o b a l t i s the n i c k e l content. In a l l cases, n i c k e l , s i l i c o n and i r o n are the major i m p u r i t i e s . Z i n c , l e a d , and other elements t h a t have been shown to have d e l e t e r i o u s e f f e c t s on the t e n s i l e p r o p e r t i e s of c o b a l t are w e l l below c r i t i c a l l e v e l s 8 2 . A l l t hree grades of c o b a l t were obtained as c o l d worked rod. The diameter of the "as r e c e i v e d " m a t e r i a l was as f o l l o w s : TABLE IV Spect r o g r a p h i c A n a l y s i s of Co b a l t M a t r i x Element 9 9 . 7 % + 9 9 . 9 % + 99 .998% + 99.998%* % % % P.P.M. Ni 0 . 1 0.02 <0.005 N.D. S i 0 .05 N.D. <0.005 7 Fe 0.005 <0.01 - 3 A l 0.005 - - - i ) Elements quoted a t l e v e l s l e s s than 100 P.P.M. (<0.01%) i n a l l specimens by S h e r r i t t Gordon — As, Cd, L i , Te, Zn. i i ) Elements d e t e c t e d a t l e v e l s of 1 P.P.M. or l e s s by Kock L i g h t L aboratores i n the 99.998% m a t e r i a l -- Ag, Ca, Cu, Mg. i i i ) The f o l l o w i n g elements were s p e c i f i c a l l y sought but not de t e c t e d (N.D.) — By S h e r i t t Gordon Ag, B, Ba, Be, B i , Ca, Cr, Cu, Ge, Kg, Mg, Mn, Mo,Pb, Sb, Sn, T i , V, Zr. -- By Kock L i g h t A l , As, Au, B, Ba, Be, Cd, Cr, Cs, Ga, Ge, Hg, In, I r , K, Le, Mn, Mo, Na, Nb, Os, Pb; Pt, Rb, Re, Rh, Ru, Sb, Se, Sn, Sr, Ta, Te, T i , T l , V, Yl, Zn, Zr. A n a l y s i s by r e s e a r c h and development d i v i s i o n , S h e r i t t Gordon Mines L i m i t e d , For!t : Saskatchewan, A l b e r t a , Canada. Maximum s e n s i t i v i t y quoted as 5 0 P.P.M. A n a l y s i s by Kock L i g h t L a b o r a t o r i e s , Colnbrook, England. Maximum s e n s i t i v i t y quoted as +50% of the amount pr e s e n t . 25 Nominal P u r i t y Q. "6. Diameter 99.7 3 mm (0.125") 99.9 6.25 mm (0.250") 99.998 5 mm. (0.200") The very h igh p u r i t y m a t e r i a l (99.998%) was s u p p l i e d by Kock L i g h t ; the two lower p u r i t y grades (99.7% and 99.9%) were obta ined from A . D. MacKay I n c . , New York , U . S. A . 2.2 P r e p a r a t i o n of T e n s i l e Specimens 2 .2 .1 Machining The important dimensions of the t e n s i l e specimens which were produced on a sma l l l a t h e are shown i n F i g u r e 1. From the 5 mm and 6.2 5 mm m a t e r i a l , double buttonhead specimens were machined to minimize problems r e l a t e d to g r i p p i n g c o n s t r a i n t s du r ing t e n s i l e t e s t s . For the 3 mm m a t e r i a l , a double buttonhead type of specimen would have g iven an unworkably sma l l specimen d iameter . The 3 mm m a t e r i a l was the re fore machined i n t o s i n g l e buttonhead specimens. In a l l cases the gauge l eng th was mainta ined a t ten times the reduced specimen d iameter . A l l specimens were machined 0.1 mm (0.004") o v e r s i z e to a l l o w fo r subsequent e l e c t r o p o l i s h i n g . T e n s i l e t e s t i n g g r i p s fo r the I n s t r o n were machined from tool s t e e l (At l a s Keewatin) and heat t r e a t ed to a hardness of 54-56 R . The p u l l rods and s leeves fo r the. s p l i t g r i p s were made from 316 s t a i n l e s s s t e e l . ro o LO CN - - 2 5 m m CM u 20 U-15-*) a l l .dimensions i n mm. P u r i t y 99.9% 99.998% 99.7% F i g . 1 T e n s i l e specimens and important dimensions 0 10 60 70 80 Time a f t e r e n t e r i n g furnace F i g . 2 T y p i c a l r eco rd of vacuum annea l ing treatment 2.2.2 Annealing Procedures A t y p i c a l heat treatment p r o f i l e i s shown i n Figure 2. Treatments were carried out at temperatures up to 1000°C with temperature monitered v i a a chromel-alumel thermocouple placed d i r e c t l y among the specimens undergoing heat treatment. Heat up rates were rapid, four minutes to reach 600°C from ambient temperature, increasing to a maximum of eight to ten minutes to a t t a i n 1000°C from ambient. The rate of furnace cooling through the transformation temperature range was between four and six degrees centigrade per -5 minute. Vacuum was maintained between 0.4 and 1.0 X 10 mm of Hg throughout the annealing procedures. The specimens retained an excellent surface through the heat treatments and surface markings due to the martensitic transformation could only be ascertained by r e p l i c a techniques. 2.2.3 X-Ray Analysis Quantitative x-ray analysis was adopted for determining the proportions of the two a l l o t r o p i c modifications of cobalt present i n a l l specimens. The analysis was c a r r i e d out a f t e r heat treatment and following deformation procedures. The method adopted was f i r s t put i n quantitative form by Sage and G u i l l a r d 9 0 , i n 1949, and has been u t i l i z e d by many authors 6 5 - 7 1 1 8 2 ' 8 h » 8 5 . The method does not require a standard which s i m p l i f i e s analysis.. Information regarding the presence of the two phases i s obtained by comparing the d i f f r a c t e d i n t e n s i t y of the (1011) l i n e i n the hep phase to that of the (200) l i n e i n the fee phase. When the m u l t i p l i c i t y factor and other variables are taken into account, the proportion of fee phase present may be determined from the formula: 21, fee x = fee hep ..... 3) x = proportion of metastable fee phase I, = Intensity of the (200) fee l i n e rcc I n C p = Intensity of the (loll) hep l i n e The derivation of t h i s formula and the required analysis i s presented i n Appendix 1. A l l x-ray work was car r i e d out with a P h i l l i p s PW 1011/60 diffractometer u t i l i z i n g manganese f i l t e r e d iron r a d i a t i o n . The rate at which the diffractometer was rotated varied from 1/4 to 2 degrees 20 per minute. Using iron r a d i a t i o n , the (1011) hep i n t e n s i t y peak occurs at approximately 60.3 degrees 20, and the (200) fee peak approximately 66.7 degrees 20 8 h. To allow i n t e n s i t y calculations d i r e c t l y from the x-ray chart, a slow rate of diffractometer r o t a t i o n was used (one quarter degree per minute) to provide a clear i n t e n s i t y traverse from 59 to 69 degrees 20. The areas under the respective peaks were then measured and substituted into formula 3. This method was tedious and due to inherent scatter i n t h i s type of measurement a s t a t i s t i c a l l y more r e l i a b l e method was undertaken for the majority of the x-ray analysis. The method may be o u t l i n e d as f o l l o w s : The x - r a y equipment a l lowed i n t e g r a t i o n over a g i v e n p e r i o d of t ime , or fo r a predetermined number of p u l s e s . The two i n t e n s i t y peaks i n ques t ion cou ld be comple te ly t r ave r sed w i t h i n 4 degree ranges , 59 to 63 degrees fo r the (1011) hep peak and 65 to 69 degrees fo r the fee peak. The background x - r a y count to be sub t rac ted from the t o t a l i n t e g r a t e d i n t e n s i t i e s obta ined by coun t ing a l l pu l ses over the 4 degrees 20 above, was determined by scanning 2 degrees 20 on both s ides of the peak i n q u e s t i o n . The r e s p e c t i v e angles 20 are g iven below and a t y p i c a l x - r a y c h a r t i s shown i n F i g u r e 3. Degrees 20 D e s c r i p t i o n 57-59 1/2 of background fo r hep peak (B.G. #1) 59-63 T o t a l hep peak (1011) 63-65 1/2 of background fo r hep and fee peaks (B.G. #2) 65-69 T o t a l fee peak (200) 69-71 1/2 of background for fee peak (B.G. #3) Therefore : I n t e n s i t y of hep peak d h c ) = T o t a l hep - (B.G. #1 + B . G . I n t e n s i t y of fee peak ( I f c c ) = T o t a l fee - (B .G. #2 + B . G . In p r a c t i c e , i t was found tha t the d i f f e r e n c e s between B . G . #1, B . G . #2 and B . G . #3 were very sma l l and scanning B . G . #1, and B . G . #3 was not j u s t i f i e d because the measurements d i d not improve the accuracy of the a n a l y s i s . For t h i s reason, the net i n t e g r a t e d i n t e n s i t y of the two peaks was determined by s u b t r a c t i n g twice the " B . G . #2" i n t e n s i t y from each peak. Degrees 20 F i g . 3 Raw x - r a y data fo r 99.7% c o b a l t o 31 A minimum of f i v e i n t e n s i t y integrations were carr i e d out on each specimen. Each integration was taken from a d i f f e r e n t area on the specimen and the re s u l t s from the f i v e scanning procedures were then added and substituted i n equation 3. The data obtained using t h i s method was reproducible, but the scatter i n res u l t s was always large. This problem 9 1 with quantitative x-ray analysis i s discussed by Giamei who attempted to reduce the scatter by scanning a number of peaks and solving the data v i a computer techniques. The tech- nique i s not applicable where a large number of specimens are to be analyzed because of the equipment time involved. The large number of specimens analyzed and the number of scanning procedures ca r r i e d out ensure that any trends , observed are i n fac t r e a l and not a consequence of the , . 9 1 analysis When data regarding the proportion of the two phases present i s quoted, the value given w i l l be the average value for a l l specimens that have the same purity and have undergone the same treatment. There are several facts that should be noted when considering x-ray data. D i f f r a c t i o n i s e s s e n t i a l l y a surface measurment, with the majority of the d i f f r a c t e d x-rays coming from the outer 25 microns of material. When the grain size i s of this, order, the x-ray r e s u l t s are due almost exclusively to the surface grains. The surface grains exist under d i f f e r e n t constraint than the i n t e r i o r grains and t h i s becomes important when the martensitic transformation i n cobalt i s considered. If the surface grains are less constrained, the transformation w i l l proceed further towards completion i n these grains; thus the x-ray r e s u l t s w i l l give a high value for the completeness of the transformation. This analysis leads to the conclusion that the measured amount of transformation i s a maximum, and the i n t e r i o r of the specimen may contain more metastable face-centered phase than the x-ray data reveals. Recognizing the above considerations, the x-ray data i s more accurate where a small grain size i s involved because the d i f f r a c t i o n w i l l take place from i n t e r i o r grains as well as surface grains. In any case, the analysis adopted ensures that the measured amount of transformation can be considered a maximum value. 2.3 Tensile and Hardness Tests A l l t e n s i l e tests were ca r r i e d out on a f l o o r model Instron machine using cross-head speeds between 0.2 in./min. _3 and 2 X 10 in./min. The majority of tests were c a r r i e d _ 2 out at 2 X 10 in./min. corresponding to a s t r a i n rate of -2 -2 2 X 10 per min. for the largest specimens and 3.3 X 10 per min. for the smallest. ; Testing media for the temperature range investigated were as follows: ( Media Temperature Range l i q u i d n i t r o g e n -196°C petroleum ether -140°C to -100°C e t h a n o l -100°C to 0°C water 0°C to 100°C s i l i c o n e o i l 100°C to 250°C s a l t bath (draw temper 275) 250°C to 400°C The temperature of the t e s t i n g baths was measured w i t h a copper-constantan thermocouple immersed c l o s e to the specimen. The t e s t temperature was maintained w i t h i n + 1°C while t e s t i n g was underway. T e n s i l e data are presented i n the F.P.S. system. True s t r e s s and t r u e s t r a i n data were c a l c u l a t e d on the b a s i s of instantaneous area and l e n g t h . These v a l u e s were c a l c u l a t e d assuming uniform deformation throughout the gauge l e n g t h . A t low temperatures, the baths c o u l d be changed and t e s t i n g resumed i n l e s s than a minute w h i l e a t hig h temperatures the p h y s i c a l h a n d l i n g d i f f i c u l t i e s and temperature c o n t r o l problems extended the time r e q u i r e d b e f o r e c o n t i n u i n g a t e s t to 5 to 8 minutes. During the time t h a t the temperature baths were being changed the t e n s i l e specimens were maintained i n t e n s i o n by a small c y c l i c l o a d . A l l hardness t e s t s were c a r r i e d out on a V i c k e r s Hardness T e s t e r w i t h the 10 Kg. a p p l i e d l o a d . The D.P.H. data was produced to a l l o w comparisons to be made with data a v a i l a b l e i n the l i t e r a t u r e . 2.4 Metallography The metallography of cobalt i s d i f f i c u l t because of the complex structures a r i s i n g due to the incomplete martensitic transformation i n the m a t e r i a l 9 2 ' 9 3 . The grain size, i n t e r n a l structure, and deformation mechanisms were examined o p t i c a l l y and v i a r e p l i c a techniques. 2.4.1 Optical Metallography The incomplete martensitic transformation i n cobalt can be forced towards completion by deformation. This s t r a i n induced transformation was measured at distances greater than 50 microns from a scratch. For t h i s reason, at least 100 microns were removed from a l l machined or ground surfaces by ele c t r o p o l i s h i n g before any metallography was attempted. A number of the c i r c u l a r t e n s i l e specimens were ground f l a t and then electropolished to obtain a large enough f l a t area for grain size determinations. The c i r c u l a r cross section of the t e n s i l e specimens was a b a r r i e r to good metallography. The most successful e l e c t r o p o l i s h i n g solution was found to be 15% perchloric acid i n acetic acid. The specimens were suspended i n a water cooled s t a i n l e s s s t e e l beaker i n which the polishing solution was s t i r r e d continuously. Polishing was carried out at 20 v o l t s , with the specimen rotating i n the s t i r r e d solution. The specimen was slowly inverted every 30 seconds to avoid taper. These precautions produced specimens with + 0.01 mm. maximum taper a long the gauge l e n g t h . Th i s procedure y i e l d s a surface w i t h an apparent m i r r o r f i n i s h . The surface shows l i t t l e evidence of p r e f e r e n t i a l a t t ack a t g r a i n boundaries or o ther h igh energy s i t e s . The me ta l l og raph i c fea tures of the specimens were determined by u t i l i z i n g a second anodic e t c h . The e tchant used was 5% concent ra ted h y d r o c h l o r i c a c i d i n d i s t i l l e d water . The specimen was p laced i n the e t ch ing bath and g iven a very shor t pu lse of cu r r en t at l e s s than one v o l t and then examined. The r e s u l t i n g s t r u c t u r e i s very s e n s i t i v e to the s i z e of the pu lse of c u r r e n t . Overe tch ing occurs very e a s i l y and extreme c a u t i o n must be e x e r c i s e d i f a r e p r o d u c i b l e surface i s d e s i r e d . As an adjunct to the x - r a y a n a l y s i s of the p r o p o r t i o n of the two phases p resen t , a p o l a r i z e d l i g h t technique was employed. Seve ra l problems arose when meta l lography under p o l a r i z e d l i g h t was at tempted. A p o l i s h e d or ground surface was of no use because of the s t r e s s induced t r ans fo rma t ion and an e l e c t r o p o l i s h e d surface d i d not g i v e a d e f i n i t i v e r e s u l t due to the presence of a t h i n ox ide l a y e r . Observa t ion cou ld on ly be made f o l l o w i n g the second e t c h i n g procedure and t h i s caused problems r e l a t i n g to the s c a t t e r i n g of l i g h t from g r a i n boundaries and surface f i n e s t r u c t u r e . The p e r i o d i c nature of the t r ans fo rma t ion shears g i v e r i s e to a f i n e s t r u c t u r e which can e tch to y i e l d an a n i s o t r o p i c e f f e c t a l though sma l l l a m e l l a r volumes of the fee phase may s t i l l e x i s t . For these reasons i n t e r - p r e a t i o n of p o l a r i z e d l i g h t photomicrographs was attempted c a u t i o u s l y . 36 Polarized l i g h t metallography proved to be most successful with large grained material. When the proportion of i s o t r o p i c material (fee) measured by t h i s technique was compared to the r e s u l t s of the x-ray analysis, acceptable agreement was found. 2.4.2 Electron Microscope Replicas Replicas were produced by soaking c e l l u l o s e acetate sheet i n acetone and then pressing the sheet to the surface to be analyzed. The acetate sheet was removed from the specimen and shadowed with chromium and coated with carbon. The acetate was dissolved away i n acetone, leaving the r e p l i c a to be mounted i n 150 mesh copper grids. A l l r e p l i c a s were examined i n a Hitachi HU11A electron microscope at 50 KV. The r e p l i c a procedure was carried out on specimens tested between -196°C and 250°C. To ensure protection of the surface at a l l times while testing, thick s i l i c o n e grease was spread over the specimen surface. The grease could be dissolved away i n trichlorethane when a r e p l i c a was desired. The upper temperature l i m i t (250°C) for the r e p l i c a procedure was dictated by the breakdown of the protective grease, which allowed oxide to form on the cobalt surface. Replicas were produced from annealed structures as well as from deformed specimens. The procedure was also carried out on the fracture surfaces of a number of specimens. 3. Experimental Program and Results 3.1 The Structure of P o l y c r y s t a l l i n e Cobalt This section outlines the methods used to determine the structure of the specimens on which a l l t e n s i l e procedures were carr i e d out. The data produced during th i s work are combined with information taken from the l i t e r a t u r e i n order to examine the complex structures observed. It i s then possible to predict the structures that w i l l e x i s t i n cobalt polycrystals a f t e r a given set of annealing procedures. 3.1.1 As Received Material From the cold worked cobalt rod, random samples from each purity l o t were prepared for testing. Quantitative x-ray analysis showed that the material was almost 100% hep phase. Integrating the measured peaks and substituting in equation 3 gave a fee content of less than 5%. % f c c = 2 l f c c • (100) 3) fee hep Tensile tests were carried out at room temperature with specimens from each purity grade. In a l l cases the d u c t i l i t y was found to be less than 3%. In the high purity material, (99.998%) the specimens fractured at y i e l d . 3.1.1.1 Preferred Orientation The texture i n cold worked cobalt has been investigated by several authors 6 6 ' 8 2 1 8 9 ' 9 4 . Wilcox 8 9 investigated electrodeposited cobalt sheet and sponge material. Beckers 8 2 et a l worked with bars and rods of commercial grade cobalt. Wilcox observed that electrodeposited cobalt has an as deposited {1010} texture which i s d i f f i c u l t to annihilate. After annealing above the transformation temperature and introducing 20% cold work he observed a {0001} <1120> r o l l i n g texture with the basal planes rotated 20 to 25 degrees i n the r o l l i n g d i r e c t i o n from the r o l l i n g plane normal. Beckers observed a similar r e s u l t for hot r o l l e d slabs. For extruded rods of cobalt, a preferred orientation with a high density of {0001} planes perpendicular to the 8 2 extrusion axis i s obtained . The preferred orientation in severly worked material was found to disappear when annealing treatments were carried out above 500°C 8 2. 3.1.1.2 Stacking Fault Energy and Fault Analysis The low stacking f a u l t energy of cobalt and the introduction of many stacking f a u l t s both by deformation and by transformation have led many investigators to study the f a u l t i n g densities i n cobalt. Various experimental methods have been chosen with most work performed v i a x-ray techniques 7 6 1 8 5 ' 8 6 1 9 5 ' 9 6 . Measurements of nuclear magnetic resonance (NMR)9 7 frequencies and d i r e c t observation i n the electron microscope have also been car r i e d o u t 2 1 * ' 3 6 ' 9 8 A s t a c k i n g f a u l t i s an e r r o r i n the o r i g i n a l sequence of l a y e r s i n a c r y s t a l l a t t i c e . F a u l t s a r i s e d u r i n g growth of c r y s t a l s and a l s o from deformation. The d i s t i n c t i o n between the two types of f a u l t s should be made c l e a r . The i d e a l hep s t r u c t u r e can be d e s c r i b e d as an ABABABAB sequence of close-packed p l a n e s . A f a u l t i s an e r r o r i n t h i s r e g u l a r sequence w i t h the r e s t r i c t i o n t h a t a d j a c e n t l a y e r s must be d i f f e r e n t . Thus, the growth of an hep c r y s t a l by the a d d i t i o n of c l o s e packed planes i s governed by the f a c t t h a t every second l a y e r i s i d e n t i c a l except when a f a u l t o c c u r s . The f a u l t l a y e r i s u n l i k e the pr e c e d i n g two l a y e r s . For a deformation f a u l t , i t i s presumed t h a t a p e r f e c t s t a c k i n g sequence e x i s t s b e f o r e deformation takes placi hep hep • 1 .. • , ABABABABCBCBCBCBC Growth F a u l t fee hep hep I ' H 1 . ABABABABCACACACACA Deformation F a u l t L — i — ' fee E i t h e r type of f a u l t can be formed by the growth of two out-of-phase hep l a t t i c e s t o g e t h e r . The deformation f a u l t can a l s o be formed by p a r t i a l s l i p which c o n v e r t s A planes i n t o C planes, and B planes i n t o A p l a n e s . The two f a u l t types may be d i f f e r e n t i a t e d because a growth f a u l t c o n t a i n s t h r e e planes of fee s t a c k i n g and a deformation f a u l t f o u r l a y e r s . The a n a l y s i s of x-ray data t o y i e l d d i f f e r e n t i a t i o n between growth and deformation s t a c k i n g f a u l t s has been c a r r i e d out by Ananthraman and C h r i s t i a n 9 9 . Analysis v i a NMR has been published by Toth and coworkers 9 7. The r e s u l t s of these analyses may be summarized as follows: i) In both the annealed and the deformed state the f a u l t density i s high with f a u l t s observed i n both the fee and the hep phases. A highly deformed specimen may have a t o t a l f a u l t density as high as one faulted plane i n every ten. In annealed material t h i s value may drop to one plane i n three hundred. i i ) A l l observed stacking f a u l t s are of the i n t r i n s i c type. More complex e x t r i n s i c f a u l t s are also possible but they have not been o b s e r v e d 9 7 ' 9 8 . i i i ) Both growth and deformation f a u l t s are present. The density of growth f a u l t s i s not strongly affected by annealing procedures but i s sub s t a n t i a l l y decreased by deformation and i s increased by c y c l i n g through the transformation. Deformation f a u l t s , as t h e i r name implies, increase with the amount of deformation introduced. The density of these f a u l t s i s reduced sharply by annealing procedures, even at temperatures below the transformation temperature. 3.1.2 Recovery, R e c r y s t a l l i z a t i o n and Grain Growth The annealing spectrum of cobalt has been investigated by several authors 8 1 1 0 0 - 1 0 3 . Some studies d e t a i l e d the important parameters a f f e c t i n g the annealing behaviour such as p r i o r treatment, purity, type of specimen, etc, while others did not. Thus, the data i n many cases d i f f e r s i g n i f i c a n t l y . The lack of agreement a r i s i n g from differences i n pu r i t y has been outlined by M o r r a l 8 7 and Winterhager 8 8. The most often quoted property i s diamond pyramid hardness (DPH), and for t h i s reason a record of DPH versus annealing procedures was obtained during t h i s study to allow comparisons to be made. The diamond pyramid hardness (DPH) for the as-received material was as follows: Purity DPH 99.7% Co 285 99.9% Co 279 99.998% Co 260 Figure 4 gives the d,ata gathered for the three purity levels investigated and comparable data drawn from the l i t e r a t u r e . In a l l cases, data are shown for room temperature hardness after a one hour anneal at the indicated temperature. The general conclusions drawn from t h i s data may be reported as follows: i) The room temperature hardness i s not affected by annealing below 220°C (0.28T m), even for high purity material. As the impurity l e v e l increases the temperature at which any major d i s l o c a t i o n rearrangement occurs increases. Thus, i n the temperature range 220°C to 350°C polygonization a n ^ recovery occur depending upon purity. i i ) Over the temperature range that includes the region where the martensitic transformation takes place, recovery and r e c r y s t a l l i z a t i o n occur. I t would 160 r i c r , • 99.7% Coba l t O 99.9% C o b a l t A 99.998% Coba l t Present work 200 400 600 800 Temperature, 1 h r . annea ls , °C Diamond Pyramid Hardness data for c o b a l t . 1000 appear that r e c y r s t a l l i z a t i o n at a temperature where hep cobalt i s stable, may be possible for very pure material. i i i ) Grain growth predominates at temperatures above 600°C. 3.1.2.1 Recovery Although the recovery of hardness values has been quoted as low as 220°C by Feller-Kneipmier 1 0 1 no change i n the bulk flow stress at room temperature has been observed for annealing treatments below 350°C (0.35T ). m The work by S h a r p 1 0 2 showed that following deformation at -196°C some recovery of e l e c t r i c a l r e s i s t i v i t y occured i n cobalt at 0.06T and Q.13T , but found no recovery m m of flow stress for short anneals at 0.38T . They m observed some flow stress recovery with long term anneals at 0.38 and 0.39T . m. A set of tests similar to that by Sharp1 0 2 et a l were carr i e d out i n the present study to substantiate the i r r e s u l t s for the cobalt used i n the present inve s t i g a t i o n . No reduction i n bulk flow stress was obtained for treatments below 0.35T . Annealing for several davs at m J 0.37Tm allowed recovery of only 2% of the flow stress i n the purest material. 3.1.2.2 R e c r y s t a l l i z a t i o n and Grain Growth The r e c r y s t a l l i z a t i o n temperature range for most metals l i e s between 0.4Tm and 0.5Tmx , a temperature range from 430°C to 610°C for cobalt. The annealing treatment required for r e c r y s t a l l i z a t i o n i s modified by the i n i t i a l grain s i z e , cold work present, and the purity of the specimens considered. Increasing purity tends to lower the r e c r y s t a l l i z a t i o n temperature as does increasing amounts of cold work and smaller grain sizes. Bibring and S e b i l e a u 6 5 ~ 7 1 worked with 99.5% cobalt and postulated that r e c r y s t a l l i z a t i o n occured at temperatures below the transformation temperature. They presented no metallographic evidence and with the low purity material they employed t h i s r e s u l t i s doubtful. In a more recent study, Beckers 8 2 determined that recovery started a f t e r one hour at 450°C and r e a r y s t a l l i z a t i o n was v i s i b l e a f t e r one half hour at 500°C for 99.7% cobalt. In the present work, no change was observed i n the surface structure of specimens for annealing procedures below 450°C. At 500°C, r e c r y s t a l l i z a t i o n was v i s i b l e a f t e r short time anneals. The rate at which grain growth proceeds i s influenced by the purity of the cobalt treated. As the purity increases, the number of obstacles retarding grain coalescence and reduction of high angle boundaries decreases, thus grain growth proceeds more quickly. This r e s u l t i s shown c l e a r l y i n Figure 5 where the data from the present study are plotted- Several data points drawn from the l i t e r a t u r e have been included for comparison. The method used for determining grain size was straight forward but tedious. Metallographic specimens were photo- graphed and the number of grains present were counted d i r e c t l y . 60 U c o H u •H c •H d) N •H CQ C fd a 50 40 30 20 10 A 99.998% c o b a l t 0 99.9% c o b a l t B 99.7% c o b a l t / \ Beckers- 8- 2 o M u l l e r • F r a s e r 8 1 ± 300 F i g . 5 400 800 900 1000 500 600 700 Annealing Temperature °C. V a r i a t i o n i n g r a i n s i z e f o r 1 hour anneals a t i n d i c a t e d temperatures, 4k The magnification used for analysis was varied to obtain as many grains as possible i n the f i e l d of view while retaining reasonable grain d e f i n i t i o n . The smaller grain sizes were also checked by a grain count taken from r e p l i c a s examined i n the electron microscope. When grain sizes i n p o l y c r y s t a l l i n e cobalt are c i t e d , i t should be noted that the values given refer to the high temperature fee phase. D i f f i c u l t y arises i n measuring the fee grain size because of the d i s t r i b u t i o n of hep martensitic plates i n the fee grains. The r e l a t i o n s h i p between the grain size and the fineness of the hep structure i s complex. A l l specimens are p a r t i a l l y fee after annealing regardless of the grain size, but the grain size a f f e c t s the amount of retained fee phase i n two d i s t i n c t ways. F i r s t , as the fee grain size increases above a ce r t a i n small value the amount of retained fee decreases r a p i d l y . For large grain sizes, the amount of retained fee remains constant at approximately 10%. Secondly, as the grain size increases the multivariance of the transformation changes, that i s , the manner' i n which the retained fee i s di s t r i b u t e d throughout a grain changes. This r e s u l t occurs because the distance over which each martensite plate may propogate before being obstructed changes with grain s i z e . This distance can be further divided as to " i n a d i r e c t i o n p a r a l l e l to" and " i n a di r e c t i o n perpedicular to" the martensitic plates as they grow. The main point to be drawn from what has been said above i s that the measured grain size i s not an i n d i c a t i o n of the size of regions of c r y s t a l l a t t i c e having the same c r y s t a l structure. The measured value should be considered a measure of the coarsness of the fee structure e x i s t i n g before transformation takes place. On the following pages (Figure 6 - 9 ) the annealed structures of the cobalt used i n t h i s study are presented. The grain structure i s not an equilibrium structure; the boundaries present are often straight and change d i r e c t i o n at r i g h t or acute angles. A large amount of i n t e r n a l structure i s v i s i b l e which causes d i f f i c u l t y i n determining i n d i v i d u a l grains. An analysis of t h i s i n t e r n a l structure i s presented following discussion of the completeness of the transformation. 3.1.3 Completeness of Transformation X-ray procedures were performed on various areas of i n d i v i d u a l specimens. The scatter i n data from one area of a specimen to another was found to be within +5% with occasional e r r a t i c r e s u l t s . The e r r a t i c r e s u l t s were always low and attributed to improper handling. The scatter i n r e s u l t s from one specimen to another was found to be greater than that within a given specimen. It became apparent that not only the variations i n as received material but also the specimen preparation procedures involving machining, could influence r a d i c a l l y the amount of retained fee phase. (Table V). 48 F i g . 6 Annea l ing spectrum i n 99.9% c o b a l t . 340X 49 F i g . 7 99.7% c o b a l t , annealed a t 600°C (a) and 800°C (b) 1 hr. F i g . 8 99.9% c o b a l t , annealed a t 900°r f o r 1 hr. 39u. m ' S"« * df* " r i , - . V . (a) - 9y (b) - 47y F i g . 9 99.998% c o b a l t , annealed a t 600°C (a) and 800°C (b) 1 hr. TABLE V Summary of Retained FCC Data Purity Anneal 99. 7% 99.9% A 99.9% B 99.9% C 99.9% Total 99. 998% 450°C - 1 Hr 49.5 49.5 500°C - 1 Hr 59.5 55.1 56.8 550°C - 1 Hr 50.7 43.1 46.0 600°C - 1 Hr 59. 4 49.6 41.1 42.7 40. 8 650°C - 1 Hr 38.7 30.4 33.5 700°C - 1 Hr 46. 5 45.3 37.2 41.1 31. 7 750°C - 1 Hr 31.8 31.8 800°C - 1 Hr 41. 8 41.6 25.3 34.0 30. 9 800°C - 1 Hr 27.3 27.3 900°C - 1 Hr 17.0 17.0 1000°C L Hr 14.1 14.1 A, B, C, represent d i f f e r e n t l o t s of "as received" material The differences between various batches of material could not be r e c t i f i e d "after the fac t " but the influence of specimen preparation was removed by electropolishing a minimum of 100 microns from the surface of a l l specimens before any heat treatment. In t h i s way, anomalous r e s u l t s were avoided. The r e s u l t s of the x-ray analysis on annealed specimens are given i n Figure 10. The scatter i n the r e s u l t s i s large, e s p e c i a l l y when i t i s considered that each point 60 50 u 40 u T3 (D C •H 4-> QJ PI 30 20 10 60 50 40 30 - u u m c •H 4-> 0 ) <*> 20 0 A • • • 99.7% c o b a l t G 99.9% c o b a l t A 99.998% c o b a l t I 99.9% c o b a l t annealed a t 500°C and 550°C. _L 10 20 30 40 G r a i n S i z e (u) 50 60 F i g . 10(a) % r e t a i n e d fee vs g r a i n s i z e J- g 99.7% c o b a l t 0 99.9% c o b a l t A 99.998% c o b a l t O 99.6% c o b a l t - M u l l e r 8 3 o A * io - o o J- ± ± 4. 0 0.1 0.2 7_ 0.3 .0.4 1//Grain S i z e (y . ) F i g . 10(b) % r e t a i n e d fee vs 1//Grain Si.ze , . F i q . 10 Progress of the t r a n s f o r m a t i o n as a f u n c t i o n of q r a m s i z e r e p r e s e n t s between 1 0 and 4 0 specimens ( 5 0 - 2 0 0 x-ray a n a l y s e s ) . N e v e r t h e l e s s , they are t y p i c a l of r e s u l t s p u b l i s h e d e l s e w h e r e 8 2 . The important q u a n t i t a t i v e r e s u l t s are c l e a r . The amount of r e t a i n e d fee i s an important f u n c t i o n of g r a i n s i z e , d e c r e a s i n g very q u i c k l y as the g r a i n s i z e i n c r e a s e s . A l s o , as the p u r i t y i s i n c r e a s e d , the t r a n s f o r m a t i o n proceeds f u r t h e r towards completion. These r e s u l t s may be e x p l a i n e d i n terms of d e f e c t s t r u c t u r e . A small g r a i n s i z e r e s u l t s from a low temperature anneal. The m o b i l i t y and a n n i h i l a t i o n of l a t t i c e d e f e c t s t h a t may take p l a c e a t t h i s low temperature i s more l i m i t e d than f o r annealing treatments y i e l d i n g l a r g e g r a i n e d m a t e r i a l . Many n u c l e i f o r the t r a n s f o r m a t i o n are a v a i l a b l e but r e g i o n s through which the n u c l e i may operate f r e e of strong o b s t a c l e s such as g r a i n boundaries or other m a r t e n s i t i c p l a t e s are s m a l l . Thus, we have a s i t u a t i o n where many n u c l e i are p r e s e n t but the growth of the n u c l e i i s s t r i c t l y l i m i t e d . For l a r g e g r a i n s i z e s the d e f e c t s t r u c t u r e i s l e s s dense; fewer n u c l e i are a v a i l a b l e to t r a n s f o r m the l a t t i c e from fee to hep. I f a n u c l e i begins to grow i n the l a r g e g r a i n e d m a t e r i a l , i t may propogate through a l a r g e r r e g i o n of c r y s t a l b e f o r e i n t e r f e r e n c e from other m u l t i v a r i a n t p l a t e s or g r a i n boundaries c o n s t r a i n f u r t h e r growth. I t i s c l e a r from the x-ray data t h a t t h i s l a t t e r s i t u a t i o n g i v e s r i s e to a more complete t r a n s f o r m a t i o n . The increasing d i f f i c u l t y i n completing the trans- formation as the impurity content increases i s due to subs t i t u t i o n a l atoms toughening the l a t t i c e for d i s l o c a t i o n movement. The locking of stacking f a u l t s i n t h i s manner, making i t d i f f i c u l t for them to move and transform the l a t t i c e , has been observed by A l t s t e t t e r et a l 2 8 - 3 1 . The present observations agree with data taken from the l i t e r a t u r e . Beckers 8 2 observed maximum retained fee (50-60%) by annealing at 500-600°C and observed a drop to approximately 30% fee for 800°C anneals. Grain sizes were not quoted but they may be assumed to be i n the same general range as i n the present study. F r a s e r 8 1 , also found the maximum retained face-centred phase to occur i n t h i s annealing range. M u l l e r 8 3 annealed sheet cobalt of various p u r i t i e s , between 800 and 1300°C and determined that from 300 micron to 30,000 micron grain si z e , the retained fee phase amounted to approximately 10%. For his f i n e s t grain size of 35 microns, he measured approximately 4 0% retained fee. Other data from the l i t e r a t u r e i s available but i t i s based on powder specimens 8 k ' 5 5 ~ 5 7 . As mentioned e a r l i e r , polarized l i g h t was investigated as a secondary t o o l for determining the d i s t r i b u t i o n of the two phases i n cobalt. A photomicrograph i s reproduced for a large grained specimen i n Figure 11. The material i s 99.998% cobalt with an average grain size of approximately 47 microns. Figure 11 shows the complexity of the trans- formation within a grain i n a very s t r i k i n g manner. The central grain has been strongly constrained during the transformation. It was o r i g i n a l l y a twinned fee grain and F i g . 1 1 99.9981 C o b a l t u n d e r p o l a r i z e d l i g h t . 900X the multivariant transformation shows more than 4 planes on which the transformation has proceeded. The dark areas i n t h i s grain remain dark throughout the rotation of the polarizer and are retained fee areas. X-ray analysis of t h i s specimen y i e l d s 31% retained fee phase at room temperature which approximates the value taken from the polarized l i g h t photomicrograph. 3.1.4 Discussion and Summary The following discussion outlines the structures that w i l l occur i n p o l y c r y s t a l cobalt following standard annealing procedures. The microstructures observed may be a r b i t r a r i l y c l a s s i f i e d on the basis of annealing temperature. The three types of treatment discussed are: a) annealing just above the transformation temperature (approximately 450°C) b) annealing i n the range where maximum fee phase i s retained (500 - 600°C). c) annealing above 600°C where grain growth predominates. The structures produced i n cobalt are related to an annealing treatment as outlined i n Figure 12. In a l l cases, the s t a r t i n g material i s severely cold worked and of physical dimensions large compared to the fee grain s i z e . t CD u -p ro u CD P, e CU EH A T = t time annealing temperature = time at annealing temperature = time i n fee phase A = the temperature at which the fee phase begins to form on heating M = the temperature at which the hep phase begins to form on cooling = the highest temperature at which the hep phase can be produced by deformation A^ = the lowest temperature at which fee phase can be produced by deformation M, - A, - 417°C 3 d d F i a . 12 Annealing Parameters a) Annealing just above the transformation temperature (A g) Upon heating through the transformation, the specimen undergoes recovery and polygonization. Simultaneously, the structure transforms completely to the high temperature fee phase. The transformation i s nucleated at stacking f a u l t s i n the hep phase or at retained regions of f e e 2 7 ' 7 8 . From many nucl e i , fee grains with a dense defect structure are formed. The transformation upon heating i s accompanied by an increase i n volume. The t h e o r e t i c a l maximum increase possible i s 3.6 X i o - 3 2 8 " 3 1 . (see Figure 13). The f a u l t density i n the room temperature product depends upon " t " . If t, i s very small, less than one minute, the number of deformation f a u l t s w i l l be reduced and the number of growth f a u l t s w i l l be higher than o r i g i n a l l y present. If t, i s large, the number of deformation f a u l t s w i l l approach zero, but the growth f a u l t density w i l l remain high. If t, i s greater than several minutes r e c r y s t a l l i z a t i o n begins at grain boundaries. A part of the d r i v i n g force appears to be a supersaturation of vacancies giving r i s e to r e c r y s t a l l i z a t i o n n u c l e i 1 0 1 . A one hour anneal at 450°C produces a p a r t i a l l y r e c r y s t a l l i z e d structure (Figure 6). Long time anneals at t h i s temperature do not y i e l d a f u l l y r e c r y s t a l l i z e d structure. Upon cooling, the volumes of c r y s t a l l a t t i c e where r e c r y s t a l l i z a t i o n has not occured, transform to the hep phase on the same l a t t i c e planes that operated during the 53 Heat ing Transformat ion hep fee p o s i t i v e volume change - 0.3% -3 4.2 X 10 expansion pe rpend icu l a r to b a s a l plane -3 0.3 X 10 c o n t r a c t i o n p a r a l l e l to b a s a l plane 0.3 X 10 -3 Transformat ion h a b i t plane (0001) (111) hep fee 4.2 X 10 Shear Values S c 1 9 ° 2 8 1 0.3 56 C o o l i n g Transformat ion fee -* hep decrease i n volume -0.3% -3 4.2 X 10 c o n t r a c t i o n pe rpend icu l a r to b a s a l plane -3 0.3 X 10 expansion p a r a l l e l to b a s a l plane F i g . 13 Volume changes du r ing the m a r t e n s i t i c t r ans fo rma t ion i n c o b a l t . heating c y c l e 1 1 1 2 7 ' 7 1 . The transformation proceeds i n t h i s manner because high densities of di s l o c a t i o n s are not available on planes other than the (111) variant corresponding to (0001) hep above the transformation temperature. In the areas that have undergone r e c r y s t a l l i z a t i o n , d i s l o c a t i o n densities are si m i l a r on a l l {111} planes. The planes that w i l l operate to form the hep phase upon cooling w i l l be determined by the constraints imposed on these new fee grains. The constraints ar i s e from the decrease i n volume accompanying the transformation, and the thermal anisotropy of the hep l a t t i c e . The amount of retained fee r e s u l t i n g from t h i s p a r t i a l l y r e c r y s t a l l i z e d structure at room temperature varies over a wide range, but i s invariable high (30% - 65%). b) Annealing i n the range 500 - 600°C A treatment of t h i s nature gives r i s e to complete r e c r y s t a l l i z a t i o n . A small amount of grain growth may occur at the higher temperature. The growth f a u l t density w i l l be high i n the room temperature product while the deformation f a u l t density w i l l be low. The size of grains i n any i n d i v i d u a l specimen varies over a wide range and cannot be considered an equilibrium structure. Many straight and acute angle boundaries are present as well as a va r i e t y of substructure. The v i s i b l e substructure varies according to the etching procedures 9 3. Figures 9(a) and 14 show the structure obtained by attack F i g . 14 E t c h i n g of g r a i n F i g . 15(a) 99.9% c o b a l t , boundaries and m a r t e n s i t e 4000X p l a t e s . 99.7% c o b a l t . 920X F i g . 15(b) 99.9% c o b a l t . F i g . 15(c) 99.9% c o b a l t . 10,000X 10,000X on both the grain boundaries and martensite plate boundarie It should be noted that plate intergrowth or overgrowth i n d i f f e r e n t d i r e c t i o n s at d i f f e r e n t depths into the grains i s evident. As outlined by F e l l e r 9 2 , p r e f e r e n t i a l etching of c e r t a i n l a t t i c e planes may occur i n cobalt. This phenomena i s shown i n Figure 15. The etching procedure c l e a r l y delineates regions of l a t t i c e of d i f f e r i n g o rientation. The average grain size obtained i n t h i s annealing range i s less than 10 microns for a l l purity l e v e l s investigated. Two t y p i c a l views for 99.9% Co are shown in Figure 16. Surface t i l t i n g due to transformation i s often severe i n t h i s f i n e grained material as shown i n Figure 17. This surface was electropolished before heat treatment but no further etching was performed. The shear markings due to the martensitic transformation are obvious. Optical metallography i s discouraging for cobalt and thus r e p l i c a work i s presented to confirm the detailed appearance of the surface i n small grained specimens. A range of structures i s observed on a single surface of a grain. The most common features are as follows: i) A few grains have the appearance of a single c r y s t a l upon viewing a single plane through the grain. These grains l i k e l y contain some multivarient plate growth at constrained grain boundary regions: (Figure 16 (a) ) . 62 F i g . 16 99.9% cobalt, 6.5 micron grain size, 4000X F i g . 17 Shear markings follow- ing heat treatment. 6500X F i g . 18 Annealing twin boundaries i n 99.9% cobalt. 5000X 63 i i ) Many grains exhibit d i f f e r e n t o r i e n t a t i o n i n areas delineated by annealing twin boundaries i n the fee phase; (Figures 15 and 18). i i i ) Some grains appear to have random areas of d i f f e r e n t orientation throughout. This type of substructure i s shown c l e a r l y under polarized l i g h t (Figure 11). iv) A banded structure i s detected i n some grains; (Figure 19). These bands are interpreted as hep regions d i f f e r i n g only i n operational shear d i r e c t i o n i n a given (111) type varient during transformation. A similar r e s u l t has been noted for a martensitic transformation i n the copper-germanium system 7 9 and postulated for cobalt i n discussions by Ne l s o n 2 8 . The bands resolved v i a r e p l i c a techniques are 0.1 to 1.0 microns thick and completely traverse a grain. Bands of t h i s thickness require operation of similar p a r t i a l d i s l o c a t i o n s on 150 to 1500 close-packed planes. The f a c t that t h i s banded structure i s not always observed i s explained by the fineness with which the transformation may operate with respect to shear d i r e c t i o n s . If the shear d i r e c t i o n changes every few close-packed planes, shear markings are too fine to discern by r e p l i c a techniques. Bands are observed only when the constraints on a volume of c r y s t a l y i e l d a strong preference for a given shear d i r e c t i o n . This analysis explains why for some years there was a dispute over the martensitic nature of the transformation i n cobalt. Without the aid of the electron microscope, the shear i s d i f f i c u l t to discern. F i g . 19(a) 4000X F i g . 19(b) 10,000X F i g s . 19(a) - 19(c) Banded s t r u c t u r e a r i s i n g from coplaner m u l t i v a r i a n c e i n c o b a l t . F i g . 19(c) 10,000X F i g . 20 99.998% c o b a l t , 47 micron g r a i n s i z e , 2000X 65 For a n n e a l i n g treatments w i t h T between 500 and 600°C, the r e t a i n e d fee phase i s a maximum. At room temperature, a l l specimens are 40 - 60% f e e . The r e t a i n e d phase does not occur as i n d i v i d u a l fee g r a i n s , but as r e g i o n s of fee l a t t i c e d i s t r i b u t e d w i t h i n i n d i v i d u a l g r a i n s . c) Annealing above 600°C An a n n e a l i n g c y c l e above 600°C g i v e s r i s e to g r a i n growth. For 99.998% c o b a l t , g r a i n growth i s proceeding r a p i d l y a t 600°C w h i l e f o r 99.7% c o b a l t , g r a i n growth i s b a r e l y underway. As the fee g r a i n s i z e i n c r e a s e s , the g r a i n s u b s t r u c t u r e observed a t room temperature becomes l e s s complex. The banded s t r u c t u r e noted i n f i n e g r a i n e d m a t e r i a l i s not observed f o r g r a i n s i z e s over approximately 15 microns. Large volumes of c r y s t a l t r a n s f o r m on a s i n g l e (111) v a r i e n t i n l a r g e g r a i n s . M u l t i v a r i a n c e occurs but the p l a t e s of d i f f e r e n t o r i e n t a t i o n are c o a r s e r than f o r f i n e g r a i n e d m a t e r i a l : (Figure 20 ) . As the g r a i n s i z e i n c r e a s e s the amount of r e t a i n e d fee decreases. For an fee g r a i n s i z e of 50 microns, approximately 3 0% of the l a t t i c e remains f e e . For g r a i n s i z e s over 300 microns, t h i s v a l u e drops t o 10% r e t a i n e d f e e . For the l i m i t i n g case of a s i n g l e c r y s t a l the t r a n s f o r m a t i o n proceeds to completion. The s t r u c t u r e of the c o b a l t specimens produced f o r f u r t h e r t e s t i n g may be summarized as f o l l o w s : i ) A l l specimens were r e c r y s t a l l i z e d c o b a l t , furnace c o o l e d to room temperature a t approximately 6°C per minute. T h e i r p u r i t y ranged from 99.7% to 99.998%. i i ) The g r a i n s i z e f o r the m a t e r i a l v a r i e d from l e s s than 5 to over 50 microns, w h i l e the r e t a i n e d fee decreased from over 50% to l e s s than 30%. i i i ) A l l p o l y c r y s t a l g r a i n s were a mixture of fee and hep phases. Most c r y s t a l s had hep r e g i o n s of d i f f e r e n t o r i e n t a t i o n w i t h very s t r i c t o r i e n t a t i o n r e l a t i o n s h i p s . That i s , a l l hep r e g i o n s were stack s of close-packed planes t h a t i n t e r s e c t a t angles between {111} planes i n the parent fee g r a i n . i v ) The s t r u c t u r e was not an e q u i l i b r i u m one. The thermodynamic d r i v i n g f o r c e attempting to complete the m a r t e n s i t i c t r a n s f o r m a t i o n was a v a i l a b l e , but i t was so small t h a t the c o n s t r a i n t s a r i s i n g from thermal a n i s o t r o p y and the volume change i n v o l v e d i n the t r a n s - formation r e t a i n e d m a t e r i a l i n the fee phase. v) The s u b s t r u c t u r e w i t h i n g r a i n s was v a r i e d . The shear produced by t r a n s f o r m a t i o n d e l i n e a t e d a n n e a l i n g twin boundaries i n the parent fee g r a i n s . The growth of m a r t e n s i t i c p l a t e s on more than one (111) type planes, termed m u l t i v a r i a n c e , was always pres e n t . Repeated t r a n s f o r m a t i o n i n a <112> d i r e c t i o n i n a g i v e n (111) plane produced a banded s t r u c t u r e i n f i n e g r a i n e d m a t e r i a l . 3.2 Tensile Behaviour of Cobalt Polvcrvstals 3.2.1 Tensile Results 3.2.1.1 True Stress - True Strain Curves True stress - true s t r a i n curves for cobalt at selected t e s t temperatures are shown i n Figures 21-23. The behaviour as a function of grain s^ze i s shown i n Figure 24. Several important observations may be drawn from t h i s data; i) the measured stress l e v e l s appear high for a pure metal. The ultimate t e n s i l e strength at room 3 temperature exceeds 150 X 10 p s i for fi n e grained material. i i ) the temperature dependence of the flow stress i s large. As shown i n Figures 21-23 the flow stress at y i e l d increases by greater than a factor of 2 for a temperature change from 400°C to. -196°C. The ultimate strength decreases by a factor of 5 over the same temperature range (Figure 21). i i i ) the y i e l d stress decreases by a factor of 2 as the grain size i s increased from 6.5 microns to 60 microns (Figure 24). iv) the t e n s i l e curves exhibit an i n f l e c t i o n i n the i n i t i a l portion of the curve. This anomaly i s shown c l e a r l y i n Figure 22 for 99.9% cobalt. The strength of cobalt i s compared to other common hep metals i n Figure 25 (a). The t e n s i l e behaviour for hep metals having c/a r a t i o s higher (Zn), si m i l a r (Mg), and lower (Ti) than cobalt are included. The data i s presented 400°C Ol 1 1 I 1 I I L 0 2 4 6 8 10 12 14 F i g . 21 True True S t r a i n (%) s t r e s s - t rue s t r a i n curves a t s e l e c t e d temperatures , 99.998% c o b a l t . 69 70 250 G r a i n S i z e -196°C (fee) 8 10 12 14 True S t r a i n (%) 16 18 20 22 F i g . 23 True s t r e s s - s t r a i n curves a t s e l e c t e d temperatures , 99.7% c o b a l t . 0 14 16 2 4 6 8 10 12 True S t r a i n (%) F i g . 24 True s t r e s s - t rue s t r a i n curves a t 20°C 18 20 22 c o b a l t .  for room temperature properties normalized to reduce the af f e c t s of shear modulus and melting point. The fact that cobalt undergoes a martensitic transformation during deformation whereas the other metals l i s t e d cio not, makes comparisons on the basis of c r y s t a l structure tenuous. In Table II the c r i t i c a l l y resolved shear stress for a va r i e t y of metals i s l i s t e d . It would appear that the common hep metals may be divided into two groups on the basis of flow stress. One group (Cd, Zn, Mg) which demonstrates a low c r i t i c a l l y resolved shear stress, s i m i l a r to the majority of fee metals, arid a second group comprised of Co, Zr, T i , and Be which exhibit much higher values of resolved shear stress. The importance that must be attached to the presence of grain boundaries i n the hep metals i s revealed c l e a r l y when the single c r y s t a l data i n Table II i s compared to the p o l y c r y s t a l data shown in Figure 25 (a). Single c r y s t a l s of T i are much stronger than single c r y s t a l s of the other metals shown i n Figure 25 (a) yet i n p o l y c r y s t a l l i n e form T i cannot be considered a strong hep metal when compared to Zn, Co, or Mg. This apparent contradiction occurs because T i may overcome more e a s i l y than the other metals, the requirement that coherency be retained at grain boundaries. At room temperature, titanium s l i p s on the basal, prism and pyramidal systems. Although both Mg and Zn deform at very low stresses as single c r y s t a l s , the constraint imposed by the introduction of g r a i n boundaries r a d i c a l l y i n c r e a s e s the s t r e s s l e v e l s r e q u i r e d t o c o n t i n u e deformation. In Zn, coherency a t g r a i n boundaries i s maintained by d i s l o c a t i o n motion on the c o r r u g a t e d s l i p planes i n a d d i t i o n to the b a s a l p l a n e s . The normalized s t r e s s l e v e l r e q u i r e d t o m a i n t a i n coherency 'at g r a i n boundaries appears to be high e r f o r Zn than T i . For Mg, the o p e r a t i o n of s u f f i c i e n t s l i p systems t o s a t i s f y Von Mise's C r i t e r i o n r e q u i r e s v e r y h i g h s t r e s s l e v e l s as r e f l e c t e d by the steep curve a s s o c i a t e d w i t h t h i s metal. Co wit h the same c/a r a t i o as Mg i s unique i n th a t i t i s a mixture of two c l o s e packed phases, fee and hep. The r e s u l t s f o r c o b a l t f a l l between those f o r Zn and Mg. The data o u t l i n e d above shows t h a t the observed behaviour of hep s i n g l e c r y s t a l s may not be g e n e r a l i z e d t o i n c l u d e p o l y c r y s t a l s . The l i m i t e d numbers of o p e r a t i v e s l i p systems i n hep metals r e q u i r e t h a t each metal must be i n v e s t i g a t e d i n d i v i d u a l l y . In F i g u r e 25(b) curves f o r Co and a group of fee metals are shown. Two o b s e r v a t i o n s may be made. Co b a l t i s c o n s i d e r a b l y s t r o n g e r than Ag, Cu, or A l on a normalized b a s i s . Secondly, the a f f e c t of g r a i n refinement i s c l e a r l y l a r g e r f o r c o b a l t . For s m a l l g r a i n e d c o b a l t an anomaly i n the t r u e s t r e s s - t r u e s t r a i n curves occurs a t low s t r a i n v a l u e s , F i g u r e s 22-24. The anomaly i s not as pronounced f o r 99.99 8% c o b a l t . Although p u b l i s h e d curves are a v a i l a b l e , no mention has been made of t h i s e f f e c t i n c o b a l t 8 1 - 8 3 . T h i s i s not s u r p r i s i n g , as the anomaly i s not l a r g e and becomes c l e a r o n l y a f t e r c a l c u l a t i n g t r u e s t r e s s v a l u e s f o r many value s of s t r a i n and p l o t t i n g t o a l a r g e s c a l e . 74 0 10 20 30 True S t r a i n (%) F i g . 25(b) Nominal s t r e s s - s t r a i n curves fo r Co, A g , Cu, and A l . The anomaly i s not obvious for a l l specimens, but i s most pronounced for specimens having a f i n e grain s i z e . A small grain size i s equivalent to a large i n i t i a l f r a c t i o n of retained fee, i n other words a large volume of material available for martensitic transformation. Published true stress - true s t r a i n curves for materials known to transform m a r t e n s i t i c a l l y during deformation are presented i n Figure 26. Included are data for 303 s t a i n l e s s s t e e l 1 0 5 , Hadfield's Manganese Steel 1 0 5, equi-atomic N i - T i 1 0 6 , and cobalt. / The retained high temperature phase i n 18-8 s t a i n l e s s steel and Hadfield's Manganese s t e e l i s fee. Some hep martensite i s generated by p l a s t i c deformation i n the 18-8 s t a i n l e s s . This hep martensite i s believed to be a tran- s i t i o n phase and most of the end product martensite produced i s bcci o 5. This stress induced martensite gives r i s e to the low i n i t i a l work hardening rate i n the 18-8 s t a i n l e s s steel at l i q u i d nitrogen temperatures 1 0 5. A si m i l a r explanation i s proposed |:or the anomalous behaviour i n the equi-atomic N i - T i shown. The large anomaly observed for 18-8 s t a i n l e s s and equi-atomic Ni-^Ti are not evident for Hadfield's Manganese Steel. Although a l l four materials transform to martensite while undergoing deformation, i t i s probable that no i n i t i a l low s t r a i n hardening occurs i n Hadfield's s t e e l because no s i g n i f i c a n t quantity of low energy martensite i s formed. Of a l l martensitic transformations the transformation from fee to hep i s the lowest energy form, requiring only a simple shear which need not be accompanied 76 •H LQ X IC W d) -P <L> EH 350 300 250 200 150 100 50 1 8 - 8 s t a i n l e s s s t e e l 1 1 10 20 JL 30 1 H a d f i e l d ' s s t e e l References Co - present work N i - T i - M a r c i n k o w s k i 1 0 5 18-8 s t a i n l e s s and H a d f i e l d ' s s t e e l - Raghaven 1 0 6 40 1 50 60 1 70 80 F i g . 26 True S t r a i n (%) True s t r e s s - t r u e s t r a i n curves f o r m a t e r i a l s undergoing s t r a i n induced m a r t e n s i t i c t r a n s f o r m a t i o n by further deformation to form the second phase (Table VI). Thus, while 18-8 stain l e s s s t e e l forms a low energy form of hep martensite and Ni-Ti does likewise, the Hadfield's steel probably forms a more complex martensite d i r e c t l y . Cobalt, l i k e the 18-8 stain l e s s ste e l and the N i - T i formij a simple hexagonal structure from the fee phase. The anomalies are larger for the 18-8 stain l e s s s t e e l and Ni-T i because these materials are i n i t i a l l y 100% retained face-centered phase while cobalt i s a mixture of both phases. TABLE VI M a r t e n s i t e Transformations i n Non-Ferrous M a t e r i a l s M a t e r i a l and S t r u c t u r a l A d d i t i o n a l Composition Change Deformation I n - T l (^20 a t . % T l ) fee -- f c t T, S Au-Cu (o,50 a t . % Cu) fee — o r t h o . T, P Au-Mn (^50 a t . % Mn) bee -- bet T Au-Cd (^50 a t . % Cd) bee — bet T, M, S Au-Cd ("V4 7.5 a t . % Cd) bee — o r t h o . T, M, S U-Mo (5-10 a t . % Mo) bee — o r t h o . T, F Cu-Zn (^40 wt. % Zn) bee -- o r t h o . T, E II I I bee -- fee T, c , E Cu-Al (^12 wt. % A l ) bee — o r t h o . T, E, P f l I I bee — fee F, E II II bee  t e t . F, E, P L i bee — hep T, E, p T i , Zr - bee — hep T, D, 7 Ti-Mn (^5wt. % Mn) bee — hep T, 7 U-Cr (^1 a t . % Cr) t e t . -- ortho. D, p Hg rhomb. — bet p Co fee — hep X N o t a t i o n : T Twinning X No a d d i t i o n a l deformation r e q u i r e d ? Unknown or i n f o r m a t i o n u n c e r t a i n C Tra n s f o r m a t i o n i n t h i n f o i l D Common deformation modes E T h i n f o i l o b s e r v a t i o n s made M Parent s t r u c t u r e ordered P Product s t r u c t u r e ordered S S i n g l e i n t e r f a c e t r a n s - formation observed 3 . 2 . 1 . 2 Y i e l d S t r e s s and U l t i m a t e T e n s i l e S t r e s s To determine and i s o l a t e the e f f e c t of p u r i t y on the y i e l d s t r e n g t h of c o b a l t , a l a r g e number of t e s t s were c a r r i e d out on m a t e r i a l of 99.7% and 99.998% p u r i t y w i t h s i m i l a r g r a i n s i z e s . Some v a r i a t i o n i n the i n i t i a l amount of r e t a i n e d f a c e - c e n t e r e d phase was unavoidable. From F i g u r e 5 , i t was observed t h a t 99.7% c o b a l t annealed one hour a t 700°C has a g r a i n s i z e of approximately 10 microns, as does 99.998% c o b a l t annealed one hour a t 600°C. The i n i t i a l amount of r e t a i n e d fee phase i s 46.5% f o r the low p u r i t y m a t e r i a l and 4 0.8% f o r the high p u r i t y m a t e r i a l . As shown i n F i g u r e 27, the e f f e c t of i n c r e a s i n g p u r i t y on the 0.2% o f f s e t y i e l d s t r e s s i n c o b a l t i s not l a r g e . I n c r e a s i n g p u r i t y from 99.7% to 99.998% decreases the y i e l d s t r e s s by approximately 4000 p s i f o r m a t e r i a l w i t h a 10 micron g r a i n s i z e . The d i f f e r e n c e i n s t r e n g t h between the two grades of m a t e r i a l remains constant throughout the temperature range from -196°C to +400°C. From the data presented i n F i g u r e 27, i t i s c l e a r t h a t the y i e l d s t r e n g t h of p o l y c r y s t a l c o b a l t i s not a stro n g f u n c t i o n of im p u r i t y content a t the l e v e l s i n v e s t i g a t e d . Although p u r i t y does not a f f e c t the y i e l d s t r e n g t h i n a str o n g f a s h i o n d i r e c t l y , the imp u r i t y d i f f e r e n c e s cause l a r g e v a r i a t i o n s i n y i e l d s t r e n g t h f o r i d e n t i c a l annealing treatments. In other words, the y i e l d s t r e n g t h i s a strong f u n c t i o n of g r a i n s i z e . T e n s i l e data f o r c o b a l t  has commonly been tabulated with reference to annealing temperature 8 1 < 8 2' 8 8. The discrepancies i n t h i s data would be reduced i f the t e n s i l e parameters were normalized to account for grain s i z e . For example, 99.7% cobalt and 99.998% cobalt having undergone i d e n t i c a l (one hour) annealing treatments at 800°C, d i f f e r i n y i e l d strength by approximately 30,000 p s i . (See Figure 28). The v a r i a t i o n i n stress with test temperature i s shown in Figures 28 and 29. For a l l materials, the temperature dependence of the y i e l d stress has two d i s t i n c t regions. At low temperatures, the y i e l d stress decreases very slowly with increasing temperature. At higher temperatures, the y i e l d stress drops rapidly with temperature; the e f f e c t i s not as pronounced for large grained material. (Figure 28). Due to the scatter i n re s u l t s between in d i v i d u a l test specimens, esp e c i a l l y regarding the y i e l d stress, i t was d i f f i c u l t to accurately define the two regions of temperature dependence. In an attempt to a l l e v i a t e t h i s problem a further group of specimens were tested. Single specimens were step pulled over the complete temperature range from -196°C to 400°C. Some specimens were i n i t i a l l y yielded at low temperatures and others at high temperatures. , The specimens were then retested every 20 or 30 °C for small increments of s t r a i n . An int e r s e c t method was used to subtract out the work hardening that had taken place up to the given step-pull being analyzed to arrive at the y i e l d stress for the temperature i n question. Test Temperature (°C) F i g . 28 Y i e l d S t ress data for p o l y c r y s t a l c o b a l t . 00 120 U •H M C •H X LO CO 0) -p CO 0) EH CO CO QJ u +> CC T j i H 0) - H >H 0\° 100 F i g , 99.9% c o b a l t - 42.7% fee 99.9% c o b a l t - s t e p - p u l l r e s u l t s -200 -100 300 400 100 200 Test Temperature (°C) 2 9 Comparison of y i e l d s t r e s s data obta ined by i n d i v i d u a l t e s t s and i n t e r u p t e d s i n g l e specimen t e s t i n g . 99.9-%. c o b a l t , 6 . 5 micron g r a i n s i z e CO The data provided by t h i s type of tes t must be evaluated c a r e f u l l y . In addition to physical measurement problems, there are other areas for concern. The stress relaxation that i s attendant to the martensitic transformation of cobalt can cause anomalies upon re y i e l d i n g specimens of c o b a l t 1 0 7 - 1 0 9 At higher temperatures, dynamic recovery may occur while testing and recovery procedes during the lapses while the temperature of the testing environment i s being adjusted. A large correction must be applied to the raw t e n s i l e data to adjust for the v a r i a t i o n of work hardening rate with s t r a i n and temperature. The calculations c a r r i e d out for tests of t h i s type are outlined i n Appendix 2. Figure 29 i s a plot of step-pull test data for 99.9% cobalt annealed one hour at 600°C. The data gathered from many ind i v i d u a l tests i s included for comparison. The agreement between the two sets of data i s encouraging. Further tests were carried out over various temperature ranges with a vari e t y of specimens. In a l l cases, acceptable agreement with the re s u l t s determined by many tests were found. Figure 28 presents the v a r i a t i o n i n y i e l d stress v/ith test temperature for a l l material tested. The pertinent information to be drawn from t h i s graph i s reproduced i n Table VII. Two important observations may be made. The temperature dependence of y i e l d stress has two d i s t i n c t regions and y i e l d stress i s a strong function of grain TABLE VII Polycrystal Cobalt - 0.2% Yi e l d Stress Data Grain Size (u) Puritv (%) 0.2% Yi e l d Stress (True Stress X G Q / G / True Stress) -196°C 20°C 250°C 400°C Temp, for Slope Change °C " T / T . m Slope at High Temp, Slope at Low Temp. 6. 5 99.9 104.0/101. 2 98.0/88.3 78.0/62.5 50.0/38.9 160 0.25 7.2 7. 0 99.7 99.5/ 96. 8 97.0/87.4 72.0/61.7 53.0/41.2 128 0.22 14.8 9. 0 99.998 '86 .5/ 84. 2 81.5/73.4 68.0/54.5 48.5/37.7 167 0.25 8.0 10. 3 99.7 89.0/ 86. 6 86.0/77.4 75.0/60.0 53.0/41.2 195 0.27 9.0 14. 5 99.9 88.0/ 85. 6 82.5/74.3 73.0/58.5 50.0/38.9 225 0.28 6.0 17. 5 99.7 81.5/ 79. 3 79.0/71.1 72.5/58.1 53.0/41.2 220 0.28 8.9 23. 5 99.998 78.0/ 75. 9 71.5/64.4 56.0/44.9 36.0/28.0 170 0.25 7.2 24. 0 99.9 75.0/ 72. 7 66.0/58.4 55.0/44.1 39.0/30.3 225 0.28 2.3 47. 0 99.998 48.5/ 47. 2 47.0/42.3 45.0/35.5 33.0/25.0 288 0.32 11.5 <6. 5 99.9 95.5/ 92. g* 100.4/90.4* 81.4/65.2* 62.0/48.2* - - - 60. 0 99.9 — 49.2/44.3* — — — — — * Single Tensile Test 00 The y i e l d stress behaviour of cobalt as a function of temperature i s unlike that for most common m e t a l s 3 3 . In copper, zinc, and molybdenum for example, the y i e l d stress drops steeply with increasing temperatures at low temperatures and becomes r e l a t i v e l y temperature independent at higher temperatures. Similar behaviour i s observed i n po l y c r y s t a l magnesium 3 2 and single c r y s t a l cobalt 1*. For 65 micron magnesium, the y i e l d stress decreases slowly with temperature up to 0 .21 T m (-80°C) and then drops quickly u n t i l 0 .43 T m (125°C) i s reached. Beyond 0.43 T the v i e l d stress continues to decrease at a lower m rate once again. (Figure 30). To allow comparisons between polycrystal cobalt and p o l y c r y s t a l magnesium, the data for both metals are plotted with the ordinant normalized for shear modulus and the homologous temperature plotted as abeissa. From t h i s graph, i t i s clear that the general shape of the curves are sim i l a r . Also, the temperature at which both metals change behaviour, and the temperature dependence of stress are comparable. A comparison between the y i e l d behaviour of po l y c r y s t a l and single c r y s t a l cobalt i s presented i n Figure 3 1 . The resolved shear stress (T) i n a p o l y c r y s t a l i s somewhat less than 1/2 the measured vajue for t e n s i l e y i e l d i f the Schmid factor i s considered. For t h i s reason, the po l y c r y s t a l data are plotted as 2 g . / ^ t o allow comparison with the single G 8 . 0 CO IC 0) u -p CO CG lu  rH Tj 0! O • H >• u o\° m CN 0) • x; O CO 7.0 6.0 5.0 4.0 3. 0 \- 2.0 1.0 7 LI c o b a l t 6 5 y magnesium 47 y c o b a l t 0.1 0.2 0.3 References C o b a l t - p r e s e n t work Magnesium - A h k t a r 3 2 0.4 0.5 Homologous Temperature (T°K/T^K) F i g . 30 Y i e l d s t r e s s versus t e s t temperature f o r c o b a l t and magnesium. CO c r y s t a l data. Although t h i s correction was made, i t i s s t i l l necessary to p l o t the single c r y s t a l data on a scale a factor of 10 larger than polycrystal r e s u l t s for the trends to be v i s i b l y examined. The abcissa i s shown both as a f r a c t i o n of the melting point, and as a f r a c t i o n of the transformation temperature. The l a t t e r scale i s included to provide a measure of the metastability of the fee phase present i n the cobalt p o l y c r y s t a l s . The data for fee cobalt single c r y s t a l s i s also presented to show the sharp differences in behaviour between the two phases as single c r y s t a l s . Several conclusions may be drawn from Figure 31. The p o l y c r y s t a l l i n e behaviour i s similar to that observed i n single c r y s t a l s . Although absolute values for the curves vary, the f a c t that both types of material exhibit two d i s t t n e t types of temperature dependence i s informative. A second important observation i s that the c r i t i c a l temperature at which the y i e l d stress changes behaviour, increases with increasing grain size i n a manner that yi e l d s upon extrapolation a value close to that obtained for single c r y s t a l s for very large grained p o l y c r y s t a l s . The l i n e representing t h i s trend i n Figure 28 i s also shown in Figure 31. This l i n e , determined from po l y c r y s t a l data, predicts a change i n y i e l d behaviour at 0.36Tm for cobalt that y i e l d s at 2 to 3,000 p s i . Hep single c r y s t a l s of cobalt, i n fact y i e l d at t h i s stress l e v e l and do change y i e l d behaviour at approximately 0.35 T . o 0,1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Fraction of the Transformation Temperature (T°K/M, °K ) F i g . 31 Yield stress versus temperature for cobalt single c r y s t a l s and poly c r y s t a l s 00 VO At t h i s juncture two important facts are c l e a r . The y i e l d stress of cobalt appears to be controlled by two processes. One process, which i s almost athermal at low temperatures, and a second process which i s strongly temperature dependent at higher temperatures. Secondly, the change from one process to the other occurs at higher temperatures as the grain size increases. A discussion of the processes that may be determining the temperature dependence w i l l be deferred u n t i l further aspects of t e n s i l e behaviour of cobalt have been presented. The two regions of temperature dependence noted for cobalt at y i e l d , disappear as s t r a i n increases. The temperature dependence of the flow stress at y i e l d and f a i l u r e i s shown i n Figure 32. The data i s presented for a small grained (6.5 micron) group of specimens of 99.9% pur i t y . Figure 33 shows a t y p i c a l set of data points from which Table VIII and IX were constructed. Similar curves to that shown i n Figure 33 were obtained for a l l material tested. In attempting to compare the flow stress behaviour with that of magnesium a problem a r i s e s . The limited d u c t i l i t y of pure magnesium, (less than 2% for 65 micron m a t e r i a l 3 2 ) , does not allow for comparison of the flow stress at the high values of s t r a i n that can occur i n cobalt. The two materials do exhibit p a r a l l e l behaviour over the range of s t r a i n where comparisons can be made. The disappearance of the e s s e n t i a l l y athermal behaviour of flow stress at low temperatures as s t r a i n increases may imply that the mechanism c o n t r o l l i n g the i n i t i a l deformation T6 # U . T . S . 25 -200 -100 0 100 200 300 400 500 Test Temperature (°C) F i g . 3 3 T y p i c a l data f o r determining the temperature dependence of flow s t r e s s . 99.7% c o b a l t , 7.0 micron g r a i n s i z e . vo i n cobalt at low temperatures, does not control the stress levels at large values of s t r a i n . The temperature dependence of the flow stress i s given i n Table VIII as a f r a c t i o n of the shear modulus for a change i n temperature of 100°C. It i s clear that for a l l materials tested, the temperature dependence of y i e l d at low temperature i s about an order of magnitude less than at high temperature. The amount of s t r a i n required to eliminate t h i s two stage c h a r a c t e r i s t i c decreases as the grain size becomes larger. For example, i n 99.7% cobalt, two regions of temperature dependence are observed at greater than 10% s t r a i n for 7 micron material, yet for 17.5 micron material of the same purity, no difference i s observed at 5% s t r a i n . (Table VIII). The absolute e f f e c t of purity on the flow stress i s small at a l l values of s t r a i n . In Figure 29, the difference was presented at y i e l d . This difference i n stress l e v e l remains small at a l l values of s t r a i n . Thus, the f a c t that the impurity l e v e l does not a f f e c t y i e l d i n a strong manner may now be expanded to include the complete stress- s t r a i n curve. As outlined e a r l i e r , the ultimate strength of cobalt i s very high for a pure metal. This fact was shown i n a general way previously i n Figure 25. From Table IX i t may be seen that p o l y c r y s t a l cobalt f a i l s at stress l e v e l s approaching G/50 at -196°C and G/70 at room temperature. The highest stress l e v e l sustained by pure p o l y c r y s t a l magnesium i s approximately G/100 3 2. Other pure metals f a i l at considerably lower l e v e l s 3 3 . TABLE VIII Temperature Dependence of Flov? Stress (Ao_ for 100°C temperature change) G Purity 99.7% 99.9% 99.998% Strain Grain Sizes 7. 0 10, .3 17 , .5 6, .5 14, .5 24 .0 9 .0 23 .5 47 .0 (%) 7. 6 12, .1 10, .6 19, .7 19, .7 36 .3 12, .1 15, .2 7, .6 0. 2 Low temp, slope where 25. 8 34, .0 38, .0 59. .0 68, .0 58, .0 50, .0 58, .0 39, .0 2. 0 required 50. 0 62, .0 - 107. .0 118, .0 - - - - 5. 0 Aa/G 106. 0 - - '- - - - - -• 10. 0 - - - - - - - - U.T ' .S . Temp. 0. 22 0, .27 0. .27 0. .25 0. ,28 0. .26 0. ,25 0. ,25 0. .32 of change T/T ' m 0. 26 0, .28 0, .28 0. .28 0, .29 0. .28 0. .26 - - 112. 0 109. .0 94. .0 153. , 0 118. .0 82. .0 97. ,0 109. ,0 88. ,0 0. 2 High temp. 116. 0 103. .0 100. .0 153. ,0 140. ,0 120. .0 128. ,0 102. ,0 90. ,0 2. 0 slope, or single 117. 0 115. .0 111. . 0 155. ,0 145. .0 131. .0 152. ,0 140. ,0 92. .0 5. 0 slope where required 140. 0 143. .0 120. .0 157. ,0 149. ,0 143. .0 - - - 10. 0 Aa/G 144. 0 168. .0 175. ,0 250. 0 220. ,0 190. ,0 U.T • S. VO 4* TABLE IX Ultimate Strength Data for Cobalt Polycrystals Ultimate t e n s i l e stress (true stress X G /G) / (True Stress) Grain Purity i n k s i . ° Size (y) (%)" -196°C 20°C 250°C 400°C 6.5 99.9 247/241 184/165 115/ 92 66/ 51 7.0 99.7 211/205 176/158 136/109 111/ 86 9.0 99.998 158/154 125/112 90/ 72 65/ 50 10.3 99.7 222/216 183/164 138/111 110/ 85 14.5 99.9 216/210 163/146 103/ 83 64/ 49 17. 5 99.7 226/220 183/164 135/108 105/ 81 23. 5 99.998 142/138 125/112 78/ 62 57/ 44 24.0 99.9 192/147 145/130 94/ 75 60/ 47 47.0 99.998 116/113 95/ 85 70/ 56 55/ 43 Note: 99.998% cobalt exhibits much less d u c t i l i t y than the lower purity grades. The s t r o n g v a r i a t i o n i n y i e l d s t r e n g t h w i t h changing g r a i n s i z e i s shown very c l e a r l y i n F i g u r e 31. The y i e l d s t r e s s f o r 47 micron m a t e r i a l i s l e s s than one h a l f t h a t f o r m a t e r i a l having a g r a i n s i z e of 7 microns. G r a i n boundaries a f f e c t the s t r a i n hardening and s t r e n g t h of metals v i a two r o u t e s . G r a i n boundaries a c t as b a r r i e r s t o s l i p , and secondly to m a i n t a i n coherency between g r a i n s d u r i n g deformation of a p o l y c r y s t a l l i n e aggregate, complex modes of deformation must take p l a c e w i t h i n i n d i v i d u a l g r a i n s . During the i n i t i a l stages of deformation, d i s l o c a t i o n s p i l e up a t g r a i n boundaries. As p i l e ups form they i n c r e a s e the back s t r e s s on d i s l o c a t i o n sources i n h i b i t i n g f u r t h e r d i s l o c a t i o n p r o d u c t i o n . At the head of the p i l e up, s t r e s s e s i n c r e a s e u n t i l d i s l o c a t i o n movement i s i n i t i a t e d a c r o s s the boundary i n another g r a i n . The measured s t r a i n hardening from t h i s avenue w i l l depend upon the ease of i n i t i a t i n g s l i p i n a d j o i n i n g g r a i n s . In the case of fee or bec metals, where ample s l i p modes have been observed, the e f f e c t i s not l a r g e . In the hep metals a l a r g e r e f f e c t i s observed due to the l i m i t e d s l i p systems a v a i l a b l e . In the o u t l i n e above, p i l e ups of d i s l o c a t i o n s a t g r a i n boundaries were p o s t u l a t e d . I t i s not necessary to assume r e g u l a r a r r a y s of d i s l o c a t i o n s i n t h i s manner. An exact d i s t r i b u t i o n of the d i s l o c a t i o n s .is not important; the important p o i n t i s t h a t there i s a s t r o n g s t r e s s f i e l d around the end of a s l i p band. When the s t r e s s f i e l d i n i t i a t e s s l i p i n an adjoining grain, the back stress on the i n i t i a l sources i s reduced and the hardening due to the back stresses increases less r a p i d l y . The effectiveness of grain boundaries as d i s l o c a t i o n b a r r i e r s i s most important during the i n i t i a l portion of the s t r e s s - s t r a i n curve while the d i s l o c a t i o n p i l e ups are forming. Thus, the e f f e c t of grain boundaries on the t e n s i l e parameters i s more marked i n the i n i t i a l portion of the t e n s i l e curve. For a number of metals, grain size and y i e l d stress may be related through an equation of the form: a Q = a ± + K D _ 1 / 2 4) a = y i e l d stress o J = f r i c t i o n stress opposing motion of di s l o c a t i o n s K = measure of the i n t e n s i t y of d i s l o c a t i o n p i l e ups at b a r r i e r s D = grain diameter The derivation of t h i s r e l a t i o n s h i p i s given i n most standard texts 3 1*. The slope of a plo t of a versus D -"^ 2 o determines K. K i s assumed to be almost independent of temperature, varying with the square root of the shear modulus, a . i s the stress reauired to force a d i s l o c a t i o n 1 against the resistances a r i s i n g from impurities, sub- grain boundaries, the Peierls-Nabarro force, etc. Therefore i t i s temperature and composition dependent, but independent of the externally applied stress. A plot of the y i e l d strength versus 1//D for cobalt i s shown i n Figure 34. Data for zinc a l l o y s 1 1 0 and copper 3 3 are also shown for comparison. Two values for 98.6% cobalt 98 References 120 100 «! 80 v. in cu u -p 60 o 40 20 F i q , • 99.7% cobalt O 99.9% cobalt A 99.998% cobalt Q 98.6% cobalt - M u l l e r 6 3 Zn a l l o y s - Risebrough 1 1 o Cu - McLean s 3 Present work 0 . 1 0. 2 0.3 0 . 4 0 . 5 (Grain size) 1 / / 2 ( m i c r o n ) " 1 ^ 34 Yield stress versus r e c i p r o c a l square root of grain size. drawn from the recent work by M i i l l e r 8 3 are included as they deal with large grained cobalt of low purity. The values for and K, for t h i s v a r i e t y of material are reproduced i n Table X. and K are quite large for cobalt when compared to values for other metals. A large value for a^, i s not unexpected. The heterogeneity of the cobalt l a t t i c e a f t e r cooling through the transformation i s well documented. The large amount of l a t t i c e debris present has been outlined by Ye g o l e y e v 8 5 ' 8 6 and o t h e r s 3 6 ' 7 6 . Even i n single c r y s t a l cobalt, the di s l o c a t i o n density i s found to be much higher than i n well annealed c r y s t a l s of other m e t a l s 2 5 . The extremely high values for K require explanation. It i s not reasonable to expect the bar r i e r s i n cobalt to be 10 times as d i f f i c u l t to overcome as those i n copper, or a factor of 5 stronger than those i n zinc. An expression providing the important parameters included i n K may be written as follows: K<x(Gba c) 1 / 2 5) G = shear modulus b = Burger's vector a c = c r i t i c a l stress at the head of a p i l e up required to i n i t i a t e s l i p i n a neighbouring grain. C l e a r l y , i f metals with very d i f f e r e n t shear moduli are to be compared, the data should be normalized for 1/2 shear modulus. The r a t i o (G„ /G_, ) i s about 0.66. Zn' Co If we normalize the K value for cobalt by t h i s factor we find that K for cobalt at room temperature i s 120,000 psi/p 1/2 TABLE X Parameters From an Ecruation of the Form: °yield a. + KD - V 2 l Test °C Temperature T/T ' m c. I p s i K • / 1/2 psi/u Comments -196 0.04 22,000 212,000 Cobalt - 99.7 - 99.998% 20 0.17 19,500 182,000 Cobalt - 99.7 - 99.998% 20 0.17 24,000 230,000 Cobalt - 98.6% 100 0.21 18,500 182,000 Cobalt - 99.7 - 99.998% 250 0.30 16,000 126,000 Cobalt - 99.7 - 99.998% 400 0.39 13,500 81,000 Cobalt - 99.7 - 99.998% -100 20 0.25 0.22 11,000 3, 000 44,000 26,000 Zinc A l l o y s 1 1 0 - Zn, Cr, T i , ZnO, Ni Copper 3 3 o o 101 compared to 44,000 psi/y / for zinc a l l o y s . The difference i n Burgers vector between the two materials should not y i e l d important differences. If cr i s a strong function of temperature i n cobalt, K values must be compared at s i m i l a r homologous temperatures. From Figure 35, i t may be seen that K for cobalt does vary with temperature. Between -196°C and 100°C the v a r i a t i o n i s not large, but K drops considerably above t h i s temperature. If K values at 250°C (0.3 T ) are compared to values for the zinc a l l o y s at (0.25 T ) we f i n d that the K value for cobalt i s 1.8 times that for zinc a l l o y s . In Figure 34 a dotted l i n e has been inserted to represent a curve for cobalt normalized for G and homologous temperatures to allow comparison to the curve for zinc a l l o y s . The coincidence of CK values for the two curves should be judged fortuitous as o\ for d i l u t e zinc-aluminum a l l o y s 1 1 1 i s approximately 0, whereas the zinc a l l o y s that, give r i s e to the l i n e plotted i n Figure 34 e x h i b i t a strong contribution to from p r e c i p i t a t e hardening. The only parameter which has not been analysed i s D. If the grain size D has been measured i n c o r r e c t l y , the measured values of K are also i n error. The D values used to assemble Figures 34 and 35 are the values associated with the fee grain s i z e . In section 3.1 i t was shown that the fee grain size i s only a measure of the coarsness of the high temperature phase. The regions of c r y s t a l l a t t i c e that may be considered i n d i v i d u a l grains depends upon the multivarianee of the transformation. The boundaries between 102 • rH CO T3 rH •r-i >• O 120 - 100 X 80 CO- CO 0) >H - P CC 60 40 20 0 20°C l i n e from F i g . 34 • 99.7% cobalt O 99.9% cobalt A 99.998% cobalt -196°C 0.1 0.2 0.3 -1/2 (Grain size) (miron) F i g . 35 Y i e l d stress versus rec i p r o c a l sauare root of grain size. 0 . 4 -1/2 100°C 250°C 400°G 0.5 m u l t i v a r i a n t areas are not t r u e g r a i n boundaries, but they are c l e a r l y s t r o n g e r b a r r i e r s than s u b g r a i n boundaries. Although, i t i s p h y s i c a l l y i m p o s s i b l e to a s c e r t a i n the s i z e of the v a r i o u s transformed r e g i o n s (except i n t h i n f i l m s i n the e l e c t r o n microscope) these v a r i o u s r e g i o n s of l a t t i c e must be s m a l l e r than the fee g r a i n s i z e . In view of the above o b s e r v a t i o n s , the s l o p e s determined i n F i g u r e 34 and 35 should be lower than as shown because the d i s t a n c e between boundaries t h a t a c t as d i s l o c a t i o n b a r r i e r s i n c o b a l t i s s m a l l e r than the diameter of the fee g r a i n s . I f i t i s assumed t h a t a normalized K f o r c o b a l t i s s i m i l a r to t h a t f o r z i n c , a p o i n t on the normalized c o b a l t curve i n F i g u r e 34 may be p r o j e c t e d back onto the curve f o r z i n c a t constant s t r e s s to y i e l d a measure of D f o r the m i s o r i e n t e d r e g i o n s of c o b a l t l a t t i c e . For example: Move data p o i n t A, r e p r e s e n t i n g 47 micron c o b a l t of 99.998% p u r i t y to p o s i t i o n A' to r e p r e s e n t n o r m a l i z i n g f o r G and homologous temperature. Then move to A" which i s assumed to r e f l e c t t h e . e r r o r i n measurement of D. The " G r a i n " s i z e determined i n t h i s manner i s approximately 10 microns. Upon comparing t h i s v a l u e w i t h F i g u r e 11, a photomicrograph, of 47 micron, 99.998% c o b a l t under p o l a r i z e d l i g h t , the r e s u l t i s not unreasonable. Although an a c c u r a t e "average" s i z e f o r r e g i o n s of l a t t i c e having s i m i l a r o r i e n t a t i o n i s i m p o s s i b l e , i t i s c l e a r t h a t the "average" i s not over 15 microns nor l e s s than 5 microns. Although the complex microstructure i n cobalt makes an accurate evaluation of K d i f f i c u l t , i t i s cl e a r that K i s large as i n other metals that lack a m u l t i p l i c i t y of s l i p systems at room temperature. The measured v a r i a t i o n i n K, and a^, with temperature i s i n t e r e s t i n g . (Table X). C l e a r l y both parameters d i f f e r l i t t l e between -196°C and 100°C, K drops only 15%, yet between 250°C and 400°C, a temperature change only one half as large, K decreases 35%. S i m i l a r l y o\ decreases more rapidl y at higher temperatures. These observations p a r a l l e l the e a r l i e r observations regarding t e n s i l e behaviour above and below 0 .25 T . m o\ i s a measure of the force necessary to drive a d i s l o c a t i o n against the resistance of impurities, p r e c i p i t a t e p a r t i c l e s , subgrain boundaries, and the Peierls-Nabarro force. Of a l l these terms, the P e i e r l s force i s strongly temperature dependent whereas the others are not. Thus a sharp change i n with temperature may r e f l e c t the change in the P e i e r l s force. The P e i e r l s force, or the force required to drive a d i s l o c a t i o n over a s l i p plane i s small on close packed s l i p planes. Thus, i t i s not large i n the fee metals. In the bee metals, where the s l i p plane i s not close packed, the P e i e r l s force i s large. In hep metals, the P e i e r l s force required to drive d i s l o c a t i o n s over the basal plane i s generally considered to be small, but to obtain "corrugated s l i p " on the {1122} planes may require a very high P e i e r l s force. Thus, one p o s s i b i l i t y for the sharp drop i n a. above 105 0.25 T i n c o b a l t i s t h a t t h e P e i e r l s s t r e s s f o r d i s -m l o c a t i o n m otion on t h e {1122} <1123> s l i p system becomes r a t e c o n t r o l l i n g . The f a c t t h a t CK does not drop as q u i c k l y a t low t e m p e r a t u r e s may r e f l e c t t h e f a c t t h a t some o t h e r mechanism o p e r a t e s , r e d u c i n g t h e need f o r c o r r u g a t e d s l i p . The m o t i o n o f t r a n s f o r m a t i o n d i s l o c a t i o n s on v a r i o u s {111} p l a n e s i n t h e f e e p o r t i o n s o f t h e l a t t i c e would be one example o f an a t h e r m a l p r o c e s s w h i c h c o u l d reduce t h e n e c e s s i t y f o r movement o f d i s l o c a t i o n s on t h e c o r r u g a t e d s l i p p l a n e . The two f a c t o r s t h a t may y i e l d t he t e m p e r a t u r e dependence of K a r e G 1 / / 2 and a^1^2. Between -196°C and 100°C, G 1 / / 2 d e c r e a s e s about 5%, thus two t h i r d s o f t h e drop i n K between -196°C and 100°C must be due t o a r e d u c t i o n i n t h e c r i t i c a l s t r e s s (a ) r e q u i r e d t o i n i t i a t e s l i p i n a 1/2 n e i g h b o u r i n g g r a m . To propose t h a t oc ' d e c r e a s e s 10% as te m p e r a t u r e i n c r e a s e s from 0.04 T t o over 0.2 T i s m m r e a s o n a b l e . On the o t h e r hand, t h e change i n K between 250°C and 400°C i s 35% and o n l y 2% o f t h e v a r i a t i o n may 1/2 1/2 be a t t r i b u t e d t o a change i n G ' ; t h u s , p ' must d e c r e a s e by over 30%. Th,is i s e q u i v a l e n t t o s a y i n g t h a t the c r i t i c a l s t r e s s a t t h e head of a p i l e up r e q u i r e d t o i n i t i a t e s l i p i n a n e i g h b o u r i n g g r a i n , d e c r e a s e s by o v e r 50% between 0.30 T^ and 0.38 T . C l e a r l y some s t r o n g l y t e m p e r a t u r e dependent d i s l o c a t i o n p r o c e s s i s o p e r a t i v e a t t h e s e t e m p e r a t u r e s . 106 P r e s e n t a t i o n o f t h e y i e l d s t r e s s as a f u n c t i o n o f t h e r e c i p r o c a l square r o o t o f g r a i n s i z e and t h e e n s u i n g d i s c u s s i o n has uncovered s e v e r a l i m p o r t a n t f e a t u r e s r e g a r d i n g y i e l d i n p o l y c r y s t a l c o b a l t . The y i e l d s t r e n g t h i n c o b a l t i s a f f e c t e d i n a s t r o n g manner by t h e g r a i n b o u n d a r i e s p r e s e n t . As b a r r i e r s t o d i s l o c a t i o n m o t i o n , t h e g r a i n b o u n d a r i e s i n c o b a l t p r o v i d e a s t r e n g t h e n i n g e f f e c t s i m i l a r t o t h a t found i n o t h e r hep m e t a l s t h a t do not e x h i b i t a m u l t i p l i c i t y o f s l i p systems a t room t e m p e r a t u r e . The s t r e s s l e v e l s measured i n c o b a l t a r e much h i g h e r t h a n f o r z i n c , cadmium, o r magnesium because o f d i f f e r e n c e s i n shear modulus and m e l t i n g t e m p e r a t u r e . The f r i c t i o n a l s t r e s s , a^, i n c o b a l t i s v e r y h i g h . I n f a c t , a f t e r n o r m a l i z i n g f o r G and homologous t e m p e r a t u r e , pure c o b a l t e x h i b i t s v a l u e s o b t a i n e d f o r z i n c a l l o y s c o n t a i n i n g a h i g h d e n s i t y o f p r e c i p i t a t e p a r t i c l e s . The v a r i a t i o n i n a. and K above and below 0.25 T i m i m p l i e s t h a t some te m p e r a t u r e dependent d i s l o c a t i o n mechanism becomes i m p o r t a n t o n l y above 0.25 T . A t lov; te m p e r a t u r e s i s l a r g e b u t does n o t v a r y s t r o n g l y w i t h t e m p e r a t u r e . A t h i g h t e m p e r a t u r e , drops q u i c k l y w i t h t e m p e r a t u r e . S i m i l a r o b s e r v a t i o n s a p p l y t o K. One p r o p o s a l c o n s i s t e n t w i t h t h e ob s e r v e d r e s u l t s i s t h e r e l a t i o n s h i p between P e i e r l s s t r e s s on t h e {1122} c o r r u g a t e d p l a n e i n hep c p b a l t and t h e s t r e s s i n d u c e d m a r t e n s i t i c t r a n s f o r m a t i o n t h a t o c c u r s i n c o b a l t . A d i s c u s s i o n o f t h i s r e l a t i o n s h i p must be d e f e r r e d u n t i l t h e d a t a r e g a r d i n g t h e m a r t e n s i t i c t r a n s f o r m a t i o n has been p r e s e n t e d . 107 3 . 2 . 1 . 3 D u c t i l i t y and Fracture The d u c t i l i t y of cobalt (% elongation) i s not well defined i n the l i t e r a t u r e with measured values from almost n i l to as high as 25% being quoted 8 3. The low d u c t i l i t i e s measured i n work ca r r i e d out p r i o r to 1940 were undoubtedly due to impurities i n the cobalt. If the concentrations of sulphur, zinc, or lead exceed very low l e v e l s , (20, 100, and 20 parts per m i l l i o n respectively) cobalt behaves i n a b r i t t l e manner 8 2. Although the basic impurity e f f e c t s have been uncovered i n recent years, low d u c t i l i t y readings are s t i l l i n evidence for very pure p o l y c r y s t a l c o b a l t 8 3 . Sulphur, zinc, and lead are well below the l e v e l s where they cause b r i t t l e behaviour i n a l l grades of cobalt used for the present study. Although hundreds of specimens were tested to f a i l u r e , no c l e a r picture regarding the d u c t i l i t y of cobalt emerged. The values for the three grades of cobalt investigated are presented i n Table XI. The scatter i n r e s u l t s was always large and mean values are shown i n the table. A large scatter i s also prevalent i n other studies where raw data has been published. The d u c t i l i t y of 99.7% cobalt i s high for a l l grain sizes tested, averaging 19.2% s t r a i n for the 55 specimens pulled to f a i l u r e . The differences i n d u c t i l i t y for the various grain sizes are too small to be able to propose, v/ith authority, any trend, although there i s a trend towards lower d u c t i l i t y as the test temperature i s increased. TABLE XI Summary of True Strain Data For Polycrystal Cobalt Purity Annealing Temp. (1 Hr.) Grain Size • (y) Strain (%) at F a i l u r e Average -196°C + 20°C 250°C 400°C 99.7% 600 - 800°C 7 - 17.5 19.2 21.6 19.7 17.3 15.4 99.9% 500°C <6.5 23.9 25.0* 20.5 29.9* 24.8* 550°C <6.5 22.9 11.8* 22.2* 33.2* .23.6* 600°C 6.5 20.8 24.7 21.8 18.9 16.9 650°C 10.0 21.7 14.6* 26.4* 14.5* 30.5* 700°C 14.5 10.8 14.4 11.7 9.0 7.2 800°C 24.0 5.6 8 .3 6.3 4.2 2.8 1000°C 60.0 5.9 - 5.9 - - 99.998% 600 - 800°C 9 - 4 7 4.5 4.8 4.1 3.4 9.5 * Single Specimen Tested t-1 o CO 109 For 99.9% cobalt, the scatter i n r e s u l t s i s large, b u t the trends i n d u c t i l i t y are more pronounced. Except for very small grained material, which has over 20% d u c t i l i t y at a l l temperatures, the d u c t i l i t y decreases as the test temperature increases. The d u c t i l i t y also drops r a p i d l y with increasing grain s|ze, decreasing from over 20% for 6.5 micron material to less than 6% for 60 micron material. The r e s u l t s show that the small grained 99.9% material behaves s i m i l a r l y to the 99.7% cobalt, but as the grain size increases the former exhibits less d u c t i l i t y . For example, 17.5 micron cobalt of 99.7% p u r i t y y i e l d s approximately 20% elongation whereas 14.5 micron 99.9% cobalt f a i l s a f t e r 11% s t r a i n . After testing several specimens of 99.998% cobalt, and noting the low d u c t i l i t y values, the material was examined to determine i f any physical defects were present. Upon car e f u l polishing and washing (no etching) a few small elongated pores became v i s i b l e . They were less than 1 micron i n cross-section perpendicular to the t e n s i l e axis and were a maximum of several microns i n length p a r a l l e l to the t e n s i l e axis. They did not appear to be contaminated and probably arose during a zone-refining procedure. The cold work introduced d u r i n g production did not close a l l the pores. Problems attendant to obtaining a further supply of 99.998% material made i t imperative that the material available be used. Attempts were made to swage and draw the material to close the pores. The low d u c t i l i t y , paired with contamination problems occuring at the temperatures required for working, thwarted every e f f o r t to eliminate the pores. Thus, the material was annealed and tested with the porosity present. While parting the high purity cobalt rods into lengths convenient for machining further t e n s i l e specimens, 50 random sections were taken. These sections were examined on planes perpendicular and p a r a l l e l to the t e n s i l e axis for porosity. No defects were observed i n 80% of the sections. The porosity, as a f r a c t i o n of cross-sectional area i s n e g l i g i b l e and should not a f f e c t the y i e l d strength or the work hardening rate, but the pores may influence the d u c t i l i t y by acting as nuclei for fracture processes. The d u c t i l i t y of 99 T998% material below 0.33 T^ (350°C) i s low for a l l annealing procedures. As with the other grades of cobalt, there |s a trend to lower d u c t i l i t y as the test temperature and grain size increase. Above 0.33 T m the d u c t i l i t y of 99.998% material increases rapidly, reaching 10% by 400°C. In t h i s very high purity material, 350°C may be s u f f i c i e n t for the onset of the high d u c t i l i t y region observed by other authors surrounding the transformation temperature 8 1 1 8 2 , 1 0 9 . They att r i b u t e the high elongation values observed to the tfansformation proceeding during deformation and r e l i e v i n g stress concentrations. The behaviour of 99.7% and 99.9% c o b a l t as a f u n c t i o n o f g r a i n s i z e i s i n agreement wi t h data presented r e c e n t l y by M i i l l e r 8 3 . The s m a l l e s t g r a i n s i z e examined i n h i s work was 35 microns. Although the m a j o r i t y of the r e s u l t s a v a i l a b l e from the p r e s e n t study are f o r g r a i n s i z e s s m a l l e r than t h i s , i n the areas where comparisons can be made th e r e i s g e n e r a l agreement. D u c t i l i t y decreases up to a c e r t a i n g r a i n s i z e , beyond t h i s , the d u c t i l i t y remains constant a t 4 to 6%. T h i s behaviour a l s o p a r a l l e l s the amount of r e t a i n e d fee phase as.a f u n c t i o n of g r a i n s i z e . Although a d e t a i l e d study of the f r a c t u r e processes i n c o b a l t was not attempted, m e t a l l o g r a p h i c evidence r e g a r d i n g the f r a c t u r e s u r f a c e s was compiled. F i g u r e 36 shows a f r a c t u r e s u r f a c e f o r 99.9% c o b a l t having a g r a i n s i z e of 6 .5 microns. The specimen f a i l e d a t approximately 20% s t r a i n . The f a i l u r e i s d e f i n i t e l y d u c t i l e , as evidenced by the d u c t i l e cusps v i s i b l e throughout the f r a c t u r e s u r f a c e . F i g u r e 37 i s a l a r g e g r a i n e d (47 micron) specimen of 99.998% c o b a l t t h a t f a i l e d a t l e s s than 5% s t r a i n . Although the s u r f a c e does not e x h i b i t the same i n t e n s i t y of d u c t i l e cusps as the p r e c e e d i n g r e p l i c a i t may s t i l l be c o n s i d e r e d a d u c t i l e f r a c t u r e . In both f i g u r e s , t h e r e i s some evidence of shear f a i l u r e i n s e l e c t e d areas. The specimens shown i n F i g u r e s 36 and 37 were t e s t e d a t room temperature. R e p l i c a s were taken from f r a c t u r e s u r f a c e s o btained a f t e r t e s t s a t -196°C, 20°C, and 250°C. 112 F i g . 37 F r a c t u r e s u r f a c e , 99.998% c o b a l t t e s t e d a t 20°C. 47 micron g r a i n s i z e . 5000X No change i n the g e n e r a l f e a t u r e s of the f r a c t u r e s u r f a c e were uncovered. R e p l i c a s of the f r a c t u r e s u r f a c e s a t 400°C were not o b t a i n a b l e due to the t e s t i n g environement ( s a l t ) and the oxide l a y e r t h a t formed on the specimens f o l l o w i n g f a i l u r e . 3.2.1.4 Work Hardening Behaviour Before d i s c u s s i n g the temperature dependence of the work hardening r a t e , a d e s c r i p t i o n of the change i n work hardening behaviour with s t r a i n i s necessary. The anomalous work hardening behaviour i n the i n i t i a l p o r t i o n of the t e n s i l e curves was noted p r e v i o u s l y . A p l o t of the work hardening parameter; 0 (the slope of the t r u e s t r e s s - t r u e s t r a i n curve) i s presented f o r v a r i o u s t e s t temperatures i n F i g u r e 38. The data are taken from the t e s t r e s u l t s shown i n F i g u r e 22 f o r 6.5 micron, 99.9% c o b a l t . The s m a l l g r a i n s i z e was chosen because the anomalous behaviour i s more pronounced f o r t h i s type of m a t e r i a l . In F i g u r e 38, the e f f e c t of the m a r t e n s i t i c t r a n s f o r m a t i o n i s q u i t e c l e a r . Instead of a smooth drop i n 0 as s t r a i n i n c r e a s e s beyond y i e l d , c o b a l t e x h i b i t s a r e g i o n where 0 remains e s s e n t i a l l y c onstant b e f o r e c o n t i n u i n g to drop i n a normal f a s h i o n . For t e s t s c a r r i e d out above -196°C, the work hardening r a t e a c t u a l l y i n c r e a s e s f o l l o w i n g t h i s anomalous r e g i o n b e f o r e c o n t i n u i n g to drop i n v a l u e . A second o b s e r v a t i o n i s t h a t the anomalous behaviour p e r s i s t s f o r a l a r g e r p o r t i o n of the Data taken from the t r u e - s t r e s s - true s t r a i n curves shewn i n F i g . 22, cobalt •rH & O i H u. C'. C •i—i c u m u o i © 1000 - 0 2 5 10 15 True F-train (%) F i a . 38 V a r i a t i o n of work hardening rate v.'ith s t r a i n f o r 99.9% cobalt. n w o J-t E-i 0) -P ri B -P 200 100 115 t e n s i l e curve as the tes t temperature increases. At -196°C, the region of constant work hardening rate disappears at 3% s t r a i n , at 0°C i t disappears at about 5% s t r a i n , at 400°C a constant value i s maintained to over 8% s t r a i n . Both observations are due to the martensitic transformation. It w i l l be shown i n the section dealing with deformation and the transformation that the regions where the anomalous work hardening rates ex i s t correspond to s t r a i n values where the retained fee l a t t i c e i s transforming to hep at a high rate. For p o l y c r y s t a l l i n e aggregates that f a i l i n a d u c t i l e manner, the elongation at which necking begins i n a t e n s i l e test i s related to the work hardening rate. P l a s t i c i n s t a b i l i t y occurs when the slope of the true stress - true s t r a i n curve (o) becomes equal to the value of true stress. This r e s u l t i s known as Consideres' C r i t e r i o n . The derivation of th i s r e s u l t i s available i n most standard texts 3 1*. The veracity of t h i s r e s u l t for cobalt i s shown i n Figure 38. Data points representing the maximum stress and elongation at f a i l u r e for the specimens giving r i s e to the work hardening curves i n Figure 38 are included for comparison. C l e a r l y the specimens neck and f a i l i n accordance with the c r i t e r i o n outlined above. Similar curves were produced for a l l grain sizes investigated. For 99.7% and 99.9% cobalt, r e s u l t s similar to those i n Figure 38 were uncovered. The r e s u l t s c l e a r l y show that the increased d u c t i l i t y observed for 99.7% and 99.9% p o l y c r y s t a l cobalt at low temperatures i s a r e f l e c t i o n of Considere's C r i t e r i o n . The r e s u l t s for 99.9,98% cobalt do not obey Considered C r i t e r i o n . Specimens of t h i s material f a i l while 0 i s s t i l l an order of magnitude higher than the true stress, and l i t t l e or no necking i s observed. These r e s u l t s substantiate the proposal that the porosity present i n t h i s high purity material promotes fracture at low s t r a i n values. The rate at which p o l y c r y s t a l cobalt work hardens as a function of temperature i s shown i n Figure 39. Curves of similar shape and magnitude are also observed for a l l other materials tested. Two general observations are clear: The work hardening rate i s not a strong function of grain size or purity. On the other hand, the work hardening behaviour changes sharpely with temperature, dropping very steeply from -196°C (0.04 T ) to approximately 0.2 5 T and decreasing at a lower rate above t h i s temperature. m c This observed change i n behaviour i s recorded for work hardening rates taken at 2% s t r a i n . At 10% s t r a i n , the e f f e c t i s not as clear. The temperature at which t h i s break i n behaviour occurs i s approximately the same f r a c t i o n of the melting point at which the two stage behaviour of the y i e l d stress and flow stress i s observed. Figure 40 traces the change i n work hardening behaviour versus temperature at various values of s t r a i n to outline how the two stage behaviour of the work hardening rate disappears as s t r a i n increases. For low s t r a i n values, the anomalous e f f e c t shown in Figure 38 i s also r e f l e c t e d i n Figure 40. The work hardening data i n Figure 40 i s for 99.9% cobalt having a 6.5 micron grain size. The work hardening curves for t h i s material lose the 0 ) c r-f o 1000 800 600 400 200 s t r a i n s t r a i n 2% s t r a i n - 2% s t r a i n - 10% s t r a i n 300 400 -200 -100 0 100 200 Temperature (°C) F i q . 39 The work hardening behaviour of c o b a l t as a f u n c t i o n of temperature Temperature (°C) F i g . 40 V a r i a t i o n i n work hardening behaviour w i t h i n c r e a s i n g s t r a i n . 99.9% c o b a l t , 6.5 micron g r a i n s i z e . two stage c h a r a c t e r i s t i c between 10% and 15% s t r a i n . Upon r e f e r r i n g t o Table V I I I i t may be seen t h a t the two stage c h a r a c t e r i s t i c of the flow s t r e s s i s no l o n g e r e v i d e n t at 10% s t r a i n . The s t r a i n above which the two sl o p e s on the work hardening curves merge f o r v a r i o u s g r a i n s i z e s i s shown i n Table X I I . The range of temperature a t which the s l o p e change i s observed i s a l s o l i s t e d . S i m i l a r i n f o r m a t i o n r e l a t i n g t o the flow s t r e s s i s i n c l u d e d f o r comparison. 3.2.1.5 D i s c u s s i o n and Summary At t h i s j u n c t u r e , i t i s c l e a r t h a t the t e n s i l e behaviour of c o b a l t i s d i f f e r e n t above and below 0.25 T . Pronounced m d i f f e r e n c e s i n the temperature dependence of y i e l d s t r e s s , flow s t r e s s , and work hardening r a t e have been uncovered. The d i s t i n c t i o n between behaviour above and below 0.25 T m disappears as s t r a i n i n c r e a s e s , and disappears a t lower values of s t r a i n as the g r a i n s i z e i n c r e a s e s . The y i e l d s t r e s s and flow s t r e s s e x h i b i t a l e s s i n t e n s e temperature dependence below 0.25 than above. On the o t h e r hand, the work hardening r a t e shows a s t e e p e r temperature dependence below 0.25 T^ than above. As a f u r t h e r approach t o c l a r i f y the d i f f e r e n c e s i n behaviour above and below 0.25 T , a number of s t e p - p u l l t e s t s were c a r r i e d out. Specimens were y i e l d e d a t a g i v e n temperature and s t r a i n e d a s m a l l amount. The t e s t temperature was then changed and a f u r t h e r increment of s t r a i n was i n t r o d u c e d . T h i s procedure was continued, TABLE XII The Two Stage Behaviour of Flow S t r e s s and Work Hardening Rate as a F u n c t i o n of. Temperature G r a i n S i z e P u r i t y (Microns) (%) S t r a i n (%) and Temperature (T/T ) S t r a i n (%) and Temperature (T/T ) Above Which the Two Stacre m Above Which the Two Staae m C h a r a c t e r i s t i c of the Work Hardening Rate i s not Observed C h a r a c t e r i s t i c of the Flow S t r e s s i s not Observed True S t r a i n (%) T/T m True S t r a i n (%) T/T ' m 6.5 99.9 10 0.28 - 0.29 5 0.25 - 0.28 7.0 99.7 10 0.23 - 0.26 10 0.22 - 0.26 9.0 99.998 2 0.24 - 0.25 2 0 .25 10. 3 99.7 5 0.22 - 0.27 5 0.27 - 0.28 14.5 99.9 5 0.27 - 0.28 5 0.28 - 0.29 17 .5 99.7 2 0.26 2 0.27 23.5 99.998 2 0.25 2 0 .25 24.0 99.9 2 0.30 2 0.27 47.0 99.998 2 0.28 2 0.32 Note: Curves P l o t t e d For 2 , 5 , 10, 15, 20% S t r a i n Only. O 121 a l t e r n a t i n g temperature between two v a l u e s , u n t i l f a i l u r e occured. The r e s u l t s were then p l o t t e d f o r the s t e p - p u l l specimens. Data from i d e n t i c a l specimens t h a t had undergone a l l deformation a t the i n d i v i d u a l temperatures being s t u d i e d were a l s o p l o t t e d . F i g u r e s 41 and 42 p r e s e n t the data from a s e r i e s of s t e p - p u l l t e s t s as w e l l as s t r e s s - s t r a i n curves f o r specimens t e s t e d i n the normal f a s h i o n . The data has been c o r r e c t e d to remove the a f f e c t of change i n shear modulus w i t h temperature. Three types of t e s t s are shown: i ) T e s t s i n v o l v i n g a temperature change between -196°C/20°C where both temperatures were below 0 .25 T . r m i i ) T e s t s w i t h both temperatures above 0.25 T , 250°C/385°C. i i i ) T e s t s where the low temperature 20°C (0.17 T ) was below the break i n the curves, the hig h m 3 temperature 250°C (0.30 T ) above. m From F i g u r e 41 the r e s u l t s imply t h a t the s t r u c t u r e s formed a t -196°C and 20°C are very s i m i l a r . The agreement between the s t e p - p u l l curves and the i n d i v i d u a l s t r e s s s t r a i n curves i s very c l o s e . The segments of the s t e p - p u l l t e s t , determined by the i n t e r s e c t technique o u t l i n e d i n Appendix 2 , e x h i b i t work hardening s l o p e s t h a t agree c l o s e l y w i t h the i n d i v i d u a l t e s t s . A t s t r a i n v a l u e s approaching f a i l u r e some v a r i a n c e o c c u r s . 250 - Step-pull - i n i t i a l y i e l d @ 20°C, second t e s t @ -196°C, e t c . Step-pull - i n i t i a l y i e l d @ -196°C, second t e s t @ 20°C, e t c . 100 150 100 Step-pull - i n i t i a l y i e l d @ 250°C, second t e s t @ 3S5%C, e t c . O Mean of 2 spec. @ -196°C • Mean of 2 spec. @ 20°C A Mean of 2 spec. @ 250°C O Mean of 2 spec. @ 385°C A . O A O O A A O 50 O _L JL _L JL _L F i g . 2 4 6 8 10 12 14 True S t r a i n (%) 41 Temperature change t e s t s , 99.9% cobalt - 6.5 micron grain s i z e . 16 18 • H X w in o w 0) 3 rH 200 150 100 50 o4 Step-pull - i n i t i a l y i e l d @ 250°C, second t e s t @ 20°C, etc. • Mean of 2 spec. @ 20°C A Mean of 2 spec. @ 250°C JL _L _L JL _L 0 2 4 6 8 10 12 14 True S t r a i n (%) F i g . 42 Temperature change t e s t , .99.9% cobalt - 6.5 micron gr a i n s i z e . 16 18 ro CO The r e s u l t s a t 250°C/385°C do not superimpose as a c c u r a t e l y as t h o s e f o r -196°C/20°C. The 250°C segments of t h e s t e p p u l l c u r v e f a l l s l i g h t l y below the mean d a t a f o r specimens p u l l e d a t 250°C, whereas t h e 385°C segments f a l l above c o r r e s p o n d i n g d a t a f o r i n d i v i d u a l t e s t s . Thus, i t i s proposed t h a t t h e s t r u c t u r e s g i v i n g r i s e t o s t r a i n h a r d e n i n g a t 385°C must be l e s s r e s t r i c t i v e t o f u r t h e r d i s l o c a t i o n m o t i o n t h a n t h e s t r u c t u r e s formed a t 250°C. A s m a l l amount of r e c o v e r y i s a l s o o c c u r i n g a t t h e s e h i g h t e m p e r a t u r e s , b u t t h e change i n s t r e s s l e v e l from t h i s avenue i s v e r y s m a l l (See S e c t i o n 3.1.2). The t e s t s f o r t e m p e r a t u r e s s t r a d d l i n g 0.25 T , (20°C/250°C) show a l a r g e v a r i a n c e w i t h t h e i n d i v i d u a l s t r e s s s t r a i n c u r v e s ( F i g u r e 42). The room temp e r a t u r e segments of t h e c u r v e f a l l much below t h e c o r r e s p o n d i n g d a t a f o r i n d i v i d u a l specimens. The 250°C segments o f t h e c u r v e f a l l above t h e c o r r e s p o n d i n g i n d i v i d u a l d a t a . The work h a r d e n i n g s l o p e s shown by t h e i n d i v i d u a l s t e p p u l l segments ar e a l s o i n dis a g r e e m e n t w i t h t h e d a t a from t h e normal t e n s i l e t e s t s . I t a p p e a r s , t h a t t h e b a r r i e r s t o d i s l o c a t i o n m o t i o n f o r m i n g a t 250°C a r e f a r l e s s r e s t r i c t i v e t h a n t h o s e o c c u r i n g a t 20°C. A f t e r u n d e r g o i n g a s m a l l amount o f s t r a i n a t 250°C and t h e n f u r t h e r s t r a i n i n g the specimen a t 20°C, t h e work h a r d e n i n g s l o p e f o r the room temp e r a t u r e segment i s h i g h e r t h a n would o c c u r f o r a specimen h a v i n g had a l l s t r a i n i n t r o d u c e d a t 20°C, b u t t h e s t r e s s l e v e l i s l o w e r . The work h a r d e n i n g s l o p e i s e q u i v a l e n t t o t h e s l o p e f o r a 20°C t e n s i l e t e s t a t a lower va lue of s t r a i n . The s t r e s s l e v e l s r e q u i r e d to cont inue deformat ion a t 250°C f o l l o w i n g some s t r a i n hardening a t 20°C r e f l e c t the more r e s t r i c t i v e s t r u c t u r e in t roduced a t 20°C. The s t r e s s l e v e l s are h igher than those observed f o r a standard t e s t a t 250°C and become l e s s r e p r e s e n t a t i v e of a 250°C t e s t as more s t r a i n i s in t roduced a t 20°C. Th is set of t e s t s appear to s u b s t a n t i a t e s e v e r a l o b s e r v a t i o n s made e a r l i e r . The f a c t t h a t the r e s u l t s of the s t e p - p u l l t e s t s w i t h both temperatures below 0.25 T , superimpose very a c c u r a t e l y w i t h i n d i v i d u a l s t r e s s s t r a i n curves throughout the major p o r t i o n of the s t r e s s - s t r a i n curves i m p l i e s t h a t s i m i l a r b a r r i e r s to d i s l o c a t i o n motion are c o n t r o l l i n g the f low s t r e s s a t both temperatures . The temperature dependence of the f low s t r e s s r e f l e c t s the degree to which the b a r r i e r s become t r a n s p a r e n t to d i s l o c a t i o n s as temperature i n c r e a s e s . The o b s e r v a t i o n t h a t the work hardening r a t e s are a l s o c o i n c i d e n t w i t h those f o r a normal s t r e s s s t r a i n c u r v e , suggest t h a t the r a t e a t which b a r r i e r s to d i s l o c a t i o n motion are f o r m i n g , are s i m i l a r a t both temperatures . I f e i t h e r r e s u l t i s i n c o r r e c t a d i f f e r e n t set of r e s u l t s would o c c u r , u n l e s s some very complex thermal behaviour i s p o s t u l a t e d f o r the c o n t r o l l i n g mechanism. For example: If the rate at which obstacles are formed with increasing s t r a i n i s higher at -196°C than at 20°C, the segment of s t r a i n at 20°C following a segment at -196°C would necessarily exhibit a stress higher than that obtained at similar s t r a i n for a normal t e n s i l e t e s t . On t h i s basis, i t i s reasonable to assume that the mechanisms c o n t r o l l i n g the major portion of the stress s t r a i n curves are the same at both temperatures. Any postulated combination of processes must be capable of producing strong b a r r i e r s to deformation to j u s t i f y the high stress l e v e l s measured and one component process must be temperature dependent, as i t i s clear that the barr i e r s to d i s l o c a t i o n motion are more e a s i l y overcome as temperature increases. For the tests where one temperature i s above 0.25 T m and the other below, the r e s u l t s r e f l e c t a difference in behaviour at the two temperatures. To y i e l d the behaviour observed regarding flow stress l e v e l s , two p o s s i b i l i t i e s e x i s t . Either more or d i f f e r e n t b a r r i e r s are forming at 20°C than at 250°C, or the obstacles formed at 20°C are more e a s i l y overcome at 250°C. The higher work hardening rate observed for a segment of the step p u l l tests at 20°C, following a segment at 250°C, implies that the s t r a i n introduced at 250°C forms ' a structure that could be formed by far less s t r a i n at 20°C. For example: If the 20°C segments of the step p u l l tests i n Figure 42 are transposed back onto the curve for the normal t e n s i l e test, maintaining the measured stress l e v e l s , 127 c o i n c i d e n c e of the curves i s observed. T h i s l a t t e r o b s e r v a t i o n r e g a r d i n g the work hardening behaviour, r e i n f o r c e s the p r o p o s a l t h a t s i m i l a r b a r r i e r s t o d i s l o c a t i o n motion are forming a t both temperatures, but t h a t the t o t a l number of b a r r i e r s produced i s lower a t 250°C. To o b t a i n equal amounts of s t r a i n a t both temperatures there must be e q u i v a l e n t amounts of d i s l o c a t i o n motion. I f e q u i v a l e n t amounts of d i s l o c a t i o n motion take p l a c e , but fewer b a r r i e r s form, t h i s i m p l i e s t h a t some mechanism has come i n t o prominence a t t h i s higher temperature, a l l o w i n g s i m i l a r amounts of d i s l o c a t i o n motion as a t low temperatures, without forming the same d e n s i t y of b a r r i e r s . The r e s u l t s f o r the t e s t s where both temperatures are above 0 .25 T r e f l e c t s i m i l a r behaviour to t h a t d i s c u s s e d m above. As the temperature i n c r e a s e s , the number of o b s t a c l e s t h a t form f o r a g i v e n i n p u t of s t r a i n , c o n t i n u e s t o decrease. The decrease i n s t r e s s l e v e l s r e q u i r e d to co n t i n u e deformation i s due to a second mechanism t h a t p r o v i d e s s t r e s s r e l i e f above 0 .25 T . m As would be expected from the data presented f o r other aspects of the t e n s i l e deformation of c o b a l t , the measured work hardening r a t e s are high, approaching G/10 a t 2% s t r a i n f o r t e s t s a t -196°C. Two important f a c t o r s t h a t may g i v e r i s e to the high work hardening v a l u e s are the low s t a c k i n g f a u l t energy and the m a r t e n s i t i c t r a n s f o r m a t i o n . 128 Both factors are important i n d i v i d u a l l y and are additive. The low stacking f a u l t energy ensures that the majority of d i s locations present i n cobalt are dissociated. Continued movement of extended di s l o c a t i o n s af t e r i n t e r s e c t i o n i s d i f f i c u l t and gives r i s e to work hardening. As the martensitic transformatiqn proceeds on d i f f e r e n t (111) planes, the martensitic lamallae formed intersect and growth of the lamallae i s i n h i b i t e d . Dislocations within the lamallae must cross a boundary, s i m i l a r to a twin boundary, to move out of the martensite, or i n t i a t e s l i p across the boundary. S i m i l a r i l y , other d i s l o c a t i o n s outside the lamallae must move through these boundaries or i n i t i a t e s l i p across them to allow continuing deformation. Another way of viewing the multivariant transformation, as related to work hardening, i s to accept the formation of the various martensite lamallae as formation of new boundaries i n the c r y s t a l l a t t i c e . This boundary formation i s similar to a continuing grain refinement. If the transformation i s viewed i n t h i s manner, i t would be expected that the strong e f f e c t s that grain boundaries impose upon p o l y c r y s t a l l i n e material during the i n i t i a l portion of the stress s t r a i n curve, may continue to be evident as long as the transformation proceeds. The d i f f i c u l t y a r i s i n g when dis l o c a t i o n s encounter obstacles of the type a r i s i n g from martensitic transformations has been observed by several authors 3 6 ' 3 7 1 1 0 5 • 1 0 6 . M a r c i n c o w s k i 1 0 5 1 1 0 6 observed that widely dissociated 129 d i s l o c a t i o n s on d i f f e r e n t (111) p l a n e s l o c k each o t h e r v e r y e f f e c t i v e l y when th e y i n t e r s e c t . He a l s o o b s e r v e d t h a t m a r t e n s i t i c l a m a l l a e form f o r m i d a b l e b a r r i e r s t o d i s l o c a t i o n m o t i o n . He p roposes t h a t d i s l o c a t i o n g e n e r a t i o n must o c c u r t o a l l o w c o n t i n u e d d e f o r m a t i o n . B a r r e t t 7 8 w o r k i n g w i t h copper-germanium p o s t u l a t e d s i m i l a r s t r o n g o b s t a c l e s t o d e f o r m a t i o n i n t h i s system where a s i m i l a r m a r t e n s i t i c t r a n s f o r m a t i o n o c c u r s . The t r a n s m i s s i o n s t u d i e s c a r r i e d out by V o t a v a 3 6 ' 3 7 i n f e r t h a t s i m i l a r h a r d e n i n g mechanisms a r e r e s p o n s i b l e f o r t h e h i g h work h a r d e n i n g r a t e s i n c o b a l t . 130 3.2.2 Deformation and the A l l o t r o p i c Transformation Many of the r e s u l t s outlined to t h i s point, may be explained i n terms of the martensitic transformation. As described e a r l i e r a l l test specimens u t i l i z e d for t h i s study contained a large f r a c t i o n of fee phase. The i n i t i a l retained fee phase for a l l annealing treatments was summarized i n Table V. A number of step-pull tests were carr i e d out to trace the progress of the transformation towards completion. The data are presented as a function of s t r a i n to allow d i r e c t comparison to the s t r e s s - s t r a i n curves. (Figures 43, 44). The progress of the transformation as a function of stress did not y i e l d data that could be r e a d i l y analysed. The retained fee phase i s also plotted against a logarithmic scale for s t r a i n to allow observation of the progress of the transformation at low s t r a i n values. (Figures 45-47). The data y i e l d s linear r elationships when plotted i n t h i s manner. This r e s u l t implies that the r e l a t i o n s h i p between s t r a i n and the fee phase may be represented by an equation of the form: log e = log A + m(% fee) ....6) or equivalently ,. / 1 r t Xm(%fcc) e = A (10) ....7) Where: e = true s t r a i n A = s t r a i n value where % fee = 0 % fee = (% fee). ... . - (% fee). - , i n i t i a l transformed Certain l i m i t s must be placed on the equations. The volume % fee phase may only vary between the amount present before testing and the amount present at f a i l u r e . For  P u r i t v G r a i n r i z e fee i n i t i a l (%) fu) (%) 0 I 1 1 1 1 I I 0 5 10 . 1 5 20 25 True S t r a i n (%) F i g . 4 4 Room temperature t e n s i l e s t r a i n induced t r a n s f o r m a t i o n f o r c o b a l t of v a r i o u s g r a i n s i z e s . •<-> u> to d r a i n s i z e fee i n i t i a l (M) (%) 0.05 0.1 0.2 0.5 1.0 2.0 5.0 10 20 50 True S t r a i n (%) P i g . 4 5 Room temperature t e n s i l e s t r a i n induced t r a n s f o r m a t i o n f o r c o b a l t of v a r i o u s g r a i n s i z e s (semilog). M LO LO Grain s i z e (y) fee i n i t i a l r u r i t y (%) (%) 9 9 . 7 99.9 99.998 1 I I I I I 1 1 1 1 I I I I I I I I I I I I I I I I l l I I I I I 0.05 0 .1 0.2 0.5 1.0 2.0 5.0 10 20 50 True S t r a i n (%) Fig.46 T e n s i l e s t r a i n induced t r a n s f o r m a t i o n of c o b a l t a t room temperature (semilog). U) • 385°C True S t r a i n (%) F i g . 47 T e n s i l e s t r a i n induced t r a n s f o r m a t i o n f o r c o b a l t a t v a r i o u s temperatures, (semilog). CO p o l y c r y s t a l c o b a l t the maximum fee phase t h a t may be r e t a i n e d f o l l o w i n g a normal a n n e a l i n g treatment i s approximately 60%. The amount prese n t a t f a i l u r e v a r i e s from around 2% a t -196°C to over 10% a t temperatures above 0.25 T . Table X I I I p r e s e n t s the s o l u t i o n s to the above m c equation f o r the curves shown i n F i g u r e s 45 - 47. A l i n e a r r e l a t i o n s h i p has been assumed f o r t e s t s above 0 .25 T as m w e l l , although t h i s may npt be j u s t i f i e d . The g e n e r a l r e s u l t s of t h i s s e r i e s of t e s t s are as f o l l o w s . As s t r e s s i n c r e a s e s , very l i t t l e t r a n s f o r m a t i o n takes p l a c e b e f o r e macroscopic y i e l d o c c u r s . T h i s r e s u l t i s shown i n F i g u r e 45 f o r 99.9% c o b a l t t e s t e d a t room temperature. The curves have been e x t r a p o l a t e d t o the s t r a i n v a l u e where the amount of r e t a i n e d fee presen t p r i o r t o t e s t i n g o c c u r s . For the v a r i e t y of g r a i n s i z e s shown, the s t r a i n a t which t r a n s f o r m a t i o n begins i s between 0,07% and 0.11% s t r a i n . S i m i l a r r e s u l t s are obtained f o r a l l m a t e r i a l t e s t e d below 0 .25 T . At 0.2% s t r a i n , a m ' n o t i c a b l e amount of t r a n s f o r m a t i o n has taken p l a c e a t a l l temperatures below 0 .25 T . Above 0 .25 T the s i t u a t i o n m m i s not as c l e a r although the data i m p l i e s t h a t the s t r a i n induced t r a n s f o r m a t i o n begins a t higher s t r a i n v a l u e s . The r a t e a t which the t r a n s f o r m a t i o n proceeds slows as s t r a i n i n c r e a s e s . At f r a c t u r e the t r a n s f o r m a t i o n remains incomplete. 3 . 2 . 2 . 1 P u r i t y To i s o l a t e any d i f f e r e n c e s i n behaviour due to i m p u r i t y l e v e l s , small g r a i n e d specimens of 99 .7%, 99.9% and 99.998% TABLE XIII Behaviour of the Strain Induced Transformation i n Cobalt : Expressed as an Equation of the F orm: m(%fcc) £ = A(10) E = true s t r a i n , %fcc = Volume %fcc Grain Size (u) Purity (%) A m Test Temp. °C e at v/hich Transformation begins (%) Volume % transformed at 0.2% e £ t x 7.0 9 9.7 44.8 - 0 . 0 5 5 20 0.07 8.0 12 .3 6 .5 99.9 33.5 - 0 . 0 6 0 20 0.09 6.0 8 . 1 9 .0 99.998 16.7 - 0 . 0 6 6 20 0.07 7 .5 9.4 <6.5 99.9 85.0 - 0 . 0 5 9 20 0.08 7 .5 10.0 <6.5 99.9 64.5 - 0 . 0 6 3 20 0.09 5 . 5 8 .5 6 .5 99.9 33.5 - 0 . 0 6 0 20 0.09 6.0 8 . 1 10,0 99.9 51.3 - 0 . 0 9 8 20 0 .11 2.5 6.6 24 .0 99.9 38.8 - 0 . 1 0 4 20 0.07 4 .5 6 .5 60.0 99.9 21.8 - 0 . 1 2 0 20 0.09 3.0 No Sol'n 6 . 5 99.9 33.5 - 0 . 0 6 -196 0.09 6.0 8 . 1 6 .5 99.9 33.5 - 0 . 0 6 20 0.09 6.0 8 . 1 6 .5 99.9 33.5 - 0 . 0 6 100 0.09 6.0 8 . 1 6 .5 99.9 87.0 - 0 . 0 6 250 0.29 0 No Sol'n 6 . 5 99.9 195.0 - 0 . 0 6 385 0 .71 0 No Sol'n c o b a l t were s t e p - p u l l e d to f a i l u r e . The r e s u l t s are shown i n F i g u r e s 43 and 46. Three o b s e r v a t i o n s may be drawn from the d a t a . From F i g u r e 43 , i t i s c l e a r t h a t a l l grades of m a t e r i a l f a i l p r i o r t o complete t r a n s f o r m a t i o n . F r a c t u r e occurs when the volume of r e t a i n e d fee phase reaches a v a l u e between 5 and 7 volume % a t room temperature. In F i g u r e 47 , i t may be seen t h a t a somewhat jower l i m i t a p p l i e s a t -196°C and a higher l i m i t a t 250°C and 385°c. Secondly, the t r a n s f o r m a t i o n begins betv/een 0.06% and 0.09% s t r a i n and i s independent of p u r i t y (Figure 46, Table XIIJ. A f i n a l o b s e r v a t i o n i s t h a t the progress of the s t r a i n induced t r a n s f o r m a t i o n w i t h r e s p e c t to s t r a i n does not vary a p p r e c i a b l y between the v a r i o u s p u r i t y grades. T h i s r e s u l t i s i n c o n t r a s t to the e a r l i e r o b s e r v a t i o n t h a t p u r i t y was found to a f f e c t the amount of r e t a i n e d fee phase i n a s t r o n g manner. As the p u r i t y of c o b a l t i n c r e a s e s , the t r a n s f o r m a t i o n proceeds f u r t h e r towards completion f o l l o w i n g an a n n e a l i n g treatment. As there i s l e s s r e t a i n e d fee a v a i l a b l e i n higher p u r i t y m a t e r i a l , a s m a l l e r i n p u t of s t r a i n i s r e q u i r e d to b r i n g t h i s m a t e r i a l to approximately 5 volume % f e e , where f r a c t u r e o c c u r s . The equations d e s c r i b i n g the t r a n s f o r m a t i o n show t h i s r e s u l t v e r y c l e a r l y . I f 5 volume % r e t a i n e d fee i s accepted as the l i m i t f o r c o n t i n u i n g deformation a t room temperature, s u b s t i t u t i o n of t h i s v a l u e i n the a p p r o p r i a t e equations i n Table X I I I . should y i e l d the measured elongation. Upon substitution, the results are 7.7% for 99.998% material, 17.9% for 99.9% material, and 23.9% for 99.7% cobalt. If these values are compared to the d u c t i l i t y values for the f i n e grained material presented i n Table XI reasonable correspondence i s observed. The fact that the progress of the s t r a i n induced transformation does not vary s i g n i f i c a n t l y with purity i s not unexpected. The d r i v i n g force tending to complete the transformation upon cooling i s very small. It has been estimated that i t wpuld be equivalent to an applied stress of several hundred p s i 2 8 - 3 1 . At these stress lev e l s i t would be expected that small differences i n the l a t t i c e would y i e l d measurable differences i n behaviour. In f a c t , i t has been observed that increasing purity does allow the transformation to proceed further towards completion upon; cooling. The stress lev e l s present during s t r a i n induced transformation are an order of magnitude larger and therefore any differences i n the manner i n which the s t r a i n induced transformation proceeds due to impurity content should not be s i g n i f i c a n t . 3.2.2.2 Grain Size The progress of t h e transformation with s t r a i n for various grain sizes i s shown i n Figures 44 and 45. The i n i t i a l fee phase available p r i o r to testing decreases markedly as the grain size increases. The only important difference between t h i s set of curves and those dealing with purity i s that the rate at which the s t r a i n induced transformation proceeds decreases as grain size increases. Although the s t r a i n values at which transformation begins and the fee phase remaining at f a i l u r e are s i m i l a r , the slopes of the curves change as grain size increases. The difference i n slopes means that a larger imput of s t r a i n i s required to y i e l d an equivalent amount of s t r a i n induced transformation for material having a larger grain s i z e . This reduction i n the rate of s t r a i n induced transformation i s not s u f f i c i e n t to overcome the decrease i n available fee phase. Thus, the measured elongation to f a i l u r e decreases as the grain size increases because the amount of retained fee reaches the value where f a i l u r e occurs with less s t r a i n imput. A dotted l i n e has been included i n Figure 44 and 45 to represent the data for large grained material tested by M i i l l e r 8 3 . He quotes an i n i t i a l fee content of approximately 10% and measured 4 to 6% elongation for material ranging from 300 to 30,000 microns. This l i n e may be assumed to represent a l i m i t on the v a r i a t i o n of behaviour with grain s i z e . 3.2.2.3 Temperature Step-pull tests were performed above and below 0.25 T , to ascertain the differences i n transformation behaviour that occur. Typical x-ray r e s u l t s for 99.7% and 99.9% cobalt are shown in Figures 48 and 49. The r e s u l t s are plotted i n Figure 47. Cobalt tested at -196°C, 20°C, and 100°C exhibit similar behaviour. In Table XIII a single equation i s presented for behaviour at a l l three temperatures. The r e s u l t s d i f f e r for material tested at 250°C (0.3 T ) m and 385°C (0.37 T ). Although the slopes of the curves are similar at a l l temperatures, a much larger amount of fee phase i s retained at any value of s t r a i n for tests above 0.25 T . m At f a i l u r e , the transformation i s 98% complete for material tested at -196°C, approximately 95% complete for material tested at room temperature and 100°C, and only 80 to 90% complete for material tested above 0.25 T . 1 m This v a r i a t i o n r e f l e c t s the stress lev e l s attained at the d i f f e r e n t temperatures. At lower temperatures the stress levels are much higher which i s equivalent to applying a larger dr i v i n g force for transformation. This f i n a l set of r e s u l t s , provides further information that may be compared to the v a r i a t i o n i n t e n s i l e properties with temperature. The volume f r a c t i o n of s t r a i n induced martensite that forms i n the i n i t i a l 0.2% s t r a i n during a t e n s i l e test i s l i s t e d i n Table X I H . C l e a r l y , the behaviour below 0.25 T d i f f e r s from that above. To obtain macroscopic m ^ v i e l d below 0.25 T , s t r a i n induced transformation must m occur. Above 0.25 T , t h i s bulk transformation does not m appear necessary. 20°C Test (% S t ra in/% fee) 250°C Test F i g . 48 X - r a y data f o r 99.9% c o b a l t , s t e p - p u l l e d a t 20°C and 250 6.5 micron g r a i n s i z e . 143 (% St ra in/% fee) 20°C Test 250°C Test F i g . 49 X - r a y data f o r 99.7% c o b a l t , s t e p - p u l l e d a t 20°C and 250°C 7 micron g r a i n s i z e . The amount of s t r a i n induced martensite formed as a function of s t r a i n i s plotted i n Figure 50 for various test temperatures. The amount of transformation that has taken place at any value of s t r a i n , i s similar for tests at -196°C, 20°C, and 100°C. I t can be seen that the volume f r a c t i o n of s t r a i n induced martensite i s much smaller, at any value of s t r a i n , for material tested above 0 .25 T . J m The s a l i e n t features of the s t r a i n induced transformation i n p o l y c r y s t a l cobalt have been presented. The r e l a t i o n s h i p between s t r a i n and retained fee phase may be represented by an equation of the form e = A ( 1 0 ) m ( % f c c ) . » m« varies l i t t l e with purity or test temperature, but changes rapid l y with grain size. "A" represents the s t r a i n that could be introduced into p o l y c r y s t a l cobalt i f fracture coincided with completion of the martensitic transformation. The i n i t i a l fee phase present following an annealing procedure and the s t r a i n value at which the s t r a i n induced transformation begins determine "A". "A" varies v/ith purity, grain si z e , and test temperatures above 0 .25 T . ^ m Eefore comparing these observations to the re s u l t s obtained from the t e n s i l e tests, a thorough discussion of the martensitic transformation as related to deformation of p o l y c r y s t a l cobalt i s required.  3 . 2 . 2 . 4 Von Mises C r i t e r i o n A c c o r d i n g to Von Mises C r i t e r i o n , a p o l y c r y s t a l r e q u i r e s 5 independent shear systems t o undergo homogeneous s t r a i n without change i n volume. P o l y c r y s t a l c o b a l t undergoes a s l i g h t volume change d u r i n g deformation and thus i n a s t r i c t sense, Von Mises C r i t e r i o n should not be a p p l i e d . The change i n volume accompanying deformation of c o b a l t i s very s m a l l , about 1/3 of 1% f o r complete t r a n s f o r m a t i o n . For m a t e r i a l used i n t h i s study o n l y about 25% to 40% of the bulk transforms d u r i n g deformation e q u i v a l e n t to a r e d u c t i o n i n volume of 0.10% to 0 .13%. T h i s f a c e t of the t r a n s f o r m a t i o n cannot y i e l d a major c o n t r i b u t i o n to the shape change of i n d i v i d u a l g r a i n s . B a s a l s l i p i s the major s l i p mode observed i n c o b a l t . T h i s system p r o v i d e s no e x t e n s i o n p a r a l l e l to the c a x i s and p r o v i d e s o n l y two independent shear systems. The volume change upon t r a n s f o r m a t i o n from fee to hep p r o v i d e s a small c o n t r a c t i o n p e r p e n d i c u l a r to the c a x i s and a s m a l l expansion p a r a l l e l t o the c a x i s . (Figure 13). The combination of b a s a l s l i p and the volume change does not s a t i s f y Von Mises C r i t e r i o n . I f i t i s accepted t h a t non b a s a l s l i p i s extremely d i f f i c u l t i n hep cobalt 1*, the s a t i s f a c t i o n of Von Mises C r i t e r i o n must a r i s e from other sources. 147 As outlined i n the review by P a r t r i d g e 7 , other deformation modes have been observed to s a t i s f y Von Mises C r i t e r i o n where i n s u f f i c i e n t s l i p systems are available. Kink Boundary formation, grain boundary s l i d i n g , as well as contributions from twinning shear are a l l recognized as processes that may supply the needed degrees of freedom to allow deformation of a p o l y c r y s t a l l i n e aggregate. According to Kocks 7, cross s l i p may also reduce the required number of independent s l i p systems. Over the temperature range investigated, grain boundary s l i d i n g should not be an important source of s t r a i n i n cobalt. Due to the very low stacking f a u l t energy of cobalt, cross s l i p may also be discounted.as a major route to an independent shear system. I f these processes are discarded as unfavourable, further independent shear systems may arise from twinning and kink boundary formation. Twinning elements y i e l d i n g both contraction and expansion perpendicular to the basal plane have been observed i n cobalt; {1012}, {1011}, and .{112n}twins have a l l been observed during single c r y s t a l deformation. A large shear value for {112n} type twins has been postulated 7. Thus, a large twinned volume may enhance the d u c t i l i t y of cobalt considerably. Reed-Hill 9 postulates that the amount of s t r a i n that may be accommodated by twinning i s arrived at as follows: e •= 1//2 (V) (S) 8) 148 VThere: e = s t r a i n 1//2 = average Schraid factor for p o l y c r y s t a l s V = volume f r a c t i o n twinned S = shear value for twinning mode considered as an example. Reed-Hill substitutes values for {1012} twinning i n zirconium. S = .17 V = .50 Therefore: e = (0.707) (0.50) (0.17) = 0.06 Thus {1012} twinning may account for up to 6% s t r a i n i n zirconium. A s i m i l a r equation for cobalt would be: e = 1//2 ( V ) { 1 0 i 2 } ( S ) { 1 0 i 2 } + 1//2 ( V ) { 1 Q l l } ( S ) { l o I l } + etc. 9) In cobalt, the volume f r a c t i o n twinned would have to be very large as occurs i n zirconium to y i e l d more than a few percent s t r a i n . The retained fee phase that i s d i s t r i b u t e d throughout the grains of the low temperature phase may aid grain shape change. The retained areas of fee have no lack of s l i p systems available, but s l i p and transformation are c l o s e l y related. Deformation of the fee phase i s probably synonomous with continuation of the transformation. If deformation i s possible i n the fee phase without transformation, non basal s l i p traces should be observed. If s l i p occurs on a given {111} plane i n the fee phase, transformation on a d i f f e r e n t {111} variant becomes d i f f i c u l t 1 * . The manner i n which the disappearance of the fee phase may provide s t r a i n i n cobalt may be stated i n two ways. The ongoing transformation may be viewed as s l i p on various {111} planes, thus y i e l d i n g a number of independent shear systems. The continuing transformation may also be viewed as a type of twin formation. The s i m i l a r i t y between twinning and martensitic formation i s very close i n cobalt because the fee to hep transformation i s a low energy transformation requiring only a simple shear, with no additional complex shuffles i n the plane of shear. (Table VI). The formula used by Reed-Hill to account for the manner i n which twinning, in addition to s l i p processes, may s a t i s f y Von Mises C r i t e r i o n , should be applicable to the martensitic transformation i n cobalt. Transformation occurs on many {111} planes i n a given fee grain; thus we have a deformation process that y i e l d s contraction and expansion i n various di r e c t i o n s i n the parent grain. The t h e o r e t i c a l shear value for the transformation i s S = 0.353 and shear up to 35% was observed by A l t s t e t t e r 2 8 - 3 1 for applied stresses of several thousand p s i i n single c r y s t a l s . For the high stresses involved during p o l y c r y s t a l deformation, the transformation may c l e a r l y provide large amounts of shear. If the formation of martensitic plates i n cobalt i s considered equivalent to the formation of twins the maximum st r a i n available from t h i s source may be determined as for twinning: e = 1//2 (S) (V) 8) £ = 1//2 ( S ) T x ( V ) T x 1 0 ) Where: S = 0.353 v£* = 0.25 to 0.40 Therefore:' e = 0.25 (V) Tx 11) For every 4% of the fee phase transformed a s t r a i n of 1.0% could t h e o r e t i c a l l y be obtained from transformation alone. In a l l material produced for the present study, between 30% and 60% fee phase was retained i n the annealed material. As the transformation i s forced near completion during deformation, anywhere from 7 1/2% to 15% s t r a i n could t h e o r e t i c a l l y be accomplished through operation of the martensitic transformatiqn. i n fa c t , i f the transformation does y i e l d the th e o r e t i c a l maximum shear, '£ = 0.25 (v* t ) , i t i s possible for the transformation to provide a l l the shear necessary i n the i n i t i a l portion of the t e n s i l e curve for example: e = A ( 1 0 ) m ( % f c q ) 7) and e = 0.25 (Vfc ) .....11) but (%fcc). ... . - (%fcc) = V. i n i t i a l tx therefore (%fcc) = (%fcc). . . . , - V. i n i t i a l tx and (%fcc) = (%fcc). .,. , - 4̂ i n i t i a l Substitute i n equation #7 e = A ( 1 0 ) m ( % f c a i n i t i a l - 4E> 12) Solve for log E + 4m£ - [log A + m(% fee). ... ,] =0 ....13) 151 If the equation i s solvable for e, the value found w i l l correspond to the s t r a i n value at which the transformation can no longer provide a l l the shear required. The progress of the transformation for a given s t r a i n imput decreases with increasing s t r a i n . Thus, the value found i s the amount of true s t r a i n that may be introduced without requiring some other shear mechanism to operate. If the equation i s not solvable for any pos i t i v e value of e, then some shear mechanism other than the martensitic transformation must be required at y i e l d and -throughout the t e n s i l e curve. The f i n a l column i n Table XIII l i s t s the value obtained from equation 13 above. The column i s t i t l e d e. . From Table XIII tx i t may be seen that there are two situations where no solution e x i s t s . The f i r s t case i s for large grain sizes. This i s not unreasonable as the i n i t i a l retained fee phase i s very low. Secondly, the ecruations for tests above 0.25 T . m cannot be solved for posit i v e s t r a i n values. This l a t t e r observation indicates a change i n behaviour at higher temperatures. In the analysis above i t has been assumed that a l l transformation taking place would contribute to the t e n s i l e s t r a i n . This i s c l e a r l y not the case and the basal s l i p mode i s undoubtedly operative throughout the s t r e s s - s t r a i n curve. Kink boundary formation has been observed by T h e i r i n g e r 2 4 1 2 5 . in cobalt at a l l temperatures with the amount of kink formation increasing with temperature. The observation that t h i s deformation mode i s more common a t h i g h temperatures i s u s u a l l y e x p l a i n e d as f o l l o w s : Although the s t r e s s r e q u i r e d to n u c l e a t e and propogate twins i s not w e l l understood, i t i s g e n e r a l l y accepted t h a t the n u c l e a t i o n process r e q u i r e s higher s t r e s s l e v e l s than does growth. At h i g h e r temperatures, i t i s proposed t h a t s t r e s s l e v e l s are not s u f f i c i e n t t o n u c l e a t e c e r t a i n twins ( i . e . {112n}) and the formation of kink boundaries takes p l a c e as an a d j u n c t to c o n t i n u i n g deformation. F i n a l l y , i t should be r e c a l l e d t h a t i n a d d i t i o n to a v a r i e t y of twinning modes, c o r r u g a t e d {1122} <1123> s l i p has been observed i n s i n g l e c r y s t a l c o b a l t by Seeger 1 h . The avenues whereby coherency a t g r a i n boundaries may be maintained i n p o l y c r y s t a l c o b a l t are m a n i f o l d . A summary of the probable deformation modes i s presented below: i ) B a s a l s l i p i i ) Twinning Modes, {1012}, L e n t i c u l a r Twins {1011}, {112n}, Th i n Twins {1121}, Zig-Zag Twins i i i ) Volume Tr a n s f o r m a t i o n of r e t a i n e d fee r e g i o n s y i e l d i n g shear on v a r i o u s {111} p l a n e s . i v ) Corrugated S l i p , {1122}, <1123>, Second Order Pyramidal v) Duplex S l i p i n r e t a i n e d fee phase. 153 3 . 2 . 2 . 5 M e t a l l o g r a p h i c Observat ions P r e s e n t a t i o n of the m e t a l l o g r a p h i c o b s e r v a t i o n s made d u r i n g the deformat ion of p o l y c r y s t a l c o b a l t has been d e f e r r e d t o t h i s p o i n t as the p r i o r i n f o r m a t i o n presented i s r e q u i r e d to e x p l a i n the su r face f e a t u r e s t h a t a r i s e . F i g u r e 51 i s presented to show the macroscopic shear t h a t may occur d u r i n g t r a n s f o r m a t i o n . Gross amounts of t r a n s f o r m a t i o n tend to obscure a l l o ther s u r f a c e r e l i e f as s t r a i n i n c r e a s e s . F i g . 51 M a r t e n s i t e shear markings in t roduced by a su r face s c r a t c h i n 99.9% c o b a l t . 1900X 154 The s t r u c t u r e s produced d u r i n g deformation of p o l y c r y s t a l c o b a l t are not documented i n the l i t e r a t u r e . Annealed 81 8 2 s t r u c t u r e s are shown i n a few cases * and the a f f e c t s of t r a n s f o r m a t i o n on very l a r g e g r a i n s has been o u t l i n e d by Bebring and S e b i l e a u 7 1 . The s t r u c t u r e s a s s o c i a t e d w i t h hardness i n d e n t a t i o n s have been photographed by L o z i n s k y , and W i l c o x 8 9 . Jagged, shear type, f r a c t u r e zones have a l s o been photographed by L o z i n s k y . A u c o u t u i r e r and Lacombe 1 1 2 d e l i n e a t e d the h i g h temperature fee g r a i n s by an auto- radiography technique and compared the observed fee boundaries with the s t r u c t u r e determined by e l e c t r o p o l i s h i n g the same areas. Three major o b j e c t i v e s were pursued d u r i n g the experimental work: Attempts were made to f o l l o w a d e f i n e d s u r f a c e area throughout the t e n s i l e curve w h i l e v a r y i n g p u r i t y , g r a i n s i z e , and t e s t temperature. A v a r i e t y of specimens were s t e p - p u l l e d to o b t a i n the r e q u i r e d d ata. A f t e r a specimen was s t r a i n e d s e v e r a l p e r c e n t i t was removed from the I n s t r o n machine, x-rayed, examined m i c r o s c o p i c a l l y and then r e p l i c a t e d . The specimen was then r e t e s t e d and the procedures continued u n t i l f a i l u r e occured. T e s t s were c a r r i e d out at -196°C, room temperature, 100°C, 250°C, and 380°C. The o b j e c t i v e s were not f u l l y r e a l i z e d as i t was found i m p r a c t i c a b l e to o b t a i n r e p l i c a s from the same•area a f t e r each segment of a s t e p - p u l l t e s t . The two methods of examination are complimentary. The re p l i c a s show much more d e t a i l than the o p t i c a l observations, but as s t r a i n increases the r e p l i c a s become so complex that the o v e r a l l s i t u a t i o n becomes obscure. The o p t i c a l work c l a r i f i e s t h i s gross picture while deleting the fin e structure. 3.2.2.5.1 Purity and Grain Size The e f f e c t s of d i f f e r i n g purity on the surface features of p o l y c r y s t a l cobalt are minimal. The only noticable difference i s that the i n t e n s i t y of surface rumpling at f a i l u r e i s lower for an increase i n purity. This difference r e f l e c t s the lower amount of transformation that occurs pr i o r to f a i l u r e . S i m i l a r l y , any differences observed between specimens of d i f f e r e n t grain size were differences i n scale and in t e n s i t y only. As grain size increases, the amount of s t r a i n induced transformation, and the elongation p r i o r to f a i l u r e decrease y i e l d i n g less severe microstructures. Based on these i n i t i a l findings, further work was concentrated on the v a r i a t i o n i n observed deformation with s t r a i n and temperature. 156 3 . 2 . 2 . 5 . 2 O p t i c a l M e t a l l o g r a p h y F i g u r e 52 t r a c e s t h e p r o g r e s s o f a l a r g e g r a i n e d s p e c i m e n f r o m y i e l d t o f a i l u r e a t 250°C. A t y i e l d , t h e l a r g e s t g r a i n e x h i b i t s o n l y o n e s e t o f o b v i o u s s h e a r m a r k i n g s (1), a s e c o n d s e t (2) a r e b a r e l y v i s i b l e . A r u m p l e d b a n d t r a v e r s e s t h e l a r g e g r a i n c o m p l e t e l y . T h i s b a n d i s p r o b a b l y a n f e e a n n e a l i n g t w i n w h i c h h a s b e e n r e o r i e n t e d d u r i n g t h e c o o l i n g t r a n s f o r m a t i o n . A t 2.3% s t r a i n t h e s i t u a t i o n h a s c h a n g e d r a d i c a l l y . A l a r g e a m o u n t o f s h e a r o n t w o s y s t e m s (1 a n d 2) i s s h o w n c l e a r l y . A t w i n i s a l s o f o r m i n g i n t h e c e n t r a l g r a i n . T h e i n c r e a s i n g c o n s t r a i n t i n t h e s y s t e m h a s a l s o c a u s e d t h e s m a l l g r a i n i n t h e u p p e r l e f t t o t w i n . T h e s u r f a c e i s r u m p l e d s o s e v e r e l y t h a t s o m e s m a l l g r a i n s a r e t i l t e d o u t o f f o c u s . A t f a i l u r e , t h e t w i n f o r m i n g a t 2.3% s t r a i n h a s p r o p o g a t e d a n d r e f l e c t e d f r o m t w o b o u n d a r i e s t o t a k e u p a z i g - z a g c o n f i g u r a t i o n . T h e t w i n h a s n o t t a k e n o n a l e n t i c u l a r s h a p e d u r i n g g r o w t h , i n f e r r i n g a h i g h s h e a r v a l u e . T w i n s o f t h i s z i g - z a g t y p e h a v e b e e n o b s e r v e d i n s i n g l e c r y s t a l c o b a l t b y D a v i s 1 1 a n d p o l y c r y s t a l t i t a n i u m b y R o s i 1 5 . B o t h i n v e s t i g a t o r s d e t e r m i n e d t h a t t h e t w i n s h a d a {1121} h a b i t p l a n e . F i g u r e 53 p r e s e n t s a d i f f e r e n t a r e a i n t h e s a m e s p e c i m e n a t f a i l u r e . T h r e e i m p o r t a n t s h e a r p l a n e s h a v e b e e n o p e r a t i v e i n a s i n g l e g r a i n . 157 F i g . 52 Deformation of 99.998% c o b a l t , 850X 158 F i g . 53 Deformation markings i n 99.998% cobalt at f a i l u r e . 1000X cn • H X rt CD C CD E H F i g . 54(a) 1 . 9 % s t r a i n F i g . 54(b) 6.6% s t r a i n F i g . 54 G r a i n shape change i n 99.9% c o b a l t . 1 0 0 0 X 159 F i g u r e s 52 and 53 show c o b a l t having the l a r g e s t g r a i n s i z e , lowest d u c t i l i t y , and l e a s t s t r a i n induced t r a n s f o r m a t i o n of any m a t e r i a l used i n the presen t study. A l l other m a t e r i a l s show very s i m i l a r behaviour, although the rumpling and shear i n c r e a s e i n i n t e n s i t y . F i g u r e 54 shows the amount of g r a i n shape change t h a t may occur w i t h l i t t l e i n c r e a s e i n t e n s i l e s t r a i n . The t e n s i l e a x i s i s shown and the d i s l o c a t i o n a c t i v i t y appears to be l i m i t e d to a s i n g l e s l i p system i n a m a j o r i t y of t h i s g r a i n . Although o p t i c a l metallography was found t o be of l i m i t e d use i n determining the presence or absence of non- b a s a l s l i p , F i g u r e s 55 and 56 show the complexity of twinning t h a t occurs i n p o l y c r y s t a l c o b a l t . Very few twins are observed a t low s t r a i n v a l u e s . At f r a c t u r e a l l specimens e x h i b i t a very complex twinned s t r u c t u r e . P u r i t y , g r a i n s i z e , and t e s t temperature have l i t t l e a f f e c t on t h i s f a c e t of the deformation. F i g u r e 55 shows the twinning p r e s e n t f o l l o w i n g a t e s t a t -196°C, F i g u r e 56 a f t e r a t e s t a t 350°C. F i g u r e 56 shows a s i n g l e g r a i n a f t e r t e s t i n g a t 350°C. S e v e r a l twins have taken on a l e n t i c u l a r c o n f i g u r a t i o n and are probably {1012} twins, whereas the t h i n s t r a i g h t twins probably represent'{1 0 1 1} and {112n} h a b i t p l a n e s . Over a dozen h a b i t planes are represented i n t h i s s i n g l e g r a i n . The appearance of the t h i n twins a t high temperature i n f e r s t h a t high i n t e r n a l s t r e s s c o n c e n t r a t i o n s were a v a i l a b l e to nu c l e a t e them. 160 F i g . 56 Twinning i n cobalt at 350°C. 850X 161 The i n f o r m a t i o n gained by o p t i c a l meta l lography may be summarized as f o l l o w s : i ) P u r i t y and g r a i n s i z e do not a f f e c t the observed deformat ion modes. A r e d u c t i o n i n p u r i t y or g r a i n s i z e s imply inc reases the i n t e n s i t y of the s t r u c t u r e s observed. i i ) L i t t l e d i f f e r e n c e was noted between deformat ion above and below 0.25 T . Surface rumpl ing was somewhat l e s s m severe a t h igh temperature which s imply r e f l e c t s the sma l l e r volumes of s t r a i n induced mar tens i t e formed at. these temperatures . i i i ) Deformation i s very heterogeneous. Some g r a i n s e x h i b i t gross amounts of deformat ion a t low s t r a i n va lues w h i l e ne ighbour ing g r a i n s appear undeformed. i v ) .Macroscopic shear occurs on two or more planes w i t h i n the reg ions d e l i n e a t e d by an fee g r a i n boundary. The amount of shear tha t may occur on any plane i s very l a r g e . v) Twins are observed i n c o b a l t specimens t e s t ed a t a l l temperatures between -196°C and 380°C. The amount of twinn ing observed a t y i e l d i s n e g l i g i b l e but i nc reases w i t h s t r a i n . Z i g - z a g t w i n n i n g , assumed to occur i n the {1121}- h a b i t p lane , i s a common obse rva t i on a t a l l temperatures . L e n t i c u l a r {1012} twins as w e l l as s t r a i g h t t h i n twins of probable h a b i t planes {1011} and {112n} are a l s o observed. Al though a m u l t i p l i c i t y of twinn ing modes are observed, the tw inn ing volume remains s m a l l . 162 3.2.2.5.3 Replica Observations The features observed by r e p l i c a techniques are d i f f i c u l t to correlate with those delineated o p t i c a l l y . As shown i n Figure 57 for a small grained specimen of 99.7% cobalt, the e f f e c t of s t r a i n on the surface topography i s very pronounced. To allow comparison to the o p t i c a l observations r e p l i c a s taken af t e r limited amounts of s t r a i n are presented. In Figure 58, the majority of shear has taken place on two s l i p systems approximately at r i g h t angles. Where one region abutts the other, twins have been i n i t i a t e d to r e l i e v e stress. Although evidence of twinning does e x i s t i n t h i s case, a t o t a l lack of v i s i b l e stress r e l i e f i s more common. In Figure 59, shear has taken place on three d i s t i n c t systems. The amount of shear i s large i n a l l cases, yet no evidence of twinning at points of inte r s e c t i o n i s observed. The observed pattern shown i n Figure 59 involving two or three shear systems i s the most commonly observed surface feature i n p o l y c r y s t a l cobalt. The topography i s c l e a r l y a r e s u l t of the multivariant martensitic transformation. The large step heights r e f l e c t the passage of many dislocations over a single s l i p plane. Therefore, i t may be inferred that the stress system producing transformation on some planes i s cabable of continuing d i s l o c a t i o n production on these planes. 163 F i g . 57 Deformation of 99.7% cobalt at 250°C. 3000X 1 6 4 F i g . 59 T y p i c a l surface shear markings i n c o b a l t . -196°C T e s t . 6500X In contrast to the markings shown i n Figure 59 are the twins shown i n Figures 60 and 61. S l i p on martensitic transformation planes i s characterized by noticable shear on many p a r a l l e l planes with gross amounts on occasional planes. The twins, on the other hand, are characterized by a single volume of sheared l a t t i c e . In Figure 61, a large l e n t i c u l a r twin appears i n the center of the grain and another twin has formed i n zig-zag fashion between the l e n t i c u l a r twin and a grain boundary. The r e p l i c a work was undertaken to ascertain i f non- basal s l i p occured i n p o l y c r y s t a l cobalt. A second goal was to determine whether the fine d e t a i l s of deformation d i f f e r above and below 0.25 T . m Non-basal s l i p was observed during tests at 250°C (0.30 T ) but no similar observations were made at -196°C, m ' 20°C, or 100°C. Figure 62 shows s l i p markings on a second system. The non-basal traces are assumed to occur on the {1122} <1123> system, as t h i s i s the only non-basal s l i p system that has been observed i n single c r y s t a l cobalt 1 "*. The appearance of non-basal s l i p i s not observed i n a l l grains. This i s to be expected i n view of the heterogeneity of deformation. One further observation may be drawn from the surface features above and below 0.25 T . Below 0.25 T a l l shear m m markings were very straight, and remained so u n t i l f a i l u r e occured. Although large amounts of shear occured on some planes they exhibited very l i t t l e bending or waviness. Figure 63 demonstrates t h i s s i t u a t i o n . At temperatures 1 6 6 F i g . 60 Twinning i n c o b a l t a t -196°C. 3700X F i g . 61 Twinning i n c o b a l t a t 2 5 0 ° C . 3 7 0 0 X F i g . 62 Non -basa l s l i p i n p o l y c r y s t a l c o b a l t t e s t e d a t 250°C. 7500X above 0.25 T the s i t u a t i o n d i f f e r e d . In areas, where m l a r g e amounts of shear were v i s i b l e on s e v e r a l systems, one s e t of shear markings o f t e n took up a curved or wavy o r i e n t a t i o n . F i g u r e 64. T h i s non l i n e a r i t y of the s l i p bands may a r i s e from an i n c r e a s e i n the amount of g l i d e p o l y g o n i z a t i o n occuring, a l l o w i n g v i s i b l e changes i n s l i p band o r i e n t a t i o n . 3.2.2.5.4 Summary The m e t a l l o g r a p h i c evidence presented f o r p o l y c r y s t a l c o b a l t agrees wi t h the behaviour p o s t u l a t e d e a r l i e r and with o b s e r v a t i o n s made i n s i n g l e c r y s t a l m a t e r i a l 1 * ' 1 h . P u r i t y and g r a i n s i z e had l i t t l e a f f e c t on the observed deformation mechanisms. As g r a i n s i z e and p u r i t y i n c r e a s e d the s u r f a c e topography became l e s s i n t e n s e due to l e s s s t r a i n induced t r a n s f o r m a t i o n o c c u r i n g . The m a j o r i t y of the s u r f a c e s t r u c t u r e i s r e l a t e d t o the a l l o t r o p i c t r a n s f o r m a t i o n . The m u l t i v a r i a n c e w i t h i n fee g r a i n s p r o v i d e s s e v e r a l b a s a l o r i e n t a t i o n s w i t h i n an fee g r a i n boundary. Shear i s commonly observed on more than one b a s a l system and i s extremely heterogeneous. A v a r i e t y of twinning modes occured a t a l l temperatures The number of twins i n c r e a s e d w i t h s t r a i n ; l e n t i c u l a r and z i g - z a g twins as w e l l as many s t r a i g h t t h i n twins were observed. The l e n t i c u l a r twins were {10l2} twins common to hep metals. The twins t a k i n g up a z i g - z a g c o n f i g u r a t i o n were 1 6 9 assumed to belong to the {1121} twinning plane, as twins of similar configuration were i d e n t i f i e d i n single c r y s t a l cobalt by D a v i s 1 1 . The thin straight twins probably belong to the { l u l l } , {1122}, or {1124} twin systems as a l l three have been observed i n cobalt single c r y s t a l s 4 , 1 k. Non-basal s l i p was observed above 0.25 T but not c m below. It i s postulated that the s l i p occurs on the {1122} <1123> system, as corrugated s l i p has been observed in single c r y s t a l cobalt 1 1*. A further observation o u t l i n i n g a difference i n behaviour above and below 0.25 T i s the non l i n e a r i t y of m basal s l i p traces. The observed bending and waviness may r e f l e c t concentrations of dislocations of si m i l a r sign on p a r a l l e l s l i p planes. 171 3.2.2.6 Discussion and Summary It remains to compare the data regarding the s t r a i n induced transformation to that determined from t e n s i l e procedures. The easiest way to avoid confusion while discussing the numerous observations made i n t h i s study i s to deal with various measured parameters i n a tabular form. A summary of the experimental r e s u l t s i s presented i n Table XIV. A series of footnotes are included for those observations that do not lend themselves to the tabular format. 3.2.2.6.1 The Y i e l d Stress A great deal of information has been gathered regarding the y i e l d stress. The most important observation i s the difference i n behaviour above and below 0.25 T . (Table XIV.) m This r e s u l t i s mirrored i n the r e s u l t s for the s t r a i n induced transformation. Below 0.25 T , the i n i t i a t i o n of m the s t r a i n induced transformation occurs at 0.05% to 0.10% s t r a i n and i s well underway at the 0.2% o f f s e t y i e l d stress. On the other hand, as the temperature i s increased above 0.25 T , the i n i t i a t i o n of the transformation i s delayed to higher values of s t r a i n . At 0.2% s t r a i n , l i t t l e i f any transformation has occured i n specimens tested at 0.30 or 0.37 T . This combination of r e s u l t s leads to the m conclusion that the e s s e n t i a l l y athermal y i e l d behaviour observed below 0.25 T , i s due to the onset of bulk transformation m of fee cobalt. 172 TABLE Xfff Summary of Experimental Results As Purity As Grain Size At Test Temperatures Increases Increases <0.25 T m >0.25 T m % retained fee decreases rapidly decreases rapidl y N/A N/A 0.2% y i e l d stress decreases s l i g h t l y decreases rapidl y ^constant decreases ra p i d l y Elongation to Fai l u r e decreases decreases rapidl y decreases decreases Work Hardening Rates l i t t l e e f f e c t l i t t l e e f f e c t decreases rapidl y decreases slowly Total Work Hardening decreases decreases decreases decreases Ultimate Strength decreases decreases decreases decreases Strain at which Tx. Begins l i t t l e e f f e c t l i t t l e e f f e c t constant increases Volume Tx. at 0.2% s t r a i n l i t t l e e f f e c t l i t t l e e f f e c t large n i l Volume Tx. at Fa i l u r e decreases decreases decreases decreases Rate of Strain Induced Tx. l i t t l e e f f e c t decreases l i t t l e e f f e c t l i t t l e e f f e c t Volume Tx. at any Strain l i t t l e e f f e c t l i t t l e e f f e c t constant decreases ra p i d l y - Fracture surfaces exhibit d u c t i l e f a i l u r e at a l l temperatures. - High values are observed for c. and K i n a Hall-Petch r e l a t i o n s h i p and both parameters decrease rapid l y above 0.25 T . - The re l a t i o n s h i p between percentage fee and strai^^may be represented by an equation of the form e = A(10) ° 173 The behaviour i s athermal because the dr i v i n g force for transformation a r i s i n g from thermodynamic considerations i s very small when compared to the stress l e v e l s involved. Above 0.25 T , i t i s postulated that i n i t i a t i o n of m di s l o c a t i o n a c t i v i t y on the corrugated s l i p plane can occur at stress l e v e l s below those required for martensitic transformation. Thus, s l i p on the second order pyramidal system controls y i e l d above 0.25 T . The sharp decrease i n y i e l d strength measured i s due to the temperature dependence of the P e i e r l s stress on the corrugated s l i p plane. This r e s u l t was outlined during discussion of the e f f e c t of grain size on the y i e l d strength. The r e s u l t s presented i n Section 3.2.2.4 on the s t r a i n induced transformation are consistent with the postulated behaviour, but do not dismiss the p o s s i b i l i t y that some other strongly temperature dependent mechanism may be responsible for the behaviour. The large increase i n y i e l d stress as grain size decreases was discussed e a r l i e r . A change i n grain size has l i t t l e a f f e c t on the manner i n which the s t r a i n induced transformation proceeds i n the region of y i e l d . It was noted during discussion of the t e n s i l e r e s u l t s that the temperature at which the y i e l d stress changes behaviour increased as the grain size increased. This r e s u l t i s also consistent with the behaviour postulated above. The change i n temperature dependence occurs at higher temperatures as the grain size increases because the stress le v e l s accomplished during deformation d i f f e r r a d i c a l l y . In Figure 65, two l i n e s have been drawn to represent corrugated s l i p and bulk transformation at y i e l d . As the applied stress increases y i e l d w i l l occur when Von Mises C r i t e r i o n can be s a t i s f i e d . At low temperatures, y i e l d occurs when transformation begins. Above 0.25 T , i t i s ^ m postulated that y i e l d occurs when the stress l e v e l i s s u f f i c i e n t to i n i t i a t e d i s l o c a t i o n motion on the corrugated s l i p plane. If material of a d i f f e r e n t grain size i s tested, a d i f f e r e n t set pf curves apply. As outlined e a r l i e r , the y i e l d stress may be considered as a r i s i n g from a combination of factors; o^, the l a t t i c e f r i c t i o n and K, a factor representing the d i f f i c u l t y with which s l i p may be i n i t i a t e d across a boundary. It was determined that both and K decrease more ra p i d l y above 0.25 T . As grain size increases, the y i e l d stress drops rapidl y r e f l e c t i n g the large value of K. At temperatures greater than 0.25 T , the value of K i s decreasing rapi d l y and therefore a less severe drop i n y i e l d stress i s observed. A second set of l i n e s representing the behaviour of 24 micron, 99.9% cobalt are shown in Figure 65. These li n e s are consistent with the t e n s i l e observations and the postulated behaviour. Purity has l i t t l e e f f e c t on the s t r a i n induced trans- . formation. This p a r a l l e l s the r e s u l t s for the 0.20% y i e l d stress, where purity was not found to be an important parameter. s t r e s s r e q u i r e d to i n i t i a t e c o r r u g a t e d s l i p i n 6.5 )j c o b a l t . s t r e s s r e q u i r e d to i n i t i a t e c o r r u g a t e d s l i p i n 24 JJ c o b a l t . s t r e s s r e q u i r e d to i n i t i a t e bulk t r a n f o r m a t i o n i n 6 s t r e s s r e q u i r e d to i n i t i a t e bulk t r a n s f o r m a t i o n i n 24 JJ c o b a l t . _L Temperature 0.25 T m F i g . 65 Mechanisms c o n t r o l l i n g y i e l d i n p o l y c r y s t a l c o b a l t 176 3.2.2.6.2 Flow Stress The observed t e n s i l e c h a r a c t e r i s t i c s of the flow stress are d i r e c t l y related to the s t r a i n induced transformation. The two stage temperature dependence of flow stress disappears as s t r a i n increases, p a r a l l e l i n g the observation that as s t r a i n increases the amount of transformation taking place during I any s t r a i n increment i s also dropping. As less transformation i s occuring at higher s t r a i n s , the athermal behaviour attributed to the s t r a i n induced transformation also disappears, and the flow stress becomes more representative of the other c o n t r o l l i n g deformation mechanisms. The anomalous behaviour noted i n the i n i t i a l portion of the s t r e s s - s t r a i n curve i s simply a further manifestation of the high rate of transformation at low s t r a i n values. 3.2.3.6.3 Elongation to F a i l u r e Based on the observations made i n t h i s study, i t i s not surprising that the d p c t i l i t y of p o l y c r y s t a l cobalt quoted elsewhere forms no recognizable pattern. Elongation varies v i a a complex i n t e r - r e l a t i o n s h i p between purity, grain s i z e , and test temperature. The reasons behind the behaviour only become clear when the amount of fee phase present, and the manner in which t h i s fee phase disappears with s t r a i n , i s understood. P o l y c r y s t a l cobalt fractures when either of two c r i t e r i a are s a t i s f i e d . F i r s t , p o l y c r y s t a l cobalt w i l l f a i l when the volume percent of fee phase i s reduced to a c r i t i c a l value. If the stress l e v e l i s very high, as i n tests at -196°C, the transformation may come within 2% of completion before f a i l u r e occurs. At room temperature, the c r i t i c a l value i s about 5% retained fee phase. The second l i m i t i s due to Considere's C r i t e r i o n ; When the work hardening rate becomes equal to the applied true stress, i n s t a b i l i t y occurs and f a i l u r e becomes imminent. The measurable parameter that determines the d u c t i l i t y of p o l y c r y s t a l cobalt i s the amount of fee phase present i n the material following an annealing procedure. The rate at which the fee phase disappears with s t r a i n does not vary with purity, or te s t temperature. Thus, the lower d u c t i l i t y measured for high purity material simply r e f l e c t s the reduced amount of fee phase available following heat treatment. The observed decrease i n d u c t i l i t y as te s t temperature increases arises from Considere's C r i t e r i o n . The rate at which the s t r a i n induced transformation proceeds decreases as the grain size increases, also the retained fee phase present p r i o r to testing decreases as the grain size increases. The l a t t e r factor i s larger and . thus, the measured elongation for po l y c r y s t a l cobalt decreases as grain size increases. 178 3.2.2.6.4 Work Hardening Behaviour E a r l i e r , work hardening behaviour i n po l y c r y s t a l cobalt was compared to that for metals undergoing a sim i l a r martensitic transformation. The e s s e n t i a l l y constant work hardening rate observed at low s t r a i n was attributed to the transformation taking place at a high rate. The monitored progress of the transformation v e r i f i e s that the majority of s t r a i n induced martensite forms during the i n i t i a l portion of the t e n s i l e curve. The two stage temperature dependence of the work hardening rate was also attributed to the martensitic transformation, as was the disappearance of the two stage behaviour as s t r a i n increased. These re s u l t s p a r a l l e l the observed behaviour of t h e flow stress and may be explained i n l i k e manner. At low temperatures and low s t r a i n values, the rate at which martensite platqs are forming i s very high, thus, the structure through which dislocations must move i s increasing i n int e n s i t y very quickly. As s t r a i n increases, the rate at which the transformation proceeds drops o f f rapidly. Simultaneously, the stress l e v e l i s increasing, i n i t i a t i n g other deformation mechanisms to r e l i e v e stress concentrations. Eventually, there i s i n s u f f i c i e n t fee phase available to allow further deformation or the work hardening rate becomes equal to the stress l e v e l and f a i l u r e occurs. Above 0.25 T , the onset of bulk transformation occurs m at some point following y i e l d while corrugated s l i p i s postulated as occuring throughout the stress s t r a i n curve. Transformation does take place, but at any value of s t r a i n far less s t r a i n induced martensite has formed than at temperatures below 0.25 T . The structure formed during deformation above 0.25 T^ i s probably less intensive than that formed below. Less l a t t i c e debris and fewer martensite boundaries due to transformation are produced. In addition, s l i p may be more e a s i l y i n i t i a t e d across boundaries due to the reduction i n P e i e r l s stress on the corrugated s l i p plane. Therefore the measured work hardening rates are lower above 0.25 T . m Although l i t t l e v a r i a t i o n i n work hardening rates were recorded for changes i n purity or grain si z e , the t o t a l work hardening between y i e l d and fracture (and the ultimate strength) decreases with an increase i n either parameter. This r e s u l t r e f l e c t s the reduction i n d u c t i l i t y that accompanies increasing purity or grain s i z e . 4 Co n c l u s i o n s i ) Although the hep a l l o t r o p e i s the s t a b l e form f o r c o b a l t below 417°C, p o l y c r y s t a l hep c o b a l t i s o n l y a t h e o r e t i c a l p o s s i b i l i t y T C o b a l t e x i s t s as a two phase mixture of fee and hep c r y s t a l l a t t i c e s f o l l o w i n g normal heat t r e a t i n g procedures. i i ) The amount of fee phase r e t a i n e d i n c o b a l t f o l l o w i n g an a n n e a l i n g treatment decreases w i t h i n c r e a s i n g p u r i t y and i n c r e a s i n g g r a i n s i z e . The maximum amount of metastable fee phase t h a t may be r e t a i n e d i s approximately 60%, the minimum 10%. i i i ) The r e t a i n e d fee phase pres e n t i n p o l y c r y s t a l c o b a l t transforms m a r t e n s i t i c a l l y to the hep m o d i f i c a t i o n as deformation i s in t r o d u c e d y i e l d i n g t e n s i l e p r o p e r t i e s t h a t may be compared to other metals t h a t undergo a s i m i l a r t r a n s f o r m a t i o n . The r e l a t i o n s h i p between s t r a i n and the r e t a i n e d fee phase may be d e s c r i b e d by an equation of the form e = A (10) °~ . The t r a n s f o r m a t i o n i n t e r f e r e s w i t h comparisons between c o b a l t and other common hep metals. iv) The y i e l d s t r e s s of c o b a l t , below the tr a n s f o r m a t i o n temperature, has two d i s t i n c t r e g i o n s of temperature dependence. Below 0 .2 5 T^ the y i e l d s t r e s s i s e s s e n t i a l l y temperature independent and i s determined by the s t r e s s necessary to i n i t i a t e bulk t r a n s f o r m a t i o n of r e t a i n e d fee phase. Above 0 .25 T i t i s p o s t u l a t e d t h a t L m the strong temperature dependence observed i s due to the de c r e a s i n g v a l u e of the P e i e r l s s t r e s s on the cor r u g a t e d {1122} s l i p p l a n e s . v) The s t r e n g t h e n i n g e f f e c t of g r a i n boundaries i n c o b a l t i s l a r g e , as i s the case f o r other hep metals which do not e x h i b i t a m u l t i p l i c i t y of s l i p systems a t room temperature. v i ) The d u c t i l i t y of c o b a l t i s r e l a t e d to the amount of r e t a i n e d fee phase p r e s e n t i n the p o l y c r y s t a l aggregate. A l a r g e r i n i t i a l p r o p o r t i o n of fee phase y i e l d s higher d u c t i l i t y . The observed decrease i n d u c t i l i t y as t e s t temperature i s i n c r e a s e d i s due to Considere's C r i t e r i o n . v i i ) The work hardening r a t e s measured f o r p o l y c r y s t a l c o b a l t are h i g h and may be compared to the behaviour of other m a t e r i a l s t h a t t r a n s f o r m m a r t e n s i t i c a l l y d u r i n g deformation. A two stage temperature dependence of the work hardening r a t e i s observed a t low s t r a i n v a l u e s . v i i i ) The commonest s u r f a c e f e a t u r e i n deformed c o b a l t i s the heterogeneous shear t h a t occurs on b a s a l planes of more than one o r i e n t a t i o n w i t h i n an fee grain-boundary. The i n t e n s e s u r f a c e shears a r i s e from t r a n s f o r m a t i o n from fee to hep on these planes combined w i t h continued d i s l o c a t i o n p r o d u c t i o n on these p l a n e s . ix) A number of twinning modes are observed i n c o b a l t a t a l l temperatures from 0.04 T to 0.38 T . c m m Although many twins form the twinned volume i s s m a l l ( s e v e r a l x) Non-basal s l i p occurs above 0.25 T but not 1 m below. The secondary s l i p system i s p o s t u l a t e d as the {1122} <1123> second order pyramidal system. 182 5 Suggestions f o r Future Work The r e s u l t s of the p r e s e n t study open many avenues f o r f u r t h e r study. The most obvious areas where f u r t h e r work i s r e q u i r e d are o u t l i n e d below. i ) I f more i s to be l e a r n e d about the deformation modes, s t u d i e s must be c a r r i e d out with v e r y l a r g e g r a i n e d specimens. T h i s would a l l o w d i r e c t measurement of planes and d i r e c t i o n s i n v o l v e d i n deformation a l l o w i n g a c c u r a t e v e r i f i c a t i o n of the o p e r a t i v e s l i p and W i n n i n g modes i n c o b a l t . i i ) A second §rea where u s e f u l i n f o r m a t i o n c o u l d be gained i s i n a study of the s t r a i n induced t r a n s f o r m a t i o n . From what has been found i n the p r e s e n t study i t should be p o s s i b l e to produce some very d u c t i l e , h i g h s t r e n g t h c o b a l t v i a a s e r i e s of ausforming procedures or by v a r i a t i o n s i n a n n e a l i n g procedures. C e r t a i n combinations should y i e l d l a r g e volumes of r e t a i n e d fee phase and thus y i e l d high d u c t i l i t y coupled w i t h h i g h s t r e n g t h . i i i ) From the high K v a l u e s and a. v a l u e s found i n pure p o l y c r y s t a l c o b a l t , i t i s reasonable to assume t h a t j u d i c i o u s a d d i t i o n s of a l l o y i n g elements should y i e l d c o b a l t a l l o y s w i t h extremely high t e n s i l e p r o p e r t i e s a t room temperature. To extend the u s e f u l s t r e n g t h to higher temperatures r e q u i r e s a l l o y i n g a d d i t i o n s t h a t would move the a l l o t r o p i c t r a n s f o r m a t i o n to higher temperatures w h i l e m a i n t a i n i n g u s e f u l p r o p o r t i o n s of the metastable, high temperature, phase. I 183 Appendix 1 X-Ray A n a l y s i s The f o l l o w i n g o u t l i n e fo r the quan t a t a t i ve a n a l y s i s of volume f r a c t i o n s of fee and hep c o b a l t i s based on work done by Sage and G u i l l a u d 9 0 and a thorough treatment of the procedure p rov ided by L a n n e r s 8 4 . The method u t i l i z e s d i f f r a c t i n g planes tha t are a f f ec t ed s i m i l a r l y by any p re f e r r ed o r i e n t a t i o n p resen t . Anomalies tha t occur i n c e r t a i n d i f f r a c t e d i n t e n s i t i e s are d i s cus sed and a l lowed f o r . The anomalies uncovered by Sage and G u i l l a u d and Lanners are the same and i t i s assumed tha t t h e i r r e s u l t s a P P l v to the m a t e r i a l u t i l i z e d fo r the present work. When the fee cub ic s t r u c t u r e t ransforms to hep, c e r t a i n (111) p lanes become (0002) p l anes . The number of d i f f r a c t i n g atoms i s cons tan t but the t r ans fo rma t ion preserves on ly two planes out of e i g h t e x i s t i n g i n the cub i c s t r u c t u r e . The p o s i t i o n of the d i f f r a c t e d l i n e does net change but i t ' s i n t e n s i t y i s reduced by a. f a c t o r of f ou r . 1 (0002) = 1 "(111) ^ . . . . 1) In a mix ture of mx grans of cub ic c o b a l t and m( l -x ) grams of hep c o b a l t , the common l i n e c o n s i s t s of a f r a c t i o n due to the cub i c phase and a f r a c t i o n due to the hep phase. 1 (111) = 4mx = 4x J (0002) R ( 1 _ x ) ( 1 ~ X ) ••••2) 184 The r e l a t i v e i n t e n s i t i e s of p a i r s of l i n e s i n the hep or fee phase have been c a l c u l a t e d . For example: I ( 1 1 D - = 2 . 2 2 I (200) 3) ' ( 0 0 0 2 ) = 0.28 •(1011) 4) The c a l c u l a t i o n g i v i n g r i s e to the r a t i o s above assumes tha t the i n t e n s i t y of the l i n e s are independent of the d i f f r a c t i o n ang le . The va lues fo r these r a t i o s determined by Sage and G u i l l a u d are 1.85 and 0.27 r e s p e c t i v e l y 9 0 . Combine equat ion 2 , 3 , 4 . x _ -""(111) _ 1 I ( l l l ) . -""(lOll) . I (200) 1 X 4 I ( 0 0 0 2 ) 4 I (200) I (0002) 1 (1011) \ . 2.22 . 1 (200) _ 1.93 T (200) 4 0.28 I ( 1 0 1 1 ) I (1011) 5) x = 2 I (200) 1 X I ( 1 0 l l ) 6) Edwards and L i p s o n 5 5 c a r r i e d out t h e i r a n a l y s i s u s ing the l i n e s (200) and (1010) . The present work compares (200) and (1011) as d i d Lanners and Sage and G u i l l a u d . The (1011) l i n e i s four t imes as in tense as (1010) and a l l o w s for more accura te c a l c u l a t i o n s e s p e c i a l l y when the amount of hep phase i s s m a l l . Both Lanners 8 1 * and Troiano 5 1 * found anomalous i n t e n s i t i e s fo r the (111) and (0002) l i n e s . By e l e c t r o n microscopy they determined tha t the r e s u l t s were due to a p r e f e r r e d p r e s e n t a t i o n 185 of these planes to the x-ray beam, t h a t i s , a t e x t u r e e x i s t e d . T h i s abnormally high p r e s e n t a t i o n of (0002) and (111) i m p l i e s normal p r e s e n t a t i o n of (200) and (1011). The equation used f o r q u a n t i t a t i v e a n a l y s i s i s not a f f e c t e d by these anomalies. L e t the enhanced i n t e n s i t i e s f o r the (111) and (0002) planes be: 1 1 (0002) 0 , 2 8 H I ( 1 0 1 1 ) T 1 = 2 22 C T (111) ' U X (200) .7) .8) (111) (0002) = 2.22 C I n (200) 0.28 HI (1011) from equation 6 X ' (111) 4 . • I'(0002) !l-x) from equations 9 and 10 I' x (1-x) 1 4 H C . ( I l l ) I' (0002) 1 4 H r 2.22 C 0.28 II I (200) (1011) (200) (1011) .9) 10) 6) The d i f f e r e n c e between the equations used by Sage and G u i l l a u d and Lanners i s as f o l l o w s : (1-x) x (1-x) 2 (200) 1 ( l O l l ) 1.5 I(200) 8 k used bv Lanners 6) (1011) 9 0 used by Sage and G u i l l a u d 11) 186 Although a l a r g e d i s c r e p a n c y appears obvious, c a l c u l a t i o n shows t h a t the d i f f e r e n c e s observed are a c c e p t a b l e when c o n s i d e r e d i n l i g h t of the normal experimental s c a t t e r i n r e s u l t s . For example see the c h a r t below. Measured R a t i o (200) % f e e , eqn. 6 % f e e , eqn. 11 1 (1011) 1 66 60 1/2 50 43 1/10 16 13 Equation 6 was chosen f o r the p r e s e n t work because a l l the r e c e n t i n v e s t i g a t i o n s have used t h i s formula, i . e . B e c k e r s 8 2 , M i i l l e r 8 3 . 187 Appendix 2 Measurement of Tensile Parameters by an Intersect Method The following paragraphs outline a method for determining the y i e l d stress versus temperature relationship from data taken from a step-pull t e s t . Figure 66 shows the step p u l l results for a specimen i n i t i a l l y strained at -196°C and retested af t e r increasing the temperature i n 40°C steps. The data i s plotted as true stress versus true s t r a i n , and i s also normalized for the change i n G with increasing temperature. Due to the parabolic shape of the curve upon retesting, the proper slope to apply to the i n d i v i d u a l segments of curve was found from graphical data s i m i l a r to that shown i n Figure 38. From curves of t h i s type, the work hardening rate at any value of s t r a i n and temperature can be determined. This slope was then applied to each i n d i v i d u a l segment of the curve to determine the stress l e v e l corresponding to the s t a r t of the s t r a i n seg- ment under scrutiny. The manner i n which the data i s determined i s shown i n Figure 67. The data for the complete t e s t shown i n Figure 66 i s presented i n Table XV. Because a l l data i s to be normalized to 0.2% s t r a i n , this value i s tabulated for the i n i t i a l step p u l l i n Table XV. At f i r s t glance, i t would appear that i f the summation of A a values due to work hardening was subtracted from the in t e r s e c t y i e l d strength a p l o t of y i e l d strength versus temperature would r e s u l t . Some curve i s found i f t h i s i s done, but i t i s inco r r e c t , because no work hardening rate 175 L True S t r a i n (%) F i g . 66 Step-pull t e n s i l e t e s t . 99.9% cobalt, 6.5 micron g r a i n s i z e . I n t e r s e c t Y i e l d Strength 0 f o r 100°C t e s t a t vL0% s t r a i n 0 f o r 140°C t e s t a t ^11% s t r a i n 9 . 3 11.5 10.4 10.4 True S t r a i n (%) -> 67 Determination of the i n t e r s e c t y i e l d s t r e n g t h from s t e p - p u l l data. TABLE XV T y p i c a l D a t a From a S t e p - P u l l T e n s i l e T e s t S p e c i m e n ADJ - 99.9% c o b a l t a n n e a l e d 1 h r . a t 600°C P u l l Temp. T r u e S t r a i n I n t e r s e c t y i e l d Maximum Aa U n c o r r e c t e d C o r r e c t e d f o r (#) (°C) (%) s t r e s s s t r e s s y i e l d s t r e s s 9 and t o C ).2% ( k s i ) ( k s i ) ( k s i ) ( k s i ) 1 -196 0 - 1 .5 104.0 123.9 19.9 104.0 102.0 2 - 1 9 6 1.5 - 2 .2 126.9 131.4 4.5 107.0 101.2 3 -140 2.2 - 3 .4 125. 0 131.1 6.1 100.6 98.4 4 -100 3.4 - 4 .6 127. 0 131.4 4.4 96.5 97.8 5 - 60 4.6 - 5 .7 126.9 129.8 2.9 92.0 96.7 6 - 20 5.7 - 6 .9 125.1 127.3 2.2 87.3 96.2 7 20 6.9 - 8 .2 122.7 123.9 1.2 82.7 95.1 3 60 8.2 - 9 .3 118.8 119.4 0.6 77.6 93.4 q 100 9.3 - 10.4 114.4 115.0 0.6 72.6 92.5 10 140 10.4 - 11.5 108.4 109.7 1.3 66.0 90.2 11 180 11.5 - 12.7 102.1 103.7 1.6 58.4 86 .5 12 220 12. 7 - 13.8 93.8 95.2 1.4 48.5 81.0 13 • 260 13. 8 - 14.6 84.8 85 .2 1.4 38.1 74.6 14 300 14.6 - 16.1 75.6 77.7 2.1 27 .5 65.9 15 340 16.1 - 17.7 66.2 67.4 1.2 10.0 59.5 16 380 17.7 - 19.0 52.9 55.5 2.6 1.5 46.9 17 400 19.0 - f a i l 50.7 50.. 8 — -3.3 45.6 'O O c o r r e c t i o n s h a v e b e e n a p p l i e d t o t h e Ac v a l u e s . ?.. s a m p l e c a l c u l a t i o n b e s t e x p l a i n s t h e p r o b l e m . F o r e x a m p l e , d e t e r m i n e t h e 0.2% y i e l d s t r e s s a t -100°C. From T a b l e XV t h e s t r e s s 3 l e v e l s m e a s u r e d a r e 127 X 10 p s i a t 3.4% s t r a i n t o 131.1 3 X 10 p s i a t 4.6% s t r a i n . To d e t e r m i n e t h e y i e l d s t r e s s a t -100°C, s u b t r a c t o u t t h e wo r k h a r d e n i n g t h a t o c c u r s f o r t h e s t r a i n i n t r o d u c e d a t -140°C a n d -196°C. T h u s , a y i e l d (-100°C) = a i y s " ( A a - 1 9 6 ° C + A a - 1 4 0 ° C ) Where a . = i n t e r s e c t y i e l d s t r e n g t h l y s J ^ A G - 1 9 6 ° C " w o r ^ h a r d e n i n g i n t r o d u c e d a t - 1 9 6 ° C . ( S i m i l a r l y f o r a l l A a T O r ) F r o m T a b l e XV A • I T / i n n o - s = 127.0 - (19.9 + 4 . 5 + 6.1) = 96.5 X 10" y i e l d (~100°C) p s x T h i s v a l u e d o e s n o t a p p e a r o u t o f l i n e ; b u t f o r t h e t e s t s a t 400°C. °yield (400°C) = 5 0 , 7 " E A ° T ° C <0 and t h u s a n e r r o r h a s b e e n made. The m i s s i n g e l e m e n t i s t h a t t h e wo r k h a r d e n i n g r a t e i s a s t r o n g f u n c t i o n o f t e m p e r a t u r e and s t r a i n . T h e r e f o r e , a l l w o r k h a r d e n i n g i n t r o d u c e d p r i o r t o t h e t e s t u n d e r s c r u t i n y m ust be n o r m a l i z e d t o t h e t e m p e r a t u r e a t w h i c h t h e y i e l d s t r e s s i s d e s i r e d . F o r t h e y i e l d s t r e s s a t -100°C, v;e t h e n h a v e : V l e l d (-100-C) = a i y s - [ A a - 1 9 6 ° C ( ^ I 0 0 ° C @ 1 % £ > -196°C @ l % e + A a - i 4 o ° c ( 0 - i o o ° c g 2 % £ ) 1 0-14O°C @ 2%e V-7here 0 i « r , o ^ o -, a i s the work hardening r a t e f o r -100°C @ l%e ^ m a t e r i a l t e s t e d a t -100°C a t 1% s t r a i n . ( S i m i l a r l y f o r o ther 0 T < , C & % £ ) a y i e l d ( -100-C) = 1 2 7 ' ° - 2 0 ' 2 = 9 7 ' 8 I f c a l c u l a t i o n s of t h i s type are c a r r i e d out f o r each segment, reasonable agreement i s found between the r e s u l t s of the s t e p - p u l l t e s t s and the r e s u l t s from many i n d i v i d u a l t e s t s . The advantage of the s t e p - p u l l t e s t i s t h a t i t a l l o w s a more accura te d e t e r m i n a t i o n of the temperature a t which the 0.2% y i e l d s t r e s s changes temperature dependence. C l e a r l y , t h i s n o r m a l i z i n g procedure i s on l y approx imate . 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