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High temperature deformation of cobalt single crystals Holt, Richard Thomas 1968

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THE HIGH TEMPERATURE DEFORMATION OF COBALT SINGLE CRYSTALS by R.T. HOLT B.Met., The U n i v e r s i t y of S h e f f i e l d , 1960 M.Sc, The U n i v e r s i t y of London, 1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY  We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of DOCTOR OF PHILOSOPHY  THE UNIVERSITY OF BRITISH COLUMBIA August, 1968  In p r e s e n t i n g  for  this  thesis  in partial  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  that  the Library  Study.  thesis  shall  I further  make i t f r e e l y  agree that  Columbia,  I agree  f o r r e f e r e n c e and  f o r extensive  copying of this  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 b y t h e Head o f my  publication  of this  w i t h o u t my w r i t t e n  Department o f  thesis  Metallurgy  S e p t e m b e r 19,  Columbia  1968  It i s understood  for financial  permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a Date  of British  available  permission  D e p a r t m e n t o r b y h.i;s r e p r e s e n t a t i v e s .  or  f u l f i l m e n t of the requirements  gain  shall  that  copying  n o t be a l l o w e d  ii ABSTRACT Single c r y s t a l s of cobalt have been deformed i n tension over the temperature range 20°C to 600°C.  On heating a transformation  from the hexagonal close packed (hep) s t r u c t u r e to the face centred cubic (fee) s t r u c t u r e occurs at 430°C. The deformation behaviour i n the hep phase has been compared to that f o r other hep metals, and i t has been shown that only basal s l i p occurs even i n unfavourable o r i e n t a t i o n s .  Twinning may occur, but has  not been found to be associated w i t h an increase i n the work hardening rate. S i m i l a r l y the p r o p e r t i e s i n the fee phase have been compared to those of fee metals. The e f f e c t of deformation on the transformation has been studied on specimens which have been thermally cycled through the transformation during t e n s i l e t e s t s .  I t has been found that the (111)/  (0001) transformation h a b i t plane may be c o n t r o l l e d by deformation. R e c r y s t a l l i s a t i o n may occur i f two s l i p systems operate, but t h i s i s a f u n c t i o n of c r y s t a l o r i e n t a t i o n . S l i p may be induced on an unfavourably orientated g l i d e plane i n the fee phase, and t h i s i n d i c a t e s that deformation d i s l o c a t i o n s on the (0001), /(111) plane are not affected by the transformation. h c  However,  g l i d e d i s l o c a t i o n s on any {111} plane, which does not form the b a s a l plane on cooling do not a f f e c t the work hardening behaviour i n the hep phase. In previously deformed specimens, the flow s t r e s s i s a function only of the deformation h i s t o r y , i . e . the y i e l d point i n the hep phase may be raised  iii  by a factor of 10 or the yield point i n the fee phase may be lowered by a factor of 3.  However, the work hardening rate depends only on the crystal  structure and i s always higher (by 20 to 100 times) i n the fee phase than i n the hep phase.  iv TABLE OF CONTENTS PAGE 1.  INTRODUCTION . . . .  1  1.1  The Cobalt Transformation  1  1.1.1  The h y s t e r e s i s of Transformation  2  1.1.2  Thermal Cycling through the Transformation  4  1.1.3  Thermodynamics of the Transformation  4  1.1.4  Mechanisms f o r the Transformation  5  1.1.5  Observations i n Thin Films  5  1.2  Deformation of Cobalt 1.2.1  7  The T e n s i l e Deformation of hep Cobalt S i n g l e Crystals  1.2.2 1.3 2.  The E f f e c t of Stress on the Transformation  10  The Purpose of t h i s I n v e s t i g a t i o n  11  EXPERIMENTAL WORK  13  2.1  13  C r y s t a l Growth 2.1.1  3.  8  C r y s t a l Quality Compared with Previous Work  ....  .......  13  2.2  T e n s i l e Specimen Preparation  2.3  T e n s i l e Tests  15  2.4  Specimen Examination  15  RESULTS OF TENSILE TESTS IN THE HCP PHASE 3.1  14  19  General Behaviour i n the Temperature Range 20°C to 425°C  19  3.1.1  The Shape of the S t r e s s - S t r a i n Curve  19  3.1.2  Work Hardening Parameters  23  3.2  Comparison with Other hep Metals  29  3.3  O r i e n t a t i o n Dependence  32  V  PAGE 3.4  X-Ray and Metallographic Observations  during  hep Deformation  35  3.4.1  The Occurrence of Twins . . .  3.4.2  Observations  35  on Specimens w i t h a very low Schmid  factor 3.4.3 3.5  Examination of Fracture  37  S l i p and Twin Trace Analysis  42  3.5.1  Results of S l i p Analysis  53  3.5.2  The I r r e g u l a r Occurrence of Twinning  55  3.6  Recovery Experiments . . .  56  3.7  Change i n S t r a i n Rate Tests  62  3.8  Discussion  62  3.8.1  Temperature Dependence of the Flow Stress  63  3.8.2  S l i p Line Studies  64  3.8.2.1 R e l a t i o n Between S l i p Studies and Work Hardening Curve 3.8.2.2 D i s l o c a t i o n s i n Thin Films 4.  35  the 65 67  DEFORMATION OF FCC COBALT  74  4.1  General Behaviour i n the Temperature Range 430°C to 600°C.  74  4.1.1  The P a r a b o l i c Nature of the S t r e s s - S t r a i n Curve . .  76  4.1.2  The Y i e l d Point  78  4.1.3  The E f f e c t of Specimen Size  79  4.1.4  Interrupted T e n s i l e Tests  79  4.1.5  The S i g n i f i c a n c e of Stage I I I  • • •  81  4.2  Comparison w i t h Other fee Metals  82  4.3  Experimental Observations  87  4.3.1  90  S l i p Line Observations w i t h Increasing Shear S t r a i n  vi PAGE  5.  4.4 Discussion  107  4.4.1  The Nucleation of the Transformation  108  4.4.2  S l i p Studies  I l l  SPECIMENS DEFORMED IN BOTH THE HCP AND FCC PHASES . . . . . .  116  5.1  116  P r e s t r a i n i n hep Followed by Deformation i n fee . . . .  5.2 Annealing Experiments 5.2.1  A Summary of the E f f e c t of Annealing on the Work Hardening Parameters  5.2.2 5.3  124  .  The Latent Hardening E f f e c t  5.3.1  Metallographic Examination  132 133  T e n s i l e Tests on Specimens Thermally Cycled  138  5.4.1  I n t e r m i t t e n t l y Deformed  138  5.4.1.1  Tests S t a r t i n g Above the Transformation  138  5.4.1.2  Tests S t a r t i n g Below the Transformation  140  5.3.1.3  Specimen Examination  142  5.4.2  5.5  131  Comparison Between an Annealed Specimen and a Non-Annealed Specimen  5.4  130  Continuously Deformed  144  5.4.2.1  Tests S t a r t i n g Above the Transformation  144  5.4.2.2  Tests S t a r t i n g Below the Transformation  146  5.4.2.3  Metallographic and X-Ray Examination . .  146  Discussion  150  5.5.1  P r e s t r a i n Without Anneal  154  5.5.2  P r e s t r a i n followed by Anneal  157  5.5.3  Specimens thermally cycled through the Transformation P o s s i b l e Explanations f o r the Behaviour i n terms  160  5.5.4  of D i s l o c a t i o n Theory  161  5.5.4.1  The hep Phase  161  5.5.4.2  The fee Phase  161  vii PAGE 6.  SUMMARY  163  6.1  The Transformation  163  6.2  Deformation Behaviour i n the hep Phase  164  6.3  Deformation i n the fee Phase  165  6.4  The E f f e c t of Deformation During Thermal Cycling . . .  166  7.  CONCLUSIONS  168  8.  SUGGESTIONS FOR FUTURE WORK  170  9.  APPENDICES  171  9.1  .  C a l c u l a t i o n of Recovery Rates by D i f f u s i o n Controlled Processes  10.  171  9.2  C r y s t a l O r i e n t a t i o n at High Temperature  9.3  The V a r i a t i o n of Shear Modulus w i t h Temperature  REFERENCES  .  173 . . .  179 181  viii TABLES PAGE TABLE I  TABLE I I TABLE I I I TABLE IV TABLE V TABLE VI TABLE V I I TABLE V I I I  Transformation Temperatures and Thermodynamical Data on the Cobalt Transformation compiled from Adams and A l t s t e t t e r (1°) .  3  Comparative Tensile Properties of Cobalt Single C r y s t a l s Tested at Room Temperature .  22  D e t a i l s of Tensile Tests at Temperatures between 18°C and 427°C . .  24  Work Hardening Parameters of C r y s t a l s with Two S l i p D i r e c t i o n s almost equally Fabourable  33  P o s s i b l e Planes i n the fee Phase which could give r i s e to Traces shown i n F i g s . 15 (a) to (d) . . . . . .  40  Orientations of Specimens used f o r S l i p and Twin Trace Analysis i n the hep Phase  43  Summary of S l i p Line Data on Specimens Deformed i n the hep Phase  52  The R e l a t i o n between Stacking Fault Energy and the Extent of easy g l i d e i n some fee Metals  TABLE IX  Comparison of SFE by ^^±±  TABLE X  Analysis of S l i p Line Studies of C r y s t a l s of Various Orientations  m e t n  ° d s and other methods . .  76 86  ....  88  TABLE XI  I n i t i a l O r i e n t a t i o n of Specimens described i n Table X .  89  TABLE X I I  Influence of O r i g i n a l O r i e n t a t i o n on Deformation Behaviour i n the fee Phase  TABLE X I I I  Data on Stage I I Hardening i n some fee Metals  TABLE XIV  Behaviour of Specimens Deformed i n fee Phase a f t e r P r e s t r a i n i n hep Phase Flow Stress and Work Hardening Parameters of fee Deformation of Specimens Prestrained i n the hep Phase at 350°C Flow Stress and Work Hardening Parameters of Specimens Prestrained i n hep Phase then Annealed before fee Deformation at 480°C  TABLE XV TABLE XVI  91 114 117 124 128  ix PAGE TABLE XVII TABLE XVIII TABLE XIX TABLE XX  Summary of X-Ray and Metallographic Observations i n Specimens Cycled through the Transformation . . . .  149  Temperatures of the Transformation averaged from s e v e r a l sources  163  A Summary of the E f f e c t s of Stress on the Transformation Hysteresis  163  D i f f u s i o n Data f o r Hexagonal Metals  172  X  FIGURES PAGE FIG.  1  Apparatus f o r Spark-Machining a S'quare Section Tensile Specimen  15  FIG.  2  Examples of Specimens with Square and C i r c u l a r CrossSection and the Gripping Technique Employed . . . . . .  15  FIG.  3  Schematic Resolved Shear Stress-Shear S t r a i n Curve f o r hep Cobalt  20  T y p i c a l Resolved Shear Stress (T) - Shear S t r a i n (y) Curves f o r hep Cobalt at Various Temperatures  21  The Temperature Dependence of the C r i t i c a l Resolved Shear Stress  25  FIG. FIG. FIG.  4 5 6  The V a r i a t i o n of the Work Hardening Rate QjG with Temperature  26  FIG.  7  Comparison of Data i n F i g . 5 with Previous Work  27  FIG.  8  Comparison of Data i n F i g . 6 with Previous Work  28  FIG.  9  FIG.  10  V a r i a t i o n of Comparison V a r i a t i o n of Comparison  FIG. FIG.  FIG. FIG. FIG.  11 12  13 14  9 /G with Temperature f o r Cobalt i n to Other hep Metals T / G with Temperature f o r Cobalt i n to Other hep Metals A  30  D  31  The E f f e c t of O r i e n t a t i o n near the [0001] - [1010] Boundary Work Hardening Parameter  34  L e n t i c u l a r Twins Observed i n a R e p l i c a taken from Specimen Number 31  36  Secondary S l i p Markings i n the V i c i n i t y of the Tip of a Crack  36  Reproduction of an X-Ray Back R e f l e c t i o n P a t t e r n , from same Areas as F i g . 13  36  15(a) A R e p l i c a of the Fracture Surface of a Specimen which has a Schmid Factor of 0.06 (x = 4°) X10.000 (b) The Fracture and S l i p Traces i n the Same Specimen  38 ....  (c) An O p t i c a l Micrograph (X230) of the Same Fracture Face as 15 (a) (d) A Replica of the Fracture at High M a g n i f i c a t i o n showing Point Bands of Twins  38 39 39  xi PAGE FIG.  FIG.  16  D i a g r a m o f t h e F r a c t u r e P l a n e ( F i g . 15) f o r t h e C a l c u l a t i o n o f Angles Between t h e Traces and t h e T e n s i l e A x i s . . . .  17  A Stereographic P r o j e c t i o n i n d i c a t i n g the p o s s i b l e Planes which could give r i s e to the Traces shown i n F i g . 15 ( a ) t o ( d ) . . . . . . . . . . .  FIG. I8(a-h)  FIG.  FIG.  39  19(a-j)  20(a-h)  Development o f S l i p i n S p e c i m e n S2  and Twin Traces w i t h \,:  .  41  Strain 45-46  Development o f S l i p L i n e s w i t h I n c r e a s i n g S t r a i n i n S p e c i m e n S 3 D e f o r m e d a t 20°C  47-48  D e v e l o p m e n t o f S l i p L i n e s i n S p e c i m e n S12 D e f o r m e d a t 360°C  50-51  FIG.  21  The D i s p l a c e m e n t  FIG.  22  Schematic  FIG.  23(a)  The R e c o v e r y  of Cobalt Annealed  a t 323°C  58  The R e c o v e r y  of Cobalt annealed  a t 397°C  58  (b) FIG.  24(a) (b)  FIG.  25(a) (b)  FIG.  26  due t o S l i p  54  Representation of Slip  54  A T / T V . A n n e a l i n g T i m e a t 323°C  59  AT/T v.  59  after Annealing  1 h r . a t 327°C  A T / T v . A n n e a l i n g T i m e a t 397°C  60  AT/T v.  60  a f t e r A n n e a l i n g 1 h r . a t 327°C  A F o r c e - D i s t a n c e Curve f o r t h e S t r e s s F i e l d a Dislocation  Round  .  66  FIG.  27(a-c)  Transmission E l e c t r o n Micrographs  FIG.  28  FIG.  29  T h e o r e t i c a l C o n s t r u c t i o n o f a S t r e s s S t r a i n Curve, i n Comparison t o an E x p e r i m e n t a l l y Determined Curve . x - y C u r v e s o v e r a r a n g e o f T e m p e r a t u r e 450°C to  of Cobalt  600°C  69  70 75  FIG.  30  l o g (T - T ) v . l o g y  77  FIG.  31  I n t e r r u p t e d T - Y C u r v e a t 550°C  80  FIG.  32  T /G  FIG.  33  9  d  0  v . T f o r C o , Pb. a n d A g . .  /G v . T e m p e r a t u r e f o r V a r i o u s f e e M e t a l s  83 84  V  xii PAGE FIG.  34  log  v. Temperature f o r A l , Cu, Au, Co . . . . . 80  FIG.  35(a-m)  Development of S l i p with Increasing Strain i n Specimen S13  93-94  FIG.  36(a-k)  Deformation of Specimen R4 . . . . .  FIG.  37(a-f)  X-Ray Patterns during Deformation of R4  98  FIGi 38(a-f)  Deformation of Specimen R27  .  100  FIG.  39(a-f)  Deformation of Specimen R39  ...  102-104  FIG.  40(a-d)  Deformation of Specimen R70  FIG.  41  Small Twin Traces a f t e r fee Deformation. most l i k e l y Habit Plane i s {112}  FIG.  FIG.  42(a-e)  43  . 95-97  106 The 106  X-Ray Back Reflection Patterns of Specimens Deformed to Fracture i n the fee Phase a f t e r Prestrain i n the hep Phase at 350°C  119  Resolved Shear Stress-Shear Strain Curves f o r Specimens Prestrained at 350°C, and Deformed at 480°C  121  FIG.  44(a-d)  Stress-Strain Curves f o r Specimens Prestrained i n the hep Plane, Annealed and Deformed at 480°C . 125-127  FIG.  45  An Exaggerated Schematic Curve showing the Stages of the Curves i n Fig. 44  FIG.  46  The E f f e c t of hep P r e s t r a i n on the Latent Hardening Ratio  FIG.  47(a): (b)  FIG.  48(a) (b)  FIG.  49(a) (b)  FIG.  50  127  S l i p Lines i n Specimen 118.  133 X600  Replica of Surface of Specimen 118. S l i p Lines i n Specimen 145.  X6.000  . . . .  X650  Replica of Surface of Specimen 145. S l i p Lines i n Specimen 125.  . . . . . . . . .  133 135 ;  X9.000  . . . .  X750  Replica of Surface of Specimen 125.  133  135 136  X15.000 . . . .  136  Replica of the Surface of Specimen 143 after Deformation  136  FIG.  51  T - y Curve f o r Specimen R64 Intermittently Deformed  139  FIG.  52  T - y Curve f o r Specimen R67 Intermittently Deformed  141  xiii PAGE FIG. 53(a)  S l i p Structure i n Specimen R67. X600  143  Replica of Surface of Specimen R67. XIO.OOO . . . . .  143  FIG. 54  T - y Curve f o r Specimen 122  145  FIG. 55  T - Y Curve f o r Specimen 124  147  FIG. 56  S t r e s s - s t r a i n curves on l a t e n t systems i n stage I I hardening of ^copper  151  The E f f e c t of the hep P r e s t r a i n on the fee Work Hardening Rate f o r Annealed and Non-Annealed Specimens Deformed at 480°C  159  (b)  FIG. 57  FIG.  58  Back R e f l e c t i o n Patterns at Various Stages of Deformation i n Specimen S13  176  FIG. 59(a-b)  Stereographic Projections f o r Orientation of the fee Phase  177-178  FIG.  V a r i a t i o n of the Shear Modulus with Temperature  60  ...  180  ACKNOWLEDGMENTS The author takes pleasure i n thanking h i s research d i r e c t o r , Dr. E. Teghtsoonian,for valuable guidance this project.  throughout  Many h e l p f u l discussions w i t h other f a c u l t y members  and f e l l o w graduate students are g r a t e f u l l y acknowledged.  Thanks  are also due to s e v e r a l members of the t e c h n i c a l s t a f f and to  :  Miss Webster f o r help i n preparing the t h e s i s . F i n a n c i a l assistance f o r the work was obtained i n the form of a grant from the Cobalt Information Centre, Brussels.  1 1.  Introduction Cobalt i s an i n t e r e s t i n g metal to study because i t undergoes  an a l l o t r o p i c transformation from the high temperature fee phase to the low temperature hep phase.  The present investigation was undertaken to  extend the knowledge of the t e n s i l e properties of cobalt single c r y s t a l s . ( 1 2 3) Up to this date only three studies have been made with the hep phase.  '  , a l l dealing  Since deformation on p o l y c r y s t a l l i n e cobalt has been  shown to influence the t r a n s f o r m a t i o n ^  i t was hoped that a single  c r y s t a l study might lead to a better understanding of the mechanisms involved.  Reports of work relevant to the present study w i l l be b r i e f l y  reviewed i n this introduction. 1.1. The Cobalt Transformation Various temperatures associated with the transformation w i l l be frequently referred to throughout this text, and are defined as follows:A^  The lowest temperature at which the fee phase can be produced by deformation.  A  s  A^  The temperature at which the fee phase begins to form on heating, The temperature at which the hep  •+  fee transformation i s  completed. A  0*3  The temperature at which the transformation on heating i s 50% complete. The highest temperature at which the hep phase can be produced by deformation.  M  g  Mf  The  temperature at which the hep phase begins to form on cooling.  The temperature at which the fee •+ hep transformation i s completed.  M 0*3  The temperature at which the transformation on cooling is 50% complete  T  £  The equilibrium temperature of the transformation lying between A s and Ms , at which the free energy of the two phases i s equal,  The transformation is martensitic and the general properties of such a transformation a l l of which apply to cobalt are given i n reference (13) page 14. 1.1.1. The Hysteresis of the Transformation The difference between the transformation temperatures on heating and cooling (AT = A - M ) i s due to the strain energy induced s s by the volume change (AV) of the transformation, and i s greater, the larger AV. Theoretically, the expansion from hep to fee should be small (.616%) and this i s substantiated by calculations based on measurements at room temperature by Taylor and Floyd values of .46% and .345% respectively.  and Marick^^^ which give (12) Yegolayev et a l  showed that  a lattice expansion occurs i n the hep -*• fee transformation (A = 460°C, g  A.„ = 500°C) and a contraction occurs on cooling (M = 310°C, M s  x  Values of A , A_ c , M , and M  n  = 240°C).  i  ^ for single and polycrystals  are given i n table I, compiled from a recent paper by Adams and A l t s t e t t e r ^ ^ , The hysteresis i s greater for polycrystals (30°C) than single crystals (13°C) and increases with thermal cycling through the transformation. work by Hess and B a r r e t t G a u n t  Previous  and Christian^"^ and Yegolayev et a l ^ ^  gave similar results, the differences probably arising from the purity of the material used i n the different investigations.  3  TABLE 1.  Transformation Temperatures and Thermodynamical Data on the Cobalt Transformation Compiled from Adams and A l t s tetter(16)  Single Crystals  Polyerystals  1st cycle  6th cycle  1st cycle  430.7  435.3  439.2  440.2  434.0  440.1  447.0  450.1  132.0  113.1  106.0  113.5  4th cycle  On heating A  s  °C  AH(To) cal/mole AG(T  Q  5  ) cal/mole  -2.46  -3.16  -4.28  -5.24  On cooling 417.0  410.2  407.8  400.6  414.0  405.8  390.0  390.0  AH(To) cal/mole  81.3  73.6  32.0  AG(TQ  -1.01  -2.36  5  )  cal/mole  57.9  —  —  A H ( T o ) i s the enthalpy change at a temperature To where To i s the average of a l l the M and A temperatures of the transformation cycles each s s specimen (and i s assumed to be close to the equilibrium temperature T ) e  AG(T_  c ) i s the free energy change calculated from s p e c i f i c heat data,  from the value of A H at T = T. °C.  4  1.1.2.  Thermal C y c l i n g Through the Transformation The h a b i t plane of the transformation i s the close packed  basal (0001) plane which converts to a (111) plane i n the fee phase. The same o r i e n t a t i o n r e l a t i o n s h i p i s maintained by thermal c y c l i n g a s i n g l e c r y s t a l between 600°C and 20°C  V  , but c y c l i n g between 1000°C and 20°C  destroys.the "memory", and the transformation may occur on more than one (111) plane to give a p o i y e r y s t a l l i n e sample. found that a long, high-temperature  S i m i l a r l y i t has been  anneal gives r i s e to a m u l t i v a r i a n t  transformation. 1.1.3.  Thermodynamics of the Transformation Also included i n Table I .  w i t h the transformation.  i s thermodynamic data associated  On heating, the enthalpy change i n a s i n g l e  c r y s t a l i s about 113 cal/mole, and on c o o l i n g i t i s 84 cal/mole.  Hence  i t i s assumed that the enthalpy d i f f e r e n c e between the two p e r f e c t phases i s 100 cal/mole, and that 15 cal/mole are needed to create defects each time the transformation occurs.  The nature of the defects has not  been e s t a b l i s h e d , but there are three p o s s i b i l i t i e s to account f o r t h i s energy: (i)  a growth stacking f a u l t on every 5 or 10 planes.  (ii)  a d i s l o c a t i o n density of about 10  (iii)  an increase i n vacancy concentration of 0.04%.  11  2 /cm  The t h i r d a l t e r n a t i v e was favoured by Adams and A l t s t e t t e r who concluded from the thermal c y c l i n g data, that transformation-induced defects impede the n u c l e a t i o n of the transformation more than i t s propagation.  1.1.4.  Mechanisms f o r the transformation Three models have been developed. (19)  (a)  Christian  proposed that adjacent (111) planes shear an amount  Si  .•£•[211] by the spreading of stacking f a u l t s across the (111) planes. However l a t e r observations by Anantharaman and C h r i s t i a n ^ ^ that p l a s t i c deformation was associated with the transformation led (21) B a s i n s k i and C h r i s t i a n to develop a pole mechanism to e x p l a i n the transformation based on B i l b y ' s d e s c r i p t i o n of twinning (22) (23) (b)  The pole mechanism which has been widely accepted i s due to Seeger  who proposed that the fee •+ hep transformation occurs by the r o t a t i o n of p a r t i a l d i s l o c a t i o n s i n opposite d i r e c t i o n s around a screw d i s l o c a t i o n l y i n g normal to the (111) plane*.  Various modifications have been suggested  mainly to account f o r metallographic observations, but most observations i n t h i n f i l m s seem to favour the mechanismj(see r e f s . 8 and 18). (25) (c)  F i n a l l y a proposal by Bollman  that the transformation occurs  by the i n t e r s e c t i o n and c r e a t i o n of stacking f a u l t s OP. various (111) planes has riot received much support. 1.1.5. Observations i n Thin Films (26  The transformation i n t h i n f i l m s has been studied by Votava  27)  '  (28)  and Drapier et a l  . Using p o l y c r y s t a l l i n e specimens which had been  r o l l e d , annealed and e l e c t r o l y t i c a l l y thinned, the f o l l o w i n g conclusions were reached. (24) * The d e s c r i p t i o n i s p a r t l y reproduced i n E n g l i s h i n Cobalt Monograph pp 79-81 and i t should be pointed out that one important t r a n s l a t i n g e r r o r has been found, v i z . page 80 l i n e 26, r e f e r r i n g to the e f f e c t of p r i o r deformation on the transformation. "An increase i n the transformation temperature i n t h i s d i r e c t i o n may thus be expected". A t r a n s l a t i o n of the o r i g i n a l paper gives "Thus, one expects i n the reverse d i r e c t i o n ( i . e . hep ->• fee) no measureable increase i n the transformation temperature".  1.1.4.  Mechanisms f o r the transformation Three models have been developed. (19)  (a) 9.  Christian  proposed that adjacent (111) planes shear an amount  ——  •£•[211] by the spreading of stacking f a u l t s across the (111) planes. However l a t e r observations by Anantharaman and C h r i s t i a n ^ ^ that p l a s t i c deformation was associated with the transformation led (21) Basinski and C h r i s t i a n  to develop a pole mechanism to e x p l a i n  the transformation based on B i l b y ' s d e s c r i p t i o n of twinning.^22) (23) (b)  The pole mechanism which has been widely accepted i s due to Seeger  who proposed that the fee •+ hep transformation occurs by the r o t a t i o n of p a r t i a l d i s l o c a t i o n s i n opposite d i r e c t i o n s around a screw d i s l o c a t i o n l y i n g normal to the (111) plane*.  Various modifications have been suggested  mainly to account f o r metallographic observations, but most observations i n t h i n f i l m s seem to favour the mechanismi(see r e f s . 8 and 18). (25) (c)  F i n a l l y a proposal by Bollman  that the transformation occurs  by the intersection and creation of stacking faults on various (111) planes has not received much support. 1.1.5. Observations i n Thin Films (26 27) The transformation i n t h i n f i l m s has been studied by Votava  '  (28) and Drapier et a l  . Using p o i y e r y s t a l l i n e specimens which had been  (24) r o l l e d , annealed and e l e c t r o l y t i c a l l y thinned, the following conclusions * The d e s c r i p t i o n i s p a r t l y reproduced i n E n g l i s h i n Cobalt Monograph pp 79-81 and i t should be pointed out that one important t r a n s l a t i n g error were reached. has been found, v i z . page 80 l i n e 26, r e f e r r i n g to the e f f e c t of p r i o r deformation on the transformation. "An increase i n the transformation temperature i n t h i s d i r e c t i o n may thus be expected". A t r a n s l a t i o n of the o r i g i n a l paper gives "Thus, one expects i n the reverse d i r e c t i o n ( i . e . hep -*• fee) no measureable increase i n the transformation temperature".  1.  In hexagonal cobalt at room temperature, numerous stacking f a u l t s are present, and i t was region was  postulated that the faulted  hep whereas the unfaulted region was  untransformed  fee. 2.  On heating, these stacking faults started to disappear at 450° C forming perfect d i s l o c a t i o n s . at 800°C.  However i t was  were actually present remained  No stacking f a u l t s were v i s i b l e  shown that the same stacking faults  at both 20°C and 550°C, and that the widths  constant.  Hence either the range of the transformation or the heating of the f o i l was 3.  i n thin films i s very large  not uniform.  Cooling to 300°C allowed the reformation take place. films was faults  of stacking f a u l t s to  The results also showed that the behaviour i n thin  d i f f e r e n t from bulk material as the number of stacking  rfter  one heating cycle was  considerably  diminished.  It i s stated that the observation that stacking f a u l t s contribute to the mechanism.  transformation  i s consistent with Seeger's t h e o r e t i c a l  However, presuming the stacking f a u l t energy i n the fee (29)  phase i s also very low Drapier et a l why transformation  , there i s no explanation by Votava or  a perfect d i s l o c a t i o n should be more stable above the  than an extended d i s l o c a t i o n . (29)  Ericsson  measured the temperature dependence of the  stacking f a u l t energy of cobalt and cobalt-nickel alloys between 20°C and 700°C.  Using the node technique, the relationship SFE = 15 + 0.03|T - Te| 2  was  established, where SFE i s the stacking f a u l t energy i n ergs./cm , T(°K)  the specimen temperature and T  (°K) i s the transformation  temperature.  7  Hence the stacking f a u l t energy i s a minimum of 15 ergs/cm  2  at the  transformation, and increases l i n e a r l y with increase or decrease i n temperature.  Extended an unextended d i s l o c a t i o n s were seen i n both  the hexagonal and  the cubic phases, and the frequency of stacking  f a u l t s was i n v e r s e l y p r o p o r t i o n a l to the stacking f a u l t energy. I t i s not s u r p r i s i n g that the stacking f a u l t energy does not decrease to zero at the transformation, since the stacking f a u l t energy according to H i r t h and L o t h e ^ ^ i s a combination of several terms. (i)  an energy term associated with the bonds across the f a u l t plane which are sheared by the f a u l t .  ( i i ) an energy term associated with the change i n length of the l a t t i c e normal to the close-packed (0001)^^/(111^ planes,  ( i i i ) an energy term a r i s i n g from the d i l a t a t i o n w i t h i n a close-packed l a y e r near the f a u l t plane. However, a c a l c u l a t i o n of these terms based on a hard sphere model does not give an accurate assessment of the S.F.E., since the uncertainty involved i n the i n d i v i d u a l c a l c u l a t i o n s i s often greater than the a c t u a l energy value. cobalt by Heidenreich  The e a r l i e s t estimate of the S.F.E. of (31) and Shockley was based on twice the 2  f r e e energy of transformation, g i v i n g a value of S.F.E. as 20 ergs/cm . This i s probably a reasonable estimate considering the c/a r a t i o f o r cobalt i s almost i d e a l . 1.2. Deformation of Cobalt The deformation of pure p o i y e r y s t a l l i n e cobalt i s not w e l l documented, and there i s u s u a l l y some doubt as to the r e l a t i v e proportion of each phase present.  Three studies of the t e n s i l e deformation of hep  8 cobalt s i n g l e c r y s t a l s are a v a i l a b l e , and the main findings w i l l be presented. 1.2.1.  The T e n s i l e Deformation of hep cobalt Single C r y s t a l s Previous work by D a v i s ^ was concerned w i t h the t e n s i l e  deformation behaviour of cobalt s i n g l e c r y s t a l s tested at temperatures between 150°C and -196°C.  The r e s u l t s showed that the curves of resolved  shear s t r e s s ( x ) versus shear s t r a i n ( y ) were s i m i l a r i n shape to the other hexagonal metals.  The d u c t i l i t y and work hardening rate i n  stage A were comparable, but the c r i t i c a l resolved shear s t r e s s ,  x ,  was an order of magnitude greater. Davis also concluded that:1.  The C o t t r e l l - S t o k e s Law was not obeyed f o r e i t h e r temperature change  or s t r a i n - r a t e change t e s t s .  This was explained i n terms of the r e l a t i v e  ease of non-basal g l i d e , but none was a c t u a l l y observed. 2.  Twinning was uncommon, and was only observed at low temperatures  a f t e r extensive deformation.  There were two forms of twin, a long  narrow twin w i t h a (1121) habit plane, and a small l e n t i c u l a r twin, which might have been a sub-boundary.  Deformation markings were  observed, which were p o s s i b l y twins induced by the m a r t e n s i t i e transformation. 3.  The a c t i v a t i o n energy f o r p l a s t i c flow was c a l c u l a t e d from s t r a i n -  rate change t e s t s was approximately 35 kT. 4.  A c r y s t a l when extended to 200% at room temperature, d i d not r e c r y s t a l l i s e  on annealing at 600°C, nor d i d the transformation remove a l l the l a t t i c e strain. (2) Seeger et a l  showed the work hardening curves f o r three  d i f f e r e n t temperatures, and several conclusions were drawn.  9  1.  The d u c t i l i t y was high i n Stage A, and much higher than, say, zinc  at 90°K. 2.  The dependence of T  q  and of 9^ on temperature i s s i m i l a r to other  hexagonal metals (with r e s e r v a t i o n s ) . 3.  Deformation proceeded by s l i p on the basal plane.  4.  The s l i p plane spacing remained constant, and the step-height increased  w i t h s t r a i n i n Stage A. 5.  Twinning occurred on (1122) and (1124) planes. This work was followed by a study on high p u r i t y c r y s t a l s by (3)  Boser  (who had collaborated w i t h Seeger i n r e f . (2) ). I t appears  as though c r y s t a l s grown by the Bridgeman technique may have a higher concentration of impurity, p o r o s i t y or some other s t r u c t u r a l defect than those used i n the present work, since the values of T any temperature have a wide v a r i a t i o n .  q  and 9^ at  I n order to overcome t h i s  problem, each specimen used by Boser was given a small deformation at room temperature, before cooling or heating to the t e s t temperature. The value of T  q  at the t e s t temperature was then re-evaluated i n terms  of the value of T  q  at room temperature.  Both T  q  and 9^ were found to  decrease w i t h increasing temperature. From these preliminary i n v e s t i g a t i o n s i t appears d i f f i c u l t to compare cobalt w i t h magnesium, zinc or cadmium.  I n general the  deformation behaviour seems to be s i m i l a r , but there are d i f f e r e n c e s , e.g. T  q  i s much higher, non-basal s l i p i s not observed, and the twin  planes most common i n hep metals have not been observed i n cobalt. There are s e v e r a l reasons why cobalt might behave d i f f e r e n t l y .  (a)  The a l l o t r o p i c transformation may a f f e c t the mechanical properties of the hep phase.  (b)  The low stacking f a u l t energy of cobalt may account f o r some differences.  (c)  V a r i a t i o n s occur i n the c/a r a t i o from one element to another.  (d)  Z i n c , cadmium, and magnesium a l l have low melting p o i n t s , and hence i t i s p o s s i b l e that the d i f f u s i o n c o n t r o l l e d recovery processes which are e f f e c t i v e i n these metals at room temperature, do not operate i n cobalt u n t i l much higher temperatures.  (See  Appendix I ) . This makes cobalt the most suitable-hep metal to study by both o p t i c a l microscopy and e l e c t r o n microscopy.  For example  using the same c a l c u l a t i o n s as given i n Appendix I , the recovery time at 220°C  would be at l e a s t 3 hours.  Unfortunately no  measurements of the d i f f u s i o n rates of hep cobalt have been made. 1.2.2.  The E f f e c t of Stress on the  Transformation  B i b r i n g and S e b i l l e a u ^ c o n s i d e r e d the d i f f e r e n c e between the e f f e c t of p r i o r cold work and applied deformation during the transformation.  They concluded  that the former gives r i s e to heterogeneous  stresses and that these l o c a l i n t e r n a l stresses (which a l s o occur on quenching) cause an increase i n the number of transformation n u c l e i and the l a t t e r gives a uniform homogeneous s t r e s s which lowers the As and r a i s e s the Ms temperatures,i.e.  closes the h y s t e r e s i s .  P o l y c r y s t a l l i n e cobalt consists of a mixture of the two phases. Cold work increases the amount of hep, and the A reduced^'.  g  temperature i s  Yegolayev et a l ^ ^ found that p r i o r cold work gave r i s e  to a l a t t i c e c o n t r a c t i o n on heating through the transformation, and t h i s anomalous r e s u l t was a t t r i b u t e d to s t r e s s r e l a x a t i o n . Deformation above the transformation increases the h y s t e r e s i s loop^'"*"^.  Kamel and Halin/"'""''^ attempted to show the e f f e c t of the transformation on the mechanical properties of p o i y e r y s t a l l i n e cobalt by performing two t e n s i l e t e s t s at a c e r t a i n temperature, one on a specimen with an hep s t r u c t u r e , and the other with an fee s t r u c t u r e . However, the technique employed f o r obtaining hep and fee specimens i s very dubious, and hence the r e s u l t s are not considered  meaningful.  (9) Nelson and A l t s t e t t e r  found that e l a s t i c compressive  stresses i n s i n g l e c r y s t a l s (a) lowered the As temperature and  (b)  r a i s e d the Ms temperature according to the r e l a t i o n dM ^  -  dA ^  -  .03 °C mm  2  /g.  The s t r e s s a did not a f f e c t the transformation habit plane or the shear direction. 1.3.  The purpose of t h i s I n v e s t i g a t i o n Previous work has i n d i c a t e d that deformation can a f f e c t the  transformation i n c o b a l t , and thereby a f f e c t other p r o p e r t i e s .  A study  of t h i s would therefore lead to a b e t t e r understanding of both the deformation mechanisms and the transformation mechanism.  Also the  t e n s i l e behaviour of hep cobalt has not been adequately covered ( p a r t i c u l a r l y at higher temperatures) and no information at a l l i s a v a i l a b l e on the mechanical properties of fee s i n g l e c r y s t a l s of cobalt.  Hence i t i s hoped that by comparing the t e n s i l e properties of  cobalt to hep and fee metals such studies may  eventually help i n the  development of cobalt and i t s a l l o y s , p a r t i c u l a r l y i n the c o n t r o l of properties using the transformation. presented i n three sections  covering:-  The experimental  r e s u l t s are  The t e n s i l e behaviour i n the hep phase (20°C to 425°C) compared w i t h other hep metals. The t e n s i l e behaviour i n the fee range (430°C to 600°C) compared w i t h other fee metals, and Ni-Co a l l o y s . The e f f e c t of p r i o r deformation i n one phase on the deformation behaviour i n the other phase.  2.  Experimental Work The cobalt used i n t h i s i n v e s t i g a t i o n was  supplied by Koch L i g h t Laboratories L t d .  of high p u r i t y  The nominal composition was  as follows (where numbers r e f e r to parts per m i l l i o n by  2.1.  weight).  Ca  <  1,  Mg  =  1,  Ni  =  6 to 8  Cu  ~  1 to 2,  Al  •* . 1,  Si  =  3  Fe  =  3 to 5,  Ag  <  Na  <  1  1,  C r y s t a l Growth Single c r y s t a l s were grown i n an e l e c t r o n beam f l o a t i n g zone  furnace using a s i n g l e pass on 3 ina diameter rods and 2 passes on 5 mm diameter rods.  The traverse rate i n each case was  vacuum was maintained at 10 current was  t o r r or b e t t e r .  25 cm/hr, and  Although the  approximately constant, close supervision was  the  emission  required  throughout the growth o f the c r y s t a l , t o ensure a uniform c r o s s - s e c t i o n . A small v a r i a t i o n i n temperature" a t ' t h e molten zone could cause the l i q u i d to become very unstable, and, r u i n the specimen. I t was p o s s i b l e to seed a specimen such that the t e n s i l e axis of the c r y s t a l was w i t h i n 5° o f ' t h e seed.  Because of the r e s t r i c t i o n s  of the apparatus, i t was not p o s s i b l e t o grow a c r y s t a l of any a r b i t r a r y o r i e n t a t i o n , although i t was u s u a l l y p o s s i b l e to get w i t h i n 10° of the desired o r i e n t a t i o n . 2.1.1.  C r y s t a l Quality Compared with Previous Work The c r y s t a l s had a completely  smooth and highly r e f l e c t i n g  surface and did not contain s t r i a t e d deformation markings i n the as-grown c o n d i t i o n , as reported by Davis ^ \  Some of the o r i g i n a l c r y s t a l s were  tested to provide a comparison with other work:( i ) I t was  found that by thermal c y c l i n g 6 times through the  transformation, the o r i e n t a t i o n of the hep phase remained unaltered,  hence the "memory" of the transformation was constant. (ii)  Using a L e i t z hot stage, specimens were heated to  500°C i n an argon atmosphere, and X-ray back r e f l e c t i o n exposures made. These were compared to Laue patterns taken at room temperatures, and hence the (0001)/(111),[1120]/[110] r e l a t i o n s h i p was v e r i f i e d . 2.2.  T e n s i l e Specimen Preparation The length of the s i n g l e c r y s t a l i n a 3 mm rod was about 15  (plus seed) and the 5 mm rods were about 11 cm long.  A f t e r taking a  Laue p i c t u r e at each end, the c r y s t a l s were cut by spark machining i n t o 5 cm lengths. Several techniques were attempted f o r specimen machining to give a c i r c u l a r c r o s s - s e c t i o n . E l e c t r o - p o l i s h i n g techniques d i d not give a uniform c r o s s - s e c t i o n a l area along the gauge, and machining on a j e w e l l e r s l a t h e was impossible, i n s p i t e of very c a r e f u l procedure. These d i f f i c u l t i e s were overcome by using a s p e c i a l l y b u i l t spark erosion l a t h e .  The t o o l piece was a large copper d i s c , 3.5 inches i n  diameter, and 1 inch wide.  The edges were rounded to give smooth  shoulders on the specimen which was held i n a pin-chuck g r i p .  I n the  3 mm rods a 1 inch gauge was machined to a diameter of about 1.65 mm by r o t a t i n g the t o o l at 15 rpm and the specimen at 30 rpm. F i g . 1 shows the p o s i t i o n of the specimen with respect to the t o o l .  During  the operation the capacitance could be decreased to give a f i n e r spark. The f i n a l surface f i n i s h was very smooth, and the depth of the damaged l a y e r was l i g h t , estimated at l e s s than 25 microns, t h i s conclusion was reached a f t e r examination of the surface by both o p t i c a l microscopy and X-ray back r e f l e c t i o n patterns.  On the as-  machined surface there were numerous p i t s and the spots on the Laue pattern were streaked.  However, no asterism was noticed a f t e r  15  Fig.  2  Examples of Specimens w i t h Square and C i r c u l a r C r o s s - s e c t i o n , and the G r i p p i n g Technique employed.  e l e c t r o l y t i c a l l y removing 15 microns from the surface.  A f t e r the  removal of the f u r t h e r 10 microns, no p i t s associated with the machining could be observed. In the 5mm  rods, the gauge length was again 1.00  but the specimens were given a square cross s e c t i o n , w i t h 1.75 mm.  inches  sides about  The same t o o l was used, but the specimen was not rotated.  When a cut of the correct depth had been made on one face, the specimen was rotated about the axis through 90° and the operation S i m i l a r l y f o r the other two s i d e s .  repeated.  N a t u r a l l y , the faces so formed  were s l i g h t l y concave, the centre being0.030 mm lower than the edge, but t h i s e f f e c t i s b e n e f i c i a l as e l e c t r o p o l i s h i n g i s more r a p i d at the edge.  The specimens were then annealed i n a vacuum furnace f o r 1 hour  at 320°C. The most s u c c e s s f u l p o l i s h i n g s o l u t i o n was 15% p e r c h l o r i c a c i d , 80% g l a c i a l a c e t i c a c i d and 5% d i s t i l l e d water, at about 22 to 25 v o l t s , 10 to 20°C f o r about 60 seconds. The current density was 2 about 0.3 amp/cm .  Approximately  50u of m a t e r i a l was removed from  the surface, and the gauge length was maintained  c i r c u l a r by r o t a t i n g ,  and p a r a l l e l by i n v e r t i n g the specimen during the p o l i s h .  After  e l e c t r o p o l i s h i n g the specimen had a h i g h l y r e f l e c t i n g surface with no etch p i t s * , and examples are shown i n f i g . 2. F i n a l l y , the o r i e n t a t i o n of each c r y s t a l was determined from an accurately measured Laue p a t t e r n , such that the values of X (the angle between the t e n s i l e axis and the s l i p plane) and A (the angle between the t e n s i l e a x i s and the s l i p d i r e c t i o n ) could be quoted to w i t h i n a - 1° e r r o r . * Later i n order to assess d i s l o c a t i o n d e n s i t i e s , various etching s o l u t i o n s were t r i e d , but none gave r i s e to etch p i t s .  2.3.  T e n s i l e Tests The specimen dimensions were accurately measured with a  t r a v e l l i n g microscope reading to .001 cm.  Tensile tests were performed  on a f l o o r model Instron, and the high temperature experiments were done i n a furnace under an argon atmosphere.  Above 300°C the temperature  of the specimen agreed c l o s e l y w i t h that of the furnace, and the c o n t r o l was - 1°C. A heavy blue oxide f i l m formed on specimens l e f t i n the furnace f o r 3 days, and a s l i g h t oxide f i l m (undetected by o p t i c a l microscopy) which formed a f t e r a few hours i n the furnace was to be the cause of some poor q u a l i t y r e p l i c a s .  thought  However, the presence  of an oxide f i l m d i d not a f f e c t the t e n s i l e behaviour*as a specimen deformed at room temperature gave the same r e s u l t s as one which had been heated i n the furnace to 450°C f o r f i v e hours, cooled to room temperature and then tested. The p u l l - r o d assembly was made from Inconel 700 and type 316 s t a i n l e s s s t e e l , and the specimen holders were machined from 316 stainless steel.  Several gripping techniques were t r i e d , but the  only r e l i a b l e one involved supporting the specimens at the shoulders, as shown i n F i g . 2.  The specimen chamber was flushed with argon f o r  2 hours before being placed i n the furnace, and the specimen temperature was s t a b l i s e d f o r 15 mins before t e s t i n g .  The recorded load-elongation  curve was transcribed to a resolved shear stress-shear s t r a i n curve by the use of the p l o t t e r output with an IBM-IBFTC computer programme. 2.4.  Specimen Examination Specimens were examined both during and a f t e r the  t e n s i l e tests by one or more of: (a)  o p t i c a l microscopy  (b)  r e p l i c a studies by e l e c t r o n microscopy  (c)  X-ray back r e f l e c t i o n  The r e p l i c a s were made w i t h c e l l u l o s e acetate which was shadowed w i t h chromium and covered with carbon f i l m .  On smooth samples  the r e p l i c a was released from the acetate by dropping molten p a r a f f i n wax onto the carbon surface, and the acetate was then d i s s o l v e d i n acetone.  The r e p l i c a was then freed from the wax i n b o i l i n g acetone. S l i p and twin trace i d e n t i f i c a t i o n was c a r r i e d out by  a two surface a n a l y s i s (on both square and round specimens where p o s s i b l e ) and t h i s could be extended to deformation i n the fee phase by using the method described i n appendix 2.  19 3.  R e s u l t s o f T e n s i l e T e s t s i n hep  3.1.  Phase  G e n e r a l B e h a v i o u r , i n - t h e T e m p e r a t u r e R a n g e 20°C t o 425°C  3.1.1.  The  Shape o f t h e S t r e s s - S t r a i n  A r e s o l v e d shear s t r e s s (Fig.  3) f o r t h e p u r p o s e  Curve  (x) - s h e a r s t r a i n  of explaining  terms  and  ( y ) c u r v e i s shown  symbols  used i n the  text.  T h i s c u r v e i s t y p i c a l f o r room t e m p e r a t u r e , i n t h a t s t a g e B i s w e l l developed.  As  stage B i s reduced linearity r a t e has  i n f a c t i n some s p e c i m e n s  been n o t i c e d b e f o r e  critical  parabolic.  The  some w o r k e r s  t o be  until i t yields,  first  d e v i a t i o n from  t h e CRSS, b u t  this  as  and  l i n e a r ) and t h e CRSS,  at  the s t r e s s  thereafter  of the r e s u l t s  i s raised,  the  can  crystal  the s t r e s s - s t r a i n curve i s r e g i o n i s taken  i s rather d i f f i c u l t  by  t o d e f i n e and i s  I f the shear s t r a i n s c a l e i s  to p r o j e c t back the curve  (which i s almost curve i s taken  as  0  initial  parabolic region usually  extends  25% s h e a r s t r a i n , b u t has been o b s e r v e d  the work h a r d e n i n g r a t e decreases  end  hardening  x .  b e t w e e n 1 0 % and  up  the  (CRSS) h a s b e e n m e a s u r e d  the i n t e r s e c t i o n w i t h the e x t r a p o l a t e d e l a s t i c  The  linear  a r e d u c t i o n i n work  the l i n e a r e l a s t i c  t h e r e f o r e n o t a c o n s i s t e n t measurement. expanded, then i t i s p o s s i b l e  no d e v i a t i o n f r o m  i n order that a comparison  T h i s i s d e f i n e d as f o l l o w s :  deforms e l a s t i c a l l y  the extent of  fracture.  resolved shear stress  t h e same m a n n e r a s D a v i s ^  b e made.  i s raised  u n t i l a t 400°C t h e r e i s v i r t u a l l y  o f s t a g e A,  The in  the deformation temperature  t o 100 to 4 0 0 %  of the i n i t i a l  up  t o a c o n s t a n t v a l u e , and  shear s t r a i n ,  depending  i s not observed  t o 40%.  However  the curve  remains  on t h e t e m p e r a t u r e .  p a r a b o l i c r e g i o n (which i s a l s o  high temperatures  a t room t e m p e r a t u r e  temperature  a t a l l ) the f l o w s t r e s s  At  dependent,  i s called  x  the and  to  Fig. 3  Schematic Resolved  Shear S t r e s s - S h e a r S t r a i n Curve of hep  Cobalt.  22 (i.e.  trie s t a r t of trie i i r i e a r region, stage Aj and trie shear s t r a i n i s Y .  .,..,.„.,_,,  ,  ,  A  i  S i m i l a r l y the end of the l i n e a r curve i s l a b e l l e d T.  and t, . A2 Aj  A s e l e c t i o n of T - t curves at various temperatures i s shown i h F i g . 4. arid 9  i t i s c l e a r that both' t£ (the c r i t i c a l resolved shear stress)  (the i i r i e a r work hardening siope i n stage A) decrease with increasing  A  temperature.  The minimum work hardening sibpe may be about i b % lower, btit  occurs over a smaller range at high values of y• as has been observed i h some Hep metals.  Stage A i s riot parabolic  y* •»taken as the l i m i t of stage A, A  2  increases markedly w i t h temperature, although the o v e r a l l d u c t i l i t y i s much less a f f e c t e d . I t should be noted here that i n most work on hexagonal s i n g l e c r y s t a l s , the l i m i t of stage A i s denoted by Y » which i s the i n t e r s e c t i o n a  of the l i n e a r portions of stage A arid stage B.  However iri the present work  t h i s nomenclature i s meaningless, due to the s m a l l aihoiiht of d u c t i l i t y i n stage B, e s p e c i a l l y at higher temperatures.  i f ; f o r example, the specimen i n  Figure 3 had broken at poirit P; the l i m i t of stage A woiiid have been y^. For the same reason; values of Gg are riot quoted, except iri brie instance, to compare specimens iri trie present work with' those of both bavis etal  ( 2 )  and Seeger  . TABLE I I  Comparative Terisile P r o p e r t i e s o f Cobalt Sirigle Crystals Tested at Room Temperature i  Davis Commercial High P u r i t y ( 1 5  Property T © T Y  0 A a  A  Kg/mm Kg/mm Kg/mm  2  2  2  Kg/mm-  4 Kg/mm  2  Y  F  0.97 1.40 2.5 1.4 2.5 5.4 3.5 1.78  0.70  i.ob  Seeger et a l  1.1 0.7  1.7  1.3 2.86 2.80 2.0 4.1  (2)  Boser  .85 2.5 7.0 2.8  (3)  Present Work 0.75 0.65 1.15 ,45 ,02 ,5 ,1 ,65  23 3.1.2.  Work Hardening  Parameters  I n T a b l e I I specimens  of a p p r o x i m a t e l y the same o r i e n t a t i o n ,  t e s t e d a t room temperature show a range of v a l u e s of x , 0 , 9  e t c . and  0  the d i f f e r e n c e s a r e p r o b a b l y due to s e v e r a l f a c t o r s , n o t a b l y c o m p o s i t i o n , method of specimen p r e p a r a t i o n , specimen s i z e , and s t r a i n r a t e .  The  fact  t h a t i n d e p e n d e n t l y performed experiments on s i n g l e c r y s t a l s produce a s e r i e s of r e s u l t s which are so c l o s e to each o t h e r i s v e r y e n c o u r a g i n g .  I n most  measurements, the v a l u e o b t a i n e d i n the p r e s e n t work i s w i t h i n 10% of t h a t o b t a i n e d e l s e w h e r e , and as the quoted v a l u e s a r e the average of a t l e a s t t h r e e t e s t s i n each c a s e , i t may  be assumed t h a t the c o b a l t used i n the  p r e s e n t work i s of c o n s i s t e n t q u a l i t y .  Where more than one t e s t has been performed under the same c o n d i t i o n s , the v a l u e s of x and v a l u e s of y  0  have been w i t h i n ±6%, v a l u e s of 0  and Yp w i t h i n ±20%.  within  ±15%  These e r r o r s a r e a c c e p t a b l e , and are  much s m a l l e r than those i n the s i m i l a r t e s t s performed by Davis and Seeger e t a l . T a b l e I I I c o n t a i n s d a t a on about twenty specimens  of v a r i o u s  o r i e n t a t i o n s , t e s t e d a t d i f f e r e n t t e m p e r a t u r e s , w i t h a c r o s s head speed of -4 .02 i n c h e s / m i n u t e (a s t r a i n r a t e of 3.3 x 10 i n t h i s t a b l e a s e r i e s of r e l a t i o n s h i p s may  ins/in/sec.). be p l o t t e d .  From the v a l u e s  F i g . 5 shows the  temperature dependence of the c r i t i c a l r e s o l v e d shear s t r e s s x , and F i g . 6 0  shows the v a r i a t i o n of the work h a r d e n i n g r a t e of s t a g e A (77-)  w i t h temperature.  (The v a r i a t i o n of shear modulus G w i t h temperature i s d i s c u s s e d i n Appendix 3 ) . (1 2 3) The same c u r v e s are shown, a l o n g w i t h p r e v i o u s d a t a A l t h o u g h Seeger's d a t a r e p r e s e n t s o n l y f i v e specimens  ' '  i n F i g s . 7 and  8.  tested at three d i f f e r e n t  t e m p e r a t u r e s , and D a v i s t e s t e d a t o n l y two t e m p e r a t u r e s , the agreement between the f o u r s o u r c e s i s f a i r l y good i n comparison to r e s u l t s on o t h e r m e t a l s by d i f f e r e n t workers.  The v a r i a t i o n i n e l e c t r o n beam m e l t e d c r y s t a l s i s l e s s  i n those grown by the Bridgemanntechnique.  The a c t u a l v a l u e s of T / G  than  TABLE I I I Spec. No.  54 62 20 42 50 52 47 40 41 58 45 25 19* 16* 46 43 18 17 10* 11* 29 * 31*  2 3  Note: 1  Temp. °C  18 18 20 103 105 190 259 302 341 350 371 380 385 390 400 400 402 406 410 410 418 422 427  Schmid Factor  0.352 0.302 0.066 0.377 0.297 0.187 0.345 0.383 0.306 0.331 0.463 0.452 0.420 0.247 0.080 0.406 0.278 0.01 0.282 0.288 0.423 0.333 0.294  DETAILS OF TENSILE TESTS AT TEMPERATURES BETWEEN 18°C AND 427°C  X°  24 20 4 29 21 12 22 25 19 22 34 34 36 18 5 32 18 0 19 18h 36 25 18  ]o 2 Kg/mm  3 16 26 5 4 13 39 38 35 17 4 19 3 6 16 5 18 17 11 18 2 1 40  0.91 0.74 0.55 0.76 0.90 0.70 0.70 0-60 0.60 0.56 0.53 0.54 0.53 0.43 0.56 0.78 0.51 0.22 0.40 0.40 0.40 0.39 0.41  I n i t i a l Flow load Stress = 2 area Kg/mm 2.82 2.50 8.50 2.02 3.04 3.78 2.04 1.57 1.98 1.71 1.15 1.20 1.19 1.76 7.60 1.93 1.85 22.40 1.44 1.41 0.98 0.92 1.22  1  1  2  1  Linear —°  A  G i 10 n"* x x 10"  0.89 0.712 0.387 0.58 0.673 0.334 0.283 0.392 0.277 0.182 0.334 0.266 0.320 0.091 0.206 1.49 0.388 0.084 0.063 0.332 0.478 0.079  V a l u e s o f G a r e c o r r e c t e d f o r Temperature Dependence a c c o r d i n g  End  To 4  1.18 0.960 0.715 1.02 1.21 0.98 1.02 0.90 0.93 0.87 0.836 0.86 0.848 0.69 0.905 1.26 0.825 0.358  T  Stage A Y  Fracture T  Y  1.55 1.50 0.73  1.35 1.55' 0.66  4.55 4.2 0.73  3.05 3.3 0.66  1.30 1.25 0.9  1.50 1.6 1.6  3.3 2.8 1.8  3.2 3.3 3.4  0.75  1.7  1.40  3.7  0 .85 0.95  4.4 2.7  0.85 0.95  4.4 2-7  0.20  4.8  0 .20  4.8  0.65 0.657 0.66 0 .66 0.57  4.6  0 .57  4.6  t o F i s h e r and Dever.'  W i t h a low Schmid F a c t o r , t h e e r r o r i n measuring x has a c o n s i d e r a b l e i n f l u e n c e on t h e v a l u e o f T . i . e . an e r r o r o f 1° a t x = would g i v e x = .55 ± 14. Specimen showed e x t e n s i v e t w i n n i n g d u r i n g d e f o r m a t i o n . Some i n d i c a t i o n s o f t w i n n i n g on l o a d - e x t e n s i o n c h a r t . Q  4  0  2 *  _A G -4  0.9x10  0.7  0.5  0.3  0.1x10"  o  o  I  100  200  300  400 TemD.  Fig.  6  The V a r i a t i o n o f the Work Hardening Rate Q ^ / G w i t h Temperature, d i r e c t i o n s are l i k e l y to o p e r a t e i n the same p l a n e ( i . e . i f (A-^ i n t h i s graph.  C  T e s t s where 2 s l i p A2) 5°) not i n c l u d e d <  N3  ON  A V  -4 2.0 x 10  •  \ \ \ \ V \  3  0  0  *  \  -4 1.0 x 10  (2) Seeger et a l Davis (1) Low P u r i t y High P u r i t y O Davis • T / G - Boser^ ) x /G (red) - Boser curve shown i n F i g . 5 A  \  \ • \  •  \  \  A  s  A  \  -4 1.2 x 10  O O  -4  0.8 x 10  0.4 x 10  100  200  300  400  500  600 Temperature  Fig. 7  Comparison of Data i n F i g . 5 with Previous Work.  700 K  100  200  300  400  500  600 Temp. °K  Fig. 8  Comparison of data i n F i g . 6 w i t h P r e v i o u s Work. to  oo  29  obtained by Boser  (3)  are shown i n F i g . 7 as open squares.  The adjusted  values (to compensate f o r the c r y s t a l defects) are shown as s o l i d squares. Although the number of c r y s t a l s tested at the higher temperatures was small, the values are i n close agreement w i t h the present work.  The drop i n x / G  w i t h temperature was small over the e n t i r e temperature range. value of 3.2.  Q  The minimum  from Boser i s shown by open squares i n F i g . 8.  Comparison with other hep metals. Cobalt i s compared to the other hexagonal metals (which deform  by s l i p on the basal plane) i n F i g s . 9 and 10 except that i n the case of cobalt the transformation temperature (taken i n the present work to be 432°C) * i s used i n place of the melting temperature . The curves f o r magnesium zinc (33) and cadmium are taken from a recent review by Bocek et a l  , and i t i s  encouraging to note that the r e s u l t s f o r zinc and cadmium are very close indeed to those reported by Seeger and Trauble  and Risebrough  However, f u r t h e r work on Mg by Sheely and Nash that of Bocek.  From F i g . 9 i t can be seen that  between 0.26 and 0.5 T . m  greater temperature range.  and Akhtar  respectivly. d i f f e r from  decreases markedly  Whereas Q^/G f o r cobalt decreases l e s s r a p i d l y over a The decrease i n the work hardening parameter i s  caused by some dynamical recovery process operating over t h i s temperature range but i t would appear that cobalt does not behave i n the same manner. d i f f e r e n c e , f o r instance i s the shape of the x - y curves.  A major  Cobalt specimens  f r a c t u r e e i t h e r at the end of stage A or early i n stage B, but z i n c , cadmium and magnesium have a l l been deformed i n t o stage C.  Stage B i s associated w i t h an  (32) * Ardell has calculated the h y p o t h e t i c a l melting points of the low temperature phase of most polymorphic metals, but d i d not include cobalt because of the magnetic transformation which occurs at 1105°C. However, by comparison w i t h other metals, i t i s not expected that the melting point of the hep phase would d i f f e r by more than 5° from 1495°C.  32 increase i n the twin density, although i t i s not c e r t a i n that the onset of twinning coincides with the end of stage A.  In magnesium and cadmium i t  has been found that the length of stage A i s independent of temperature up to 370°K, but above t h i s point i t increases w i t h temperature. cobalt the length of stage A increases w i t h temperature. the r a t i o Q^/O.  In zinc and At room temperature  i s about 5 i n the present work (see Table I I ) and t h i s i s  somewhat lower than the values f o r other hep metals, eg. f o r magnesium the r a t i o (37) (35) i s about 19 , w h i l e f o r cadmium i t v a r i e s with temperature remaining at 27.6 up to .26 T , and decreasing to 4 at .5 T . m  m  In F i g . 10, the v a r i a t i o n of x /G w i t h temperature i s shown f o r Q  the same metals, and here i t can be seen that i n both zinc and cadmium i s constant up to about 0.4 T  m  T G  /G  and decreases markedly at that temperature.  On the other hand x /G f o r magnesium decreases l i n e a r l y w i t h temperature up D  to about 0.37 T , and above t h i s temperature the CRSS i s independent of temperature.  Neither Bocek, Sheely and Nash, nor Akhtar made any measurements  above 460°K, but the r e s u l t s of both Schmid and S i e b e l ^ ^ \ and Bakarian and (39) Mathewson i n d i c a t e that x /G f o r magnesium does decrease with increasing temperature between 500°K and 600°K. (0.54 to 0.65 T ). m G  r  In summary, the general features of the s t r e s s - s t r a i n curve f o r a l l metals which s l i p on the basal plane vary, and the differences are probably due to the r e l a t i v e ease of recovery.  For cobalt the flow s t r e s s  over the e n t i r e temperature range i s three to four times higher than the other metals considered.  There i s a sharp drop i n x /G w i t h temperature when Q  0 .15Te<T < 0.4 T . e  Between 0.4 T  e  and about 0.7 T  Q  the value i s constant,  and thereafter decreases with i n c r e a s i n g temperature up to the transformation. 3.3  O r i e n t a t i o n Dependence In a l l the experiments so f a r described (including the other hexagonal  33  metals), the specimens have been orientated f o r basal s l i p , w i t h values of x ranging from 15° to 45°.  I f x i s greater than 45°, work softening  or inhomogeneous deformation may occur. the c r i t i c a l resolved shear s t r e s s T  Although  q  i s constant at  a given temperature, the a c t u a l i n i t i a l flow s t r e s s a , (where a = load  s  cross s e c t i o n a l area  }  v a r i e S  W l t h  o r i e n t a t i o n  according to the Schmid r u l e ,  and there i s no a n i s o t r o p i c e f f e c t . TABLE IV  Work Hardening Parameters of c r y s t a l s with 2 s l i p d i r e c t i o n s  Specimen No.  A " (—) G 9  2 ~  X  A  l  9  A  —  G  54 29 23 45 19 50 42  3 2 1 4 3 4 5  9  A  '  =(—) v  G  J  Expected from c  Fig. 6  0.89 0.332 0.478 0.334 0.32 0.673 0.580  0.74 0.135 0.135 0.180 0.170 0.530 0.537  G  A  (—) G  '  9  A  - (—) K  A " (—)  G  "  J  9  0.203 1.49 2.54 0.855 0.880 0.270 0 .080  In Table IV the o r i e n t a t i o n s of the specimens are given, and the values of  - A^) i s an i n d i c a t i o n of the p o s s i b i l i t y of duplex s l i p .  A^  i s the angle between most favourable s l i p d i r e c t i o n and the t e n s i l e a x i s ; i s f o r the next most favourable.  Therefore, the lower (\^ - A^) the greater  i s the p o s s i b i l i t y of A^ coming i n t o operation.  I t might be expected that the  work hardening r a t e increases considerably w i t h duplex s l i p when A^ = Fig.  \^  11 attempts to show t h i s g r a p h i c a l l y .  and  The data f o r t h i s graph i s i n  Table I I I and the specimens were tested at various temperatures so that the A a c t u a l value of (—) G G  A ' which w i l l be c a l l e d (—) must be compared to that for a G 9  specimen i n which A„ - A., i s greater than 11° and tested at the same temperature. A This value of (—) 9  G  i s read from the graph, F i g . 6,  Unfortunately no specimen  34  F i g . 11  The E f f e c t o f O r i e n t a t i o n (near the [0001] [1010]boundary) on the work h a r d e n i n g parameter.  35 had two e q u a l l y f a b o u r a b l e d i r e c t i o n s , and i t i s g e o m e t r i c a l l y n o t p o s s i b l e f o r another system t o o p e r a t e d u r i n g normal d e f o r m a t i o n . C o n s i d e r i n g t h a t A i s measured t o ±1°, then t h e e r r o r i n (A  2  - A^) i s ±2°, which i s more than adequate t o account f o r the s c a t t e r  on t h e graph.  Hence i t can be assumed t h a t i f \^ i s g r e a t e r than A^ by  more than 4° the work h a r d e n i n g s l o p e i s u n a f f e c t e d . 3.4  X-Ray and M e t a l l o g r a p h i c O b s e r v a t i o n s d u r i n g hep D e f o r m a t i o n  3.4.1.  The Occurrence o f Twins A l t h o u g h t w i n n i n g i r i cadmium was n o t i c e d t o s t a r t a t t h e  b e g i n n i n g o f s t a g e B by R i s e b r o u g h  ( 35)  o ( a t l e a s t below 20 C) t w i n n i n g  was n o t thought t o be t h e r e a s o n f o r t h e end o f s t a g e A.  In cobalt  e v i d e n c e o f t w i n n i n g has been observed on t h e t e n s i l e c h a r t , i n 6 o f the 26 specimens  t e s t e d i n t h e hep phase.  S m a l l twins ( l e n t i c u l a r -  have been observed i n r e p l i c a s , (see F i g . 12) a f t e r t e s t i n g a t room temperature and a l s o i n specimens  ( t e s t e d a t h i g h e r temperatures)  break b e f o r e t h e end o f t h e easy g l i d e r e g i o n .  A l s o some  which were f r a c t u r e d i n s t a g e B d i d n o t c o n t a i n t w i n s .  which  specimens  Therefore,  i n c o b a l t i t i s u n l i k e l y t h a t t w i n n i n g i s the main h a r d e n i n g mechanism i n s t a g e B. 3.4.2.  O b s e r v a t i o n s on Specimens w i t h a Very Low Schmid F a c t o r Twins have o c c a s i o n a l l y been observed under t h e o p t i c a l  microscope p a r t i c u l a r l y where t h e b a s a l p l a n e was p a r a l l e l t o t h e tensile axis.  Even here the m a j o r i t y o f d e f o r m a t i o n occured on t h e  b a s a l p l a n e s e e F i g . 18, and no p r i s m a t i c s l i p was observed.  The  f r a c t u r e p l a n e was (1011) - c a l c u l a t e d by 2 s u r f a c e t r a c e a n a l y s i s ( w i t h F i g s . 18(d) and 18(e)) t o w i t h i n 2°.  On a  36  F i g . 12  L e n t i c u l a r twins observed i n r e p l i c a taken from Specimen R31.  F i g . 14  o s  Reproduction of an X-ray back reflection p a t t e r n from same a r e a as shown i n F i g . 13.  37  c i r c u l a r c r o s s - s e c t i o n specimen of the same o r i e n t a t i o n s e v e r a l cracks had propagated along the {1011} planes and had ceased before f r a c t u r e . reasonable  I t seems  to assume that the high s t r e s s concentration at the t i p of the crack  caused some of the metal to transform, and thus prevented of the crack.  f u r t h e r propagation  (For i t w i l l be shown l a t e r that the fee phase i s very much  stronger than the hep phase).  S l i p l i n e s on a completely d i f f e r e n t system are  seen i n the v i c i n i t y of the t i p of one crack which stopped propagating, F i g . 13. ( I t was only p o s s i b l e to do a s i n g l e surface trace a n a l y s i s on these s l i p l i n e s , as they d i d not reappear on a d i f f e r e n t surface and assuming a favourable Schmid Factor, the most l i k e l y s o l u t i o n i s (1120) or (110).  Close to the  f r a c t u r e an X-ray back r e f l e c t i o n photograph showed sets of double spots which were equivalent distances from the beam a x i s . (Fig. 14).  Other spots appeared s i n g l e .  A s i m i l a r e f f e c t had been noted but not explained by Davis  (p. 67) and i t has a l s o been observed i n the present work i n specimens deformed above the transformation temperature (see l a t e r ) .  Therefore, t h i s e f f e c t  may w e l l be associated w i t h a transformed product, which f u r t h e r suggests the idea that the transformation can be s t r e s s induced.  This e f f e c t may take  place by a broadening of the stacking f a u l t due to the applied s t r e s s .  A  s i m i l a r e f f e c t has been reported elsewhere i n metals of low stacking f a u l t e n e r g y H e n c e  the formation of double spots which are small arcs of  Debye r i n g s could be due to r e f l e c t i o n s from both the hep and fee l a t t i c e s . In the transformation c e r t a i n planes are p e r f e c t l y orientated and p a r a l l e l e.g.  (111)//(0001),  (011)//(120),  (112)//(10l0), some are s l i g h t l y misorientated.  for instance the s e t of double spots at ~22° and~23° from the basal plane resp, could be r e f l e c t i o n s from ( 2 l l 8 ) and (231), which occur at 22° and 22 .21° resp. 3.4.3.  Examination of Fracture F i g . 15(a) i s a fractograph, i . e . a photograph of a r e p l i c a taken  from the f r a c t u r e surface of another specimen of the same o r i e n t a t i o n .  In  F i g . 15 (b)  The F r a c t u r e and S l i p Traces X150.  39  F i g . 15 (c)  F i g . 15 (d)  Same f a c e  X230.  as F i g . 15 (a)  F a i n t bands o f twins i n the F r a c t u r e P l a n e X22,000.  photograph o f f r a c t u r e F i g . 16  D i r e c t i o n of maximum shear  plane Diagram o f the F r a c t u r e Plane f o r the c a l c u l a t i o n of angles between the t r a c e s and the t e n s i l e axis.  40 F i g . 15 (b) the f r a c t u r e i s shown, and the s l i p t r a c e s a r e almost p a r a l l e l to the t e n s i l e a x i s .  To o r i e n t a t e t h e c r y s t a l l o g r a p h i c d i r e c t i o n s shown i n  F i g . 15 ( a ) , an o p t i c a l m i c r o g r a p h was t a k e n of t h e same s u r f a c e F i g . 15 ( c ) . I t has a l r e a d y been mentioned t h a t t h e p l a n e i s (1011) and the d i r e c t i o n of the arrow i n F i g . 15 ( c ) i s t h e d i r e c t i o n o f maximum shear.  The t e n s i l e a x i s i s  v e r y c l o s e t o the [ 4 3 1 0 ] d i r e c t i o n , hence knowing the angle between the t e n s i l e a x i s and the f r a c t u r e f a c e (= 55° from F i g . 15 ( c ) ) , a l s o the angle between the y,  t r a c e s i n F i g . 15 ( c ) and t h e edge o f the photograph (52°), then the a n g l e , between the t e n s i l e a x i s and the t r a c e d i r e c t i o n can be c a l c u l a t e d . R e f e r r i n g t o F i g . 16 i t can e a s i l y be shown by v e c t o r a n a l y s i s t h a t cos y  =  c o s  OL  c o s  6 =0.615 x0.574, and t h e r e f o r e Y  =  70°.  to assume t h a t t h e major t r a c e s o f F i g . 15 ( c ) correspond  I t i s reasonable t o t h e major t r a c e s  of F i g s . 15 (a) and 15 ( d ) , and hence t h e r e p l i c a s may be o r i e n t a t e d . F i g . 15 (d) i s an enlargment showing f a i n t l e n t i c u l a r twins formed i n bands, and  these t w i n t r a c e s a r e p a r a l l e l t o t h e secondary t r a c e s i n F i g . 15 ( a ) . F i g . 17 i s a s t e r e o g r a p h i c p r o j e c t i o n showing t h e zone  plane  (1011), and i n t h i s zone the primary  of the f r a c t u r e  and secondary t r a c e s have been marked.  Zone I c o n t a i n s a l l t h e planes w h i c h c o u l d g i v e r i s e t o the primary  t r a c e , and  s i m i l a r l y zone I I c o n t a i n s p l a n e s w h i c h c o u l d g i v e t h e secondary t r a c e s o r t w i n s . Low i n d e x p l a n e s  i n t h e h e x a g o n a l system have been marked i n F i g . 17, and T a b l e V  c o n t a i n s t h e low i n d e x p l a n e s i n t h e f e e phase which c o u l d g i v e r i s e t o the t r a c e s ; TABLE V  P o s s i b l e p l a n e s i n t h e f e e phase which c o u l d g i v e r i s e t o t r a c e s shown i n F i g s 15 (a) and (d) TRACE I I  TRACE I HCP  FCC  II20 2131 1103 0223 1232  Oil 012 001 013  A  FCC lib 212 102 133  B  HCP  FCC  1210 0221 1232 1122  221 111 113  A  iio •  I f (0001) a (111), then A i s f o r (1010)= (121)and B i s f o r (1010)=(121).  FCC 101 310 211  B  41  1010 S F i g . 17  A S t e r e o g r a p h i c P r o j e c t i o n o f Fractogram Traces ( F i g . 15 (a) - ( d ) . The T e n s i l e A x i s (g> i s c l o s e t o [ 4310]. I t was c a l c u l a t e d t h a t the p r i m a r y t r a c e I makes an a n g l e of 70° w i t h the t e n s i l e a x i s . On F i g . 3.15 (a) t h e secondary t r a c e I I was measured t o make an a n g l e o f 50 w i t h the primary trace I . .*. I t may be c a l c u l a t e d t h a t t r a c e I I i s a t an a n g l e o f 56° t o t h e t e n s i l e a x i s . Z o n e © contains a l l the planes w h i c h c o u l d give r i s e to the p r i m a r y t r a c e I , s i m i l a r l y zone (rp f o r secondary t r a c e II. The i n t e r s e c t i o n o f these zones i s o b v i o u s l y the f r a c t u r e p l a n e , and i s c l o s e t o (1011).  42  Further i n t e r p r e t a t i o n from the a v a i l a b l e evidence i s impossible, and to i d e n t i f y the traces would require a lengthy technique of s e c t i o n i n g f o r complete analysis. I t i s suggested, however, that the angular boundary, seen i n F i g . 15(a) could be the phase boundary between the regular hep traces) and a region of fee which has been transformed stress.  (containing the  under the applied  In t h i s region the f r a c t u r e surface i s not so regular but does  contain traces. The 'twins' i n F i g . 15(d) are s i m i l a r i n shape and d i s t r i b u t i o n to those i n F i g . 12.  But i t i s not p o s s i b l e that trace I I could agree with  Davis' observations of (1121) twins although Seeger's (1122) twins are possible. (1012).  The traces could not a r i s e from the usual hep twinning mode of, The f r a c t u r e plane of (1011) i s sometimes quoted as a s l i p plane i n  hexagonal metals, but no evidence of s l i p l i n e s on t h i s plane were seen i n any of the four specimens tested.  (1011) has not been c i t e d i n the (13)  l i t e r a t u r e on a twin plane i n cobalt, although C h r i s t i a n  p r e d i c t s that  the three most favouable twin planes should be (1012) (2241) and 3.5  (1011).  S l i p and Twin Trace A n a l y s i s On a l l the specimens (of c i r c u l a r cross section) deformed i n the  hep r e g i o n , only basal s l i p was seen to operate.  Twins were sometimes  observed, but the traces could not be followed f a r enough to work out accurately the twin h a b i t plane. Therefore a s e r i e s of specimens was prepared w i t h square cross s e c t i o n , and they were h i g h l y polished f o r metallographic observations. specimen (of known o r i e n t a t i o n , see Table VI) was  Each  t e n s i l e tested at a  p a r t i c u l a r temperature, and the tests were i n t e r r u p t e d at various stages of  43 the deformation i n order that the specimen could be examined, both by o p t i c a l metallography and by r e p l i c a of the surface studied i n the e l e c t r o n microscope. TABLE VI Orientations of Specimens used for S l i p and Twin Trace A n a l y s i s i n the hep Phase Specimen Number  O r i e n t a t i o n of Basal Plane  Test Temp. °C  Observed at values of  Y  X  A  S2  2  15  20  S3  20  30  20  0.16,  0.55, 1.8,  3.06,  S12  19  24  360  0.14,  0.28, 0.93,  1.70  A l l three specimens s l i p p e d e x c l u s i v e l y on the basal plane. F i g s . 18, 19 and 20 show the development of s l i p i n S2, S3 and S12 r e s p e c t i v e l y . The surface of S2 was so smooth that i t was impossible to make r e p l i c a s :  even  when great care was taken w i t h the wax technique the carbon f i l m broke up. Hence of t h i s specimen only o p t i c a l micrographs are shown. The main feature of these photographs are (a)  S l i p i s uniformly d i s t r i b u t e d throughout the specimen and does not occur i n bands.  (b)  The s l i p l i n e s are long and s t r a i g h t , i n agreement with other hexagonal metals deformed i n the easy g l i d e region.  (c)  No evidence of branching of s l i p l i n e s , s i m i l a r to the e f f e c t found i n (34) zinc,  and a t t r i b u t e d to climb of edge d i s l o c a t i o n s , has been found  i n cobalt. (d)  Cross s l i p has not been observed.  44  (e)  Except at low s t r a i n s , an a n a l y s i s (which w i l l be discussed l a t e r ) shows that the number of s l i p l i n e s remains constant. by i n c r e a s i n g the step height. about  Deformation proceeds  The average s l i p l i n e spacing i s  0.2P.  Specimen S2 - Figs. 18(a) to (h) The increments of deformation between 18(a) and 18(d) are very small.  At f r a c t u r e , the specimen extension was only about 0.3%, which  roughly corresponds  to a shear s t r a i n of 30%.  The s l i p traces l i e p a r a l l e l  to the t e n s i l e a x i s (the specimen edge i s shown at the top of F i g s . 18(a) to (d), i . e . the Schmid f a c t o r i s very low.  Despite t h i s , no other s l i p  l i n e s were observed i n the specimen, but twins were observed, F i g s . 18(f) to (h).  As has already been mentioned, specimens with t h i s o r i e n t a t i o n  f r a c t u r e on the (1011) plane, and long p a r a l l e l twins were analysed as (1011) type twins.  L e n t i c u l a r twins were a l s o observed and these appeared  to be of the (1012) type.  The l a t t e r i s a commonly occuring twin i n  hexagonal metals, but n e i t h e r of these h a b i t planes has previously been reported i n c o b a l t , p o s s i b l y because t h i s o r i e n t a t i o n has not been used. Although the density of s l i p l i n e s i n t h i s specimen does appear to increase w i t h s t r a i n , the a n a l y s i s i s incomplete without r e p l i c a evidence as f i n e s l i p can only be resolved i n the e l e c t r o n microscope. Specimen S3 - F i g . 19(a) to ( j ) F i g s , (a) and (b) show o p t i c a l and r e p l i c a micrographs (c) and (d) a f t e r y =  0.55  (e) ( f ) and (g) a f t e r y =  1.80  (h) ( i ) and ( j ) a f t e r y =  3.06  after y =  0.16  45  Figs. 18 (a) to (h) Deformation of Specimen S2.  46  47  F i g s . 19 (a) t o ( j )  Deformation o f Specimen S3.  F i g . 19 (a) Y = 0.16, X250  F i g . 19 (c) Y = .55, X700  F i g . 19 (e) Y  = 1.8, X700  Fig.  19 (b)  Y = 0.16, X20.000  F i g . 19 (d) Y  = .55, X20,000  F i g . 19 ( f ) Specimen r o t a t e d 9 0 ° , y = 1.8, X250.  48  Fig. 19 (i) Y = 3.06, X20,000  Fig. 19 (j) Rotated 35° y = 3.06, X230  49  There i s very l i t t l e d i f f e r e n c e between the o p t i c a l micrographs at various s t r a i n s hence the magnifications have been v a r i e d .  I t can be  seen from the r e p l i c a s , a l l at a mag. of 20,000X, that the density of s l i p l i n e s i s constant above y =.16 and that the displacement at each s l i p step increases w i t h s t r a i n .  L e n t i c u l a r twins appeared a f t e r y = 3.06, but  were not a common f e a t u r e , and none were observed i n the r e p l i c a s . F i g . 19 (j) i s a twinned area on the face, o r i g i n a l l y 90° from the face shown i n a l l the other photographs (except ( f ) ) , but now the angle i s 35°. twins were very close of (0112).  The  Back r e f l a c t i o n X-ray patterns were  taken at each stage, and spots were very c l e a r , even a f t e r  fracture.  Specimen S12 - F i g . 20(a) to ( j ) (a) and (b) are o p t i c a l and r e p l i c a micrographs a f t e r y = 0.14 (c) and (d) a f t e r y = 0.28 (e) and (f) a f t e r y = 0.93 (g) and (h) a f t e r y = 1.70 The o v e r a l l e f f e c t i s s i m i l a r to spec. S3, and the data i s summarised i n Table V I I .  Again, no twins, except p o s s i b l y the band i n  F i g . 20(h), were seen i n the r e p l i c a s , but i n F i g . 20(i) i s shown a t y p i c a l (1011) type twin at a m a g n i f i c a t i o n of 236X, and i n F i g . 20(j) are seen (1012) twins i n the same face.  The analyses f o r t h i s specimen showed  that the s l i p plane agreed to less than 1° w i t h the basal plane, hence the error i n measuring  the twin planes i s very small.  In two cases, the (1011)  twins, passed completely through the specimen, and i n appearance were very s i m i l a r to Neumann bands. Calculations have been made to determine the CRSS of twinning  50  F i g s . 20 (a) t o ( j )  D e f o r m a t i o n o f Specimen S12.  F i g . 20 (a)  F i g . 20 (b)  Y = .14, X230  Y = .14, X20.000  F i g . 20 (c)  F i g . 20 (d)  Y = .28, X230  Fig. Y  =  20  (d)  .93,  X230  Y = .28, X20.000  F i g . 20 (e) Y = .93, X20,000  F i g . 20 (g) = 1.70, X650  Y  F i g . 20 ( i ) Y  = 1.70, X236  F i g . 20 (h) Y - 1-70, X20.000  F i g - 20. ( j ) Y - 1-70, X650  TABLE V I I SUMMARY OF SLIP LINE DATA ON SPECIMENS DEFORMED IN HCP PHASE Spec. S t r a i n Shear No. e % Strain y  FACE (1) Trace Measured Calc. Nl N Slip Angles width d i s p l a c e - ( i n (measured Spacing Face 1 Face 2 w tensile ment normal =5/N(y) a x= w axis) 3 (v) to trace) cos g  No. of s l i p (a-a ) (u) L cm. l i n e s per cm. a f t e r deformation =N x2000x (1+ e ) 100 (xlO" ) Q  1  4  S3 S3  4 14 47 82 104 4 10 30 56  Z  S3 S3* 1  S3 S12 -i S12 S12" S12 5  1  2  3  4  0.16 0.55 1.8 3.06 3.84 0.14 0.28 0.93 1.70  17 24 27 25 30 25 22 27 20  0.294 0.208 0.185 0.200 0.167 0.200 0.227 0.185 0.250  14 15 13 13 15 39 42 42 41  84 84 84 84 84 28 26 22 16  0.02 0.03 0.07 0.12 0.12 0.04 0.05 0.07 0.09  0.192 0.286 0.675 1.140 1.140 0.045 0.J054 0.076 0.094  4.1 6.5 7.0 6.5 6.75 15.7 14.7 18-0 13.0  0.855 1.48 2.06 2.36 2.76 3.76 3.24 4.68 4.06  0.0468M 0.0945 0.228 0.348 0.377 0.012 0.031 0.064 0.138  0.36 0.50 0.44 0.53 0.50 0.16 0.18 0.23 0.21  N i s the number of s l i p l i n e s measured i n a 10 cm. distance i n a r e p l i c a at 20,000X m a g n i f i c a t i o n (the measurement i s made normal to the trace). N"*" i s the number of s l i p l i n e s i n the d i r e c t i o n of the t e n s i l e a x i s .  / „ \ i•s calculated -i i ^ , from £ length (a-a_J —Increase — —i_n Specimen . ,. — Number of s l i p l i n e s per cm. a f t e r deformation per s l i p step. r  6  e/100 N-- x 2,000 x (1 + e/100) = extension 1  (a-a ) should be p r o p o r t i o n a l and close i n value to the step height displacement, x. Q  53  from the f i r s t i n d i c a t i o n on the load-extension chart.  I t has not been  p o s s i b l e to determine which mode of twinning operated i n i t i a l l y i n any specimen, but knowing the values of x and X f o r (a) {1012}<1011> and (b) {1011}  twins.,> and knowing the load and extension of the specimen when  twinning i s f i r s t observed, then the CRSS f o r {1012} type twins i s about 2 2 .90 to 1.00 Kg/mm and f o r {1011} i t i s between 1.30 and 1.45 Kg/mm . 3.5.1.  Results of S l i p A n a l y s i s Also i n Table VII are shown estimates of the s l i p l i n e length  L on face (1).  These values were c a l c u l a t e d s t a t i s t i c a l l y  from the number  of a r r e s t s seen i n a p a r t i c u l a r s e c t i o n (with the o p t i c a l mocroscope). The. values are therefore probably only correct to about ±30% and i t i s evident that both specimen dimensions and s l i p plane o r i e n t a t i o n are the r e s t r i c t i n g f a c t o r s , as i n specimen S3 the traces were longer, due to the lower angle between t r a c e and t e n s i l e a x i s .  In specimen S12 the average  s l i p length i s almost as long as the specimen c r o s s - s e c t i o n would allow. I t was not p o s s i b l e to measure the s l i p step height by i n t e r ferometry, as used f o r fee metals close together.  (41)  because the s l i p traces were too (42)  I t was hoped that the method due to Mader  could be  employed, but we were unable to obtain the necessary l a t e x spheres. However, from these r e p l i c a studies i t i s p o s s i b l e to estimate the step displacement, because f o r each specimen, the same face has been used i n the production of the r e p l i c a , and f o r each stage of the deformation the s l i p trace angle on the face at r i g h t angles to the r e p l i c a has been measured. As the s l i p step i s not normal to the surface the width (w) of the step increases w i t h i t s displacement  (x) see F i g . 21.  54  Fig.  21  The increase i n displacement due to slip.  6 decreases gradually w i t h s t r a i n , because of the r o t a t i o n of the s l i p plane towards the t e n s i l e a x i s . tan Bi  Referring to F i g . 22  =  w.  1  cos  Let AC  =  a  CB  =  a  Then a  Q  g,  Q  i s p a r a l l e l to the o r i g i n a l t e n s i l e  axis.  a  i s p a r a l l e l to the t e n s i l e axis a f t e r a c e r t a i n deformation, g i v i n g r i s e to a s t r a i n AB i s the s l i p d i r e c t i o n .  e.  55  In Table VII c a l c u l a t i o n s f o r specimens S3 and S12 are given; and i t can be seen that i n specimen S3 there i s some discrepancy between x and (a - a ) because the angle g i s l a r g e , but f o r specimen S12 the Q  agreement i s good.  Obviously, s l i p l i n e measurements are dependent on the  l i m i t of r e s o l u t i o n , and t h e r e f o r e , s l i p steps of less than 100A° would not be recorded.  From these observations i t may be stated that as  deformation proceeds, the number of a c t i v e s l i p planes increases up to Y  :  0.25 and remains constant t h e r e a f t e r , but the amount of deformation  occuring on each s l i p plane increases. This i s the same conclusion as that reached by Seeger and Trauble  f o r z i n c , and Seeger et a l  f o r cobalt, and i t would appear  therefore that Seeger's theory of work hardening i n stage A agrees w i t h the observations, that the density of d i s l o c a t i o n sources i s constant during (43) deformation.  Observations on Mg by H i r s c h and L a l l y  show that the  number of sources increases with s t r a i n , and t h i s i s consistent with Hirsch's theory of work hardening. 3.5.2.  The I r r e g u l a r Occurrence of Twinning The incidence of twinning i n cobalt has been shown to be s t r a i n  rate dependent i.e-. occurs more frequently at higher s t r a i n r a t e s , and does not occur i f k. < 1 x 10  sec.  I t has not been p o s s i b l e to p r e d i c t  whether twinning w i l l occur i n a specimen i f the o r i e n t a t i o n , t e s t temperature, and s t r a i n rate are a l l known.  Therefore, i t i s assumed that twinning i s  a random e f f e c t and i s dependent on l o c a l i s e d s t r e s s r a i s e r s i n the specimen, and as such i s not an important process i n work hardening.  Twinning i s  r a r e l y observed i n stage A deformation of other hexagonal metals, except at low temperatures, and usually twinning i s associated with stage B, although  56  (35) i t i s not n e c e s s a r i l y the reason f o r the increased work hardening rate I t i s i n t e r e s t i n g that the twins observed i n the present work do not correspond to those reported by Davis ^  or Seeger et a l ^ ,  whom were dealing with lower temperatures.  .  both of  I t might be p o s s i b l e that at  the higher temperatures used i n t h i s study that the twins are more akin to  (44) annealing twins than mechanical twins.  Hall  has reported annealing twins  of the (1012) type, i n cobalt. 3.6  Recovery Experiments The s t r e s s - s t r a i n curves of specimens S3 and S12 showed no  s t r e s s r e l a x a t i o n on the resumption of the tests a f t e r each period of observation.  However, i n v e s t i g a t i o n s on p o l y c r y s t a l l i n e cobalt by S e b i l l e a u and  B i b r i n g , ^ Feltham,  and Sharp, M i t c h e l l and C h r i s t i a n a l l  indicate  that dynamic recovery can take place at temperatures as low as 77°K. S e b i l l e a u and B i b r i n g found that the cold-worked state could be recovered by annealing a t 300°C, and Sharp, M i t c h e l l and C h r i s t i a n showed that i n t h i n f o i l s , the d i s l o c a t i o n density of deformed cobalt could be d r a s t i c a l l y decreased by annealing a t 270°C f o r 94 hours.  No change i n mechanical  properties was found, however, u n t i l the annealing temperature was increased to 393°C.  R e s i s t i v i t y measurements on deformed s i n g l e crystals (4 7)  by B i l g e r and Kronmuller  show that the recovery of hep cobalt i s s i m i l a r  to that i n fee metals. Accordingly, two s i n g l e c r y s t a l s w i t h Schmid Factors 0.356 (X = 26°, X = 36°) and .407 (x = 28, X = 30°) were deformed a t 323°C and 387°C r e s p e c t i v e l y .  A f t e r each small s t r a i n increment (Ay = 0.2 to 0.4)  the load was almost completely removed and the specimen was annealed i n s i t u a t the temperature of the deformation.  The r e s u l t s f o r each specimen  57  were q u i t e d i f f e r e n t , as shown i n F i g . 23. At 323°C there i s a s l i g h t decrease i n the flow s t r e s s a f t e r annealing, F i g . 23 (a)) but an i n i t i a l increase i n flow s t r e s s was observed at 397°C ( F i g . 23(b)).  I n the l a t t e r case, as the s t r a i n was  increased the flow s t r e s s f e l l to the o r i g i n a l value of the flow s t r e s s t£.  Although only two tests of t h i s nature were performed, i t has been  p o s s i b l e to show the r e l a t i o n s h i p s between A T / T ^ and ( i ) the time of anneal and  ( i i ) the resolved shear s t r a i n .  At/t£  I n F i g . 24(a) i t can be seen that  increases w i t h annealing time, (5, 15, 60 or 600 mins. were used)  when the annealing temperature i s 323°C.  Note that A T i s a decrease i n  flow s t r e s s , and that the e f f e c t i s more marked at lower shear s t r a i n s (a conclusion reached despite the high degree of s c a t t e r ) . for  F i g . 24(b) shows  the same specimen,the dependence of amount of recovery on the shear  strain.  The gradient of the graph i s greater than i f A T had been p l o t t e d ,  as T^ increases with y. Fig.  25(a) and (b) show the same p l o t s f o r specimen R19 tested  at 397°C, where i n t h i s case A T i s an increase over the flow s t r e s s T^. AT/T£  does not increase with annealing time, and now the e f f e c t i s more  marked a t higher s t r a i n s , which can be seen i n F i g . 25(b). In the 323°C anneals on cobalt and i t i s expected that during the anneal, the d i s l o c a t i o n density has been reduced, consequently  the e l a s t i c  i n t e r a c t i o n of p a r a l l e l d i s l o c a t i o n s i s lower, and therefore the flow s t r e s s i s reduced.  At 397°C, i t i s c l e a r that some i n i t i a l  hardening  mechanism i s operating, and such a y i e l d - p o i n t e f f e c t has not been previously recorded f o r hep metals.  However, Haas en and K e l l y  found a s i m i l a r  e f f e c t i n the stage I deformation of aluminium and n i c k e l s i n g l e c r y s t a l s ,  Fig.  23 (a)  »at  Fig. Fig.  23  23 (b)  Reproductions o f I n s t r o n l o a d - e x t e n s i o n curves showing the e f f e c t o f a n n e a l i n g f o r 1 hour when the d e f o r m a t i o n and a n n e a l i n g temperature a r e (a) 323°C, (b) 397°C. In both c a s e s , the c r o s s head speed was .02 inches per minute and the c h a r t speed 1 i n c h per minute. D u r i n g the anneal the l o a d was h e l d a t about 0.25 l b . to keep the specimen a l i g n e d , and b o t h specimens have been deformed to Y - 3.0 i n s t a g e A.  59  ) Fig. 24 (b) AT. f T  v  1  ,  1  2  Y  f o r  1  h o u r  anneals at 323°C  1-  3  60  ,  1  ,  _ _  2  Fig. 25 (b) Ax v y for 1 hour anneals at 397°C.  r-  3  61 and the conditions are summarized below. 1.  The magnitude of Aa increases w i t h a (where a i s the flow s t r e s s ) .  2.  Must age under reduced load to show: the e f f e c t .  3.  Ao increases when aging at temperatures greater than the deformation temperature.  A.  The e f f e c t i s l e s s marked at higher temperatures of t e s t i n g .  5.  Ao seems independent of the time of. aging. Conditions 1 and 5 have been v e r i f i e d on hep c o b a l t , and the  explanations by B l e w i t t ^ ^ and Noggle^"^ which depend on the formation of C o t t r e l l atmospheres and the consequent l o c k i n g of d i s l o c a t i o n s by vacancies during p l a s t i c flow do not agree with the observations. S i m i l a r l y Cupp and C h a l m e r s s u g g e s t  that d i s l o c a t i o n s are locked by  s o l u t e atoms, e i t h e r s u b s t i t u t i o n a l o r ' i n t e r s t i t i a l .  Haasen and K e l l y  propose an anchoring of dislocations;, during unloading, rather than the thermally a c t i v a t e d migration of point' defects to d i s l o c a t i o n s , and t h i s i s responsible f o r the y i e l d point effect.; A s i m i l a r explanation could be true f o r the e f f e c t i n cobalt. I t w i l l be shown i n s e c t i o n 5 that a specimen pre-strained i n the hep phase, and followed by deformation i n the fee phase e x h i b i t s greater strength i f the hep deformation i s followed by an anneal between 360°C and 480°C. Experiments have shown, therefore, that the work hardening mechanisms change considerably as the temperature i s r a i s e d between room temperature and the transformation temperature. x  0  Between 360°C and 420°C,  decreases markedly, but remains constant below 360°C.  Also the annealing  o experiments prove that the s t a t i c recovery at 323 C i s quite d i f f e r e n t to  62  that at 397 C.  No i n d i c a t i o n of r e c r y s t a l l i s a t i o n was observed, e i t h e r by  back r e f l e c t i o n X-ray photographs, or by o p t i c a l microscopy. A s t r a i n aging e f f e c t has been reported by P f e i f f e r and Seeger i n s i n g l e c r y s t a l s of Ni-Co a l l o y s ( i n the fee phase).  (52  In stage I an  increase i n flow stress Ax i s found a f t e r a p r e s t r a i n followed by aging, even at 20°K. Ax increases with x^ and s l i p l i n e s were seen homogeneously throughout the specimen, hence they concluded that the y i e l d point e f f e c t was not akin to Liiders band formation.  The e f f e c t was independent of the  aging time, and therefore does not seem to be d i f f u s i o n c o n t r o l l e d . 3.7  Change i n S t r a i n Rate Tests At 360°C a t e n s i l e test was performed where the s t r a i n rate was  a l t e r e d by a f a c t o r of 100.  The resultant change i n flow stress was less  than 1%, i n d i c a t i n g that at that temperature the deformation process i s athermal.  However, at temperatures between 360°C and 420°C change i n  s t r a i n rate tests should give a more pronounced change i n flow s t r e s s , but such tests have not yet been performed. 3.8  Discussion of Results x /G i s constant at 1.06 x 1 0 ^ between 18°C and 220°C, and -  Q  gradually  decreases with temperature to 0.86 x 10 * between 220°C and 380°C.  Between 380°C and 425°C x /G decreases sharply to about 0.66 x 10 0  .  (Refer  to F i g . 5 ) . Over the same temperature range, the v a r i a t i o n of work hardening rate 0 /G i s not so marked (see F i g . 6) and another difference i s that 9 /G A  decreases less r a p i d l y w i t h increasing  A  temperature.  63  Hence,it appears that the factors c o n t r o l l i n g the flow s t r e s s vary i n three temperature ranges, (A i s the transformation temperature on g  heating, taken as 435°C). (i)  0.15 A  g  < T < 0.4 A  - where x / G decreases with increasing T. Q  s  0.4 A s < T < 0 . 7 A s - where xo/ G i s constant,  (ii) (iii)  0.7 A  < T < A  s  s  - where x / G decreases with increasing T. Q  (53) Using Seegers nomenclature are  the contributions to the flow stress  given by (i) T  =  T  G  (w) +  T  , +  G  T  '  s  where x_ i s the temperature independent component due to e l a s t i c i n t e r a c t i o n s , G  and i s sub-divided as T „ ^ \ the s t r e s s opposing the movement of a d i s l o c a t i o n G  due to e l a s t i c i n t e r a c t i o n s w i t h p a r a l l e l d i s l o c a t i o n s on a d i f f e r e n t g l i d e plane but i n the same s l i p system, and x„^ ^ i s the s t r e s s due to e l a s t i c W  i n t e r a c t i o n s between i n t e r s e c t i n g d i s l o c a t i o n s .  This c o n t r i b u t i o n i s  expected to be s m a l l i n hep metals where s l i p i s confined to the basal plane. x  i s the s t r e s s required f o r a d i s l o c a t i o n to overcome obstacles by a *  g  thermally a c t i v a t e d process and i s sometimes designated x .  As a l l the  mobile d i s l o c a t i o n s l i e i n the s l i p plane, and there i s no evidence of nonbasal s l i p , the c o n t r i b u t i o n of x x s  i s expected to be small compared to x^. (3) From experimental observations, Boser concluded that both and 1/v increased w i t h deformation (v i s the a c t i v a t i o n volume). From  x /G Q  g  v temperature curves, x decreased l i n e a r l y w i t h increasing temperature, g  to zero a t 425°K, and increases again between 550°K and 650°K.  (Note i n  the present work, x i s zero between 300°K and 500°K, but above t h i s s temperature range T / G decreases w i t h i n c r e a s i n g temperature up to the O  transformation, i n d i c a t i n g that some dynamic recovery process, i . e . c r o s s - s l i p  64  or climb i s probably o c c u r r i n g ) . According to Boser^agglomerates of i m p u r i t i e s formed during the c r y s t a l preparation act as thermally surmountable obstacles to the dislocations.  Vacancies created during deformation increase the number  of o b s t a c l e s , e x p l a i n i n g the r i s e i n x , although i t i s shown by e l e c t r o n microscopy that the density of f o r e s t d i s l o c a t i o n s does not increase. 3.8.2.  S l i p Line Studies The s l i p l i n e observations on cobalt agreed more c l o s e l y with the  observations on zinc (34) than with the observations on magnesium (43) and from these observations i t i s p o s s i b l e to c a l c u l a t e the work hardening (53) rate. According to Seeger et a l !A G  JL !_. r  9TT  {  L  3 / 4  } 2  where d i s the distance between s l i p planes, and  i s the s l i p l i n e length  (due to screws). From the data given i n Table V I I , the smallest observed value of d c a l c u l a t e d normal to the s l i p plane i s 1.67  x 10 ^ cm, and L i s ~0.50  cm.,  -4 therefore, Q^/G = 1.01 x 10  at room temperature.  This value i s s l i g h t l y  higher than the observed values, but as the s l i p l i n e length i s probably r e s t r i c t e d by the c r y s t a l dimensions (for example i n zinc L then the c a l c u l a t e d value of 6./G  would be lower.  2  i s about 2 cm.),  Hence i s seems reasonable  to a t t r i b u t e the low work hardening i n easy g l i d e to the e l a s t i c i n t e r a c t i o n between p a r a l l e l d i s l o c a t i o n s on adjacent g l i d e planes, assuming that e i t h e r the d i s l o c a t i o n density on the g l i d e planes or the number of obstacles increases s l i g h t l y with s t r a i n .  ( I f not, the number of d i s l o c a t i o n s  crossed would equal the number passing out of the c r y s t a l and no work hardening would r e s u l t ) .  65 3.8.2.1.  R e l a t i o n between s l i p studies and the work Hardening  curve.  The y i e l d s t r e s s at which p l a s t i c flow commences i s close to but slightly  lower than the quoted value of x , and i s probably the s t r e s s  necessary to operate a Frank-Read source of length x , or more l i k e l y a (54) modified source as described by Washburn and Murty Gb i.e. x = — o  x  therefore, at room temperature x  2.4 x 10  -4  cm, or about a quarter of the 6 2 d i s l o c a t i o n spacing i f the d i s l o c a t i o n density i s about 10 /cm . However, =  i t i s probable that many such sources are surface activated i n which case -4 the length would be reduced to 1.2 x 10  cm.  Two other forces must also  be considered. (a)  the back s t r e s s x on the source by a newly created d i s l o c a t i o n loop Gb 1 a distance x i from the source (where x i > x).xv = -r— . — 2TT X^ the s t r e s s x required to move a d i s l o c a t i o n loop through the l a t t i c e v  x  (b)  A  m  2G T  m  (1-v)  -2Tra/b(l-v) 6  In c l o s e packed l a t t i c e a = /2 b and x i s about0.037 Kg/mm . m  Hence both x and x are less than x and assuming no other forces were v m o present, x would be a s u f f i c i e n t s t r e s s to continue the p l a s t i c deformation. o r  However, r e f e r r i n g to Table V I I , i t i s p o s s i b l e to deduce that the density of observed s l i p l i n e s increases during the early stages of deformation, hence i t i s p o s s i b l e to c o r r e l a t e t h i s observation w i t h the i n i t i a l p a r a b o l i c work hardening r a t e seen i n the i n i t i a l stages of the x - y curve. If x - x  0  =  K  n Y  2 where K and n are constants then average values f o r K and n are0.45 Kg/mm and 0.7, i . e . (x - x ) = 0.45 y°' . o 7  66  I f the e l a s t i c i n t e r a c t i o n between d i s l o c a t i o n s on p a r a l l e l s l i p planes follows the normal force-distance r e l a t i o n s h i p (shown schematically i n F i g . 26,)then as the distance between the s l i p planes d decreases, the a t t r a c t i v e force increases u n t i l i t i s at a maximum when the separation of the planes i s d . Q  Force  d Fig.  26  Q  Distance  A force - distance curve f o r the s t r e s s f i e l d round a dislocation.  For edge d i s l o c a t i o n s (which give r i s e to a much higher s t r e s s f i e l d than screw d i s l o c a t i o n s ) , the maximum force F i s given by F  =  Gb  2  r 2TT(1-V)  -r—r,  x  1 4d  Q  Thus the applied s t r e s s x needed to overcome t h i s force i s app Gb 1 app  2TT(1-V)  4d  3  1  Q  E = NbL  Also  where a t a p a r t i c u l a r s t r a i n e, the d i s l o c a t i o n density has increased to N and a d i s l o c a t i o n has moved a distance L before being held up. h If d =N Hence the shear s t r e s s x opposing the motion of these d i s l o c a t i o n s i s Q  67  G 2TT(1-V)  T  fiF J  L  thereby p r e d i c t i n g a p a r a b o l i c r e l a t i o n s h i p between stress and s t r a i n  due  to the long range stress f i e l d created by the e l a s t i c i n t e r a c t i o n between d i s l o c a t i o n s l y i n g i n p a r a l l e l g l i d e planes. In c o b a l t , Lomer-Cottrell b a r r i e r s are not expected to form as there i s no evidence of p r i s m a t i c or pyramidal g l i d e .  Twinning i n the hep  phase i s not thought to contribute to work hardening as i t was observed only i n about 25% of the t e s t s .  The occurrence of twinning seems to be random  i n that i t i s not temperature or o r i e n t a t i o n dependent, and i s therefore unpredictable.  I t probably occurs at some c r y s t a l imperfection, but  the  phenomenon has not been i n v e s t i g a t e d . 3.8.2.2.  D i s l o c a t i o n s i n Thin Films Examination of t h i n f i l m s of hep cobalt by transmission e l e c t r o n  microscopy has shown that cobalt i n the undeformed s t a t e contains a high density of stacking f a u l t s .  For example, F i g . 27(a) reproduced from a paper  by T h i e r i n g e r s h o w s extended d i s l o c a t i o n s i n a (1103) plane of an undeformed c r y s t a l . 5 x 10  cm.  The spacing between stacking f a u l t s was  ( i . e . about 2000 close packed planes) and t h i s distance  decreased to 1 x 10 ^ cm. up to a shear s t r a i n of 0.20, thereafter.  found to be  and remained  constant  This observation i s i n good agreement with the present work  which shows that the density of s l i p l i n e s increases up to a shear s t r a i n of 0.25  and remains approximately constant t h e r e a f t e r , and also the minimum  average observed s l i p spacing i s about 1.67  x 10  Assuming Thieringers observations these values f o r d i n equation 3.1,  cm.  to be correct then s u b s t i t u t i n g  the stress necessary to overcome the 2  e l a s t i c i n t e r a c t i o n increases from0.23 Kg/mm at y =0,  to 1.15  at y = 0.2. Hence froi  t h e o r e t i c a l considerations i t has been shown that i n the i n i t i a l region of  68  the s t r e s s - s t r a i n curve, the work hardening rate i s expected to increase p a r a b o l i c a l l y from the y i e l d s t r e s s T to a flow s t r e s s of about 1.15 2 Kg/mm at y = 0.2. Above t h i s s t r a i n , the density of d i s l o c a t i o n sources 9A -4 remains about constant and a l i n e a r work hardening rate ( ~10 ) i s q  A  G  expected,with  d i s l o c a t i o n s being held up at insurmountable obstacles such as (53)  c r y s t a l defects as envisaged by Seeger et a l  .  A theoretical stress-  s t r a i n curve constructed w i t h t h i s data i s shown i n F i g . 28, compared w i t h an experimentally determined curve. In Thieringers specimens the d i s l o c a t i o n density of the undeformed 8 specimens was about 5 x 10 /cm lower, see F i g . 27(b).  2 , whereas i n the present work i t was  probably  In t h i s photograph the plane of the f o i l i s close  to (1015) and the long s t r a i g h t d i s l o c a t i o n s l i e i n the [1210] d i r e c t i o n . They presumably r e s u l t from the transformation and l i e i n the (0001) plane. Other d i s l o c a t i o n s (which may be i n (0001) plane) form i n networks. shear s t r a i n of 0.16  After a  the d i s l o c a t i o n density i n Thieringers specimens 9 2  increased to about 4 x 10 /cm  , but i t f l u c t u a t e d and was high i n areas  containing groups of l i n e a r [1120]dislocations.  I t was proposed that  these d i s l o c a t i o n s were formed during the transformation on c o o l i n g , and that they act as b a r r i e r s to s l i p .  D i s l o c a t i o n s often appeared i n p a i r s ,  or s t a b i l i s e d themselves through a multi-pole arrangement. (also by Thieringer)the Burgers vector i s normal to the f o i l . 9 2 s t r a i n of 0.48  the d i s l o c a t i o n density was about 5 x 10 /cm  hardly increased during t h i s increment of s t r a i n . accumulation  In F i g . 27(c) A f t e r a shear , i . e . i t had  There i s a large  of screw d i s l o c a t i o n s which are seen (depending on t h e i r  p o l a r i t y ) as l i g h t and dark dots l y i n g i n rows along the basal plane (shown by a dashed l i n e ) .  The edge d i s l o c a t i o n s (dark contrast) are described as  " c r e a t i n g w a l l s which move i n a d i r e c t i o n perpendicular to the basal plane,"  F i g . 27  Transmission E l e c t r o n of Cobalt.  Micrography  F i g . 27 (b) Undsformed c o b a l t w i t h the p l a n e of the f o i l (1015) X30.000.  F i g . 27 (c) A f t e r a d e f o r m a t i o n of 0.48 shear s t r a i n w a l l s of edge d i s l o c a t i o n s may be observed. A l s o from Thieringer(55) X22.000.  Kg/mn/  Increase i n number of a c t i v e s l i p planes  Work Hardening by Long range dislocation interaction  1.2  0.8 . Theoretical Curve Experimentally Determined Curve  0.4 '  i  0.1 F i g . 28  i  0.2  0.3  Y  Theoretical construction of stress s t r a i n curve, shown i n comparison to an experimental curve at 20°C.  o  71  i.e.  t h e e f f e c t shown i n F i g . 2 7 ( c ) i s a t t r i b u t e d t o p o l y g o n i s a t i o n by t h e  climb  o f edge d i s l o c a t i o n s .  These o b s e r v a t i o n s H i r s c h and L a l l y cross-slip and  and  ' and A k h t a r  occurs.  ' who h a v e shown t h a t d u r i n g  This process  hence i n c r e a s e s  dipoles.  do n o t c o r r e s p o n d t o t h o s e o n m a g n e s i u m by  lowers  the p r o p o r t i o n  the density  stage A  of the screw d i s l o c a t i o n s ,  o f edge d i s l o c a t i o n s w h i c h r e a r r a n g e  The n e t w o r k s s o f o r m e d a c t a s b a r r i e r s t o t h e g l i d e d i s l o c a t i o n s ,  eventually  the work h a r d e n i n g r a t e i n c r e a s e s  associated with  stage  t o s t a g e B.  Twinning i s  B.  H e n c e one o f t h e m a i n d i f f e r e n c e s b e t w e e n c o b a l t a n d probably  in  lies  i n t h e f a c t t h a t magnesium has a f a i r l y h i g h  magnesium  stacking  fault  2 energy  (> 200 e r g s / c m ) a n d t h e r e f o r e c r o s s - s l i p , w h i c h r e q u i r e s  recombination Cobalt, with as  of p a r t i a l d i s l o c a t i o n s , i s e n e r g e t i c a l l y a low s t a c k i n g f a u l t  energy i s not l i k e l y  t h e work h a r d e n i n g r a t e , and t h e e x t e n t  process also occurs At  during  deformation,  would be expected  allow climb that both  that a dynamical climb.  i n the d i f f u s i o n  t o o c c u r more r e a d i l y , and t h e r e f o r e i t  the c r i t i c a l  h a r d e n i n g r a t e be reduced w i t h  to c r o s s - s l i p , but  probably  t e m p e r a t u r e s a b o v e 300°C, t h e i n c r e a s e  c o e f f i c i e n t should  favourable.  o f t h e easy g l i d e r e g i o n a r e  c o m p a r a b l e i n c o b a l t and magnesium i t i s q u i t e l i k e l y recovery  increasing  resolved  s h e a r s t r e s s and t h e w o r k  temperature.  However, i n c o b a l t , t h e r e a s o n f o r t h e i n c r e a s e rate giving rise have been  i n work  t o s t a g e B has not been determined, although  considered.  the  hardening  several factors  72  1.  I t i s not due to twinning as twinning can occur i n stage A, and yet i s not always observed a f t e r deformation  2.  i n stage B.  No other s l i p systems have been observed.  The occurrence of non-  b a s a l s l i p i s not w e l l understood, but i s probably the r e s u l t of s e v e r a l f a c t o r s , i n c l u d i n g the c/a r a t i o . a c/a r a t i o of 1.622 c/a r a t i o of 1.623  However, magnesium with  e x h i b i t s p r i s m a t i c s l i p , w h i l e cobalt with a  does not e x h i b i t any type of non-basal s l i p .  Therefore, v a r i a t i o n s i n the c/a r a t i o are not expected to make any c o n t r i b u t i o n to work hardening parameters i n hexagonal metals oriented f o r s l i p on the b a s a l plane. 3.  From p l o t t i n g the change i n o r i e n t a t i o n w i t h deformation, i t i s c l e a r that the specimen axis rotates towards the pole of the operative s l i p d i r e c t i o n , and therefore does not cross a boundary i n the stereographic t r i a n g l e such that two s l i p systems would be equally favoured. behaviour then, i s not responsible f o r stage B.  This  Furthermore, the extent  of stage A i s not greatly a f f e c t e d by having the i n i t i a l o r i e n t a t i o n near to the [0001] - [1010] boundary, although no specimens were tested where two s l i p d i r e c t i o n s were equally favoured. 4.  The p o s s i b i l i t y of a s t r a i n induced transformation has been ruled out because X-ray back r e f l e c t i o n photographs show no signs of an fee phase. Also t h i s e f f e c t would be more l i k e l y to occur at higher temperatures where stage B i s not observed or i s very weak.  5.  The property which causes the high work hardening rate of stage B at lower temperatures must be annealed out of the l a t t i c e at higher temperatures, and therefore might be vacancies or s e s s i l e d i s l o c a t i o n s which i n the c r y s t a l during the growth, or the subsequent the c r y s t a l cools to room temperature.  accumulate  transformation as  73  According to Seeger and Trauble  the t r a n s i t i o n from stage A  to stage B i n zinc occurs when the production of vacancies i s at such a high rate that they cannot be absorbed by the climb of edge d i s l o c a t i o n s and they then form s e s s i l e loops i n the b a s a l plane.  I t i s not c l e a r how  the vacancies are generated, but i t seems l i k e l y that a s i m i l a r mechanism may operate i n cobalt.  7k  4.  Deformation of fee Cobalt  4.1.  General Behavior i n the Temperature Range 430°C to 600°C In the temperature range 430°C to 600°C* the  T  - y curves  were constructed w i t h the o r i e n t a t i o n data obtained by the method described i n Appendix Fig.  2.  29 shows a s e r i e s of T -. y curves over a temperature  range of 436°C to 600°C (approx. 0.4 to 0.5 T ) . m  The curves at  temperatures of 436, 490, 550 and 600°C represent specimens whose axis lay i n the centre of the stereographic t r i a n g l e , and metallographic examination showed that s l i p p r i m a r i l y occurred on one system.  Specimen  490 B was s i t u a t e d c l o s e to the (100) - (111) boundary, and observations on a specimen of the same o r i e n t a t i o n showed that two s l i p systems operated a f t e r a shear s t r a i n of 30%. Unless the t e s t i n g conditions are favourable, i t i s d i f f i c u l t to o b t a i n a three stage work hardening curve f o r most fee metals. the o r i g i n a l theory by T a y l o r ( s u b s e q u e n t l y modified by M o t t ^ " ^ ) developed to e x p l a i n the p a r a b o l i c s t r e s s - s t r a i n curve.  In f a c t was  Metals of high  stacking f a u l t energy e.g. aluminium, do not show stage I , except at very low temperatures.  Metals such as copper show a l i m i t e d stage I at room temperature;  and a l l o y s of low stacking f a u l t energy such as a brass show good three-stage (58) curves at room temperature *  o 600 C was chosen as the upper l i m i t of t h i s work, as below t h i s temperature thermal c y c l i n g though the transformation of p o i y e r y s t a l l i n e or s i n g l e c r y s t a l specimens r e s u l t s i n transformations on the same v a r i a n t close packed plane (see Nelson and A l t s t e t t e r ( 9 ) ) . M u l t i v a r i a n c e (transformation on more than one close packed plane r e s u l t i n g i n a p o i y e r y s t a l l i n e specimen) occurred i f the specimens are cycled between room temperature and a temperature greater than 600°C.  76  In Table V I I I the other  fee metals are  stacking fault  compared t o the  s t r a i n r a t e at various  extent  temperatures).  energies  of  c o b a l t and  of easy g l i d e  Even though the  (for  stacking  some constant  fault  (29) energy i s low as  the  i n cobalt  temperature of  the  , i t i s not  s u r p r i s i n g t h a t no  transformation  is relatively  stage I i s seen  high.  TABLE VIII  THE  RELATION BETWEEN STACKING FAULT ENERGY AND EXTENT OF EASY G L I D E I N SOME FCC METALS  Metal  a  1.5  22 5  Brass  80  Copper  Temp  Y/Gb  S.F.E. y ergs/cm see Ref. 62  Cobalt  -7  x  10  3 x  10  5 x  -3 10 -2 10  135  3 x  Nickel  180  -2 2 x 10  The  P a r a b o l i c Nature of  Several the  the  0.4  -4  Aluminium  4.1.1.  0.4 0.34 0.10 0.03 0.01  °K  Ref.  T,m  Present Work  0.24 0.35 0.22 0.37 0.32  T,m  0.17  T, m  r  r  58  m m m m  58 41,59, 60,61 42  S t r e s s - S t r a i n Curve  a u t h o r s (^1>59,60,61) j  i  a  y  e  g^g^  t h a t a t room  temperature,  s t r e s s - s t r a i n curve f o r aluminium s i n g l e c r y s t a l s i s p a r a b o l i c .  generally  assumed t h a t s t a g e I I I o f  hence the  curves f o r c o b a l t have been analysed  the  Assuming w h e r e K and the  THE  n are  constant,  l i n e a r p o r t i o n of  the  From f i g . 2 9 , a p l o t o f  and  T  d  s t r e s s s t r a i n curve i s p a r a b o l i c ,  (T - x ) i s t a k e n as  c u r v e w h e n y = 0. log  (x - x ), Q  It is  v.  as =  follows: KY*  1  the p r o j e c t e d Then l o g  value  of  x  from  (x - x ) = l o g K + n l o g  l o g y i s shown i n F i g .  30.  y,  77  The l o c a t i o n of p o i n t P corresponds to the b e g i n n i n g of s t a g e I I I and i s t h e r e f o r e , e q u i v a l e n t to the arrows i n F i g . 29.  78  Each point  P.  At  strains  above  consist  of  low P  two  parabolic  Neglecting  0.60  to  0.81  4.1.2.  in  over  the  The Y i e l d  observed.  linear large  stage as  tire w o r k  T  value  of  T  II  to  in  the  of  system  been  this  has  is h i g h l y  observed,  For  example  1.9  x  10  -3  where  from  the  stress  600°C,  n  =  = 1  stage  II  ±  .02,  the  T -  where  and  at  curves  y  n - 1 ,  and  a  0.65.  to  ( T -  whereas  Therefore  in  n  1.00  n  = 0.65  T )  at  0  the  P  value  is  is  interesting.  constant  of y  at  P  at  7.5  increases  from  range.  to  Fig.  hep  29  of  strain,  rate  is  0.05  and  with  no  experiment  T  is  taken  q  At  high,  constant  in  and  phase.  this the  and  0.1  over  the a  as  value  yield  it  an  easy  three  (about  80  decreases  hardening  rate  range  temperature,  glide  extrapolation  about  point  gradually  work  has  the is  considerable  increasing  generally  usually  been  favoured.  the  work  assumed found  slip  hardening  system)  that two  region  of  times -  as T ) Q  increasing  reaches  a  uniform  II).  Fig.  the  90% o f  with  (stage  (see  and  slip  systems  i n c o b a l t (see  However,  i n F i g . 29 the t w o (1  as  of  at a  intersecting  The  32)  but  is  orientation.  It i s I I , and  III  slope  .10.  region  (P)  value  decreases  independent  stage  zero  remains  q  ±  same  The  Betweeny= and  0.65  a  lines,  Point  hardening  strain. level,  q  are  linear  and  Referring been  has  490B,  436°C  straight  line  crossover  specimen  between  2  as  a  two  each  slopes  parts,  region  of  consists  strains  the  The  Kg/mm  plot  in  cases  curves 2.1  x  10  -3  (2  only  is  at 490°C  have  slip  even  later),  where  coefficient  operate  one  only  values  during  when  slip  about  system  10%  of S ^ / G  systems).  one  stage slip has  lower.  of  79  4.1.3.  The E f f e c t of Specimen Size Although a l l of the c i r c u l a r specimens tested had gauge diameters  between 1.40  and 1.60 mm,  an estimation of the effect of c r y s t a l diameter  has been made using two specimens, one of 1.09 mm diameter, and the other of 1.91 mm diameter. specimen of 1.46  In both cases the T - y curves corresponded to a  mm diameter tested at the same temperature  (470°C).  This  ( 63^  result does not agree with the findings of Fourie  who  concluded from  experiments on copper single crystals that the length of stage II was a direct function of c r y s t a l s i z e , and as stage II i s a surface phenomenon, i t would not appear at a l l i n an i n f i n i t e l y large c r y s t a l .  As such the  t r a n s i t i o n from stage II to stage I I I should not depend on any physical property of the metal. 4.1.4.  Interrupted Tensile Tests While i t i s true that evidence of c r o s s - s l i p may also be observed  i n the l i n e a r region of stage II (see a description of the metallography of specimen S13 l a t e r i n this chapter), a t y p i c a l x - y curve for an interrupted t e n s i l e t e s t i s shown i n F i g . 31, and i t can be seen that there i s a difference i n behaviour i n stages II and I I I . When the test i s halted arid the specimen removed from the furnace for observation during stage I I , and then returned for further testing the y i e l d stress i s exactly the same as the flow stress before. transformations w i l l not a f f e c t the work hardening behaviour.  Hence two However, i f  the procedure i s repeated during stage I I I , then y i e l d i n g occurs at a much lower stress, and a higher work hardening rate i s necessary to advance the flow stress to the value i t would have been at i f the test had been continuous. Furthermore, the  decrease i n y i e l d stress i s greater, the further into stage  81  I I I the t e s t has proceeded.  This e f f e c t has been noticed i n several  t e s t s , and i t i s suspected that some s t a t i c recovery i s occurring during the period when the specimen i s unloaded and subsequently reheated to the t e s t temperature. The slope of the curve on r e t e s t i n g i s the same as  there-  fore the dynamical recovery process i s not occurring during t h i s stage, but A  re-appears at the expected flow s t r e s s - see dotted l i n e on F i g . 31.  Hence,  t h i s observation i n d i c a t e s that there i s d e f i n i t e l y a d i f f e r e n c e between the behaviour i n stages I I and I I I , and as i t has already been established the specimen dimensions d i d not a f f e c t the p r o p e r t i e s , then the p o s t u l a t i o n made by Fourie, that stage I I i s a surface phenomenon, and therefore that ^2.11 does not have any p h y s i c a l s i g n i f i c a n c e does not seem to hold true f o r cobalt. 4.1.5.  The S i g n i f i c a n c e of Stage I I I In F i g . 29, ^2.11 * t  ie s t r e s s  a t  t n  e onset of stage I I I i s  i n d i c a t e d by an arrow, and i s taken as the s t r e s s at which the x - y curve s i g n i f i c a n t l y deviates from the area stage I I .  T  ni i  s  n o t  affected by  o r i e n t a t i o n but decreases markedly with increasing temperatures.  Therefore  i f stage I I ends when a c e r t a i n recovery process comes i n t o operation, then the recovery process needs a certain'tatress"level"to• operate;'-' ;  ;:  ' •.  This s t r e s s l e v e l decreases with i n c r e a s i n g temperature, which i n d i c a t e s that x » the thermal component of the flow s t r e s s , plays an important p a r t s  i n the recovery. x decreases w i t h increasing temperature, and at 0.35 T makes s m  an i n s i g n i f i c a n t c o n t r i b u t i o n i n most fee metals.  However, s i l v e r has a  low stacking f a u l t energy, and the value of x decreases with increasing Q  82  temperature. Seeger e t a l the  (53)  comment " i n low s t a c k i n g f a u l t energy  fee m e t a l s ,  f o r m a t i o n o f j o g s i n screw d i s l o c a t i o n s h o u l d g i v e a n o n - v a n i s h i n g  x  s  c o n t r i b u t i o n , even a t r a t h e r h i g h temperatures."  The (see  temperature dependence o f T  q  f o r c o b a l t i s g r e a t e r than s i l v e r  F i g . 32 f o r a comparison), and t h e r e f o r e a s i m i l a r e x p l a n a t i o n i s v a l i d .  4.2.  Comparison  Two  w i t h Other f e e M e t a l s  i m p o r t a n t r e s u l t s which a r e p r e d i c t e d by Seeger's  theory o f  . , , , (53,64) work h a r d e n i n g . are: _3 (a)  G  i ] / G i s c o n s t a n t , about 3 x 10 This implies  f o r a l l metals a t a l l temperatures.  t h a t the geometric p r o c e s s e s i n d e f o r m a t i o n are  temperature  insensitive. (b)  Log  (T) i s a l i n e a r f u n c t i o n o f a b s o l u t e temperature. (53)  (a)  The f i r s t p o i n t has been shown to be t r u e f o r copper, g o l d , n i c k e l  but does not seem v a l i d  for aluminium^^,  lead  or f o r c o b a l t - see F i g . 33.  Over the s m a l l temperature range t e s t e d , the v a l u e o f Q^/G x 1 0 ~ / ° K , compared to 3.2 6  In  decreases by  x 1 0 ~ / ° K f o r l e a d as g i v e n by B o i l i n g e t 6  the metals not a g r e e i n g w i t h Seeger's  ,  t h e o r y , some temperature  1.57  al^  6 6  ^.  dependent  h a r d e n i n g mechanism must o p e r a t e on a system o t h e r than t h a t of the primary slip  system. A l s O j C o b a l t appears  to have a v a l u e o f  somewhat lower  than  t h a t o f the o t h e r f e e m e t a l s , a l t h o u g h Q-j^/G i s about 5 times g r e a t e r than the  v a l u e of 0.,/G  i n the hep phase a t room  temperature.  B (b)  F i g . 34 shows the r e l a t i o n s h i p f o r l o g  vsT(°K) f o r aluminium,  copper,  (53) and g o l d  (taken from Seeger e t a l  l i n e a r has been i n t r o d u c e d .  ) and the curve f o r c o b a l t which i s a l s o  The graphs have been used by Seeger e t a l to  c a l c u l a t e the s t a c k i n g f a u l t energy  (SFE) f o r these metals  (by a method known  00  •  *L1 -3 3.0 x 10  0  CT  2.0  &8 o 69 o  a B  o 8  o 9  -3  x 10  -3 x 10  • 8 O  0  100  Cobalt Lead  Present work 66a  Aluminum  53  Copper  53  Nickel  53  Ni/50% Co  53  Ni/60% Co  53  200  <8>  <8>  Ref.  Metal  1.0  •  300  400  500  600  700  800  900  Temp. (°K) F i g . 33.  Q n  v. temperature f o r v a r i o u s f e e m e t a l s .  fault energy.  86  as the T-QI method) and although the r e s u l t s do not correspond favourably w i t h those of other techniques, they do show the general trend, i . e . the slope i s i n d i c a t i v e of the SFE as i t i s f a i r l y w e l l established that SFE values decrease;  A l > Cu > Au.  The c a l c u l a t i o n of SFE by t h i s method i s given by C h r i s t i a n and Swann^ ^ ^ but i t has not been repeated f o r cobalt as numerous tests at various s t r a i n rates are required and a l s o i t i s necessary to know the number of d i s l o c a t i o n s i n a p i l e - u p which would give a high enough applied s t r e s s to b r i n g together, completely, a p a i r of p a r t i a l d i s l o c a t i o n s .  In  other words i t i s assumed that T-^-Q i s the s t r e s s at which c r o s s - s l i p i s i n i t i a t e d , but even i f c r o s s - s l i p i s not common (as i n c o b a l t ) , the technique may s t i l l be applied to c a l c u l a t e SFE i f i t i s assumed that at T  lll * t  ie r e c o v e r v  Process which comes i n t o operation and causes the work  hardening r a t e to decrease, must i n v o l v e the recombination of p a r t i a l dislocations. Table IX shows the slopes of the curves i n F i g . 34 and the comparison of SFE by t h i s and other techniques. TABLE IX COMPARISON OF SFE BY Metal  Al Ni Cu Pb Au Co  T l n  Slopes from F i g . 34  -.0074 -.0031 -.00122 -.00043  , METHOD AND OTHER METHODS SFE by . T  lll  m e t n o c  * 2  230 erg/cm. 300 170 25 30  Widely accepted value of SFE of other methods 2 135 erg/cm. 180 80 50 15 to 25  87  These r e s u l t s Indicate that i f the SFE of cobalt was  c a l c u l a t e d by the 2  T  lll  m e t n o <  ^»  t n e  r e s u l t would be between 10 and 20 ergs/cm , which i s  c e r t a i n l y of the correct order, and therefore i t may be assumed that the dynamic recovery process which gives r i s e to stage I I I involves the recombination 4.3  of p a r t i a l d i s l o c a t i o n s .  Experimental  Observations  Three techniques have been employed to study the e f f e c t of deformation  on the l a t t i c e .  (a) O p t i c a l microscopy (b) E l e c t r o n microscopy of r e p l i c a surfaces (c) Back r e f l e c t i o n X-ray photographs Table X shows an a n a l y s i s of s l i p l i n e studies ( s i m i l a r to those described i n the previous section) on f i v e specimens, S13, R4, R39 and R70. Table XI.  R27,  The i n i t i a l o r i e n t a t i o n of these specimens i s shown i n The two a l t e r n a t i v e s were constructed according to the method  given i n Appendix 2, and the correct s o l u t i o n was discovered a f t e r a small amount of deformation  gave r i s e to s l i p l i n e s .  For example, a f t e r 14%  formation at 550°C a s l i p trace a n a l y s i s on S13 showed that x  =  Appendix 2), and therefore the second a l t e r n a t i v e was c o r r e c t .  32°  de-  (see  For  convenience a l t e r n a t i v e (2) i s the correct s o l u t i o n f o r each specimen.  It  w i l l be noted from the t a b l e , that i n only one of these.specimens (R70) i s the o r i g i n a l b a s a l plane the most favourably oriented f o r (111) s l i p . The other specimens a l l have at l e a s t one (111) plane more favourably oriented, and the d i s t i n c t i o n between the specimens then l i e s i n the r e l a t i v e Schmid f a c t o r s of the d i f f e r e n t (111)  planes.  TABLE X  SUMMARY OF SLIP LINE DATA ON SPECIMENS DEFORMED IN FCC PHASE  N Spec. S t r a i n Shear FACE (1) Calc. Trace Measured No. N Slip Angles width displace(in e % Strain (measured Spacing w ment tensile Y x= W normal axis) = 5/N(u) Face 1 Face 2 (M) to trace) a e cos g 1  snl  6.4 18.4 S13 S13 42 R4 5.1 R42p 11.9 R4 s 11.9 R^P 34 R4 s 34 R271 5.3 R27 p 10 R27 s 10 R39 25 R39 60 R70 27 82 R70 2  3  1  0.14 0-40 0-87 0-09 0.21  2  0.63  4  2  0.17 0.33  2  2  3  1  2  0.49 1.19 0.45 1.48  12 26 24 15 13 12 11 8 18 14 11 9 18 21 19  0.416 0.194 0.208 0.330 0.385 0.416 0.455 0.625 0.279 0.357 0.455 0.555 0.278 0.238 0.263  62 67 64 18 17 45 14 40 85 83 12 68 37 35  32 29 26 87 87 38 87 37 18 17 54 35 80 80  D  0.02 0.02 0.05 0.02 0.06 0.06  0.0235 0.0228 0.0560 0.388 1.130 0.076  0.04 0.055 0.04 0.05 0.05 0.06 0.14  0.043 0.058 0.068 0.061  10.5 2.24 x 1 0 23.6 5.6 6.09 21.4 4.65 0.975 3.84 0.855 8.4 1.88 3.2 0.86 5.1 .1.37 18 3.78 14 3.08 2.3 0.505 8.3 2.08  0.34 0.81  12.6 10.8  p refers to the primary s l i p system, s refers to the secondary s l i p system For an explanation of terms N , N \ (a-a ) etc. see Table V I I . Q  No. of s l i p (a-a ) l i n e s per (y) cm. a f t e r deformation  3.2 3.94  4  L cm.  0.029 0.033 0.069 0.052 0.139 0-063 0.390 0.248 0.014 0.032 0.198 0.120  0.024 0.016 0.013 0.040 0.032 0.021 0.034 0-051 0 .080 0.070 0.030 0.070  0.084 0.208  0 .100 0 .080  TABLE XI POSSIBLE ORIENTATIONS OF SPECIMENS USED IN SLIP TRACE ANALYSIS  Specimen Number  S13  ALTERNATIVE .{111}  X  ® ®  48 52  ®  1 8  •  *  14 32  R4  2 7  *  67*  R27  R39  R70  *  1  <110>  Schmid factor  48 52 20 20  0.497 0.484 0.290 0.229  X  54 28 69  X  U11}  0  ALTERNATIVE 2 Schmic! <110> factor A  34 O 74 • 14* O 8  42 75 20 20  0.416 0.249 0.229 0.131  43 67* 10 6  48 69 13 13  0.456 0.330 0.170  26 19* 14  36 24 24  0.356 0.298 0.221  42 28 11* 81  44 36 27 81  0.481 0.380 0.169 0.154  34* 22 69  36 23 70  0.452 0.344 0 .320  O r i g i n a l Basal Plane. Alternative (2) represents the true fee orientation. The symbols 0 , ® and O refer to the poles shown i n F i g . 59 Appendix 2.  90  The term o r i e n t a t i o n factor has been introduced to c l a s s i f y the specimens, and i s defined by the r a t i o of The Schmid factor on the most favourably oriented (111) The Schmid factor on the transformed  basal (111)  plane  plane  In Table XII, the f i v e specimens to be discussed are tabulated as a function of the o r i e n t a t i o n f a c t o r , and although each of the experiments was  repeated,  the actual l i m i t s i n each category are arbitrary, and some  overlap might be expected as no two crystals have behaved exactly a l i k e . 4.3.1.  S l i p Line observations with increasing Shear Strain The s l i p l i n e development with increasing deformation  for  these specimens i s shown i n Figs. 35 to 40, and the observations on each specimen w i l l be described b r i e f l y : Specimen S13 - Figs.35(a)  to  (m)  After 14% shear s t r a i n (Figs. 35(a) to (d)) there was  a  considerable difference i n the appearance of the s l i p l i n e s on two at 90° to each other.  faces  Fig. 35(a) shows short wavy traces at 240X  magnification, and from X-ray data i t was  ascertained that this face was  less  than 20° from the plane containing the edge segments of the expanding d i s l o c a t i o n loops.  Hence the dislocations escaping on this face were  primarily of edge character.  The waviness indicates that the edge  dislocations emerge on d i f f e r e n t planes, and that cross-slip has  occurred.  The face at r i g h t angles contains much straighter s l i p lines (Fig. 35(d)) because on this face the screw dislocations emerge.  Only i f the edge  dislocations can climb, w i l l a screw d i s l o c a t i o n have sections lying i n a d i f f e r e n t plane, but this i s not suspected  from the nature of the s l i p l i n e s .  TABLE X I I INFLUENCE OF ORIGINAL ORIENTATION ON DEFORMATION BEHAVIOUR IN FCC PHASE Example and Specimen Number  O r i e n t a t i o n Factor » S.F. of fav. ( I l l ) S.F. of b a s a l (111) 1.0  Number of Twin or S l i p Systems  Remarks  Yes  Good spots to fracture  1, 2 or 3 at d i f f e r e n t locations  Yes  Spots, getting Work hardenl a r g e r , fewer ing curve and more d i f f u s e s i m i l a r to A. with s t r a i n  R70  B  R27  1.0 + -1.3  C  R4  -1.3 •+ -1.7  2 or 3 at d i f f e r e n t locations  D  R39  > -1.7  E  S13  > -1.7  groun  X-Ray Back R e f l e c t i o n Data  1  A  This  Is the Basal (111) Plane the primary s l i p plane?  Stage I work hardening never observed  No but w i l l operate as secondary  Spots -»- spots + Debye arcs -> r i n g formation  No change i n W.H. a f t e r recrystallization  2  No but twin bands form  S i m i l a r to C  Twinning sometimes indicated on load chart  1  No o r i g i n a l l y yes a f t e r trans formation  Clear spot pattern  Wavy s l i p traces as evidence of cross s l i p  behaves as type D i f transformation to type A not allowed to take place.  92 Hence i t i s believed that the major dynamical recovery process that occurs during deformation i s c r o s s - s l i p , and that c r o s s - s l i p may occur at a very early stage i n the deformation at 550°C, i . e . i n stage I I , w e l l below the s t r a i n at which stage I I I commences.  The r e p l i c a s d i d not contain the  same degree of waviness, but the s l i p l i n e s were not as s t r a i g h t as those observed i n the hep phase.  Some twins were observed ((c) and (d)) although  they were not indicated on the load-extension chart.  The twin plane  coincided w i t h the close-packed (111) plane which o r i g i n a l l y constituted the b a s a l plane, even though t h i s plane had an unfavourable Schmid f a c t o r . F i g s . 35 ( e ) , (f) and (g) a f t e r y = 0.40.  At 240X m a g n i f i c a t i o n  the photograph was taken s l i g h t l y out of focus to enhance the waviness of the traces, and i t appears as though there are two sets of l i n e s separated by about 9°.  At 700X i t can be seen that a branching of the s l i p l i n e s  occurs, but c l a s s i c a l c r o s s - s l i p was not observed.  No X-ray p a t t e r n was  taken a f t e r t h i s stage. F i g s . 35 (h) and ( i ) a f t e r y = 0.87.  At 240X there i s an  even more pronounced e f f e c t (which causes the shadows at about 30° to the trace d i r e c t i o n s ) and two of the four r e p l i c a s (i) showed f a i n t traces of a second s l i p system operating.  A f t e r y = 0.14  the X-ray back r e f l e c t i o n  photographs  contained good spots, w i t h a s l i g h t r o t a t i o n of the l a t t i c e .  At y = 0.87,  the X-ray p a t t e r n s t i l l consisted of c l e a r spots, but the  o r i e n t a t i o n of the hep phase was completely d i f f e r e n t , as the transformation had occurred i n such a way that the b a s a l plane was now the (111) plane on which s l i p had taken place.  The d i s l o c a t i o n density on the primary s l i p  plane would be very much higher than on any other (111) plane, even though twinning had occurred on the (0001/111) plane.  Deformation had therefore  93 F i g s . 35 (a) t o (m) D e f o r m a t i o n of specimen S13  F i g . 35 (e)  y =  .4, X240  F i g . 35 ( f )  Y = .4, X700  94  Fig.  3 5  (k) v  - 1.33,  X250  Fig, 35 (1)  y = 1.38,  X700  95  Fig.  35 (m)  y  = 1.38,  F i g . 36 (a)  X700  Y = .09 X650  F i g s . 36 (a) t o (k) D e f o r m a t i o n of Specimen  F i g . 36 (b)  Y  = .21, X650  F i g . 36(d)  Y  = .37, X650  R4  F i g . 36 ( c )  Y = .21, X5000  F i g . 36 (e) Y = .67, X650  96  changed the way i n which n u c l e a t i o n of the hep phase could be i n i t i a t e d , and the 'memory' of the transformation had been destroyed throughout the whole c r y s t a l .  The  crystallography of t h i s transformation i s described  i n Appendix 2.  The X-ray pattern s t i l l gave spots even though the  specimen had now been deformed i n t o stage I I I , and the s l i p l i n e length had decreased to about h a l f that i n 35(a). Figs. 35 ( j ) , ( k ) , (1) and (m) show further twinning occurred between y = 0.87 and y = 1.38 at f r a c t u r e .  These twins are p a r a l l e l to  the ones observed early i n the deformation i . e . o r i g i n a l l y belonged to the transformed b a s a l plane, but at l a t e r stages corresponded to the (111) plane which has rotated i n t o a more favourable Schmid f a c t o r .  In f a c t  at higher magnification (x 700) these twins appear to contain s l i p traces (1) and (m), but unfortunately no r e p l i c a s could be made of the surface, probably because s l i g h t o x i d a t i o n of -|;he surface occurred. 1  (Hence i t i s  not known whether the secondary s l i p "seen i n F i g . 35 ( i ) developed appreciably w i t h the increase i n s t r a i n ) . '  '••  Specimen R4 - F i g . 36 Fig.  36 (a) shows that a f t e r a low s t r a i n ( y = 0.09) there i s  only one s l i p system operating.  This does not correspond  to the basal  plane, but the basal (111) plane has become a s l i p plane at y = 0.21 shown at x 650 i n F i g . (b) and at x 5000 i n F i g . ( c ) .  Both s l i p systems  continue to operate up to y = 0.37 ( F i g . ( d ) ) , although the primary system seems to have remained the dominant one.  Up to t h i s point the X-ray  back r e f l e c t i o n photographs show spots, which increase i n s i z e and become more d i f f u s e as the s t r a i n increases - see F i g . 37 A  to C .  when y = 0.67 the micrographs take a d i f f e r e n t appearance;  However,  the primary  F i g . 36 ( f )  Y = .67,  F i g . 36 (g)  X5,000  Fig. 36 (j)  y  =  1.12, X650  Y  = .85, X650  F i g . 36 (k)  Y =  1.12,  X 5,000  F i g . 37 A to F - Specimen R4  The change i n back r e f l e c t i o n patterns with increasing amounts of deformation. A y = '09 w e l l defined spots. B Y C Y  =  -21 spots fewer, and large. -37 some spots broke into doublets.  =  D Y = -67 small arcs replace spots. E Y = -85 arcs better developed. F Y  =  1'12  almost complete ring pattern.  99  s l i p system now appears to be banded, and there i s also a t h i r d s l i p system appearing i n small areas (Fig.35(e)). the secondary s l i p to be fragmented. gave a mixture of spots, and short arcs  The r e p l i c a also shows  At t h i s stage the X-ray p a t t e r n of Debye r i n g s , F i g . 37  i n d i c a t i n g that some change i n s t r u c t u r e had taken place.  D ,  F i g . 36 (g)  shows that some r e c r y s t a l l i s a t i o n has taken place at y = 0.85-, increasing as y  =  1.01  ( F i g . 36 ( h ) ) . I n some of the newly created g r a i n s , a  completely d i f f e r e n t s l i p trace i s observed although the o r i g i n a l primary and secondary s l i p traces are s t i l l discernable.  A r e p l i c a taken at t h i s  stage showed s e v e r a l such boundaries (Fig36(i))«  At a s t r a i n of y =  1.12  the specimen f r a c t u r e d , and Figs.36(j) and (k) are taken near the f r a c t u r e . A complete break-up of the s t r u c t u r e was observed at 650X.  During the  l a t t e r stages of the deformation the r i n g patterns became more and more complete, although they also became broader and more d i f f i c u l t to distinguish.  D i r e c t reproduction of these patterns was impossible, and  therefore they have been traced f o r reproduction, and are shown i n Fig.  37  A  to  F .  Specimen R27 - F i g . 38 Figs 38 (a) and (b) show  t h i s specimen a f t e r a shear s t r a i n of 0.17.  Only one s l i p system was seen both i n the o p t i c a l and e l e c t r o n microscopes. The operative s l i p plane was the transformed b a s a l plane despite the fact that another (111) had a more favourable Schmid f a c t o r .  At higher s t r a i n , .33,  the b a s a l (111) plane continued as the primary, but another s l i p  system,  the one with the favourable Schmid f a c t o r , also operated, F i g s , (c) and (d).  Both s l i p systems contributed about equally to the deformation up to  the f r a c t u r e , although a t h i r d system was also observed i n small areas  Figs. 38 (a) to (f)  100  Deformation of Specimen R 27  Fig.  38 (a)  y = .17  Fig.  38 (b)  Y  X650  Fig. 38 (c)  y  = .33, X650  = .17,  X10,000  Fig.  38 (d)  Y  = .33 X 6,000  O Figs. 38 (e) and (f) Micrograph (X650) and X-ray pattern at fracture strain (Y = 1.3)  101 (Fig.  (e)).  X-ray patterns showed spots even up to the f r a c t u r e s t r a i n ,  but they were rather l a r g e , d i f f u s e and few i n number, as shown i n F i g . 38(f) reproduced from a t r a c i n g of the o r i g i n a l f i l m . Specimen R 3 9 - F i g . 3 9 At y = 0 . 2 8 there was one major s l i p system which was plane with the highest Schmid f a c t o r .  the ( 1 1 1 )  However, F i g . (a) shows that traces  of a second s l i p system appeared, although at t h i s stage i t could not be identified.  However, t h i s small amount of deformation  i s believed to be  the reason f o r the X-ray pattern showing both spots and i n d i c a t i o n s of a r i n g formation.  At higher s t r a i n Y  =  0.49,  the secondary s l i p system  developed i n t o twins, ( F i g . (b)) long twins s i m i l a r to Neumann bands which have been observed i n i r o n - s i l i c o n a l l o y s . was  i d e n t i f i e d as the basal ( 1 1 1 ) plane.  The habit plane of these traces The primary s l i p traces may  be  followed through the twin, and the displacement i s a function of the width of the twin, and i t s o r i e n t a t i o n .  In some instances s i n g l e twin boundaries  may be observed, when the s l i p traces do not change d i r e c t i o n .  It is  assumed that these traces are i n f a c t due to a double twin boundary, f i n e to be resolved, and that these boundaries separate as proceeds.  A r e p l i c a i s shown i n F i g . ( c ) .  deformation  increases w i t h s t r a i n , and at y  too  deformation  The extent of t h i s secondary =  0 . 8 3 the X-ray pattern shows  only f a i n t Debye arcs. At f r a c t u r e ( Y = 1 . 1 9 ) and  the s t r u c t u r e i s shown i n F i g s , (d), (e)  ( f ) , and secondary s l i p traces may  now be observed i n the twinned region.  These are presumably of ( 1 1 1 ) o r i e n t a t i o n .  An o p t i c a l micrograph of four  adjacent regions along the t e n s i l e a x i s of a specimen of s i m i l a r o r i e n t a t i o n i s shown i n F i g . 3 9 (g).  Here a p a r t i c u l a r twin trace can be followed along  the axis u n t i l i t disappears.  The change i n o r i e n t a t i o n of the primary s l i p  Figs. 39 (a) to (f) Deformation of specimen R39  Fig. 39 (a)  Y  Fig. 39(b)  Y  = -28, X250  = -49, X650  S  F i g . 39 (c)  Y - .49, X6,000  103  Fig. 39 (d)  Y  = 1.19, X250  Fig. 39 (f)  Y  = 1.19, X20,000  F i g . 39 (g)  A scan along the tensile axis of a specimen of the same orientation as RA. X150. The twin habit plane i s the (111) plane corresponding to the basal plane after the transformation to room temperature.  o 4S  105  plane can also be observed across the twin boundary.  Near the centre  of the p i c t u r e i s a region where the primary s l i p plane changes from one d i r e c t i o n to another without an observable boundary.  I t i s p o s s i b l e that  cross-slip might a f f e c t t h i s change-over, but i t could not be c l e a r l y resolved.  In both F i g s , (d) and (g) the primary s l i p traces can be  followed through s e v e r a l changes i n d i r e c t i o n although t h i s i s not so obvious i n the r e p l i c a s (e) and ( f ) . Specimen R70 - F i g . 4 0 This specimen was oriented such that the b a s a l (111) plane had the higher Schmid f a c t o r , and the specimen deformed completely on one s l i p system.  No twins were observed, and even at f r a c t u r e (y = 1.48) the spots  on the X-ray photograph were c l e a r and sharp.  Although the r e p l i c a s i n F i g .  40 (b) and (d) bear s i m i l a r resemblence to those of specimen S13 ( F i g . 35), the s l i p traces under the o p t i c a l microscope seen i n F i g s . 40 (a) and ( c ) , were longer and s t r a i g h t e r , but not as long as i n specimens deformed below the transformation temperature. 4.3.2  The Occurrence of Twinning i n fee Cobalt In hep metals twinning frequently occurs, as there i s only one  operative s l i p plane.  In fee metals, however, twinning i s r a r e l y observed,  and then only at very low temperatures, because the normal twin plane (111) i s also a p o s s i b l e s l i p plane.  However, i n s e v e r a l of the experiments  performed i n the fee phase evidence of twinning has been observed on the -4 load-extension chart at s t r a i n rates of 3.3 x 10  ins./in/sec.  When the  s t r a i n rate was decreased by a f a c t o r of 100 i n d i c a t i o n s of twinning were no longer observed.  On subsequent examination of the specimens only  106 F i g s . 40 (a) t o (b) Deformation  F i g . 40 (a)  Y =  .45,  of Specimen R70  F i g . 40 (b)  (c)  i  = 1.48,  = .45 X20.000  X650  F i g . 40  y  F i g . 40 (d)  Y = 1-48, X20,000  X650  ^J^i.  F i g . 41 Non-octaiedral t w i n , w i t h a probable h a b i t plane {112.} e s t i m a t e d by single s u r f a c e analysis. X700  107  large twins on (111) planes were observed, as shown i n F i g . 35 ( c ) , or 39 (b).  However, i n one specimen i n which there had been one burst of  twinning i n d i c a t e d , some smaller twins were observed  ( F i g . 41).  From the  stereographic p r o j e c t i o n a one-surface trace a n a l y s i s was used on the twin, knowing that the two major traces belonged to (111) planes, and assuming that the s l i p trace i n the twin belonged to the primary s l i p system. estimated twin h a b i t plane was 4.4.  The  (112).  Discussion Each of the specimens which has been described i n some d e t a i l  had c e r t a i n deformation c h a r a c t e r i s t i c s which were a f u n c t i o n of the i n i t i a l o r i e n t a t i o n , and a l s o the o r i e n t a t i o n i n the fee phase.  Two specimens  were tested i n each c l a s s , and the r e s u l t s always corresponded.  Therefore  i t should be p o s s i b l e to analyse the r e s u l t s i n terms of an o r i e n t a t i o n f a c t o r which i s the r a t i o of the Schmid f a c t o r of the most favourable  (111)  plane to the Schmid f a c t o r of the b a s a l (111) plane. A summary of the previous d e s c r i p t i o n i s given i n Table X I I , where i t i s p o s s i b l e to see that when the basal plane i s the operative primary s l i p plane then no r e c r y s t a l l i z a t i o n or occur.  twin  band formation can  The specimen remains as a s i n g l e c r y s t a l , even when secondary  s l i p occurs.  When the o r i e n t a t i o n f a c t o r l i e s between 1.0 and 1.3  (the  upper l i m i t i s approximate), the probable reason f o r s l i p to occur on the basal (111) plane i s that the transformation occurs on this plane a l s o , and hence the b a s a l (111) plane i s l i k e l y to contain a much higher d i s l o c a t i o n density.  S i m i l a r l y , the massive change i n o r i e n t a t i o n shown i n specimen  S13 must be due to the high d i s l o c a t i o n density on the operative (111) s l i p  108  plane before the specimen was cooled through the transformation f o r examination. strain,  I f the specimen had not been examined u n t i l a higher shear  the same conditions would then have e x i s t e d i n S13 as existed i n  R39 before the f i r s t examination, and the two specimens would have been identical. This complete change i n o r i e n t a t i o n ( b a s i c a l l y a 70° r o t a t i o n about the <110> or <1120> d i r e c t i o n ) does not appear to be connected with twinning, even though the l a r g e twins observed i n specimens S13, and R39 belonged to the b a s a l (111) plane, as i n specimen S13 t h i s twin plane was r e j e c t e d as the transformation plane in:favour of the primary s l i p plane. 4.4.1.  The Nucleation of the Transformation Undeformed c r y s t a l s have a transformation memory, which may,  or may not (according to the o r i e n t a t i o n and temperature l i m i t s ) be retained a f t e r deformation.  There are probably many nucleating s i t e s  i n the l a t t i c e and the three p o s s i b i l i t i e s of operation are: (a) that the majority of the s i t e s are a c t i v e . (b) that i n i t i a l l y few s i t e s are a c t i v e , but that the number of n u c l e i increases as the transformation proceeds. or  (c) that one nucleus grows throughout the whole c r y s t a l . Nucleation and growth probably occurs at stacking f a u l t s which  expand according to the pole mechanism described i n s e c t i o n 1.  Electron (68)  microscope studies by r e p l i c a and t h i n f i l m s on copper-germanium good evidence f o r a pole mechanism i n the fee  gave  hep transformation.  From measurements on shear markings i n the surface i t was concluded  that  r e p l i c a studies were a b e t t e r guide than t h i n f i l m studies when considering  109  the operation of a pole mechanism.  Thin f i l m studies on cobalt  '  '  seemed to support the pole mechanism, but no d i r e c t evidence of a pole d i s l o c a t i o n was  found.  When the two p a r t i a l d i s l o c a t i o n s which r o t a t e i n opposite d i r e c t i o n s around a screw d i s l o c a t i o n are separated by a distance 2c  =  2a/3,  then the a t t r a c t i v e force between them i s at a maximum and  2 has been c a l c u l a t e d at 40 Kg/mm , i . e . almost two orders of magnitude greater than the shear s t r e s s a c t i n g on the d i s l o c a t i o n s .  In order to  (23) overcome t h i s great b a r r i e r , Seeger  suggests that the process must  be dynamic rather than s t a t i c and that the d i s l o c a t i o n s acquire the necessary energy i n k i n e t i c form.  I f so, i t would be expected that the  number of n u c l e i which can a c t u a l l y grow i n the l a t t i c e would be low, but that the density of n u c l e i increases with deformation f a u l t density increases.  Homogeneous deformation  as the stacking  does i n f a c t favour  the transformation by c l o s i n g the h y s t e r e s i s loop, which supports  the  idea that m u l t i p l e n u c l e a t i o n occurs. Nucleation at any p a r t i c u l a r s i t e i s probably a f u n c t i o n of l o c a l thermal gradients i n the l a t t i c e .  Hence, the p a r t i c u l a r s i t e s  at which n u c l e a t i o n takes place should vary from one thermal c y c l e to another.  Several studies of thermal c y c l i n g have been made but no report  has been given on the a c t u a l n u c l e a t i n g s i t e s during the transformation, (27) although Votava  observed a decrease i n the number of stacking f a u l t s  i n the second c y c l e . (13) In i r o n i t has been shown that repeated transformations give r i s e to i d e n t i c a l s t r u c t u r e s of martensite, with the same n u c l e i 3 operating, and that the number of n u c l e i i s i n the order of 10  4 to 10  can  110  per sq. cm.  The observations i n the present study ( l i s t e d below)  i n d i c a t e the the density of n u c l e i i s f a i r l y low (compared to the d i s l o c a t i o n d e n s i t y ) , but that i t increases w i t h 1.  deformation.  I n specimen R27, even w i t h two operative s l i p systems, i t was s t i l l  p o s s i b l e to r e t u r n to a s i n g l e c r y s t a l i n the hep phase, and hence the transformation occurred on the (111) plane on which primary s l i p had taken place. structure.  This coincided with the basal plane of the o r i g i n a l I f there were many n u c l e i some would grow i n regions of high  d i s l o c a t i o n density on the secondary (111) plane, but as no signs of t h i s were observed on X-ray patterns or by o p t i c a l metallography,  i t was  thought that the number of transformation n u c l e i was quite s m a l l . 2.  At higher s t r a i n s i n the same specimen i s o l a t e d areas where a t h i r d  s l i p system operated were observed, and y e t one region of the c r y s t a l contained only one s l i p system. the work hardening  This inhomogeneity did not a f f e c t e i t h e r  curve, or the transformation, except that the spots on  the X-ray pattern grew l a r g e r , and some s p l i t i n t o doublets due to s l i g h t l a t t i c e misorientation.  This observation i n d i c a t e d that more n u c l e i were  operative than i n the p r e v i o u s l y considered example and that the regions of l a t t i c e inhomogeneity gave r i s e to low angle boundaries, not v i s i b l e i n the o p t i c a l microscope. 3.  I n specimens of a d i f f e r e n t o r i e n t a t i o n , r e c r y s t a l l i s a t i o n occurred  e.g. specimen R4 where the basal plane d i d not become the operative fee s l i p plane.  I n t h i s case, transformation n u c l e i on both (111) v a r i a n t s must  have been present and presumably s t a r t e d to grow at the same time, as the r e s u l t a n t g r a i n s i z e i s q u i t e uniform.  The g r a i n s i z e decreased w i t h  Ill  i n c r e a s i n g s t r a i n , i n d i c a t i n g that the number of transformation n u c l e i increased w i t h i n c r e a s i n g d i s l o c a t i o n density. that d i s l o c a t i o n s produced during deformation  Hence i t would appear (on the primary s l i p plane)  were s i m i l a r to those that c o n t r o l l e d the transformation. 4.  The change i n o r i e n t a t i o n of specimen S13 was uniform.  However,  even on the s l i p plane, the d i s l o c a t i o n density i s expected to f l u c t u a t e , and s i m i l a r l y there are l i k e l y to be regions i n the o r i g i n a l transformation plane w i t h a high d i s l o c a t i o n density. The p r o p o r t i o n of n u c l e i on each plane should depend on the amount of deformation.  Hence, a f t e r a shear s t r a i n 0.5 < y < 0.8,  the  d i s l o c a t i o n density i n the primary s l i p plane must be high enough to operate the transformation. I f the number of transformation n u c l e i was p r o p o r t i o n a l to the number of areas of high d i s l o c a t i o n density, then i f the number of n u c l e i was high, i t i s almost c e r t a i n that n u c l e i would also operate  on  the o r i g i n a l transformation plane, and give r i s e to a p o i y e r y s t a l l i n e aggregate.  In four specimens t e s t e d , the r e s u l t s always showed complete  transformation to a s i n g l e c r y s t a l hence i t was  concluded  that the number  of transformation n u c l e i was much smaller than the number of d i s l o c a t i o n i n t e r s e c t i o n s , but increased w i t h i n c r e a s i n g stacking f a u l t density . 4.4.2.  S l i p Studies When only one s l i p plane i s i n operation, the appearance of the  Measurements made on photographs by Bollman and Drapier et a l show that the number of stacking f a u l t i n t e r s e c t i o n s l i e s between 10 and 10 /sq. cm. 9  s l i p l i n e s under the e l e c t r o n microscope at low s t r a i n s i s very s i m i l a r to the hep  studies even though the work hardening rate i s very much higher.  higher s t r a i n s the s l i p tends to bunch together.  The o p t i c a l  At  micrographs  show,however,that the s l i p l i n e s are more wavy and considerably s h o r t e r . In Table X measurements on the s l i p l i n e s of specimens S13, R4, R27,  R39  and R70 are given, and c a l c u l a t i o n s have been made to f i n d approximately the s l i p step height and the s l i p l i n e length.  In most of the specimens,  the spacing between the s l i p bands i s about constant, or decreases with increasing s t r a i n .  slightly  The average displacement due to one s l i p step  seems to increase w i t h s t r a i n , although there i s a large d i f f e r e n c e between say the values of x (the s l i p displacement)- i n specimens S13 and  R4.  A s i m i l a r a n a l y s i s f o r Ni-Co a l l o y s (which are fee at room (42) temperature) i s given by Mader  .  The three stages of work hardening are  characterised by the s l i p l i n e appearance.  In stage I homogeneous f i n e  s l i p i s observed, and once easy g l i d e i s f u l l y developed, the number of a c t i v e s l i p l i n e s does not increase.  The s l i p l i n e length i s constant  and the s l i p step height increases with s t r a i n .  In stage I I s l i p i s  s t i l l homogeneous, but some s l i p bands are stronger.  Less than 10% of  e x i s t i n g s l i p steps increase i n s i z e and most s l i p takes place i n new planes.  In stage I I I i s o l a t e d cases of cross s l i p are observed, and the  s l i p l i n e s c l u s t e r to form s l i p bands. Observations i n t h i n f i l m s of Ni-Co a l l o y s are a l s o described. The most s t r i k i n g feature i s the predominance of edge d i s l o c a t i o n s , i n b r a i d s w i t h a <110>  Burgers vector.  network of d i s l o c a t i o n tangles.  arranged  Previous reports had shown a random  This i s explained by the o r i e n t a t i o n , i . e .  the plane of the f o i l s being p a r a l l e l to the g l i d e plane whereas others had used p o l y c r y s t a l l i n e specimens w i t h random o r i e n t a t i o n of the f o i l s .  As work  113  hardening it  t h e o r i e s p r e d i c t a h i g h e r p r o p o r t i o n o f screw d i s l o c a t i o n s  i s concluded  t h a t some d i s l o c a t i o n rearrangement o c c u r r e d i n the  p r e p a r a t i o n o f the f o i l . wide.  then  I n s t a g e I the b r a i d s a r e about 2y l o n g ,  D i s l o c a t i o n t a n g l e s a r e seen and t h e r e i s  0.3y  evidence o f p i l e - u p s .  The  d i s l o c a t i o n d e n s i t y i n c r e a s e s i n s t a g e I I I , b u t the b r a i d s a r e s m a l l e r ,  and  t a n g l e s i n a c e l l u l a r - t y p e s t r u c t u r e have been observed.  concluded in  t h a t t h i n f i l m o b s e r v a t i o n s a r e compatible w i t h s l i p  It is studies  replicas.  The  data f o r stage I I hardening  i n some f e e metals  - (Table XIII)  (42) is  reproduced  from  the a r t i c l e by Mader  .  The l e n g t h parameter A i s a  c o n s t a n t d e r i v e d from t h e r e l a t i o n s h i p between s l i p  l i n e l e n g t h L and shear  s t r a i n y. L  I t i s presumed t h a t the s l i p  = A  Y l i n e h e i g h t , n, i s c o n s t a n t w i t h  s t r a i n , which would be expected  increasing  i n Seeger's theory o f work h a r d e n i n g .  In  (53) f a c t Seeger e t a l  used  these v a l u e s to c a l c u l a t e  t h e o r e t i c a l v a l u e s of 8-rj.  and  these a r e a l s o i n c l u d e d i n T a b l e X I I I , t o g e t h e r w i t h the measured v a l u e s .  The  agreement i s e x c e l l e n t . 6  The same  G  can be used  formula,  q Jnb 2TT 43A  II  f o r the c a l c u l a t i o n o f Q-J--J-/G f °  a i s a geometric  r  c o b a l t , i f a i s assumed to be  c o n s t a n t w i t h v a l u e s between 0.8  and 0.9  0.85.  f o r a l l fee metals.  -4 For low s t r a i n s  (y  < 0.4)  the average v a l u e f o r s l i p b = 2.5 A °  the average v a l u e o f A(= L.y) i s 66 x 10 displacement  i s 0.05p.  the t h e o r e t i c a l v a l u e o f Q J J / G i s 1.79  v a l u e i s 2.0 x 10  _3  .  Again  the agreement i s v e r y  Therefore n x 10 close.  cm. and  = 139.  If  , and the e x p e r i m e n t a l  114  TABLE X I I I DATA ON STAGE I I HARDENING  Temperature of deformation C  Ni  Ni+ 20% Co  Ni+ 40% Co  Ni+ 50% Co  Cu  Co  -183  20  20  60  20  500  31  32  25  15  20  139  S l i p l i n e height i n atomic distance, n s l i p step (A ) Burgers Vector (A°)  5.9  Length parameter on top surface A, 10~4 cm. 9  T T  6.2  6.5  4  6  66  (theoretical) Kg/mm  21  21  20  17.2  12  12.1  (experimental) Kg/mm  23  23  23  21  13.5  11.3  2  I t has already been shown ( F i g . 33) that most fee metals with a value of about 1/300.  G-r-r/C;  i s constant f o r  The reason that cobalt has  a lower value could be that the distance Ro between the d i s l o c a t i o n sources may be greater i n c o b a l t . of a d i s l o c a t i o n loop  The maximum opposing s t r e s s to the expansion  occurs when the distance moved i s Ro.  I t i s caused by an  opposing loop on a p a r a l l e l g l i d e plane separated by a distance of Ro. nbG T  G  =  01  " 2TTRO  I f i n f a c t the transformation on heating i s accompanied by the formation of (16)  vacancies as postulated by Adams and A l t s t e t t e r e x p l a i n why  e I T  /  G  then i t i s d i f f i c u l t to  should be lower than i n other fee metals.  the d i s l o c a t i o n density n should be higher, and therefore x higher.  I f anything, G  would a l s o be  115  The d i f f e r e n c e cannot be accounted f o r by the number of a c t i v e s l i p systems, as F i g . 29 shows that at a given temperature the work hardening  slope when two s l i p systems operated was only 12% greater than  when one s l i p system predominated.  Hence the lower work hardening rate i n  cobalt must be due to some feature of the transformation, which must i n turn reduce the number of defects i n the l a t t i c e .  The higher enthalpy of 113  cal/mole on heating might therefore be due to the removal of  lattice  defects rather than t h e i r c r e a t i o n , as a s i m i l a r energy term would be required for e i t h e r .  In high p u r i t y m a t e r i a l then, i t i s p o s s i b l e that the number  of obstacles to deformation w i l l be reduced by the transformation, and i t i s a l s o a p o s s i b i l i t y that transformation d i s l o c a t i o n s do not contribute to the work hardening.  Three ways of studying the r e l a t i o n between applied  s t r e s s and the transformation have been attempted. (i) (ii)  The e f f e c t of deformation i n e i t h e r phase on the transformation, The e f f e c t of deformation i n one phase on the deformation  behaviour  i n the other, and (iii)  The e f f e c t of thermally c y c l i n g a specimen through the transformation w h i l e a t e n s i l e s t r e s s i s continuously applied.  The r e s u l t s w i l l be described i n Section 5.  116  5.  Specimens Deformed i n both the hep and the fee Phase In Section 4 i t was shown that the specimen o r i e n t a t i o n played  some part i n the deformation temperature.  c h a r a c t e r i s t i c s above the transformation  This was mainly a t t r i b u t e d to the transformation taking  place on the (111) plane which contained the higher d i s l o c a t i o n density. Several experiments w i l l be described i n t h i s s e c t i o n i n which specimens were subject to deformation above and below the transformation, i n order that the c r y s t a l l o g r a p h i c s t a b i l i t y could be examined more c l o s e l y . 5.1.  P r e s t r a i n i n hep, followed by Deformation i n fee Specimens of o r i e n t a t i o n f a c t o r 1.7  (type D i n Table XII) were  given varying degrees of p r e s t r a i n at 20°C or 350°C, followed by an extens i v e amount of deformation at 480°C. The o r i e n t a t i o n s of a l l specimens used i n t h i s  examination  were very c l o s e to each other, and are given i n Table XIV.  A f t e r the  deformation i n the hep phase, each specimen was examined under the o p t i c a l microscope, and i n each case, as expected, s l i p l i n e s were seen on only one system, and the back r e f l e c t i o n patterns were c l e a r spots.  Although  evidence of twinning was o c c a s i o n a l l y detected on the load-extension chart, no twins were seen w i t h the o p t i c a l microscope. not taken of the surfaces.  Replicas were  The specimens were then a l l deformed to  f r a c t u r e at 480°C and subsequent examination showed that the f i n a l s t r u c t u r e was q u i t e dependent on the amount of deformation i n the hep phase. (a)  Y  hcp = 0.075 There were 2 s l i p systems operating i n the fee phase although  TABLE XIV Behaviour of specimens deformed i n fee Phase a f t e r p r e s t r a l n i n hep Phase  >pecimen No.  Test Temp. i n hep phase  Prestrain hep X *  112 110  20 350  0.110 0.075  19 40 50  113 111  20 350  0.180 0.130  18 42 51  114 116  20 350  0.330 0.345  18 43 50  115 118  20 350  0.610 0.530  18 45 50  *  *  *  Orientation,in fee phase A Schmid Factor  Orientation Factor  Number of Slip Systems ( 2 )  X-ray P a t t e r n after Fracture  30 40 54  0.282 0.492 0.450  1.75  2  Rings  26 43 53  0.288 0.490 0.467  1.70  2  Rings  37 44 52  0.247 0.490 0.472  1.97  1  Rings + Spots  26 45 51  0.278 0.500 0.481  1.80  1  Streaked Spots  Basal plane i n hep phase. (1.)Calculated a f t e r taking measurements on s l i p l i n e s formed during the i n i t i a l stages of the fee deformation. (2.).A small amount of a t h i r d s l i p system was observed i n specimen 110, and small areas of a second s l i p system were observed i n specimens 114 and 116.  118 specimen 110 contained areas w i t h three s l i p systems.  P a r a l l e l to the  o r i g i n a l b a s a l plane, large bands had formed, very s i m i l a r i n appearance to those i n F i g . 39 (d).  The X-ray back r e f l e c t i o n pattern consisted  of almost continuous r i n g s , and i s shown i n F i g . 42 A. (b)  Y  hcp =  0.13 Two s l i p systems were o p e r a t i v e , and most of the deformation  occurred on the new primary s l i p plane (the (111) plane w i t h the highest Schmid f a c t o r ) .  I t could not be estimated whether or not f u r t h e r  deformation had occurred on the o r i g i n a l b a s a l s l i p plane but the metallographic appearance was again s i m i l a r to a specimen deformed i n the fee phase without hep p r e s t r a i n .  The X-ray back r e f l e c t i o n p a t t e r n  consisted of arcs of r i n g s and i s shown i n F i g . 42 (c)  Y  B.  h c p = 0.345 When the hep p r e s t r a i n i s increased from 0.13  to 0.345, the  subsequent behaviour i n the fee phase i s changed considerably.  The  deformation at 480°C had taken place almost e n t i r e l y by s l i p occurring on the o r i g i n a l b a s a l plane, even though i n these specimens, the o r i e n t a t i o n f a c t o r was very high (1.97). a l s o observed.  S l i p on a secondary  (111) system was  The X-ray back r e f l e c t i o n p a t t e r n now consisted of a  mixture of spots and s m a l l arcs of Debye r i n g s , and i s shown i n F i g . 42 C. (d)  Y  h c p =0.53 A f t e r f r a c t u r e at a shear s t r a i n of 2.12, only one s l i p system  was observed.  Hence the deformation i n the fee phase must have taken  place on the s l i p plane which operated i n the hep phase, i . e . the basal plane. With an o r i e n t a t i o n f a c t o r of 1.8 i t was not expected that these specimens would  F i g . 42  X-ray back r e f l e c t i o n patterns of specimens deformed i n the fee phase at 480°C a f t e r a p r e s t r a i n i n the hep phase at 350°C. A specimen 110 ^hep =0.057 B specimen 111 ^hep =0.13 C specimen 116 Yhcp = 0. 345 D specimen 118 ^hep =0.53 As d i r e c t p r i n t i n g of the films d i d not give a very c l e a r p i c t u r e , the patterns were traced f o r reproduction.  120 s l i p on the transformed b a s a l plane. only spots ( F i g . 42  The back r e f l e c t i o n pattern showed  D ) , and although the spots were large and s l i g h t l y  streaked, they were e a s i l y used to o r i e n t a t e the c r y s t a l . The resolved shear stress-shear s t r a i n curves f o r specimens 110,111, 116 and 118 are shown i n F i g . 43.  A l l these specimens were  hep p r e s t r a i n e d at 350°C, and t h i s p a r t of the curve i s c a l c u l a t e d f o r the basal plane being the operative s l i p plane.  Above the transformation  temperature specimens 110 and 111 deformed with d i f f e r e n t primary  slip  planes and therefore f o r these specimens d i f f e r e n t values of x and A were used.  The metallographic observations showed that specimens 116  and  118 deformed p r i m a r i l y on one s l i p system above the transformation whereas specimens .110 and 111 deformed on two. hardening  Differences i n the work  r a t e may be observed i n F i g . 43 and are summarised i n Table XV. When the amount of hep p r e s t r a i n i s low, the shape of the  T - y curve i s s i m i l a r to that of say specimen R39 s e c t i o n 4, f o r which the curve i s s i m i l a r to 490  (already described i n A  F i g . 29) but at  higher amounts of hep p r e s t r a i n the fee deformation curve has a much lower work hardening ductility.  r a t e , a lower flow s t r e s s at f r a c t u r e , and a higher  The d u c t i l i t y i s i n f a c t higher than i n specimens such as  R70 where the b a s a l (111) plane i s the favourable s l i p plane.  The most  important e f f e c t of p r e s t r a i n i n g i n the hep phase, however, i s the v a r i a t i o n of the work hardening  rate i n stage I I of the fee deformation.  0^  is  about 100 times greater than the work hardening rate i n the easy g l i d e region of the hep phase (9^).  However, a f t e r p r e s t r a i n i n g only 7.5%  the  r a t i o i s reduced to 80, and i t decreases w i t h i n c r e a s i n g p r e s t r a i n i n g to about 17 at a p r e s t r a i n of 53%.  This w i l l be discussed l a t e r with reference  TABLE XV  Specimen Number  I n i t i a l Work Hardening Rate (x 10-3)  Flow Stress and Work Hardening Parameters of fee Deformation of Specimens prestrained i n the hep Phase  112  110  113  111  114  116  115  118  2.56  2.18  2.08  1.98  1.02  0.89  0.59  0.64  0.441  0.364  0.385  0.294  0.271  0.206  0.202  0.156  F i n a l Work Hardening Rate  Q /G (x 10-3) 1Z1  p • " Ratio 9  / /  G  84  G  74  60  66  34  28  18  22  A Total Shear S t r a i n i n fee at fracture  1.18  1.35  1.24  1.41  1.80  1.92  2.15  1.99  Flow Stress at end of hep deformation. xh, Kg/mm  0.84  0.48  0.91  0.50  0.98  0.68  1.1  0.65  Flow Stress at beginning of fee deformation Kg/mm  0.90  0.45  0.92  0.52  0.86  0.61  1.02  0.63  fee Flow Stress ^ 27, o f f s e t x , Kg/mm  1.01  0.57  1.00  0.575  1.08  0.65  1.17  0.70  1.21  1.19  1.10  1.15  1.10  0.95  1.06  1.08  2  2  c  Latent Hardening Ratio =  T /T c  h  to F i g . 57. The flow s t r e s s i n both phases i s about the same, so a specimen p r e s t r a i n e d a t 20°C has a higher i n i t i a l flow s t r e s s i n the fee phase than a specimen p r e s t r a i n e d the same amount at 350°C. comparison i s given i n Table XV.  A  Also shown i n Table XV are values  of the l a t e n t hardening r a t i o which i s defined as the r a t i o of the i n i t i a l flow s t r e s s i n the cubic phase, to the f i n a l flow stress i n the hexagonal phase, i . e . LHR = xc/xh. As the y i e l d stress i n the fee phase i s d i f f i c u l t to determine, a 2% o f f s e t y i e l d has been used i n a l l c a l c u l a t i o n s .  I t can be seen  that the LHR decreases w i t h i n c r e a s i n g p r e s t r a i n and the s i g n i f i c a n c e of these measurements w i l l be discussed l a t e r . In a l l cases, the behaviour of specimens which were hep p r e s t r a i n e d equal amounts at d i f f e r e n t temperatures ( e i t h e r 20°C or 350°C) showed the same e f f e c t on the subsequent fee deformation.  Therefore i t  i s not l i k e l y that recovery occurred by rearrangement of the d i s l o c a t i o n s t r u c t u r e below the transformation temperature. the transformation temperature,  When heated to above  a l l specimens were subject to the same  temperature^and the time i n the furnace was a l s o c o n t r o l l e d .  Therefore  any annealing which could have occurred during the heating stagershould have had more e f f e c t on the specimens containing the highest d i s l o c a t i o n density, i . e . the ones which had been subjected to the greater shear strains.  I f t h i s had been the case then there i s no reason why the  basal (111) plane should continue to operate.  124  5.2  Annealing  Experiments  T h e r e f o r e , i n o r d e r to a s s e s s the p o s s i b i l i t y d u r i n g these experiments  a second  whereby specimens were g i v e n hep  of r e c o v e r y  s e r i e s of experiments were performed p r e s t r a i n s Yp °f e i t h e r about  0.20  or  0.65, and then g i v e n an a n n e a l a t e i t h e r 20°C, 350°C, 400°C or 480°C 480°C.  b e f o r e b e i n g deformed a t  Some t y p i c a l r e s o l v e d shear s t r e s s - s h e a r s t r a i n curves shown i n F i g . 44,  and i n comparison  were not annealed  ( F i g . 43)  to the t e s t s on specimens which  i t appears  a marked e f f e c t as the amount of hep those annealed in  at  t h a t a n n e a l i n g does not have such  prestrain.  A l l the curves  The i n i t i a l p a r t where the work hardening r a t e i s  i n c r e a s i n g with i n c r e a s i n g s t r a i n i s designated stage I I . s t a g e , which i s c l o s e l y  l i n e a r , i s d e s i g n a t e d stage I I I .  The The  slope i n stage I I , 9 ^  decreases w i t h i n c r e a s i n g p r e s t r a i n , and  a n n e a l i n g temperature,  and i n F i g . 44  s l o p e i n stage I I I , QJ-J-J-  (d) i s approximately  The maximum s l o p e i n stage I I  w i t h i n c r e a s i n g p r e s t r a i n but i s independent  schematic  prestrain.  final initial increasing  e q u a l to the (©"-r-r)  decreases  of a n n e a l i n g temperature  for  An e x p l a n a t i o n o f the symbols i s g i v e n i n the  c u r v e , F i g . 45.  From T a b l e X V I i t can be v e r i f i e d temperature  has  temperature  is  t h a t the a c t u a l a n n e a l i n g  some e f f e c t on the work h a r d e n i n g .  When the a n n e a l i n g  20°C the curves are very s i m i l a r to those f o r specimens  which had not been annealed, e.g. a n n e a l i n g temperature curve now  (except  20°C F i g , 44 (b)) show d i s t i n c t l y 2 stages of h a r d e n i n g  the f e e r e g i o n .  a g i v e n hep  are  of  shows the two  compare F i g s . 43 and 44  (a).  At  an  360°C t h e r e i s some e f f e c t , i . e . the fee x - y d e f i n i t e s t a g e s , see F i g . 44  ( b ) , but on t h i s  graph  F i g . 44  x - y curves f o r specimens hep p r e s t r a i n e d , annealed and deformed a t 480°C  125  T  Kg/mm  0.2  0.4  0.6  0.8  1.0  1.2  1.4 Y  F i g . 44 (b)  P r e s t r a i n and a n n e a l . a t 360°C.  127  F i g . 45  Schematic curve showing the stages of the work hardening curve from F i g . 44.  TABLE XVI  hep P r e s t r a i n Temp. Y  Spec.  °c"  Flow S t r e s s and Work H a r d e n i n g Parameters o f Specimens P r e s t r a i n e d i u hep Phase, then a n n e a l e d , b e f o r e f e e d e f o r m a t i o n a t 480°C  Anneal Temp. Time °C hrs  140  0.10  400  483  3  141  0.49  400  482  3  143  0.16  402  402  12  145  0.57  400  400  148  0.99  403  149  1.30  129  No. o f s l i p sys terns after fee  a' 9  A "  II G  9  II G  9  LIIR  III G  0.47  0.38  0.44  0.57xl0  0.56  0.51  0.55  0.48  1.81  0.40  0.98  2  0.52  0.51  0.57  1.45  2.20  0.74  1.1  12  2  0.59  0.55  0.57  1.36  2.03  0.27  0.97  403  12  ,(1)  0.65  0.66  0.67  1.00  1.57  0 .185  1.02  402  402  12  l (  l)  0.65  0.57  0.59  0.50  1.36  0.102  0.91  0.25  360  360  24  2  0 .68  0.77  0.80  1.82  2.43  1.09  1.16  125  0.66  360  360  24  0.72  0.76  0.79  1.78  2.26  0.495  1.09  142  0.22  20  20  72  2  0 .96  0 .95  1.21  2.82  -  0.435  1.25  147  0.60  20  20  72  1  0.93  0.92  1.07  1.92  -  0.296  1.15  (1) (2) (3)  1  Flow S t r e s s Kg/mm end o f beg. o f 2% hep fee offset fee  ( 1 )  ,(2)  ,(3)  _ 3  2.01xl0~  3  0.73xl0~  3  0.94  With a second s l i p system o c c u r r i n g o c c a s i o n a l l y throughout gauge l e n g t h . Second s l i p system seen near f r a c t u r e . Two secondary systems observed t o a s m a l l e x t e n t .  OO  129  i t can be seen t h a t t h e amount o f hep p r e s t r a i n has a l a r g e e f f e c t on the s l o p e s  ®'n»  ^"il  an<  i n c r e a s i n g hep p r e s t r a i n .  * ^ I I I ' "*"^ °^ ^ i a  w  c n  a  r  e  reduced w i t h  F i g s . 44 (b) and 44 (c) show t h a t when b o t h  the hep p r e s t r a i n temperature and t h e a n n e a l i n g temperature a r e r a i s e d from 360°C t o 400°C then 6 ' ^ and  i s s l i g h t l y d e c r e a s e d , 9"  i s unaffected  i s also unaffected.  T h i s i s i n t e r e s t i n g when compared t o the r e s u l t s o f t e n s i l e t e s t s g i v e n i n s e c t i o n 3.  R e f e r r i n g t o F i g . 5 i t would appear  that  between 350°C and 420°C the t e s t i n g temperature has a l a r g e e f f e c t on the c r i t i c a l r e s o l v e d s h e a r s t r e s s , and t h e r e f o r e i t i s presumed t h a t some r e c o v e r y p r o c e s s i s o c c u r r i n g i n t h i s range.  I f dynamic r e c o v e r y  o c c u r s a t say 400°C, i t must be a temperature dependent  c o n t r i b u t i o n to  the f l o w s t r e s s , and i t might then be e x p e c t e d t h a t i f t h e specimen was annealed a t t h e same temperature complete r e c o v e r y would t a k e p l a c e . Hence t h e specimen would then deform i n t h e f e e phase i n a comparable manner w i t h specimen R39 w h i c h had n o t been p r e s t r a i n e d i n t h e hep phase. But t h i s i s n o t s o , and hence t h e r e c o v e r y w h i c h takes p l a c e on a n n e a l i n g i s n o t t h e same as t h a t w h i c h o p e r a t e s under t h e c o n t i n u o u s a p p l i c a t i o n of s t r e s s d u r i n g t h e a c t u a l t e n s i l e  test.  The v a r i a t i o n o f the work h a r d e n i n g r a t e w i t h temperature ( F i g . 6) shows t h a t over t h e same temperature range, 9^/G decreases by about 30% and so t h e same d e c r e a s e i n t h e work h a r d e n i n g r a t e might be expected i n t h e fee region.  I n f a c t the decrease i n 9  1  i s o f t h e same o r d e r .  When t h e a n n e a l i n g temperature ( o f a specimen ores t r a i n e d a t 400°C) i s i n c r e a s e d from 400°C t o 480°C, t h e d i f f e r e n c e s between the v a r i o u s s t a g e s of the f e e d e f o r m a t i o n become more e x a g g e r a t e d .  F i g . 44 (d) shows t h r e e -  130  stage curves as Q'-J-J i s lower than i n the corresponding 400°C anneal (Fig. 44 ( c ) ) .  The s t r e s s at which stage I I I commences increases w i t h  i n c r e a s i n g annealing temperature up to 400°C, but i s lower f o r the 480°C anneal. Also included i n F i g . 44 (d) i s the T - y curve f o r specimen 146.  The hep p r e s t r a i n was 0.1 at a temperature of 400°C, and t h i s was  followed by an anneal at 602°C f o r 1 hour before the specimen was deformed at 602°C.  In comparison to specimen 140, annealed and deformed  at 480°C, the higher temperature causes a decrease i n ^'J-J- and 0jj-]->  D U t  9"^^ i s about the same. 5.2.1.  A Summary of the E f f e c t of Annealing on the Work Hardening  Parameters  R e f e r r i n g to F i g . 45: (a)  For a given annealing temperature T , then as y increases, A p decreases, © " J J decreases,  decreases  i s constant, Y J J J - increases T ' ^ J i s constant, T " J ^ i s constant and  Yjj.  (b)  increases s l i g h t l y  For a given y^ (i)  I f y^ i s high enough f o r the basal/(111) s l i p plane to operate i n the fee phase, then as T^ increases G'JJ. decreases, 0" Yj  II  i s constant, QJJ-J- i s constant  i s constant, Y J J J increases i s constant, T^.^ i s constant  131 (ii)  I f Yp  i s low  and  the primary  of h i g h e s t Schmid f a c t o r ,  9  II  Y II  decreases,  9  increases,  y  and  x  decrease  5.2.2  The  III  constant, 9  is  constant  plane i s the  (111)  plane  increases III  decreases  slightly  to the t r a n s f o r m a t i o n temperature,  but  temperatures.  Latent Hardening  t h e hep  t h e n as T  is  i n c r e a s e up  at higher  As in  III  II  II  fee s l i p  Effect  i n t h e t e s t s d e s c r i b e d i n s e c t i o n 5.1  p h a s e b e f o r e t h e l o a d was  r e m o v e d was  the flow  stress  a b o u t t h e same as  the  y i e l d p o i n t of the fee phase a f t e r a n n e a l i n g , i . e . the a n n e a l i n g  probably  did not a f f e c t  stress.  The  the d i s l o c a t i o n s t r u c t u r e w h i c h c o n t r o l s the f l o w  actual values  f o r t h e hep  and  E v e n f o r a s m a l l amount o f hep with  prestrain,  b u t must be  due  d e f o r m a t i o n , and  stress during a straight  480°C ( s e e s e c t i o n 4 ) . t o t h e hep  The  reason  a r e shown i n T a b l e  tensile  In both Tables  stress. not vary  The  i n hep  former  has  deformation). a value very  c o n s i s t e n t l y w i t h hep  The  XV  calculated  of the l i n e a r p o r t i o n of the x - Y curve back to Y f Q  t e s t deformed  f o r this behaviour  v a l u e s o f t h e f e e f l o w s t r e s s a r e g i v e n , one  of x  i s much  column of Table XVI,  as i n s e c t i o n 5.1  at  i s not  = c c  and  clear  XVI  s t r a i n or temperature  the l a t e n t hardening  i s d e f i n e d as  x /x^. c  two  0 (similar  o t h e r i s a 27. o f f s e t  c l o s e t o t h e hep  ratio  the  from the e x t r a p o l a t i o n to  does  of deformation  i s shown.  Broadly speaking,  the  yield  s t r e s s , and  H o w e v e r , t h e 2% o f f s e t y i e l d d o e s show some r e l a t i o n s h i p , and last  lower  d e f o r m a t i o n , w h i c h i n t u r n must s t a b i l i s e  s t r u c t u r e d u r i n g the t r a n s f o r m a t i o n .  computation  XVI.  the fee f l o w s t r e s s f o l l o w s  t h e same v a l u e as o b t a i n e d i n t h e hep  than the fee y i e l d say  fee flow stress  etc.  i n the This,  t h e LHR  decreases  132  w i t h a n n e a l i n g temperature f o r a g i v e n hep p r e s t r a i n , and f o r a g i v e n a n n e a l i n g temperature LHR decreases w i t h i n c r e a s i n g  p r e s t r a i n , except a t  h i g h t e m p e r a t u r e s , when i t remains c o n s t a n t . The v a r i a t i o n o f LHR w i t h hep p r e s t r a i n i s shown i n F i g . 46 f o r specimens  b o t h annealed a t 400°C and not annealed b e f o r e the f e e  deformation. Y, = hep 5.3.  The LHR  decreases to a c o n s t a n t v a l u e of about 1 a t about  0.6. Comparison  between an Annealed Specimen and a Non-Annealed Specimen  Comparing an annealed specimen  to one not a n n e a l e d , the f l o w  s t r e s s of the former reaches a h i g h e r v a l u e , due m a i n l y to the h a r d e n i n g i n stage I I " .  T h i s i n c r e a s e i n s t r e n g t h due to the a n n e a l i n g p r o c e s s  i s an anomaly and must a r i s e from the rearrangement  of the  dislocations  d u r i n g the a n n e a l i n g i n a s i m i l a r manner t o the s t r a i n a g i n g e f f e c t discussed i n section  3.  As a room temperature a n n e a l does not have much  e f f e c t on the subsequent b e h a v i o u r then i t would appear t h a t the r e c o v e r y temperature i s a p p r o a c h i n g 350°C, as the e f f e c t a t 400°C i s more The most l i k e l y  s o l u t i o n i s t h a t the b a s a l d i s l o c a t i o n s  t h a t a network of d i s l o c a t i o n s may  act  are " l o c k e d " o r  i s formed d u r i n g a n n e a l i n g e i t h e r of which  as o b s t a c l e s t o the moving d i s l o c a t i o n s  a certain stress  pronounced.  on the s l i p p l a n e .  At  (which depends on the a n n e a l i n g temperature) the b a r r i e r s  to d i s l o c a t i o n movement a r e b r o k e n or c i r c u m n a v i g a t e d by a dynamic r e c o v e r y p r o c e s s and s t a g e I I I commences. I t would be e x p e c t e d t h a t a f t e r a low hep p r e s t r a i n , where two s l i p systems  o p e r a t e ( p r o b a b l y because the d i s l o c a t i o n d e n s i t y on the b a s a l  p l a n e i s too low) a h i g h work h a r d e n i n g r a t e would r e s u l t due to i n t e r s e c t i o n mechanisms o p e r a t i n g .  T h i s has been found, p a r t i c u l a r l y i n specimens  not  134 annealed. 5.3.1.  Metallographic Examination Although a b r i e f d e s c r i p t i o n of the metallography has been  given, and summarised i n Table XIV and XVI, three specimens w i l l be used as examples to i n d i c a t e more c l e a r l y the differences between the annealed and non-annealed specimens. Specimen 118 —  Y, fee  c  1  Fig.  The hep p r e s t r a i n i n each case was about  0.6.  =1.55  47 (a) shows that one s l i p system operated the same as  observed at the end of the hep deformation.  The r e p l i c a 47 (b) also  contained only one s l i p system, and the s l i p l i n e s were long and s t r a i g h t , very s i m i l a r to those observed i n specimens deformed only i n the hep phase, see s e c t i o n 3. Specimen 145 — c  Y, =0,66 ' fee Fig.  48 (a) shows that a f t e r a smaller amount of deformation  i n the fee phase the primary s l i p l i n e s i n specimen 145 were coarse, and grouped i n t o bands.  They were also shorter than those i n specimen 118.  A small amount of secondary s l i p may a l s o be seen, and i t was stronger i n other parts of the c r y s t a l . (Fig.  48 (b)) compared to the primary s l i p l i n e s which are very broad.  Specimen 125 — c  In the r e p l i c a , secondary s l i p was very f i n e ,  Y  fee  =0.75  One s l i p system was observed throughout the gauge length, and occasional areas of secondary s l i p were also observed, see F i g . 49 ( a ) . This l o c a l i s e d s l i p formation must be due to some inhomogeneity i n the  Fig. 48 (a) X650.  137 c r y s t a l , and has a s i m i l a r shape and d i s t r i b u t i o n to the l e n t i c u l a r twins discussed i n s e c t i o n 3.  However, there was no evidence of twinning,  e i t h e r on the load-elongation curve, or i n the r e p l i c a s .  A t y p i c a l area  at high m a g n i f i c a t i o n i s shown i n F i g . 49 (b) and the s l i p l i n e s were again coarser than i n specimen 118. Specimen 143  Y, =0.16, hep  v. =0.86 'fee  As a comparison, F i g . 50 i s a r e p l i c a of specimen 143, where the hep p r e s t r a i n was low.  I t i s thought that the heavy, s t r a i g h t traces  were formed during the fee deformation.and were a r e s u l t of the hep deformation.  that the f i n e r , fragmented traces  In s e v e r a l instances, i n d i c a t i o n s  c r o s s - s l i p are present, and displacements at the major s l i p l i n e s  of  indicate  that these traces were present i n i t i a l l y . In general, the s l i p l i n e s on the primary s l i p system i n annealed specimens appear very coarse and banded, even at high hep  prestrain  when the transformed basal plane continues as the primary s l i p plane i n the fee phase. prestrain  However, i n non-annealed specimens with a high hep  the s l i p l i n e s are long and s t r a i g h t and much f i n e r , and i t seems  probable i n t h i s case that the fee deformation i s a continuation of the hep deformation, almost unaffected by the transformation. Hence, one of the questions to be answered i s , why 2 i n the fee phase (~  i s the CRSS  1.5 Kg/mm ) so much higher than the flow s t r e s s at  the beginning of fee deformation i n a specimen which has been hep pre-strained? Although the problem has not been solved, some headway has been mady by experiments  conducted on specimens cycled through the transformation.  138  5.4.  T e n s i l e tests on specimens thermally cycled between 350°C and 470°C  5.4.1.  I n t e r m i t t e n t l y Deformed Two specimens (or o r i e n t a t i o n f a c t o r 1.0 (specimen R57) and  1.5 (specimen R64)) were cycled through the transformation from a s t a r t i n g temperature e i t h e r ( i ) above or ( i i ) below the transformation. 5.4.1.1.  Tests s t a r t i n g above the transformation Specimens were heated to 490°C, deformed a few percent,  then with the load removed the temperature was reduced to 460°C, and the t e n s i l e load was reapplied.  This operation was repeated f o r  various temperatures down to 360°C and the r e s u l t i n g t e n s i l e curves are shown i n F i g . 51. In Specimen 64, the work hardening slope i n the fee phase -3 -5 ( 6 / G = 1.93 x 10 ) i s about 60 times that i n the hep phase (© /G = 3.1 x 10 ), IT  A  which means that  despite  the high work hardening rate i n the fee phase,  the hep phase s t i l l deforms i n stage A and therefore previous deformation i n the fee phase does not a f f e c t the work hardening rate i n the hep phase. In specimen R57 the r a t i o i s about 4 0 .  But i n both cases the stress i n the  hep phase depends on the s t r a i n and therefore the flow s t r e s s i n the fee phase, 2 i . e . a f t e r about y = 0.7 the shear s t r e s s T = 2.20 Kg/mm , which i s very much higher than i s achieved by t e n s i l e deformation i n the hep phase.  The f i n a l  s e c t i o n was taken at 460°C to show there i s a considerable d i f f e r e n c e from the previous stage at 350°C.  A f t e r deformation the specimens were examined,  and i n one case two s l i p systems were seen (when the o r i e n t a t i o n f a c t o r was 1.45).  I t i s suspected (from the work hardening rate) that only one s l i p system  operated during the hep phase even when the previous deformation had been on a  140  d i f f e r e n t s l i p system, but t h i s was not v e r i f i e d . 5.4.1.2.  Tests s t a r t i n g below the transformation Specimens R63 ( o r i e n t a t i o n f a c t o r 1.0) and R67 ( o r i e n t a t i o n  f a c t o r 1.5) were heated to 370°C and given a small amount of s t r a i n , then w i t h the load removed the temperature was r a i s e d to 390°C, and a f u r t h e r deformation was imposed.  This operation was repeated a t  i n c r e a s i n g temperature through the transformation, and down again. The r e s u l t i n g T - y curve f o r specimen R67 i s shown i n F i g . 52. The work hardening rate i n the fee phase (Qj^/G = 5.0 x 10 ) i s 21 4  times higher than i n the hep phase (where 9^/G = 2.3 x 10 "*), and again the flow s t r e s s i n the hep phase depends on the deformation history.  Likewise, the flow s t r e s s a t the end of the transformation  (about 430°C on t h i s curve) does not r i s e immediately  to a flow  s t r e s s comparable w i t h the T value of a normal fee t e n s i l e t e s t , but q  has a s i m i l a r e f f e c t to the prestrained specimens already described. Specimen R63 behaved s i m i l a r l y , 0 /G = 2.45 x 10~ , 5  A  and G-j-j/G  =  16-  Q-r-r/G  = 4.05 x 1 0 ~ , 4  Therefore the flow s t r e s s i n the fee phase i s governed  VG-  by the d i s l o c a t i o n network r e s u l t i n g from the deformation i n the hep phase.  When the temperature i s lowered through the transformation  the work hardening  rate i n the hep phase reverts back to i t s o r i g i n a l  value, i n d i c a t i n g that the deformation mode (on one s l i p system) i n the hep phase i s not a f f e c t e d by any previous deformation p o s s i b l y on two s l i p systems (although only one was observed) i n the fee phase.  (Note  however, that the flow s t r e s s i s a t a much higher l e v e l than during the f i r s t c y c l e ) .  142  5.4.1.3.  Specimen Examination The specimens were not removed f o r observation during the  tests but were examined a f t e r f r a c t u r e .  I n a l l cases two s l i p  systems were observed, but i n the specimens where the basal plane operated i n the fee phase ( o r i e n t a t i o n f a c t o r = 1) the amount of secondary s l i p was small. Specimen R67 ( o r i e n t a t i o n f a c t o r = 1.5) was p a r t i c u l a r l y i n t e r e s t i n g , and the micrographs are shown i n F i g . 53.  At 600 x  (Fig. 53 (a)) the primary (111) system can be seen, and the secondary system, which could not be i d e n t i f i e d , i s not continuous, and appears between the primary traces.  A r e p l i c a of t h i s specimen ( F i g . 53 (b))  shows that there i s some displacement of the primary trace s i m i l a r to a shear, and that the secondary traces are i n d i v i d u a l l y short, and do not appear as conventional s l i p l i n e s .  The primary trace probably  o r i g i n a t e d i n the hep phase, and i t i s p o s s i b l e that the secondary traces r e s u l t from the transformation.  I t i s also j u s t p o s s i b l e to  resolve some very f i n e s l i p , p a r a l l e l to these secondary traces. X-ray back r e f l e c t i o n photographs were taken a f t e r these tests and i n the case where the i n i t i a l deformation had been i n the fee phase, only the specimen orientated such that the basal plane was the (111) plane w i t h the highest Schmid f a c t o r i n the fee phase gave a spot pattern.  With higher o r i e n t a t i o n f a c t o r s a r i n g pattern was obtained.  However, when the i n i t i a l deformation was i n the hep region (and therefore the basal plane was o p e r a t i v e ) , then the f i n a l X-ray pattern always showed spots.  Fig. 53 (a)  Fig. 53 (b)  Deformation of Specimen R67 X600.  Replica of same face as Fig. 53 (a) XIO.OOO.  144  5.4.2.  C o n t i n u o u s l y Deformed  Two s p e c i m e n s experiments  i n which  o f t h e same o r i e n t a t i o n s w e r e u s e d i n s i m i l a r  t h e s p e c i m e n was c o n t i n u a l l y  deformed a t low s t r a i n  r a t e , a n d t h e t e m p e r a t u r e was a l s o c h a n g e d s l o w l y b u t c o n t i n u o u s l y . The  results  a r e n o t much d i f f e r e n t  x - y c u r v e s a r e shown i n F i g s . curves are the  specimen  t o t h o s e j u s t d e s c r i b e d , and t h e  54 a n d 5 5 .  temperature  (°C)  The numbers s i t u a t e d  on t h e  recorded during the  deformation.  5.4.2.1.  Tests s t a r t i n g  above t h e t r a n s f o r m a t i o n  When t h e i n i t i a l  d e f o r m a t i o n i s i n the f e e phase  the work h a r d e n i n g r a t e i n c r e a s e s v e r y s l i g h t l y A t 390°C a f a i r l y  ( F i g . 54)  as t h e t e m p e r a t u r e  falls.  d r a s t i c change i n t h e work h a r d e n i n g r a t e o c c u r s ,  a n d i t c o n t i n u e s t o d e c r e a s e t o t h e minimum t e m p e r a t u r e o f t h e c y c l e (360°C).  As t h e t e m p e r a t u r e i s r a i s e d  negative work-hardening  t h e r e a f t e r , an apparent  rate i s obtained.  Recovery  occurs i n this  temperature range, g i v i n g a decrease i n f l o w s t r e s s w i t h i n c r e a s i n g erature  (see section 3 ) .  temp-  Hence, i f t h e r a t e o f i n c r e a s e i n temperature  i s h i g h enough t h e n o r m a l work h a r d e n i n g mechanisms a r e n o t s u f f i c i e n t t o overcome t h e d e c r e a s e i n f l o w s t r e s s , and an a p p a r e n t work  softening  occurs.  A t about about  430°C t h e w o r k h a r d e n i n g r a t e i n c r e a s e s , a n d r e m a i n s  c o n s t a n t (and a p p r o x i m a t e l y p a r a l l e l  t h e maximum  t e m p e r a t u r e o f 470°C.  t o t h e o r i g i n a l v a l u e ) up t o  On t h e s e c o n d  cycle  the specimen  f r a c t u r e d w h e n t h e t e m p e r a t u r e was 376°C a n d f r o m F i g . 54 i t c a n b e t h a t a t 390°C t h e r e was o n l y a s l i g h t  change i n work h a r d e n i n g r a t e .  seen The  146  t r a n s f o r m a t i o n t o t h e hep p h a s e e i t h e r  ( i ) had n o t taken p l a c e a t a l l ,  ( i i ) had taken p l a c e i n c o m p l e t e l y o r ( i i i ) had taken p l a c e b u t t h e s p e c i m e n was now d e f o r m i n g due  i n s t a g e B o f t h e work h a r d e n i n g  to the intersecting dislocations  The  third possibility  curve, p o s s i b l y  from the f e e deformation.  i sunlikely  a s a n X - r a y p a t t e r n showed  t h a t t h e s i n g l e c r y s t a l s t r u c t u r e had been r e o r g a n i s e d , and t h e m i c r o s t r u c t u r e was  similar  to F i g . 3 6 (g).  t r a n s f o r m a t i o n temperature deformation The  had been lowered  specimen the  b y t h e e x c e s s i v e amount o f  i n t h e f e e p h a s e a n d some r e c r y s t a l l i s a t i o n h a d o c c u r r e d .  net result  would encounter other s l i p  Hence i n t h i s p a r t i c u l a r  favoured  a h i g h work hardening  boundaries.  Tests s t a r t i n g below the t r a n s f o r m a t i o n  When t h e i n i t i a l  deformation  i s i n t h e hep phase  o r i e n t a t i o n f a c t o r 1 . 3 F i g . 5 5 ) the curve  i svery s i m i l a r  first  i n d i c a t i o n o f a h i g h work hardening  rate occurred a t  GJJ/G  ( f e e ) was a b o u t  cooling tinued  30  times  t h e low work hardening to decrease  g r e a t e r than  5.4.2.3. The two  slip  (Specimen 1 2 4 ,  to Fig. 5 2 .  434°C,  The and  On s u b s e q u e n t  3 9 4 ° C , and conof the cycle 362°C. Work  r a t e was a g a i n o b s e r v e d  at  on h e a t i n g and d u r i n g t h e second c y c l e t h e  t r a n s f o r m a t i o n t o t h e f e e phase o c c u r r e d a t a t about  (hep).  t o t h e minimum t e m p e r a t u r e  softening again occurred  fractured  dislocations  o b s t a c l e s i n t h e form o f i n t e r s e c t i n g d i s l o c a t i o n s on  p l a n e s , and a l s o g r a i n  5.4.2.2.  r a t e as t h e g l i d e  460°C,  418°C,  after a t o t a l s t r a i n of  M e t a l l o g r a p h i c and X-ray  and t h e specimen  3.0.  Examination  specimens were examined a f t e r f r a c t u r e , and i n a l l cases  systems were observed.  When t h e o r i e n t a t i o n f a c t o r was 1 . 0 ,  2 mm 5.0  148  the majority of s l i p took place on the same plane i n both phases, because the f i n a l specimen dimensions were r i b b o n - l i k e .  The c r y s t a l  s t r u c t u r e was maintained throughout the deformation except when the primary s l i p plane i n the fee phase was not the transformed b a s a l plane, and the i n i t i a l deformation was i n the fee phase. Table XVII summarises the X-ray and s l i p data from o p t i c a l and e l e c t r o n microscopy, f o r both the continuously deformed and i n t e r m i t t e n t l y deformed specimens.  Adding t h i s information to the analysis of the  s t r e s s - s t r a i n curves, i t may be stated that the behaviour f o r both modes i s s i m i l a r . In a l l these experiments i t has been found that at a c e r t a i n temperature, which depends on the amount of deformation, a s i g n i f i c a n t change i n the work hardening slope occurs, e i t h e r on heating or c o o l i n g . On h e a t i n g , t h i s temperature (the transformation temperature) l i e s between 437°C f o r small amounts of hep deformation (y = 0.5) and 425°C for large amounts (y = 2.0) of deformation, i . e . the greater the amount of the p r i o r deformation, then the loweris the transformation temperature. (This agrees w e l l w i t h the e a r l i e r observations, and also with the p r e d i c t i o n s of Seegers transformation theory).  On cooling,the  transformation takes place at about 390°C to 380°C, and t h i s temperature i s usually not affected by the amount of p r i o r deformation.  This  temperature i s i n close agreement w i t h other published values (and the most commonly quoted value i n the l i t e r a t u r e f o r the transformation on heating i s 417°C.)  149  TABLE XVII Summary of X-ray and Metallographlc Observations i n Specimens cycled through the Transformation Examination a f t e r Fracture No of S l i p X-ray Pattern Systems  Specimen  Deformation  Orientation Factor  R57  i  1.0  ,(1)  Spots and Debye arcs  R64  i  1.45  2  Large rings  R63  i  1.0  ,(1)  Spots  R67  i  1.5  2  Spots  122  c  1.25  2  Rings (broken)  126  c  1.0  2  Large spots and arcs  124  c  1.3  2  Spots and Rings  128  c  1.0  2  Spots  i = i n t e r m i t t e n t deformation c = continuous deformation (1) = some secondary s l i p observed i n l i m i t e d areas  150 5.5.  Discussion Recently, two papers have been published on the e f f e c t of  p r e s t r a i n on copper s i n g l e c r y s t a l s  .  The technique involves  s t r a i n i n g a large s i n g l e c r y s t a l i n tension such that s l i p occurs on only one s l i p system, and then sectioning t h i s c r y s t a l i n such a way that a new t e n s i l e specimen i s formed which would s l i p on a d i f f e r e n t s l i p system.  As the basis of these experiments i s s i m i l a r to the work  described i n t h i s s e c t i o n , the r e s u l t s w i l l be included so that comparisons may be made. 1.  Jackson and B a s i n s k i ^ ^ - found a marked difference between (a) the  l a t e n t hardening r a t i o (LHR - which has previously been defined i n s e c t i o n 3) of specimens cut so that the new s l i p system was i n the same plane but i n a d i f f e r e n t d i r e c t i o n , i . e . coplanar, to (b) specimens whose new s l i p system was a l s o on a d i f f e r e n t plane - i . e . (a)  intersecting.  For coplanar secondary systems the LHR was found to be 1.05 ±.05  i . e . close to unity and independent of the amount of p r e s t r a i n .  Also  the work hardening rate 0 was found to be the same, and easy g l i d e d i d not reoccur i f the p r e s t r a i n was taken to stage I I .  This i s shown by  specimen B2 i n F i g . 56 (which i s reproduced from Jackson and Basinski's paper). (b)  For i n t e r s e c t i n g secondary systems the LHR decreases with increasing  p r e s t r a i n , ranging from 2.6 early i n stage I to 1.4 l a t e i n stage I I . In these specimens e.g. A2 and D l i t was p o s s i b l e to induce an extended stage I i n the secondary system as i n F i g .  56 where easy g l i d e occurred  2 at over 3.5 Kg/mm 2 0.15 to 0.2 Kg/mm ).  (and the c r i t i c a l resolved shear stress f o r copper i s Another feature i s that the extent of easy g l i d e i s  151  Fig.  increased  56  S t r e s s - s t r a i n curves on l a t e n t systems i n stage I I h a r d e n i n g of copper. Specimen B2 i s f o r c o p l a n a r systems and A2 and D l a r e i n t e r s e c t i n g systems. , Reproduced from the paper by J a c k s o n and B a s i n s k i  a f t e r p r e s t r a i n i n g and the work h a r d e n i n g r a t e i n s t a g e I I i s  l e s s than 50% of the v a l u e o f 9^^ on the p r i m a r y  system.  These r e s u l t s a r e e x p l a i n e d i n terms of the f o r e s t theory of h a r d e n i n g , i . e . d i s l o c a t i o n s on the p r i m a r y s l i p p l a n e a c t as d i s l o c a t i o n s on the secondary. should increase the i n c r e a s e density  forest  E a r l y i n s t a g e I a change i n s l i p  plane  the f o r e s t d e n s i t y by a f a c t o r of 10, and a t h i g h e r s t r a i n s  i s smaller.  When a c o p l a n a r system i s t e s t e d ,  the f o r e s t  i s unchanged.  The c o n c l u s i o n  that f o r e s t d i s l o c a t i o n s are responsible  f l o w s t r e s s v a l u e s i s r e a s o n a b l e and i t must a l s o be a c o n t r i b u t i n g when c o n s i d e r i n g  the b e h a v i o u r of the t h e r m a l l y  i n F i g s . 51 to 55.  f o r the factor  c y c l e d specimens shown  The main s i m i l a r i t i e s between the p r e s e n t work and  152  that of Jackson and B a s i n s k i are (a)  easy g l i d e on one s l i p system can take place even a f t e r extensive  s l i p on a d i f f e r e n t s l i p plane. (b)  the work hardening rate i n stage I I of the fee curve i s lower on the  secondary system. (c)  a f t e r p r e s t r a i n i n g the l a t e n t hardening r a t i o i s >1 when a new s l i p  plane operates (although Jackson and Basinski's value i s much higher than i n the present work) and when the same s l i p plane i s operating, the LHR i s approximately 1. (54) 2.  Washburn and Murty  - a l s o s t r a i n e d large s i n g l e c r y s t a l s of  copper (oriented f o r m u l t i p l e s l i p ) which were then cut such that a new s i n g l e s l i p system would operate.  I n a l l cases the LHR was about 1.25  to 1.35 i . e . much lower than Jackson and. B a s i n s k i ' s , and c l o s e r to the values f o r cobalt.  The i n i t i a l hardening rate decreased and the length  of easy g l i d e i n the secondary deformation increased with increasing p r e s t r a i n . Stage I I was also a f f e c t e d , the work hardening rate decreased, and the extent was increased w i t h i n c r e a s i n g p r e s t r a i n .  A l s o the s t r e s s l e v e l ^J-J-J- a t  which the hardening rate began to decrease was found to increase from 2.4 2 Kg/mm  2 to 4.1 Kg/mm w i t h i n c r e a s i n g p r e s t r a i n .  Three stages of the work  hardening curve were always obtained, even when the y i e l d s t r e s s i n the secondary system exceeded ^-^^ f ° the "as grown" c r y s t a l . r  Washburn and Murty made a d e t a i l e d study of s l i p l i n e s by both o p t i c a l metallography, and r e p l i c a s . In stage I the s l i p l i n e s were long, s t r a i g h t and quite f i n e . Macroscopically the s l i p was not uniformaly d i s t r i b u t e d throughout the  specimen below 3% s t r a i n and the inhomogeniety  increased with p r e s t r a i n .  The d e f o r m a t i o n took p l a c e by both the f o r m a t i o n o f new s l i p an i n c r e a s e i n d i s p l a c e m e n t on e x i s t i n g s l i p was 220u and d i d n o t change w i t h i n c r e a s i n g  In slip  s t a g e I I the s l i p  u s u a l l y propagated  lines.  l i n e s and  The average l e n g t h  strain.  l i n e s were s h o r t e r and s t r o n g e r .  The  a c r o s s the specimen i n groups of bands, and t h i s  was a l s o t r u e i n n o n - p r e s t r a i n e d specimens b u t n o t so o b v i o u s . l e n g t h o f a band decreased w i t h i n c r e a s i n g p r e s t r a i n .  The  As the s t r e s s -  s t r a i n curve always showed 3 s t a g e s , and y e t the s l i p s t u d i e s were not always c o n s i s t e n t , then i t was concluded not a v a l i d b a s i s f o r a work h a r d e n i n g be governed  that s l i p  l i n e s t u d i e s alone a r e  t h e o r y , as the flow s t r e s s s h o u l d  by areas o f s t r e s s c o n c e n t r a t i o n such t h a t primary  loops can m u l t i p l y so as to produce  dislocation  a l a r g e enough s l i p band t o s e t o f f  the avalanche o f s l i p .  3.  Sharp and M a k i n ^ ^  - s t u d i e d t h i n f i l m s o f copper  t w i s t e d , and then t e s t e d i n t e n s i o n on a d i f f e r e n t s l i p s t r u c t u r e was formed a f t e r the f i r s t  taken from specimens system.  A cell  d e f o r m a t i o n , and t h i s v a r i e d a c r o s s  the specimen b e i n g much f i n e r near the s u r f a c e .  A f t e r the second  d e f o r m a t i o n f i n e s l i p was i n i t i a l l y seen w i t h i n the c e l l s ,  and t h i s was  f o l l o w e d by c o a r s e s l i p when the s t r e s s was h i g h enough f o r s l i p to p e n e t r a t e the c e l l w a l l s .  Mutual a n n i h i l a t i o n o f p i l e d - u p groups o f  p o s i t i v e and n e g a t i v e d i s l o c a t i o n s on o p p o s i t e s i d e s o f the c e l l w a l l s c r e a t e d s o f t e n e d r e g i o n s , which spread a c r o s s the c r y s t a l to form slip  coarse  lines.  Although  these o b s e r v a t i o n s agree w e l l w i t h those of Washburn  and Murty, the l a t t e r authors suggest  t h a t d i s l o c a t i o n arrangements i n  154  t h i n f i l m s cannot be s u c c e s s f u l l y used i n formulating work hardening r e l a t i o n ships as the specimen sample i s much too small.  In f a c t the microscopic and  macroscopic d i s t r i b u t i o n of shear s t r a i n along the length of the specimen are  extremely important i n determining the slope of the s t r e s s - s t r a i n  curve. The e f f e c t s of p r e s t r a i n on copper s i n g l e c r y s t a l s as described by Washburn and Murty substantiate the work of Jackson and B a s i n s k i , and the former propose a s l i p nucleation mechanism to overcome the high density of f o r e s t d i s l o c a t i o n s .  C r o s s - s l i p acting w i t h secondary s l i p systems  i n the primary g l i d e plane i s then used to e x p l a i n the growth of s l i p bands. Although many of the experiments on cobalt are analogous, there are  a l s o some d i f f e r e n c e s which undoubtedly a f f e c t the work hardening  behaviour, the main e f f e c t being the transformation. 5.5.1.  P r e s t r a i n without Anneal When the hep p r e s t r a i n was low (specimens 110,111), s l i p i n  the  fee phase took place on a new (111) plane, hence t h i s t e s t i s very  s i m i l a r to the tests on copper, except that easy g l i d e was not observed i n fee deformation of cobalt.  So i t must be assumed that above the  transformation, the temperature i s too high f o r s i n g l e s l i p a c t i v a t i o n . As the transformation occurs on the basal plane, r e s i d u a l d i s l o c a t i o n s on the p a r a l l e l (0001)/(111) plane from both basal s l i p and the transformation could a c t as f o r e s t d i s l o c a t i o n s f o r the s l i p on the primary (111) plane.  155  Hence i t might be expected that the work hardening rate i s higher i n these specimens than i n a normal fee t e n s i l e t e s t . hardening rate i s i n f a c t about the same, which might  The work  imply that the  transformation d i s l o c a t i o n s are a c o n t r o l l i n g mechanism.  But on the  other hand, the work hardening rate i s also the same when the transformed basal plane operates as the primary s l i p plane i n Stage I I .  So the  c o n t r i b u t i o n of the transformation d i s l o c a t i o n s towards the work hardening rate cannot be very high, unless the transformation d i s l o c a t i o n s are s e s s i l e and therefore impede the g l i d e d i s l o c a t i o n s on a coplanar system to the same extent that they impede g l i d e d i s l o c a t i o n s on an i n t e r s e c t i n g system. In f a c t the work hardening rate i n stage I I i s lower f o r -3 cobalt than the other fee metals (Q^^/G = 2 x 10 i s probably a r e s u l t of the transformation.  -3 of 3 x 10  ) and t h i s  The explanation f o r one  observation therefore seems to contradict the explanation f o r another. I t i s not known why the y i e l d stress i n the fee phase should be much lower than the y i e l d s t r e s s f o r normal fee deformation but presumably  the d i s l o c a t i o n s i n the b a s a l plane r e s u l t i n g from the p r e s t r a i n  must i n some way allow or cause p l a s t i c deformation to occur more e a s i l y . When hep p r e s t r a i n i s increased the d i s l o c a t i o n density on the b a s a l plane must increase a l s o , u n t i l a t one stage i t i s high enough that s l i p i n the fee phase also takes place on the same plane, even when there are other (111) planes with a higher Schmid f a c t o r . condition  Now the  i s s i m i l a r to the coplanar t e s t s performed by Jackson and  B a s i n s k i , and so a s i m i l a r work hardening behaviour might be expected. The LHR is.indeed reduced from about 1.17 to about 1.0 but the work hardening  156 curve i n the fee phase appears to have several p o s s i b i l i t i e s : (1)  that both stages I and I I are absent and the deformation i s i n stage I I I .  (2)  that only one s l i p system i s operating, and the deformation i s s i m i l a r to stage I or hep stage A.  (The higher work hardening rate w i l l be  discussed s h o r t l y ) . (3)  That the work hardening rate i s r e a l l y a compromise between stages I and I I , (note that the work hardening.rate i n stage I I i s about the same whether two s l i p systems operate or p r i m a r i l y one - see F i g . 29). (1) i s l e a s t l i k e l y because only one s l i p system was  and the s l i p l i n e s were not wavy.  observed  (However, the only i n d i c a t i o n of  c r o s s - s l i p by wavy s l i p l i n e s has -been when only one s l i p system i n fee i s observed, but not on the transformed b a s a l plane).  E i t h e r (2) or (3)  could be correct and i n f a c t i t i s not p o s s i b l e to d i s t i n g u i s h between them.  But from these observations i t seems highly l i k e l y that i f only  one s l i p system operates i n the fee phase the work hardening rate w i l l be low. -3 2 x 10  Therefore i n a l l cases where the work hardening rate 9/G i s about we should assume that 2 s l i p systems are operating i r r e s p e c t i v e  of the c r y s t a l o r i e n t a t i o n , and no matter what the m i c r b s o p i c a l observations i n d i c a t e .  I f r e p l i c a s show only one s l i p system, then there  must be some d i s l o c a t i o n a c t i v i t y on an i n t e r s e c t i n g plane, too f i n e to be resolved, but s u f f i c i e n t to a f f e c t the work hardening p r o p e r t i e s . A s i n g l e s l i p system can operate as i n specimens 116 and 118, but only on  the transformation plane and only when the d i s l o c a t i o n density  on t h i s plane i s high, much higher than i s due to the transformation. Replicas of 118 d i d i n f a c t show s i n g l e s l i p , i d e n t i c a l to stage A deformation of the hep phase, see F i g . 47.  157  An observation from s e c t i o n 4 that deformation d i s l o c a t i o n s can d i c t a t e the transformation and therefore, that deformation d i s l o c a t i o n s are s i m i l a r to transformation d i s l o c a t i o n s i s not disproved here.  However, a complimentary suggestion may be made that transformation  d i s l o c a t i o n s are at a low density and do not give an appreciable c o n t r i b u t i o n to work hardening i n e i t h e r of two a l t e r n a t i v e s . (1)  they are g l i s s i l e and therefore increase s l i g h t l y the density of g l i d e d i s l o c a t i o n s or  (2)  they are s e s s i l e and act as b a r r i e r s to g l i d e d i s l o c a t i o n s . E i t h e r a l t e r n a t i v e would of course p r e d i c t a s l i g h t l y higher  work hardening rate than i s obtained i n easy g l i d e . 5.5.2.  P r e s t r a i n followed by Anneal Anneals a t 20°C have no e f f e c t .  However at 360°C or 400°C  the annealing gives the subsequent fee deformation two d e f i n i t e stages, w i t h a sharp t r a n s i t i o n from one to the other.  The f i r s t stage i s concave  i n that the work hardening rate a c t u a l l y increases w i t h s t r a i n .  When  the annealing temperature i s 480°C t h i s e f f e c t i s so pronounced that i t s e l f may be subdivided i n t o two stages, such that the complete curve isathree-stage fee work hardening curve. An hep p r e s t r a i n of 0.5 ensured that further deformation would take place on the transformed b a s a l plane when the specimen was heated to the fee phase.  Hence, i t was o r i g i n a l l y expected that annealing the  specimen f o r a s u b s t a n t i a l time a f t e r the p r e s t r a i n would i n fact revert the c r y s t a l back to an undeformed s t a t e .  In other words, i t was expected  that i f specimen 118 had been annealed before being tested at 480°C, then the  158  fee  T - y curve would have been the same as specimen  thereby i n c r e a s i n g the LHR to 3.  R37  ( i n F i g . 43),  T h i s was not found to be t r u e (see  T a b l e X V I ) , and even w i t h an LHR o f 1, the x - y curve appears d i f f e r e n t f o r annealed specimens than f o r say specimen  110.  quite The  d i s l o c a t i o n s t r u c t u r e a f t e r a p r e s t r a i n i s p r o b a b l y s t a b i l i s e d by an a n n e a l , and even i f two s l i p fee  systems a r e seen  ( r e f e r to T a b l e XVI) the  work h a r d e n i n g curve has t h i s c h a r a c t e r i s t i c shape, although only  one s l i p  system may o p e r a t e i n t h e lower work hardening range of stage I I ,  i n which case i t would be more c o r r e c t to c a l l the stages I , I I and I I I , r a t h e r than as d e s c r i b e d i n F i g . 45.  A f u r t h e r c o m p l i c a t i o n i s added a t the end of s t a g e I I where the work h a r d e n i n g r a t e changes a b r u p t l y .  The reason f o r t h i s sudden  change i s n o t known, b u t i t i s p o s s i b l e t h a t a t the c r i t i c a l s t r e s s T-Q-J(which d e c r e a s e s w i t h i n c r e a s i n g p r e s t r a i n a t a g i v e n a n n e a l i n g and d e c r e a s e s s l i g h t l y w i t h i n c r e a s i n g a n n e a l i n g temperature  temperature  at a given  p r e s t r a i n ) we have an e f f e c t s i m i l a r t o t h a t d e s c r i b e d by Washburn and Murty, where an inhomogeneous s l i p In  occurs i n bands a c r o s s the specimen.  a l l cases where a specimen was annealed a f t e r the p r e s t r a i n , the  primary s l i p  system appeared  evidence o f f i n e s l i p  as s h o r t e r r a t h e r c o a r s e bands, and the o n l y  ( F i g . 48 (b)) was oh the secondary o r i n t e r s e c t i n g  sys terns.  Fig.  57 shows the e f f e c t o f the amount o f hep p r e s t r a i n on  the v a r i o u s s t a g e s o f the f e e work h a r d e n i n g c u r v e s . specimens the i n i t i a l work h a r d e n i n g r a t e . O <  yp < 0.34 because  two s l i p  I n the non annealed  has a sharp break f o r 0.13  systems operate when Yp  <  0.13, but one s l i p  system,that on the transformed b a s a l p l a n e , operates when Y f i n a l work h a r d e n i n g s l o p e Q  > p  0.34.  decreases g r a d u a l l y w i t h i n c r e a s i n g  The Y . p  Q  1  -I  0  0.2  1  r  0.4  0.6  i 0.8  9  1  /G  non  '  57  t—  1.0 hep p r e s t r a i n  Fig.  annealed  1.2 Y  D  The e f f e c t of the hep p r e s t r a i n on the f e e work hardening r a t e and non annealed specimensdeformed at 480°C.  f o r annealed VO  160  6"  /G, the maximum work hardening slope of stage I I f o r the annealed  specimens  £  i s of the same order, but never exceeds the value of  Qj^/G f o r the normal fee t e s t s . The f i n a l work hardening slope f o r the annealed specimens fl i s about the same as f o r the non annealed specimens, and a l i t t l e less than i n the normal fee stage I I I hardening.  Hence i t might be true  that a s i m i l a r recovery process i s occurring i n t h i s section of the curve.  Although evidence of c r o s s - s l i p has been seen i n the annealed  specimens, the s l i p studies of the non-annealed specimens appear quite different.  The traces are not wavy to i n d i c a t e that c r o s s - s l i p might  be occurring. 5.5.3.  Specimens Thermally cycled through the Transformation No l a t e n t hardening e f f e c t has been observed i n these specimens. I f a specimen i s deformed i n one phase at a p a r t i c u l a r flow  s t r e s s , then t h i s i s the flow s t r e s s at which p l a s t i c deformation recommences i n the other phase i f the m a t e r i a l i s heated or cooled through 2  the transformation., i . e . a y i e l d p o i n t i n the fee phase of about 0.5 Kg/mm can be induced a f t e r only 7% shear s t r a i n i n the hep phase, and easy g l i d e 2 i n the hep phase can be induced a t a s t r e s s of over 6 Kg/mm . In the hep phase the work hardening rate i s about constant, depending s l i g h t l y on temperature, and i t i s independent of deformation history. In the fee phase the work hardening rate i s very dependent on the deformation h i s t o r y , and only s l i g h t l y temperature dependent.  For  example t h e v a l u e s  o f Q-j-j/G f o r s p e c i m e n s 122 a n d 124  -3 d e f o r m e d ) a r e 1.95 x 10  -3 and 0.56 x 10  124 t h e v a l u e o f  Q-r-j/G  5.5.4.  Explanations  Possible Theory.  5.5.4.1.  T h e hep  In previously low  (continuously  increased  respectively.  However, i n  _3 t o 0.96 x 10 d u r i n g the second c y c l e .  f o r t h e b e h a v i o u r i n terms o f D i s l o c a t i o n .  Phase  t h e hep phase t h e r e s o l v e d  shear stress  i slow i n a  undeformed c r y s t a l where t h e f o r e s t d i s l o c a t i o n d e n s i t y i s  b u t h i g h when p r e v i o u s d e f o r m a t i o n i n t h e f e e p h a s e h a s p r e s u m a b l y  raised  the forest density.  However, any d i s l o c a t i o n s  on a non-basal  (111) p l a n e i n t h e f e e p h a s e m i g h t b e r e m o v e d b y t h e t r a n s f o r m a t i o n , t h e r e i s no e q u i v a l e n t the  high flow stress  p l a n e i n t h e hep phase. i s due t o l o n g - r a n g e s t r e s s  d i s l o c a t i o n s must overcome. barriers  5.5.4.2.  to slip  t h ef e e phase, w i t h  g l i d e , and as t h e y i e l d dislocations primary  stress  a c t as obstacles slip  no hep p r e s t r a i n ,  i shigh,  i s low.  f o r one o f t h ea c t i v e s l i p  amount o f h e p p r e s t r a i n , w i l l  For  controls  theflow  transformation  planes  (even i f  However, i t i s n o t  then lower the resolved  r e m a i n s t h e same.  d i s l o c a t i o n arrangement b e f o r e and a f t e r and t h i s  t h e r e i s no e a s y  i t i s presumed t h a t  s h e a r s t r e s s when t h e w o r k h a r d e n i n g r a t e  similar,  are mobile the  t h e work h a r d e n i n g r a t e  plane i s thetransformed b a s a l ) .  c l e a r why a s m a l l  the  f i e l d s which the  When t h e d i s l o c a t i o n s  a r e weak and t h e r e f o r e  that  The f e e Phase  In  the  I t i s postulated  as  Presumably  the transformation i s very  stress.  a h i g h e r hep p r e s t r a i n  (y h e p >0.5)  thefee flow  stress  162  remains more or l e s s unaffected, and the LHR remains at about 1. However, deformation i n the fee phase now takes place on one s l i p system, that of the transformed basal plane and consequently work hardening rate Q  i s much lower.  the  The d i s l o c a t i o n density on  the g l i d e plane i s high, therefore the fee curve may be e i t h e r a stage I , or perhaps a combination of stages I and I I , or perhaps, but l e s s l i k e l y j u s t stage I I I . The annealing experiments have helped to solve t h i s problem. With an hep p r e s t r a i n of 0.5 an anneal between 350°and 400°C probably rearranges the d i s l o c a t i o n s , so that the i n i t i a l deformation i n the fee phase takes place on the transformed b a s a l plane, but i f during the anneal, some recovery can take place by climb, then i t i s possible that sources may act i n such a way as to promote s l i p on a second s l i p thereby  increasing the density of f o r e s t d i s l o c a t i o n s which then increases  the work hardening rate. Fig.  system,  A f t e r a shear s t r a i n y  (y-j-j-'  +  Yjj" i -  n  45) where .15 < y ^ < .3 depending on p r e s t r a i n and annealing  temperature, the work hardening rate sharply decreases to stage I I I . The flow s t r e s s of stage I I I i s lower than f o r normal fee t e n s i l e t e s t s , but higher than the p r e s t r a i n without anneal.  I n a l l cases the work  hardening rates are comparable. From observations, i t may be seen that a non-annealed  specimen  (118) contains f i n e s t r a i g h t s l i p l i n e s as seen i n the easy g l i d e region. The s l i p l i n e s i n specimen 145 are much coarser, and appear banded. i s postulated that due to d i s l o c a t i o n l o c k i n g i n the annealed  It  specimens,  there i s a greater work hardening r a t e , but at a p a r t i c u l a r s t r e s s  T  -r-r-r»  an avalanche of s l i p occurs, causing softened regions and a lower work-hardening rate i n stage I I I .  163 Section 6 6.1.  Summary  The Transformation The quoted temperatures  of the transformation d i f f e r from one  report to another, but average values are as f o l l o w s : TABLE XVIII  M,  M  480  417  390  -  450  417  410  385  A, d  A  s  f  Polycrystals  417  435  Single C r y s t a l s  417  430  d  s  f  i . e . the h y s t e r e s i s loop (A - M ) i s larger f o r p o l y c r y s t a l s than s i n g l e s s crystals. Heterogeneous s t r e s s , due to p r i o r deformation before the transformation causes an increase i n the number of transformation n u c l e i . Homogeneous s t r e s s applied during the transformation favours the transformat i o n by e i t h e r lowering the A  or r a i s i n g the M temperature. The e f f e c t s s s of s t r e s s on the transformation h y s t e r e s i s are given i n Table XIX. TABLE XIX Single C r y s t a l s  Poly C r y s t a l s A s  M  s  Hysteresis Loop  A  _  Homogeneous deformation during transformation  +  Closed  Heterogeneous deformation above  -  Widened  Heterogeneous deformation below  -  s  Closed  where - i n d i c a t e s a decrease i n temperature. + i n d i c a t e s an increase i n temperature. 0 i n d i c a t e s no change i n temperature.  0  M  Hysteresis Loop  +  Closed  s  Unchanged  164 Although no measurements on the transformation temperature have been attempted i n the present work, i t has been possible to make estimates of the transformation temperature from the slope of the work hardening curve where the temperature was changed during the deformation. I t appeared as though the A  g  temperature was lowered from about 435°C  to 428°C but there was no s i g n i f i c a n t change i n the M  g  temperature  which remained a t about 390°C. 6.2 1.  Summary of deformation behaviour i n hep phase S l i p occurred on the b a s a l plane only, even when the Schmid f a c t o r was very low.  2.  L e n t i c u l a r (1012) twins and long (1011) twins have been observed, even up to temperatures approaching the transformation. twin planes  These  d i d not correspond to any previously reported f o r  cobalt. 3.  Indications of twinning on the load-extension chart have been observed both i n stage A and.stage B to about the same extent. However, i n the specimens where twinning has been observed, a higher density of twins occurred i n specimens deformed i n t o stage B, but t h i s may be due to the lower temperature of deformation.  4.  I n the easy g l i d e region  the i n i t i a l - work hardening rate  was p a r a b o l i c , and f o r shear s t r a i n s between 0.2 and the end of stage A the work hardening rate was l i n e a r . 5.  The work hardening rate decreased w i t h increasing temperature. I t was strongly temperature dependent between 100°K and 400°K, and weakly temperature dependent between 400°K and 700°K.  165 6.  The CRSS was independent of temperature between 300°K and 500°K. Outside t h i s temperature range the CRSS decreased with increasing temperature.  7.  Cobalt deformed i n t o stage B only at the lower temperatures.  Fracture  occurred i n stage A at temperatures approaching the transformation. The extent of stage A increased with temperature, but was not s e n s i t i v e to c r y s t a l o r i e n t a t i o n , except when the Schmid Factor was low. 8.  Stage C has never been observed.  9.  S l i p trace a n a l y s i s i n d i c a t e d that during the i n i t i a l p a r a b o l i c hardening  the number of s l i p l i n e s increased with deformation, and  during the l i n e a r hardening  the number of d i s l o c a t i o n sources  remains about constant, but the step height increased with s t r a i n . This i s s i m i l a r to the observation on z i n c , but not the observations on magnesium. 10.  Recovery experiments at 397°C showed the formation of a y i e l d p o i n t , but such an e f f e c t was not observed at 323°C.  This e f f e c t has been  i n t e r p r e t e d by a pinning of d i s l o c a t i o n s when the load was released. 11.  An explanation f o r the shape of the work hardening  curve based on  these observations, and the long range s t r e s s f i e l d of e l a s t i c i n t e r a c t i o n between d i s l o c a t i o n s on p a r a l l e l g l i d e planes, as described by Seeger, has been discussed. 6.3. 1.  Summary of fee deformation The work hardening  curves showed only stages I I and I I I .  No easy g l i d e  was observed, even where one s l i p system predominated. -3 about 2 x 10  -3  2.  ®n/G  3.  The value of ( T ^ J - T ) was about constant, although T  w a s  (compared to 3 x 10 0  with i n c r e a s i n g temperature.  f o r most fee metals). q  decreases  166 4.  Cross s l i p can occur, despite the low value of stacking f a u l t energy, and has been observed i n stage I I .  5.  The metallographic observations show that the deformation behaviour i s a f u n c t i o n of the o r i e n t a t i o n f a c t o r , but that t h i s does not s i g n i f i cantly a f f e c t the work hardening curve.  6.  Deformation can a f f e c t the h a b i t plane of the transformation over the entire crystal.  I f more than one s l i p system operates, then  r e c r y s t a l l i s a t i o n may occur. 7.  Evidence of twinning on the I n s t r o n chart was only observed at -4 higher s t r a i n rates (y > 10  ins/in/sec.).  At low s t r a i n rates  (y = 3 x 10 ^ i n s / i n / s e c . ) no evidence of twinning has been recorded. Long twins on (111) planes have been i d e n t i f i e d and the twins broaden with i n c r e a s i n g deformation. 8. When a test i s halted i n stage I I and l a t e r r e s t r a i n e d , the flow s t r e s s i s not altered..  However a f t e r an i n t e r r u p t i o n i n stage I I I  there i s a drop i n flow s t r e s s i n d i c a t i n g some recovery process has occurred. 6.4 1.  Summary of the e f f e c t of deformation during thermal c y c l i n g Specimens prestrained i n the hep phase continue to deform i n the fee phase with the same flow s t r e s s .  I f the hep deformation i s greater  that -0.5 then i t i s p o s s i b l e to continue deformation on the transformed b a s a l plane even though other (111) planes have a higher Schmid f a c t o r . The work hardening rate  i s then very much lower.  of the p r e s t r a i n i s not an important f a c t o r .  The temperature  167 2.  Annealing a specimen deformed i n the hep phase does not allow recovery to take place, i ^ e . such a specimen does not deform i n the  fee phase as an "as grown" c r y s t a l .  The shape of the fee  T - y curve changes considerably, so that two s l i p systems operate even f o r large hep p r e s t r a i n s .  The maximum work hardening slope  of stage I I i s of the same order, but does not exceed the value of Gj-r/G f °  ra  normal fee t e n s i l e t e s t .  A l ^ o the s l i p l i n e s which  occur a f t e r annealing are much coarser. 3.  However, the f i n a l work hardening slopes i n both non annealed and annealed specimens are very s i m i l a r , and are dependent on the amount of p r e s t r a i n .  4.  The hep p r e s t r a i n also affectsthe LHR, (see F i g . 4 6 ) f o r both the annealed and non-annealed specimens.  The LHR decreases from  about 1 . 2 at Y . = 0 . 1 to about 1 . 0 a t y, = 0 . 6 . hep hep 5.  I n specimens thermally cycled through the transformation under a t e n s i l e s t r e s s , the value of 0 ^ i s about constant, but 6 ^ ^ depends on the deformation h i s t o r y .  6.  ^TJ/^A  var  ^-  es  f  r o m  about  20  to  100.  However, the flow stress i s purely a f u n c t i o n of the amount of previous deformation and does not change on passing through the transformation.  The behaviour was s i m i l a r when the specimens were either  i n t e r m i t t e n t l y deformed between temperature changes or when the deformation (at a low s t r a i n rate) and the temperature c y c l i n g were continuous.  (67) 7.  The r e s u l t s are compared to those of Jackson and B a s i n s k i system and re-tested on a d i f f e r e n t system. Washburn and Murty  (54)  and  , who prestrained copper c r y s t a l s on one s l i p  168 7.  1.  Conclusions  The t e n s i l e d e f o r m a t i o n the work h a r d e n i n g to  o f hep c o b a l t s i n g l e c r y s t a l s gave v a l u e s f o r  r a t e and the e x t e n t o f s t a g e A w h i c h were comparable  those f o r t h e o t h e r hep m e t a l s .  However,  T /G Q  was t h r e e o r  f o u r times g r e a t e r , and i s p r o b a b l y due t o s e v e r a l f a c t o r s : (a) a low s t a c k i n g f a u l t energy (b) t h e r e l a t i v e d i f f i c u l t y  f o r recovery processes  to operate  ( ) r e s i d u a l f a u l t s of the t r a n s f o r m a t i o n . c  The work h a r d e n i n g  i s p r o b a b l y due t o l o n g range i n t e r a c t i o n between  d i s l o c a t i o n s on p a r a l l e l g l i d e p l a n e s . 2.  The o b s e r v a t i o n s on t w i n n i n g do n o t l e a d t o the c o n c l u s i o n t h a t t w i n n i n g i s r e s p o n s i b l e f o r s t a g e B b u t t h a t i t i s a random e f f e c t depending on l a t t i c e  imperfections.  v Tnn.. o b s e r v a t i o n s by h i e r i•n g e r (71,72).  This i s contrary to recent „ i. (72) However, i. t i.has ail s o ubeen shown  t h a t t w i n n i n g i s a s s o c i a t e d w i t h d i s t u r b e d r e g i o n s i n the l a t t i c e , k i n k w a l l s , and such r e g i o n s have n o t been observed study.  Hence t h e o c c u r r e n c e  s l i p or  i n the p r e s e n t  o f t w i n n i n g p r o b a b l y depends on the  crystal preparation. 3.  I n t h e f e e phase t h e temperature must be h i g h enough t o cause t h e r m a l l y a c t i v a t e d d i s l o c a t i o n movement on secondary ( u n f a v o u r a b l e ) g l i d e p l a n e s . -3 I t must be assumed (as t h e work h a r d e n i n g interaction  rate 9  / G ' i s - 2 x 10  mechanisms a r e the main cause o f h a r d e n i n g  ) that  even when o n l y  one s l i p system i s observed. 4.  The lower work h a r d e n i n g r e c o v e r y by c r o s s s l i p .  r a t e o f s t a g e I I I i s p r o b a b l y due t o dynamic  169  5.  Deformation  can  c o n t r o l the t r a n s f o r m a t i o n h a b i t p l a n e ,  d i s l o c a t i o n s produced during deformation  6.  the  transformation.  The  observations  in  7.  Deformation  d i s l o c a t i o n s on {111}  plane  A f t e r an i n i t i a l following (a)  cause a  n o n - o p e r a b l e i n the  deformation  for  nuclei deformation.  favourably  fee phase.  i n e i t h e r phase, observations  have l e d to  the  conclusions:  t i o n do n o t  affect  the previous  i n the l a t t i c e  the flow s t r e s s .  deformation.  transformation plane  Therefore,  as  a result The  yield  of  the  transforma-  s t r e s s depends o n l y  i s not  d i s l o c a t i o n s before  a l t e r e d by  the  transformation.  they  c a n b r e a k away and  be  glide.  The  work hardening  r a t e i s a f u n c t i o n only of the c r y s t a l s t r u c t u r e  and  i s high i n the  f e e p h a s e due  the i n t e r s e c t i n g and  {111}  h e n c e t h e r e a r e no  Hence a work h a r d e n i n g 2 o f 6 Kg/mm .  on  Hence, the d i s l o c a t i o n arrangement i n  i n e i t h e r p h a s e , t h e same l o c a l s t r e s s f i e l d m u s t  overcome by  (b)  increases with  t h e b a s a l p l a n e may  t o be  D i s l o c a t i o n s present  the  a c t as n u c l e i  i n d i c a t e t h a t t h e number o f t r a n s f o r m a t i o n  an u n d e f o r m e d c r y s t a l i s q u i t e l o w , b u t  orientated  8.  may  hence,  planes  do  t o i n t e r s e c t i o n mechanisms. not  transform  effective barriers r a t e QA/G  o f 3 x 10  t o low  to s l i p  i n d e x hep  i n t h e hep  ^ can o c c u r  However, planes,  phase.  at a flow s t r e s s  170 8.  Suggestions  f o r Future Work  1.  A study of thermally a c t i v a t e d deformation by s t r a i n - r a t e change t e s t s and recovery t e s t s i n the temperature range 350°C to 600°C should give f u r t h e r information on the r a t e - c o n t r o l l i n g  processes  i n both phases. 2.  A more fundamental study of the r o l e of transformation vs. deformation d i s l o c a t i o n s c o n t r o l l i n g the transformation could be undertaken by r e s i s t i v i t y measurements on specimens thermally cycled through the transformation while a constant or v a r i a b l e s t r e s s i s applied.  3.  Cobalt deformed at high temperature should be studied by transmission e l e c t r o n microscopy i n order to compare the r e s u l t s with the recent (72) report of Thieringer  .  I f p o s s i b l e , etch p i t studies should also  be undertaken. 4.  The present data should be compared to e i t h e r a Co-33% N i or a Co-8%Fe a l l o y where the transformation occurs at room temperature.  171 Appendix I  C a l c u l a t i o n of Recovery  Rates  by D i f f u s i o n C o n t r o l l e d P r o c e s s e s  I n s e c t i o n I i t was p o s t u l a t e d t h a t d i f f e r e n c e s i n m e c h a n i c a l p r o p e r t i e s b e t w e e n c o b a l t and t h e o t h e r h e x a g o n a l and  m a g n e s i u m c o u l d b e due t o t h e f a c t  d i f f u s i o n processes  The s e l f  zinc,  cadmium  t h a t Z n , C d , a n d Mg h a v e l o w  m e l t i n g p o i n t s a n d t h a t a t room t e m p e r a t u r e by  metals,  they  e.g. c l i m b , by v a c a n c y  are subject to recovery  migration to dislocations.  d i f f u s i o n c o e f f i c i e n t D i s g i v e n by t h e A r r h e n i u s  equation D  A e C^RT)  =  Al  2 where A i s a c o n s t a n t  called  the "frequency  Q i s t h e a c t i v a t i o n energy  factor,  (cm / s e c ) .  (cal/mol/°K).  T i s the absolute temperature  (°K).  (73) Data from Metals  Reference  B o o k by S m i t h e l l s  i s shown i n T a b l e A l .  Also included i n the table are values of D (the d i f f u s i o n c o e f f i c i e n t f o r vacancies) Q/2  calculated  f o r room t e m p e r a t u r e  at the given temperatures.  b a s e d on t h e v a l u e s o f A and  The a c t i v a t i o n e n e r g y  the energy  of formation of vacancies Q  vacancies  Q.  and t h e e n e r g y  v  Q i s t h e sum o f of migration of  m  AG A G  =  V  m  AH - TAS V  =  A H  m  "  T A S  V  m  (74) AH /(AH V  AS  V  = AS  m  V  + AH ) m  i s a b o u t 0.57  h e n c e an a p p r o x i m a t i o n  that excess  vacancies  are present  v  '  and i t i s a l s o e x p e c t e d  gives Q  v  Further approximation  o f t h e known e x p e r i m e n t a l d a t a  Q  [ I t i s t h e r e f o r e assumed  i n t h e l a t t i c e as a r e s u l t o f  d e f o r m a t i o n , and t h a t t h e r e c o v e r y p r o c e s s these v a c a n c i e s ] .  = 1/2  that  mechanical  d e p e n d s o n the. m i g r a t i o n o f i s t a k e n by t h e e x t r a p o l a t i o n  ( T a b l e XX) t o room t e m p e r a t u r e ,  particularly  172 in  t h e case o f c o b a l t .  If  the dislocation density  deformed c r y s t a l , a vacancy  10  10  /cm  2  i n a highly  t h e n t h e maximum d i s t a n c e i n t h e l a t t i c e  need d i f f u s e  5 x 10 ^ cm.  over  which  t o t h e a n n h i l a t e d by a d i s l o c a t i o n i s about  From F i c k ' s second  distance L  c; i s a b o u t  the time r e q u i r e d  law of d i f f u s i o n , i n a d i f f u s i o n  f o r complete  random d i s t r i b u t i o n i s g i v e n  2 2 t = ML D  by  where M i s a c o n s t a n t depending  A2  on t h e geometry o f t h e c o n s i d e r e d  v o l u m e , e . g . f o r a s p h e r e M = 0 . 7 5 , f o r a c y l i n d e r M = 1.0 a n d f o r a s h e e t M = 1.5.  I f M = 0.75,L  = 5 x 10 ^ cm, a n d D i s t h e v a l u e  f r o m e q . A l , t h e n t h e v a l u e s o f t a r e shown i n t h e f i n a l T a b l e XX.  F o r z i n c a n d cadmium  magnesium, j u s t the m e t a l s .  a few s e c o n d s ,  calculated  column o f  t h e time i s very s h o r t indeed, f o r  t h e r e f o r e r e c o v e r y i s t o be expected i n  But f o r c o b a l t t h e d i f f u s i o n time i s p r o h i b i t i v e l y  (1 y e a r - 3 x 1 0  7  seconds)  long  and r e c o v e r y i s i m p o s s i b l e .  TABLE XX  Metal  Mg / / c  _Lc  Zn  He Jj-C lie  J t L C  Cd  Co  He  A (cm / s e c . ) 2  Q (Kcal/mol/°C)  1.0 1.5  32.2 32.2  0.13 0.58 0.076 0.39  21.8 24.3 22.0 25.0  0.05  o.io  18.2 19.1  0.51  65.5  Temp. °C  468-635  D  f o r Room Temp, (cm^/sec.)  1.88 x l O } 2.82 x 10 -  2  t (sec.)  7.45 4.96  14.4 x 10"?-° 8.9 x io"r^ 8.4 x 3.62 x 10  0.01 0.016 0.016 0.039  130-310  1.25 x lO'l 1.24 x 10  0.001 0.001  1015-1300  1 x  13 1.4 x 1 0 *  240-440 200-415  x  lO"  2 4  u  J  173  Appendix 2  Crystal Orientation  For it  high  a habit the  t o know t h e o r i e n t a t i o n  to calculate  prohibited at  t e n s i l e t e s t s p e r f o r m e d above the t r a n s f o r m a t i o n  i s essential  order  at High Temperature  the values of x  the p r a c t i c e  of taking  a  n  of the fee c r y s t a l s t r u c t u r e , i n  d A.  Experimental  i t s h o u l d be p o s s i b l e  f e e phase i f t h e o r i e n t a t i o n  However, h a v i n g  to predict  Hence f r o m a b a c k r e f l e c t i o n p i c t u r e ,  For the  into two  e x a m p l e , F i g . 59  details).  a (111) p l a n e , w i t h alternatives  shown as ®  andO.  h a s 120° s y m m e t r y .  t h e hep s t e r e o g r a p h i c  projection  f o r t h e fee o r i e n t a t i o n .  back r e f l e c t i o n p a t t e r n  t o 97 f o r f u l l  the o r i e n t a t i o n of  h a s 60° r o t a t i o n a l  symmetry about t h e c e n t r e and t h e (111) p r o j e c t i o n  two p o s s i b i l i t i e s  determined  o f t h e h e p p h a s e i s known.  U n f o r t u n a t e l y , t h e (0001) p r o j e c t i o n  gives  difficulties  a back r e f l e c t i o n d i f f r a c t i o n p a t t e r n  t e m p e r a t u r e on e a c h t e n s i l e s p e c i m e n . relationship  temperature,  (a) i s the s t e r e o g r a p h i c p r o j e c t i o n of  f i g 5 8 ( a ) of s p e c i m e n S 1 3 , ( s e e p a g e s The b a s a l p l a n e  i s assumed t o t r a n s f o r m  t h e <1120> d i r e c t i o n s  f o r the construction T h e v a l u e s of x  a n  p a r a l l e l t o <110>.  of t h e o t h e r d  90  The  {111} p l a n e s a r e  X for the various  {111} p l a n e s o f  e a c h a l t e r n a t i v e are g i v e n i n T a b l e X I .  The the  correct  orientation  angle between the primary s l i p  this value  i s t h e n o b t a i n e d by s i m p l y trace  t o t h e two p o s s i b i l i t i e s .  v a r i a t i o n o f x b e t w e e n one c o n s t r u c t i o n it  i s 14°) and t h e s l i p  trace  measuring  and t h e s p e c i m e n s a x i s  I n most c a s e s and a n o t h e r ^  and r e l a t i n g  there i s a wide ( I n s p e c i m e n SI 3  measurement gave 32°, so t h e second  a l t e r n a t i v e , shown by t h e s y m b o l © c o r r e c t one.  I n every  unquestionably  determined.  i n F i g . 59 ( a ) was  taken  t o be t h e  s p e c i m e n t h u s t e s t e d , t h e f e e o r i e n t a t i o n was  An example o f t h e use o f t h i s p r o c e d u r e w i l l be Referring again photographs  to the deformation  taken  a f t e r a s h e a r s t r a i n o f 0.14  a s h e a r s t r a i n o f 0.87 projections,  o f s p e c i m e n S13 b a c k  (Figs.  reflection  ( F i g . 58 ( b ) ) a n d a f t e r  ( F i g . 58 ( c ) ) h a v e b e e n p l o t t e d o n  59 ( a ) a n d  of a face a t r i g h t angles  59 ( b ) ) .  described.  stereographic  ( N o t e t h a t F i g . 58 ( c ) i s t a k e n  t o b o t h F i g s . 58 ( a ) a n d 58 ( b ) .  On F i g . 59 ( a ) t w i n t r a c e n o r m a l s o f F i g s . 35 ( c ) a n d ( d ) are  superimposed.  (As t h e p l a n e  o f F i g . 35 ( c ) i s a t r i g h t a n g l e s  t h e f a c e o f t h e X - r a y p a t t e r n i n F i g . 35 ( b ) , t h e s e rotated slip  through 90°).  traces l i e s  t r a c e n o r m a l s must be  I t can be seen t h a t the i n t e r s e c t i o n o f the  a t t h e (111) p o l e w i t h  the highest  Schmid f a c t o r , and  t h a t t h e t w i n t r a c e s a r e on t h e (111) p o l e w h i c h corresponded o r i g i n a l basal plane,  to  and w h i c h i s n o t f a v o u r a b l y  to the  oriented.  A f t e r a s h e a r s t r a i n o f 8 7 % , t h e t r a c e n o r m a l s o n F i g . 35 ( j ) (which again hep  i s t h e same f a c e a s t h e X-Ray P h o t o g r a p h F i g . 58 '(c)), a n d F i g . 35 ( k ) , corresponded  t o (111) p l a n e s , b u t t h e r e l a t i v e o r i e n t a t i o n i n t h e  phase has changed.  p l a n e , w h i c h means plane,  The s l i p  plane  t h a t t h e t r a n s f o r m a t i o n h a s t a k e n p l a c e o n a new  and t h a t on r e h e a t i n g  becomes t h e ( 1 1 1 ) p l a n e w i t h  through the transformation, the highest  o f F i g s . 35 ( j ) a n d ( k ) now c o r r e s p o n d i n t o a more f a v o u r a b l e  This  now c o r r e s p o n d s t o t h e b a s a l  S c h m i d f a c t o r (x  e x p e r i m e n t was r e p e a t e d  Schmid f a c t o r .  the b a s a l The t w i n  habit plane traces  t o a (111) p l a n e w h i c h has t o t a t e d has i n c r e a s e d  with other  f r o m 14  to  specimens and t h e r e s u l t  was  r e p r o d u c e a b l e when t h e t r a n s f o r m a t i o n was  b e f o r e the c r y s t a l i n d i c a t e d by lattice  this  s t r u c t u r e showed s i g n s o f r e c r y s t a l l i s a t i o n  the X-ray  pattern.  The  as  maximum s h e a r s t r a i n w h i c h  the  can undergo b e f o r e change i n the t r a n s f o r m a t i o n p l a n e i s  p r e v e n t e d , has 0.5  allowed to take p l a c e  t o 0.8.  not been a c c u r a t e l y determined Similarly,  but  i s probably  about  t h e minimum amount o f d e f o r m a t i o n t o  cause  change i n t r a n s f o r m a t i o n p l a n e i s p r o b a b l y about  0.2.  1 7 6  (b) (a)  Fig. 58  (a) (b)  (c)  (c)  Back reflection patterns of Specimen S13 Before deformation After shear strain 0.14 After shear strain 0.87  177  Fig.  59  (a)  S t e r e o g r a p h i c p r o j e c t i o n of back p a t t e r n shown i n F i g . 58 ( b ) .  reflection  The b a c k r e f l e c t i o n p h o t o g r a p h ( F i g . i s t a k e n o f t h e same f a c e as 35 ( d ) . T a b o v e a r e t h e s l i p and t w i n t r a c e f r o m 35 ( d ) . . T r a c e s S± and (from m u s t b e r o t a t e d t h r o u g h 90° i n o r d e r and t w i n p l a n e s may b e i d e n t i f i e d . 2  0  Represents the b a s a l  58  (b) S and normals F i g . 35 t h a t the 2  plane  A r e t h e two a l t e r n a t i v e p o s i t i o n s o f t h e (111) p l a n e s a b o v e t h e t r a n s f o r m a t i o n , and O was f o u n d t o be t h e c o r r e c t v a r i a n t . The i n t e r s e c t i o n of the s l i p t r a c e s l i e s c l o s e to a (111) p l a n e , and t h e t w i n p l a n e i s c l o s e t o the transformed b a s a l plane.  (c)) slip  178  N  S  Fig.  59(b)  Stereographic p r o j e c t i o n of back p a t t e r n shown i n F i g . 58 ( c ) .  reflection  S3 and T3 a r e t h e s l i p and t w i n t r a c e n o r m a l s o f F i g . 35 ( j ) . S 4 and T4 a r e t h e s l i p and t w i n t r a c e n o r m a l s o f F i g . 35 ( k ) r o t a t e d t h r o u g h 90 O r e p r e s e n t s t h e p o l e s o f t h e (111) p l a n e s i n t h e f e e p h a s e and t h e s l i p p l a n e i s t h e ( 0 0 0 1 ) / (lll) transformation plane. n  c  179  Appendix 3  V a r i a t i o n o f Shear Modulus w i t h  Temperature  I n the hexagonal phase, c o b a l t r e q u i r e s f i v e elastic  constants  strains  at a given point.  and C.  0  12  C^.  constants  a r e needed C - Q '  44  (111) p l a n e  most r e c e n t d a t a on t h e t e m p e r a t u r e crystals  f o r fee.  dependence o f e l a s t i c  moduli  of cobalt single  values  o f C., up t o 523°K (250°C) i . e . w e l l b e l o w t h e t r a n s f o r m a t i o n  due t o F i s h e r a n d D e v e r ^ " ^ 7  The r e a s o n  t o alignment  f o r this  i s acoustic attenuation,  at higher  temperatures).  s i m i l a r method on p o l y e r y s t a l s M a r i n g e r Brandis  (77)  , and P o s t n i k o v  transformation.  (78)  and M a r s h B u n g a r d t ,  have a l l p u b l i s h e d the  An average o f t h e s e r e s u l t s  temperature  exceeding the  i s shown i n F i g . 60  are approximately  A parallel,  t h e r e f o r e an e x t r a p o l a t i o n o f t h e F i s h e r and Dever curve has been  used f o r v a l u e s  o f G a b o v e 250°C.  T h i s seems j u s t i f i e d  t i o n d o e s n o t h a v e any e f f e c t o n t h e p o l y c r y s t a l l i n e i n d i v i d u a l curves temperatures be  Preisendang  o n t h e same g r a p h F i s h e r a n d D e v e r ' s r e s u l t s a r e p r e s e n t e d .  c o m p a r i s o n shows t h a t up t o 250°C t h e c u r v e s and  (possibly  However, u s i n g a  d e p e n d e n c e o f t h e s h e a r m o d u l u s up t o t e m p e r a t u r e s  and  gives  o f magnetic domains) w h i c h i n t e r f e r r e d w i t h the  recording of results  and  only  44  temperature. due  ^33  C.. i s t h e s h e a r m o d u l u s i n t h e b a s a l  f o r hep and i n t h e c l o s e - p a c k e d  The  a r e C - Q > C-j^* ^13*  The s t i f f n e s s m o d u l i  I n each case  44  plane  t o s p e c i f y t h e r e l a t i o n s h i p s between s t r e s s e s and  I n the c u b i c phase only three such  a n d C...  independent  fluctuate slightly  curve  recalculated, indicate that  (two o f  a t t h e t r a n s f o r m a t i o n , b u t as t h e  v a r y by a b o u t 50°C, t h e e f f e c t i s l o s t ) .  s t a t e d t h a t t e s t s on a s i n g l e  as t h e t r a n s f o r m a -  However, i t s h o u l d  c r y s t a l o f f e e C o - 8 % F e a t 300°K when decreases  markedly a f t e r  the transformation.  180  But  a s no f u r t h e r i n f o r m a t i o n  the e x t r a p o l a t e d appreciable  values  margin.  will  In this  i s a v a i l a b l e , i t cannot be c o n c l u d e d differ  from the c o r r e c t values  t h e s i s , reference  c o b a l t has been r e c a l c u l a t e d u s i n g  the data  that  by an  t o a l l o t h e r work on  o f F i s h e r and Dever.  F i s h e r and Dever  (75)  e x t r a p o l a t e d f o r the temperature range o f t h e p r e s e n t work a v e r a g e v a l u e s from ( 7 6 ) , (77) and(78).  — — • -  \ \  \ \  \  \  \ \ \ \  \  \ \  200 Fig.  60  400  600  V a r i a t i o n o f s h e a r modulus w i t h  Temperature temperature  K  K. G. D a v i s , Ph.D.  T h e s i s , D e p t . o f M e t a l l u r g y , U.B.C., 1 9 6 1 .  K. G. D a v i s a n d E. T e g h t s o o n i a n ,  T r a n s . TMS-AIME, 221  K. G. D a v i s a n d E. T e g h t s o o n i a n , A c t a . M e t . , 10 K. G. D a v i s  and E.  0. B o s e r , Z. M e t a l l k u n d e , 58 J.  1189. ( 1 9 6 3 ) 762.  Rapp., Phys. S t a t . S o l .  a n d H. B i b r i n g ,  T r a n s . TMS-AIME 194  (1952) 645.  I n s t i t u t e o f M e t a l s Monograph  H.  Bibring  a n d F. S e b i l l e a u ,  Compt. R e n d u .  244  ( 1 9 5 7 ) 496.  H.  Bibring  a n d F. S e b i l l e a u ,  Compt. R e n d u .  245  (1957)  C. R. H o u s k a , B. L . 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