SOLID SOLUTION STRENGTHENING OF MAGNESIUM by AINUL AKHTAR B.Sc- (Hons), Utkal U n i v e r s i t y , I n d i a , 1962 B„E., Indian I n s t i t u t e of Science, I n d i a , 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 required standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1968 In presenting for an that advanced the Study. thesis degree I further for agree make that it freely h.i;s of of this thesis may for permission. Metallurgy September 18, Columbia 1968 be for granted It is financial of British available permission representatives. by fulfilment U n i v e r s i t y of or The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada Date the purposes my w r i t t e n Department at in p a r t i a l scholarly publication without thesis Library shall Department or this for the Columbia, I reference and extensive by the requirements copying Head o f understood gain shall this my that not of agree be copying allowed ABSTRACT S o l i d s o l u t i o n strengthening -1 i n magnesium p o l y c r y s t a l s containing Zn, A l , Cd, I n and Pb as solute has been i n v e s t i g a t e d over the temperatures between 78° and 513°K with p a r t i c u l a r emphasis on the d i l u t e alloys. The v a r i a t i o n of y i e l d s t r e s s with concentration occurs i n e i t h e r two or three stages. I n stage I , the y i e l d s t r e s s increases r a p i d l y and l i n e a r l y with concentration; i n stage I I , the rate of increase of y i e l d stress i s very much l e s s than i n stage I ; i n stage I I I , the y i e l d stress decreases with solute a d d i t i o n s . the t r a n s i t i o n concentrations The s o l u t i o n hardening rates and from stage I to stage I I (C ) depend on the s i z e - d i f f e r e n c e between Mg and the solutes. T The r e s u l t s are discussed i n terms of the v a r i a t i o n with concentration of the CRSS f o r both basal and prismatic s l i p . I t i s proposed that at concentrations l e s s than C^, the increase i n CRSS f o r prismatic s l i p i s the dominant f a c t o r ; beyond C^, y i e l d i s governed by a balance between basal hardening and p r i s m a t i c softening. The e f f e c t of solute on the d u c t i l i t y of magnesium at elevated temperatures i s discussed i n terms of a s t r e s s induced polygonization process and the d u c t i l i t y maxima observed i n the Mg-Al a l l o y s are explained. Single c r y s t a l s of Mg-Zn a l l o y s oriented f o r basal s l i p have been deformed i n tension over the temperature range from 78°K to 423°K. The v a r i a t i o n of the basal d i s l o c a t i o n density caused by the a d d i t i o n of solute has been studied using transmission e l e c t r o n microscopy of t h i n f o i l s . The increase i n d i s l o c a t i o n density which was found to be proportional to the square root of the solute concentration, cannot account f o r the observed increase i n the athermal s t r e s s . A d i s l o c a t i o n etch p i t technique has been developed and used to measure the v a r i a t i o n i n the f o r e s t d i s l o c a t i o n density with solute concentration. The f o r e s t density increases l i n e a r l y and r a p i d l y up to a c e r t a i n minimum solute concentration, beyond which i t remains almost constant. The r e s u l t s are i n good agreement with the observed thermally activated flow s t r e s s f o r low solute concentrations. The observed v a r i a t i o n i n the athermal component of CRSS has been discussed i n the l i g h t of an increased f r i c t i o n s t r e s s a r i s i n g due to a random d i s t r i b u t i o n of s o l u t e . Using rate theory, i t has been shown that the f o r e s t i n t e r section remains the rate c o n t r o l l i n g mechanism up to a c e r t a i n low concentration of solute beyond which the s i n g l e solute atom pinning of d i s l o c a t i o n s becomes the rate determining process. The solute dependence of the work hardening parameters are also reported and examined i n the l i g h t of the e x i s t i n g theories of work hardening. Single c r y s t a l s of Mg - Zn and Mg- A l a l l o y s have also been deformed so as to suppress basal s l i p and induce prismatic s l i p . {1012} twinning and to The r e s u l t s have been explained i n terms of an increasing athermal stress and a decreasing P e i e r l s s t r e s s with the a d d i t i o n of s o l u t e . P e i e r l s s t r e s s has been shown to be the rate c o n t r o l l i n g mechanism below room temperature. The observed v a r i a t i o n of CRSS f o r prism s l i p with solute concentration accounts adequately f o r the concentration dependence of y i e l d s t r e s s i n the p o l y c r y s t a l l i n e aggregate. The r e s u l t s a l s o suggest that the decrease i n P e i e r l s s t r e s s with solute a d d i t i o n i s not n e c e s s a r i l y associated with a decreasing c/a r a t i o and the monovalent nature of the s o l u t e . iii ACKNOWLEDGEMENT The author g r a t e f u l l y acknowledges the advice and encouragement given by h i s research d i r e c t o r , Professor E. Teghtsoonian. Thanks are also extended to other members of the f a c u l t y and the graduate students f o r h e l p f u l d i s c u s s i o n s . F i n a n c i a l assistance i n the form.of Lead-Zinc research f e l l o w s h i p and the N a t i o n a l Research Council studentship i s g r a t e f u l l y acknowledged. iv TABLE OF CONTENTS 1. S o l u t i o n Strengthening i n P o l y c r y s t a l s Page. 1 1.1. Introduction and Objectives 1 1.2. Experimental Procedure 4 1.2.1. M a t e r i a l s and a l l o y preparation 4 1.2.2. Preparation of p o i y e r y s t a l l i n e specimens 4 1.2.3. The growth of s i n g l e c r y s t a l s 5 1.2.4. Standard sections used 7 1.2.5. Spark erosion damage 8 1.2.6. Preparation of s i n g l e c r y s t a l specimens f o r tensile tests 9 1.2.7. Testing procedure 10 1.3. Deformation c h a r a c t e r i s t i c s of p o i y e r y s t a l l i n e aggregates 12 1.3.1. Nature of the s t r e s s - s t r a i n curves 12 1.3.2. The y i e l d s t r e s s 1.3.2.1. 1.3.2.2. 1.3.2.3. 1.3.2.4. 1.3.2.5. 18 21 24 28 28 1.3.3. The c r i t i c a l t r a n s i t i o n concentration 31 1.3.4. The maximum s t r e s s v a r i a t i o n with temperature and a l l o y i n g 35 1.3.5. Flow s t r e s s i n r e l a t i o n to temperature and alloying 38 1.3.6. Ductility 44 1.3.6.1. 1.3.6.2. 1.4. The temperature dependence of y i e l d The concentration dependence of y i e l d S o l u t i o n strengthening i n stage I Strengthening above Cj The temperature dependence of the s o l u t i o n strengthening parameters Alloying effect The temperature dependence of ductility 44 44 Discussions 49 1.4.1. 49 50 Deformation modes i n Magnesium 1.4=1.1. C r y s t a l l o g r a p h i c s l i p Table of Contents (Cont) 1.4.1,2= 1.4.1.3. 1.4.1.4. Page 54 57 58 P l a s t i c deformation by twinning Grain boundary deformation C e l l formation 1.4.2. Fracture of Magnesium p o l y c r y s t a l s 59 1.4.3. Solution hardening 60 1.4.3.1. 1.4.3.2. 1.4.3.3; 1.4.3.4. 1.4.3.5. 1.4.4. .1.4.5. 2. v The v a r i a t i o n of O y p and d u c t i l i t y with solute concentration , The s o l u t i o n hardening rate (|£.) Hardening beyond.Cj The t r a n s i t i o n concentration C The flow s t r e s s 64 64 66 67 68 T The e f f e c t of temperature on d u c t i l i t y 69 1.4.4.1. 70 The d u c t i l i t y maxima Strengthening e f f e c t s i n multicomponent solutions solid 72 S o l u t i o n hardening i n a l l o y s i n g l e c r y s t a l s 75 2.1. I n t r o d u c t i o n and Objectives 75 2.2. S t r e s s - S t r a i n R e l a t i o n s h i p s i n Basal S l i p 76 2.2.1. 2.2.2. 2.2.3. 2.2.4. 2.2.5. 2.2.6. The s t r e s s - s t r a i n curves The e f f e c t of substructure on work hardening The s t r e s s - s t r a i n curves of the Mg-Zn a l l o y s Y i e l d points The c r i t i c a l resolved shear s t r e s s The rate of s o l u t i o n hardening 2.2.6.1, 2.2.6.2. 2.2.7. 76 78 80 . 84 88 91 The temperature dependence of S j The v a r i a t i o n of STT with temperature Work hardening 2.2.7.1. The work hardening rate i n Stage A, 0 The extent of easy g l i d e Stress at the onset of Stage B, r x The work hardening rate i n stage B, 9 Deformation i n stage C 93 A 2.2.7.2. 2.2.7.3. 2.2.7.4. B 2.2.7.5. 2.3. 91 93 B 93 96 100 100 103 The e f f e c t of solute on the d i s l o c a t i o n d e n s i t i e s 103 2.3.1. The basal d i s l o c a t i o n density 105 2.3.1.1. 2.3.1.2. 106 107 F o i l preparation Observations vi Table of Contents (Cont) Page 2.3.1.3. 2.3.1.4. 2.3.2. The f o r e s t d i s l o c a t i o n density 2.3.2.1. 2.3.2.2. 2.3.2.3. 2.4. The technique of d i s l o c a t i o n d i s l o c a t i o n density measurement and i t s limitations The e f f e c t of solute on the basal d i s l o c a t i o n density C r y s t a l o r i e n t a t i o n and the p i t characteristics The study of spark erosion damage i n Mg using the d i s l o c a t i o n etch p i t method V a r i a t i o n of the.etch p i t density with a l l o y i n g Discussions . 108 112 114 114 115 118 119 2.4.1. The c r i t i c a l resolved shear stress 119 2.4.2. Solution strengthening i n the athermal region 121 2.4.2.1. 2.4.2.2. 2.4.2.3. 2.4.2.4. 2.4.2.5. 122 125 126 128 2.4.2.6. 2.4.2.7. 2.4.2.8. 2.4.3. The basal d i s l o c a t i o n density Elastic interaction Chemical i n t e r a c t i o n Short range order Strengthening due to a random d i s t r i b u t i o n of the solute Strengthening at low solute concentrations. Valency e f f e c t Other hardening mechanisms 130 133 135 135 Solution strengthening at, low temperatures 136 2.4.3.1. 2.4.3.2. 140 2.4.3.3. 2.4.3.4. 2.4.3.5. Thermally activated deformation The e f f e c t of solute on the apparent a c t i v a t i o n parameters The a c t i v a t i o n volume at y i e l d Solution e f f e c t on the apparent a c t i v a t i o n energy Zinc a l l o y i n g and the thermally activated flow 2.4.3.5.1. Cross s l i p 2.4.3.5.2 P e i e r l s , Pseudo P e i e r l s and Recombination mechanisms 2.4.3.5.3. The i n t e r s e c t i o n model a) i n t e r s e c t i o n model, at low solute concentration 2.4.3.5.4. D i s l o c a t i o n pinning by the solute atoms 143 145 148 149 151 152 153 155 156 vii Table of Contents (Cont) Page 2.4.3.6. 2.4.3.6.1, 2.4.4. 159 Deviations from square array 163 Work hardening of Mg s o l i d solutions 2.4.4.1.1. 2.4.4.1.2. 2=4.4.2. 2.4.4.3. 2.4.4.4. 2.4.4.5. 2.4.5. Strengthening mechanisms i n d i l u t e alloys The easy g l i d e i n Mg Easy g l i d e i n a l l o y c y r s t a l The temperature dependence of 9 A i n alloy crystals The extent of easy g l i d e Work hardening in.stage B The stage 'C' of deformation The E f f e c t of solute on the ease of prismatic slip 2.4.5.1. 2.4.5.2. 2.4.5.2.1. 2.4.5.2.2. 2.4.5.2.3. 2.4.5.2.4. 2.4.5.2.5. 2.4.5.3. 2.4.5.3.1. 2.4.5.3.2, 2.4 s5.3.3. 2.4.5.3.4. 164 165 167 168 169 171 172 173 Introduction and objectives Experimental r e s u l t s The s t r e s s - s t r a i n curves Ductility The CRSS f o r prismatic s l i p The CRSS of Mg-Zn a l l o y s The e f f e c t of solute on the flow stress 173 174 174 181 181 183 Discussions 189 187 The d i s l o c a t i o n mechanism f o r prismatic slip 189 The e f f e c t of solute 190 The r e s u l t s of the presgnt work 192 The O r i g i n of T and T 195 g 2.4.5.3.4.1. The athermal stress 195 2.4.5.3.4.2. The v a r i a t i o n of T * with a l l o y i n g 196 3. Summary of Conclusions 198 4. Suggestions f o r Future Work 201 5. ' Appendices A. Determination of solute concentration i n the a l l o y s B. The P r e f e r e n t i a l nature of the s o l u t e - d i s l o c a t i o n i n t e r action C. The determination of Ar from s t r a i n rate change tests Bibliography 202 202 206 209 211 viii LIST OF FIGURES No. Page 1. Standard sections f o r obtaining t e n s i l e specimens from the as-grown c r y s t a l . . . . . . . . . . . . . . ... . 2. Gripping arrangement for basal s l i p specimens 3. S t r e s s - s t r a i n curves f o r Mg-Zn. a l l o y s tested at 295°K . 13 4. S t r e s s - s t r a i n curves for Mg-Al a l l o y s tested at 295°K . 14 5. S t r e s s - s t r a i n curves for 65y grain s i z e Mg 6. S t r e s s - s t r a i n curves for Mg + 0.055 a t . % A l a l l o y ... 16 7. S t r e s s - s t r a i n curves f o r Mg + 0.53 a t . % A l a l l o y . . . . 17 8. Y i e l d stress-temperature r e l a t i o n s h i p s f o r Mg-Al a l l o y s 19 9. Y i e l d stress-temperature r e l a t i o n s h i p s f o r Mg-Cd a l l o y s 20 10. The composition dependence, of Tt i n Mg-^-Al and Mg-Cd a l l o y s 22 11. Y i e l d stress-concentration p l o t for Mg^Zn a l l o y s . . . . 23 12. Y i e l d stress-concentration p l o t f o r Mg-Cd a l l o y s . . . . 23 13. Stage I s o l u t i o n hardening at 295°K f o r various a l l o y s . 26 14. Stage I slope vs s i z e m i s f i t parameter 27 15. 16. Stage I I slope vs s i z e .misfit parameter . . . The e f f e c t of temperature on the s o l u t i o n hardening curve f o r Mg-Al a l l o y s ...... ..... 27 29 17. The e f f e c t of temperature on the s o l u t i o n hardening curve f o r Mg-Cd a l l o y s . . . . . . . 30 18. C r i t i c a l . t r a n s i t i o n concentration, C^, from stage I to stage I I vs temperature for Cd solute . . . . . . . . . 32 19. Cx vs temperature for A l solute. 32 20. a) Stage I slope vs temperature for Mg-Cd a l l o y s b) 21. . . . » . 6 ...... . . . . . . . . . . . . 11 15 ..... 33 Stage I I slope vs temperature.for Mg-Cd a l l o y s . . . . . 33 Stage I slope vs temperature.for A l solute . . . . . . . 34 ix L i s t of Figures (Cont) No, Page 22. C r i t i c a l t r a n s i t i o n concentration, C from stage I to stage I I vs s i z e m i s f i t parameter . . . . . . . . . . . 34 23. Maximum s t r e s s vs. temperature f o r Mg-Al a l l o y s . . . . 36 24. Fracture s t r e s s vs. composition f o r Mg-Cd a l l o y s tested T at 295°K .... . . . . . . . . . . . . . 37 25. Flow s t r e s s vs. temperature f o r 65y Mg . . . . . . . . 39 26. Flow s t r e s s vs. temperature f o r Mg + 0.055 a t . % AI a l l o y 40 27. 28. Flow s t r e s s vs. temperature f o r Mg + 0.53 a t . % AI a l l o y T r a n s i t i o n temperature from stage I to stage I I i n the f l o w stress-temperature curves of Mg + 0.055 a t . % AI a l l o y vs. s t r a i n . . . . . . . . . . . . . . 41 29. Flow s t r e s s vs. composition f o r Mg-Zn a l l o y . . . . . . 43 30. D u c t i l i t y vs. concentration f o r various solutes . . . . 31. True s t r a i n to f r a c t u r e vs. temperature f o r Mg-Al a l l o y s 46 32. True s t r a i n , t o maximum s t r e s s vs. temperature f o r Mg-Al alloys ..... ..... 48 33. True s t r a i n associated with negative work hardening vs. temperature f o r Mg-^Al a l l o y s . . . . . . . . . . . . . 48 34. CRSS f o r basal s l i p vs. concentration (After Levine et al(74)) 63 35. Revised curves drawn f o r data from r e f . 74 63 36. S o l u t i o n hardening curve f o r Mg-Zn-In, ternary a l l o y s tested at 295°K w i t h Zn concentration f i x e d at 0.004 at.%. . . . 74 S o l u t i o n hardening curve f o r Mg-Zn-In-ternary a l l o y s tested at 295°K with Zn concentration f i x e d a t 0.007 at.%. 74 Resolved shear stress-shear s t r a i n curves f o r Mg s i n g l e c r y s t a l s oriented f o r basal s l i p ....... 77 Schematic resolved shear stress-shear s t r a i n curve 79 37. 38. 39. . . 42 45 X L i s t of Figures (Cont) No. 40. 41i 42. Page Sub-boundary.running p a r a l l e l to the t e n s i l e - a x i s i n a Mg t 0 . 0 5 4 at.%.Zn.alloy c r y s t a l deformed i n easy g l i d e at room temperature . . . . . . . . . . . . . . . 79 Resolved.shear stress-shear s t r a i n curves f o r Mg s i n g l e c r y s t a l s deformed by various workers at room,temperature 81 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg + 0 . 0 1 9 a t ; % Zn a l l o y s i n g l e c r y s t a l s 43. 45. 46. 82 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg + 0 . 0 1 9 a t . % Zn.alloy s i n g l e c r y s t a l s 44. ....... ....... 83 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn s i n g l e c r y s t a l s deformed at 3 7 3 ° K . . . . . 85 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn a l l o y s i n g l e c r y s t a l s deformed at 2 9 5 ° K . . . . . . . . 86 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn a l l o y s i n g l e c r y s t a l s deformed at 1 9 5 ° K . . . . . . . 87 47. CRSS f o r basal s l i p vs. temperature f o r Mg-Zn.single crystals 89 48. S o l u t i o n strengthening i n b a s a l s l i p vs. concentration for Mg-Zn a l l o y s 90 S o l u t i o n strengthening i n basal s l i p vs. square root.of the solute concentration ..... 90 49. 50. 51. The v a r i a t i o n of the s o l u t i o n strengthening parameter S^ with temperature . . . . . . . . . . . . . 92 The v a r i a t i o n of the s o l u t i o n strengthening parameter SJJ with temperature . . . . . . . . . . . . . . . . . 92 52. The work hardening rate i n stage A vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s . . . . 94 53. The temperature dependence of the work hardening rate i n the easy g l i d e of Magnesium as reported by various workers . . . . . . . . . . ..... 95 54. The increase i n work hardening rate i n easy g l i d e v s . Zn concentration . 97 xi L i s t of Figures (Cont) No. Page 55. The Increase i n work hardening rate i n easy g l i d e vs. square root of the Zn concentration . . . . . . . . . . 98 56. The extent of easy g l i d e as a f u n c t i o n of temperature for Mg-Zn s i n g l e c r y s t a l s . . . . . . . . . . . . . . . 99 The decrease i n the extent of easy g l i d e as a f u n c t i o n of the solute concentration . . . . . . . . . . . . . . 99 The e f f e c t of temperature and solute concentration on the s t r e s s at the onset of stage B . . . . . . . . . . 101 59. The e f f e c t of temperature on the work hardening r a t e of Mg-Zn c r y s t a l s i n stage B . . . . . . . . . . . . . . . 102 60. The increase i n the work hardening r a t e i n stage B 57. 58. vs. Zn concentration . . . . . . . . . . . . . . . . . 102 61. The s t r e s s at the onset of stage C vs. Zn concentration 104 62. 63. T y p i c a l d i s l o c a t i o n s t r u c t u r e i n as.grown Mg c r y s t a l . . E l e c t r o n micrograph showing d i s l o c a t i o n s surrounding a parti 107 64. T y p i c a l d i s l o c a t i o n s t r u c t u r e i n an undeformed Mg + 0.18 ate % AI a l l o y s i n g l e c r y s t a l . . . . . . . . . . . . . 110 65. T y p i c a l d i s l o c a t i o n structure i n an undeformed Mg + 0.38 at. % AI a l l o y s i n g l e c r y s t a l I l l 66. B a s a l - d i s l o c a t i o n density vs. square root of s o l u t e concentration f o r Mg-Al a l l o y s ..... 67. a) b) Hexagonal shape of the etch p i t s . . . . . . . . . . . D i s t r i b u t i o n of etch p i t s i n a Mg + 0.019 at.%. Zn alloy crystal . . . . . . . . . . . . . . . . . . . . . 68. D i s l o c a t i o n etch p i t s on the {0001} C l T y S _,_il • o o o a e « o « * e e o e « 113 116 116 plane of Mg s i n g l e O B O O O o e > e o H 7 69. Etch p i t density vs. Zn concentration . . . , . , , . . 117 70. The temperature dependence of y i e l d i n terms of the s t r e s s components 120 71. Comparison of the observed s o l u t i o n strenthening w i t h that expected from the increase i n the basal d i s l o c a t i o n xii L i s t of Figures (Cont) No. 72„ Page 1/2 The increase-in.CRSS of Mg vs. ( L i concentration) i n Mg-Li a l l o y s i n g l e c r y s t a l s . ..... 124 73. r v s . concentration f o r Ag s o l i d solutions ..... 134 74. The e f f e c t of solute on the T - T curve (schematic) . . 136 ft 75. 76. T v s . temperature f o r Mg-Zn s i n g l e c r y s t a l s . . . . . * (T^ ) v s . solute concentration f o r Mg-Zn s i n g l e - dT . ,. Y/Y 77. 78. 79. 80. 138 0 . crystals . . . . . . . . . . . . . . . . . . . . . . . A c t i v a t i o n volume vs. shear s t r a i n f o r Mg-Zn.single crystals . .............. A c t i v a t i o n volume at y i e l d vs. Zn concentration . . . A c t i v a t i o n volume at y i e l d vs. temperature f o r Mg and Mg + 0,045 a t . % Zn a l l o y s i n g l e c r y s t a l s . * A c t i v a t i o n volume at y i e l d vs. x f o r Mg and Mg + 0.45 a t . % Zn a l l o y s i n g l e c r y s t a l s , ..... 144 146 146 147 81. Apparent a c t i v a t i o n energy vs. Zn concentration 82. D i s l o c a t i o n pinning by solute atoms g i v i n g r i s e to low temperature f r i c t i o n s t r e s s (schematic) . . . . . . . 156 83. Comparison.of the experimental r e s u l t s with the composition dependence of a c t i v a t i o n volume as predicted by F r i e d e l ' s model 158 Concentration.dependence of CRSS extrapolated for Ag-In and Ag-Al s i n g l e . c r y s t a l s 158 84. 85. . . . 138 150 to 0°K Resolved shear stress vs. shear strain,curves f o r Mg s i n g l e c r y s t a l s oriented f o r prismatic s l i p . . . . . 86. Resolved shear s t r e s s vs. shear s t r a i n f o r Mg + 0.019 a t . % Zn a l l o y s i n g l e c r y s t a l s oriented f o r prismatic 87. Resolved shear stress vs. shear s t r a i n curves f o r Mg + 0.258 a t . % Zn a l l o y s i n g l e c r y s t a l s oriented f o r prismatic s l i p 175 177 xiii L i s t of Figures (Cont) No. 88. 89. 90. 91. 92. Page Resolved:shear s t r e s s vs. shear s t r a i n curves f o r Mg + 0.45 a t , % Zn a l l o y s i n g l e , c r y s t a l s oriented f o r prismatic s l i p . . . . . . . . . . . . . . . 178 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn-single c r y s t a l s deformed at 423°K i n prism s l i p orientation . . . . . . . . . . . . . . . . . . . . . 179 Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn s i n g l e c r y s t a l s deformed at 78°K i n prism s l i p orientation . . . . . . . . . . . . . . . . . . . . . 180 Shear-strain to-fraeture vs. temperature f o r Mg-Zn s i n g l e . c r y s t a l s oriented f o r prismatic s l i p . . . . . 182 CRSS f o r prismatic s l i p vs. temperature f o r Mg-Zn single crystals . . . . . . . . . . . . . . . . . . . 93. CRSS f o r prismatic s l i p vs. Zn concentration 94. CRSS f o r prismatic s l i p vs. temperature f o r Mg-^Al single crystals . . . . . . . . . . . . . Flow s t r e s s f o r prismatic s l i p vs. concentration f o r Mg-Zn s i n g l e c r y s t a l s tested at 78°K . . . . . . . . . 95„ . .... 184 185 186 188 96. Flow stress vs. concentration f o r Mg-Zn s i n g l e c r y s t a l s tested at 423°K ............. 188 97. A c t i v a t i o n volume at y i e l d vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s deformed i n prism s l i p o r i e n t a t i o n . . 191 98. CRSS f o r prismatic s l i p vs. temperature f o r Mg-Li a l l o y single crystals . . . . . . . . . . ... 193 99. Schematic representation of the e f f e c t of solute on the various components of flow s t r e s s i n prismatic s l i p . 194 100. Absorbance vs. Zn concentration 205 101. Solution hardening curves f o r Mg-Zn and Mg-In binary systems 207 102. The nature of the flow s t r e s s observed during s t r a i n . r a t e change t e s t s i n Mg-Zn s i n g l e c r y s t a l s . (Oriented for basal s l i p ) . . . . . . . . . . . . . . . 210 X I V LIST OF TABLES Page I Solution hardening parameters f o r p o l y c r y s t a l s 3.t 293 K o o o Q O o e > o ' o o o » o o o o o tested o o o o o 25 o e o o o 54 II S l i p systems i n hexagonal metals III Comparison of s o l u t i o n hardening rates „ » « « , » „ « 65 IV Strengthening due to increased 162 o » o o o o f o r e s t density = , 0 0 0 PART I 1. L L Solution Strengthening i n P o l y c r y s t a l s INTRODUCTION & OBJECTIVES : The systematic study of s o l i d s o l u t i o n strengthening mechanisms has lagged considerably behind i t s a p p l i c a t i o n s . e s p e c i a l l y the case f o r m a t e r i a l s with hep s t r u c t u r e . This i s Solid solutions with fee structure have been considered i n some d e t a i l during the past (1 2) decade ' . However, the l i m i t e d understanding of the deformation c h a r a c t e r i s t i c s of hep pure metals has i n h i b i t e d i n v e s t i g a t i o n s of s o l u t i o n strengthening i n t h i s c l a s s of m a t e r i a l . Of a l l hexagonal metals, titanium and magnesium have been studied i n the greatest d e t a i l because of t h e i r favourable strength to weight r a t i o . The pure metal magnesium i s not used i n many t e c h n o l o g i c a l a p p l i c a t i o n s , mainly due to i t s embrittlement during cold working. Therefore,,the problem of determining the deformation mechanisms which (3-13) c o n t r o l flow i n magnesium has been a subject of considerable i n t e r e s t As i n the engineering of other metals a l l o y i n g of magnesium has been used to obtain strength, d u c t i l i t y , w o r k a b i l i t y , c o r r o s i o n r e s i s t a n c e , low density and c a s t a b i l i t y . In r e l a t i o n to deformation behaviour much of the s o l i d s o l u t i o n work i n magnesium and i n hexagonal structures i n general has been confined to the Mg-Li a l l o y s ' ^ . Interest i n t h i s system of a l l o y s was aroused mainly because these a l l o y s showed an unusual lowering of the c r i t i c a l resolved shear s t r e s s f o r prismatic s l i p w i t h increasing solute a d d i t i o n . This anomalous s o l i d s o l u t i o n e f f e c t was a t t r i b u t e d to the decrease of c/a r a t i o i n these a l l o y s , compared to that of pure magnesium. I t was concluded that only those 2 a l l o y i n g elements which decrease the c/a r a t i o of magnesium can lower. the CRSS f o r prismatic s l i p . One of the o b j e c t i v e s of the present i n v e s t i g a t i o n was to evaluate the s i g n i f i c a n c e of the c/a r a t i o i n the ease of p r i s m a t i c s l i p and also to evaluate the e f f e c t of r e l a t i v e valence of the solute on the properties examined. For t h i s purpose the solutes chosen were Zn, Cd, A I , In and Pb. Of these Zn and Cd belong to the same valency group as Mg and have the same c r y s t a l s t r u c t u r e as w e l l , but d i f f e r i n the atomic s i z e . i t ^ ^ . Zn has l i t t l e e f f e c t on the c/a r a t i o , whereas Cd increases A I , I n and Pb belong to higher valency groups, and a l l three increase the c/a r a t i o . These elements cover a wide range of s i z e differences with respect to magnesium. A second o b j e c t i v e of the work presented i n t h i s t h e s i s was to examine the e f f e c t s of a l l o y i n g at low concentrations. Work by ( 1 8 ) Hardie and Parkins using hardness measurements had i n d i c a t e d the p o s s i b i l i t y of a very high strengthening e f f e c t at low concentrations i n Mg base a l l o y s containing a wide v a r i e t y of s o l u t e s . Many of the previous s o l i d s o l u t i o n strengthening studies have been c a r r i e d out on p o l y c r y s t a l s . I t i s p o s s i b l e to derive q u a n t i t a t i v e information concerning the d i s l o c a t i o n - s o l u t e i n t e r a c t i o n i n face centred cubic a l l o y s . However, i n the case of hexagonal s o l i d s o l u t i o n s such studies may at best be considered to provide a q u a l i t a t i v e understanding of the subject. The d i f f e r e n c e i n the two groups of close packed structures a r i s e s mainly due to the d i f f e r e n t ways i n which t h e i r p o l y c r y s t a l l i n e aggregate undergoes p l a s t i c deformation. 3 A necessary condition f o r a p o l y c r y s t a l to deform p l a s t i c a l l y and yet r e t a i n c o n t i n u i t y i s that the number of independent deformation systems be f i v e ^ ^ 22,60)^ ^ t ^ e face centred cubic structures the primary s i n g l e s l i p mode, i s capable of g i v i n g r i s e to f i v e independent s l i p systems. Since the s l i p systems are c r y s t a l l o g r a p h i c a l l y equivalent, they are affected equally by the a d d i t i o n of solute. In contrast, no s i n g l e s l i p mode i s capable of giving r i s e to f i v e independent s l i p systems i n hexagonal metals. (The second order {1122} <1123> pyramidal s l i p i s capable of g i v i n g r i s e to f i v e independent modes, but i t operates as a secondary system at high temperatures i n the case of Cd, Zn and T i . This system, however, does not operate i n magnesium). The p l a s t i c deformation of p o l y c r y s t a l l i n e magnesium involves ( 1 4 ) more than two sets of c r y s t a l l o g r a p h i c a l l y nonequivalent s l i p systems The solute d i s l o c a t i o n i n t e r a c t i o n , therefore, on the two sets of planes cannot be expected to be i d e n t i c a l . In view of t h i s l i m i t a t i o n of the p o l y c r y s t a l study, the i n v e s t i g a t i o n has been extended to include the e f f e c t of solute on s i n g l e c r y s t a l s as w e l l . The f i r s t part of t h i s thesis i s concerned with the e f f e c t of solute on the deformation behaviour of the p o l y c r y s t a l l i n e aggregates. The second part deals with studies on s i n g l e c r y s t a l s i n making q u a n t i t a t i v e estimates of the d i s l o c a t i o n solute i n t e r a c t i o n f o r various s l i p systems. 4 1.2. EXPERIMENTAL PROCEDURE: 1.2.1. M a t e r i a l s and A l l o y Preparation: High p u r i t y Mg (99.995), obtained from the United Minerals and Chemicals Corporation, N.Y. , i n the vapour deposited form, and a l l o y i n g elements having an impurity l e v e l below 0.005% were used i n the present i n v e s t i g a t i o n . Melting was c a r r i e d out at 680®C i n a c y l i n d r i c a l graphite mould, housed i n s i d e a v e r t i c a l r e s i s t a n c e heated furnace. A l l o y i n g additions were made i n the form of. pre^-weighed pure metals f o r compositions greater than 0.2 a t . % . a l l o y s were used f o r lower.concentrations. However, master A f t e r s t i r r i n g , the melt was s o l i d i f i e d i n the melting pot by sharp u n i d i r e c t i o n a l c o o l i n g i n order to avoid pipe formation. For a l l o y s containing high vapour pressure solutes (at the melting temperature) l i k e Zn and Cd, the graphite pot along with a tapered graphite plug was enclosed i n a s t a i n l e s s s t e e l bomb. This procedure minimized the l o s s of the more v o l a t i l e component from the melt, The compositions of the a l l o y s were checked and found t o be close to the nominal values. D e t a i l s of the chemical analyses are described i n appendix (A). 1.2.2. Preparation of P o i y e r y s t a l l i n e Specimens: 1 " The castings approximately 1 /Q i n diameter and 5" long were homogenized and subsequently hot r o l l e d at 430°C to 0.032" thickness. Reductions of 10 - 15% per pass were made i n the beginning to break down the cast s t r u c t u r e , followed by 2 0 - 25% reduction per pass, which c o n t r o l l e d the f i n a l g r a i n s i z e of the m a t e r i a l . The m a t e r i a l was given i n t e r m i t t e n t annealing f o r 5 minutes at 430°C before every pass. The r o l l e d sheet was sheared i n t o 3" long by 0.75" wide 5 s t r i p s , which i n turn were punched i n t o t e n s i l e t e s t specimens having a reduced gauge length of 0.8" with a width of 0.2". The t e n s i l e a x i s of the specimen was kept p a r a l l e l to the r o l l i n g d i r e c t i o n . Edges were removed by 3/0 emergy paper and the specimens were given 20 mins. anneal at 430°C. The l a s t annealing operation removed a l l r e s i d u a l stresses due to punching, and gave a c o n s i s t e n t l y uniform g r a i n s i z e of 60 - 65p. The t e s t pieces were p i c k l e d i n 20% HNO^ which removed the oxide layer.from the surface and a l s o gave s l i g h t g r a i n boundary grooving, which helped examining the microstructure 1.2.3. subsequently. The Growth of Single C r y s t a l s : Single c r y s t a l s were grown from the melt using a modified Bridgeman technique. A l l o y s were made f o l l o w i n g the procedure described 4 it " earlier. The p o l y c r y s t a l l i n e rod approximately \ /% i n diameter, arid 5" long was cleaned and kept i n a graphite mould, which was covered with a t i g h t f i t t i n g tapered graphite plug, as shown i n f i g . (1). The mould was then lowered i n a v e r t i c a l tube r e s i s t a n c e furnace at the rate of 0.4"/hr. crystals. This procedure gave c o n s i s t e n t l y good q u a l i t y s i n g l e . A shallow temperature gradient was used i n order to minimize the s o l u t e segregation i n the a l l o y c r y s t a l s . For a constant degree of supercooling, and temperature gradient, the apex angle of the n u c l e a t i o n t i p was found to i n f l u e n c e the o r i e n t a t i o n of the c r y s t a l w i t h respect to the d i r e c t i o n of growth. The o r i e n t a t i o n of the c r y s t a l s grown i n t h i s manner could be c o n t r o l l e d without seeding. A l l c r y s t a l s used i n the present work were grown such that the basal plane remained i n c l i n e d at nearly 45° to the growth d i r e c t i o n . This procedure was 6 l'3 0-12" M—0-5"—H Specimen dimensions PRISM s l i p specimen from section I I F i g . 1. Basal s l i p specimen from s e c t i o n I Standard sections f o r obtaining t e n s i l e specimens f the as grown c r y s t a l . 7 found to be most convenient i n obtaining large sections having the desired o r i e n t a t i o n . Subsequent chemical analyses on samples taken from the two ends of the r e l a t i v e l y short length of the as grown crystal did not show a detectable v a r i a t i o n i n composition. For each solute concentration i n v e s t i g a t e d , only one crystal was grown from which a l l the t e n s i l e t e s t specimens as w e l l as samples for d i s l o c a t i o n density evaluation could be 1.2.4. obtained. Standard Sections Used: The o r i e n t a t i o n of the as grown c r y s t a l was determined using X-ray back r e f l e c t i o n Laue technique. The c r y s t a l was mounted on a "V" block which i n turn was clamped on to the base p l a t e of a spark erosion machine. Using a goniometer, the c r y s t a l was rotated with respect to i t s growth axis and the spark erosion t o o l - a f l a t copper s t r i p ~ w a s adjusted such that the desired s e c t i o n could be obtained on subsequent spark erosion. Two sets of s l i c e s having a thickness of 0.1" each were used i n the present i n v e s t i g a t i o n . Section I : These s l i c e s were cut p a r a l l e l to the d i r e c t i o n of growth, keeping the {0001} plane perpendicular to the f l a t face. Tensile t e s t specimens oriented f o r basal s l i p were obtained from t h i s s e c t i o n . Section I I : The surface of t h i s s e r i e s of s l i c e s was kept p a r a l l e l to the basal {0001} plane w i t h i n 2 degrees. Samples f o r d i s l o c a t i o n density evaluations as w e l l as t e n s i l e test pieces to induce prismatic s l i p were obtained from t h i s s e c t i o n . 1.2,5. Spark Erosion Damage: In recent years spark erosion has become a more a t t r a c t i v e a l t e r n a t i v e to the acid machining methods, i n the shaping of s u i t a b l e test specimens from larger s i n g l e c r y s t a l s . The main reasons f o r the preference of spark erosion over the acid machining methods are the r e l a t i v e l y f a s t e r c u t t i n g rate and the f l a t t e r surfaces obtainable by the former technique. However, the uncertainty i n the depth of the p l a s t i c a l l y deformed l a y e r , due to spark erosion, has been a drawback. L a t e l y i n t e r e s t has been shown i n determining the depth and d i s t r i b u t i o n of spark damage. Much of t h i s work has been based on the (23) revealing of d i s l o c a t i o n s by s u i t a b l e etching techniques. SamiMels has shown that the depth of damage i n p o l y c r y s t a l l i n e 70-30 brass i s l i m i t e d to 45y below the surface. on Fe-4%Si a l l o y , of Steeds (25) v ' "(24) The work of Sestak and Libovicky on copper and of P l a t n i k (111) plane of Sb and B i and {0001} (26^ on the plane of Zn have demonstrated that with a spark energy of the order of 1C? ergs the damage i s l i m i t e d to (27) a depth of 150 y from the surface. Hazzledine working w i t h Cu-Al a l l o y s concluded that the damage was 300 y deep f o r s i m i l a r spark energy. (28) More recently Turner et a l have evaluated the e f f e c t of p l a s t i c anisotropy on spark damage i n Zn s i n g l e c r y s t a l s . 3 Spark energies of the order of 10 ergs have been used i n the present work. Using s i m i l a r spark energies and transmission e l e c t r o n (29) microscopy f o r r e v e a l i n g dislocations,, Hirsch and L a l l y have found that the b a s a l d i s l o c a t i o n density remains unaffected i f s l i c e s t h i c k e r than 1 mm are cut. However,an accurate check on the depth of damage could not be made by these authors because of the n o n - a v a i l a b i l i t y of a 9 s u i t a b l e etchant to reveal d i s l o c a t i o n s i n magnesium. In the course of the present i n v e s t i g a t i o n , an etchant has been developed to r e v e a l the non basal d i s l o c a t i o n s i n Mg and i t s d i l u t e a l l o y s . method w i l l be described i n a l a t e r chapter. etching i t was The d e t a i l s of the Using t h i s method of found that the depth of spark damage was surface layer 300M t h i c k . l i m i t e d to a I t i s important to note that the present etch p i t t i n g technique reveals the e f f e c t of spark erosion on the nonbasal edge d i s l o c a t i o n density alone. The e f f e c t of spark erosion at and below a depth of 300y the basal d i s l o c a t i o n s was checked as f o l l o w s . Two on t e n s i l e t e s t specimens were taken from the same s l i c e . One was chemically polished to a depth of 300jj and the other to 500y . The i n i t i a l flow stresses and the i n i t i a l work hardening rates of the two specimens were found to be equal w i t h i n experimental was e r r o r , i n d i c a t i n g that the spark damage on the basal planes i n s i g n i f i c a n t below a depth of 300p . 1.2.6. Preparation of Single C r y s t a l Specimens for T e n s i l e Tests; A copper t o o l was used to spark erode t e s t pieces whose f i n a l shape and dimensions a f t e r chemical p o l i s h i n g are shown i n fig=(1). m a t e r i a l used f o r obtaining the t e s t pieces was from the as grown c r y s t a l . polished i n 10-20% HNO^ each specimen was The i n the form of s l i c e s cut A f t e r shaping the specimens were chemically to remove the damaged l a y e r . The o r i e n t a t i o n of checked by the back r e f l e c t i o n Laue method. No asterism was observed, i n d i c a t i n g that the c r y s t a l s were s t r a i n f r e e . The o r i e n t a t i o n of the s l i p plane with respect to the t e n s i l e axis i s shown i n f i g . (1) f o r basal and p r i s m a t i c s l i p r e s p e c t i v e l y . 10 In the case of specimens oriented f o r basal s l i p the basal plane made an angle of 45 i 8° with the t e n s i l e axis whereas those oriented f o r p r i s m a t i c s l i p had the basal plane p a r a l l e l to the t e n s i l e a x i s w i t h i n 2 degrees. In the l a t t e r case one of the 1st.order prism planes of the form {1010} was kept at an angle close to 45° to the t e n s i l e a x i s , so as to have the maximum shear s t r e s s a c t i n g on t h i s plane. The alignment of the basal plane with the wider face of the t e s t piece f a c i l i t a t e d the i d e n t i f i c a t i o n of the prism s l i p markings on the narrow face. A l l specimens were given a 2 hr. anneal at 450°C i n order to remove any s t r a i n i n g caused during handling. The specimens were chemically polished again i n order to remove the surface layer f o r easier examination of the deformation markings. 1.2.7. Testing Procedure: A l l specimens were deformed on a Floor Model Instron. p o i y e r y s t a l l i n e specimens were tested at a s t r a i n rate of 2 x 10 The sec ; -4 -1 whereas the s i n g l e c r y s t a l s were deformed at 1.66 x 10 sec except when otherwise stated. Testing media included L i q u i d Nitrogen Petroleum ether + Dry i c e Petroleum ether cooled with l i q u i d nitrogen Air Silicone O i l 78°K 195°K 133°K to 295°K 295°K 295°K to 513°K In each case the temperature was c o n t r o l l e d to + 2°. For p o i y e r y s t a l l i n e specimens wedge g r i p s were used which provided a r i g i d t e s t i n g apparatus. Single c r y s t a l s oriented f o r p r i s m a t i c s l i p were much stronger than the p o i y e r y s t a l l i n e specimens. Hence the s p l i t jaw g r i p s were used i n t h i s case with increased precaution i n the alignment 1 1 F i g . 2. Gripping arrangement f o r basal s l i p specimens. 12 procedure. For s i n g l e . c r y s t a l specimens oriented f o r basal s l i p a separate set of grips w a s used as shown i n f i g . (2). In a l l cases cycle c o n t r o l was used i n order to prevent overloading of specimens during gripping. The data on mechanical properties of the p o l y c r y s t a l s are expressed i n FPS u n i t s , while those f o r s i n g l e c r y s t a l s are given i n CGS u n i t s . This i s done i n order to f a c i l i t a t e comparison w i t h previous work. 1.3. DEFORMATION CHARACTERISTICS OF POLYCRYSTALLINE AGGREGATES: 1.3.1. Nature of the Stress S t r a i n Curves: The true s t r e s s vs true s t r a i n curves f o r pure magnesium and representative sets of Mg-Zn and Mg-Al a l l o y s deformed at room temperature are shown i n f i g s . (3) and (A). I t i s r e a d i l y observed that at low solute concentrations the s t r e s s - s t r a i n curves f o r the a l l o y s l i e above that f o r pure magnesium. At higher concentrations of s o l u t e , however, a knee appears and the s t r e s s s t r a i n curves, f a l l below those of the a l l o y s containing lower amounts of solute. for Mg-Cd, Mg-Pb and Mg^In a l l o y s . S i m i l a r r e s u l t s were obtained These r e s u l t s are consistent w i t h the observations of Yoshinaga and H o r i u c h i ^ ^ and of Hauser et a l ^ " ^ on Mg-Li alloys. The lowest concentration of l i t h i u m studied by Yoshinaga was 0.4 a t % . The e f f e c t of temperature on the s t r e s s - s t r a i n curves of magnesium i s shown i n f i g . ( 5 ) , and f o r two of the Mg-Al a l l o y s i n f i g s . (6) and (7). I t i s observed that i n the e a r l y stages of s t r a i n i n g the work hardening curve i s parabolic at high e f f e c t i v e temperatures, however, the rate of i n i t i a l work hardening increases more r a p i d l y w i t h s t r a i n at lower temperatures. Reference to f i g s . ( 5 ) , ( 6 ) and (7) i n d i c a t e s a large amount of s t r a i n beyond the point of maximum s t r e s s 40 F i g . 4/ S t r e s s - s t r a i n curves for Mg-Al a l l o y s tested at 295°K. 0 I 0 _ i 4 1 8 1 12 1 16 I 20 I 24 I 28 True s t r a i n % F i g . 6. S t r e s s - s t r a i n curves for Mg + 0.055 at. % AI a l l o y . L 32 I 36 40 0 8 16 24 32 True s t r a i n % F i g . 7. S t r e s s - s t r a i n curves.for Mg + 0.53 at. % A l a l l o y . 40 48 18 i n specimens tested above 373°K. The Mg-Cd a l l o y s a l s o e x h i b i t e d a s i m i l a r behaviour. This behaviour was observed not to be associated with necking. 1,3.2, The Y i e l d S t r e s s : The d e f i n i t i o n of a y i e l d s t r e s s i n p o l y c r y s t a l l i n e magnesium i s d i f f i c u l t because of the gradual nature of the y i e l d process. Therefore,in the present work the s t r e s s at 0.2% o f f s e t s t r a i n w i l l be c a l l e d the y i e l d s t r e s s Oyp' .1.3.2.1. The Temperature Dependence of Y i e l d ? The temperature dependence of the y i e l d s t r e s s f o r various a l l o y s i s shown i n f i g s . (8) and ( 9 ) f o r both aluminum and cadmium solutes. The curves may be d i v i d e d conveniently i n t o three stages. At low temperatures decrease i n there e x i s t s a region of moderate and l i n e a r with i n c r e a s i n g temperature (stage I ) , followed by stage I I , i n which the y i e l d s t r e s s decreases more r a p i d l y w i t h temperature. Stage I I ends at approximately 400°K [ f i g . (8)] and a t h i r d l i n e a r stage follows where the r a t e of decrease of temperature i s s i m i l a r to that i n stage I . a vp with Y i e l d stress-temperature r e l a t i o n s h i p s have been obtained by Hauser, Landon and Dorn^*"^ , f o r p o l y c r y s t a l l i n e pure Mg of varying g r a i n s i z e s ; however, t h e i r study was not s u f f i c i e n t l y extensive as to e s t a b l i s h the various stages shown i n f i g . (8). Temperature i n *K F i g . 8. Y i e l d stress-temperature r e l a t i o n s h i p s f o r Mg-Al a l l o y s . 100 200 300 400 Temperature i n "K F i g . 9. Y i e l d stress-temperature r e l a t i o n s h i p s f o r Mg-Cd a l l o y s . 21 I t i s also i n t e r e s t i n g to note that the temperature at which t r a n s i t i o n from stage I to stage I I occurs ( T j i s a s e n s i t i v e f u n c t i o n of the solute concentration i n the low a l l o y s . However, beyond a c e r t a i n minimum concentration of s o l u t e , which we w i l l designate C , the t r a n s i t i o n temperature increases only s l i g h t l y with c increasing solute content. This i s shown i n f i g . (10), where T i s p l o t t e d against the solute concentration f o r both aluminum and cadmium solutes. The numerical values of C are 0.17 and 0.054 at % f o r c Mg-Cd and Mg-Al a l l o y s r e s p e c t i v e l y . 1,3.2.2. The Concentration Dependence of Y i e l d : The y i e l d s t r e s s at room temperature i s p l o t t e d against solute concentration f o r both Zn and Cd solutes as shown i n f i g s . (11) and (12), The curves may be divided i n t o three stages. Stage I at the lowest solute concentrations i s a region of r a p i d and l i n e a r increase i n y i e l d s t r e s s w i t h increasing s o l u t e . At a concentration C T the stage I ends and the stage I I strengthening begins, which i s also approximately l i n e a r but has a slope approximately an order of magnitude lower than that i n stage I . Stage I I ends with a gradual decrease i n q^p with f u r t h e r increase i n solute concentration during stage I I I . This type of multistage s o l u t i o n strengthening has a l s o been observed w i t h A I , Pb, Cd and In s o l u t e s , although, the stage I I I region has not been observed i n a l l cases. E a r l i e r work by Hardie and Parkins ( 1 8 ) using hardness measurements had i n d i c a t e d the p o s s i b i l i t y of a high strengthening e f f e c t at low solute concentrations followed by a l e s s r a p i d increase i n hardness at higher concentrations, i n alloys of Magnesium containing a v a r i e t y of (14) s o l u t e s . Work by Hauser, Landon and Dorn , had i n d i c a t e d a three 22 23 F i g . 12. Y i e l d stress-concentration p l o t f o r Mg-Cd a l l o y s . 24 stage strengthening e f f e c t i n Mg-Li a l l o y s , s i m i l a r to that observed i n the present work. However, neither study was s u f f i c i e n t l y complete to provide the necessary information. 1.3.2.3. Solution Strengthening i n Stage I : The stage I regions f o r a l l the f i v e systems examined at room temperature are shown i n f i g . (13), and c l e a r l y reveal the r e l a t i v e strengthening e f f e c t of the various solutes i n the order-Zn, A I , Pb, da ' Cd, In. The s o l u t i o n strengthening rate (•—) solutes are l i s t e d i n Table I i n stage I f o r various along with other relevant data. The stage I slope has been p l o t t e d as a f u n c t i o n of the s i z e d i f f e r e n c e , Ar between magnesium and the various solutes as shown i n f i g . (14). I t i s seen that the strengthening e f f e c t of the solute increases as the d i f f e r e n c e i n s i z e between the solvent and the solute becomes larger. In attempts to c o r r e l a t e the hardening e f f e c t to the s i z e d i f f e r e n c e ^ i t i s important to note that the concept of an atomic s i z e i n an a l l o y i s problematic and hence care must be exercised while making q u a n t i t a t i v e i n t e r p r e t a t i o n s i n v o l v i n g the use of such a parameter. There are two methods i n use f o r the evaluation of the s i z e m i s f i t parameter. The one i n v o l v i n g the use of the change i n l a t t i c e parameter due to a l l o y i n g i s the more commonly used method, which r e l a t e s the strengthening e f f e c t of the solute as f o l l o w s : dc ' K C a dc ; where a i s the l a t t i c e parameter, da/(j , i t s v a r i a t i o n with solute conc c e n t r a t i o n , K and n are adjustable parameters. The changes i n the l a t t i c e parameters of magnesium due to a l l o y i n g have been tabulated by B u s k ^ ^ , TABLE I Solution..har.deninR„-paramafeeES-for- polyerystals..tested at 295°K SOLUTE ELEMENT SOLUBILITY at % Max. Zn 1 T 0.5 - 0.01 345 x 10 11.5 1.6 0.067 59.5 x l 0 3 0.9 x l 0 3 12,500 Pb 8.0 1.5 0.068 42.6 x l 0 3 0.6 x l 0 3 11,400 Cd Complete 12 0.16 22.7 x 10 3 0.254 x 10 12,360 In 19.0 13 0.25 11.0 x 10 3 0.65 x 10 11,250 Al 4.0 at 25° C CRITICAL STAGE I SLOPE STAGE II SLOPE YIELD STRESS CONCENTRATION d(T d(T " AT C Crj, dc dc (J"T at % psi/at % solute psi/at % solute in psi 9 x 10 3 11,950 3 3 3 F i g . 14. Stage I slope vs s i z e m i s f i t parameter. F i g . 15. Stage I I slope vs s i z e m i s f i t parameter. 28 Hardie and Parkins (31) , von Batchelder and Rauchle (32) (33) and King However, no s i n g l e combination of n and K could give a s a t i s f a c t o r y f i t f o r the present r e s u l t s . Alternatively the difference i n size ? between the pure metals can be used as a s i z e m i s f i t parameter. l a s t mentioned approach has been taken i n the present work. The Atomic (34) r a d i i tabulated by Van Vlack have been used here. I t i s important to note that the change i n the shear modulus of the m a t e r i a l due to a l l o y i n g i s also a c o n t r i b u t i n g f a c t o r i n s o l u t i o n strengthening. I n the absence of experimental data r e l a t i n g to the v a r i a t i o n of the shear modulus with solute content, however, t h i s f a c t o r has not been considered here. 1.3.2.4. Strengthening Above C-: The s o l u t i o n hardening rates i n stage I I , at room temperature are l i s t e d i n table I f o r a l l solutes examined. F i g . (15) shows the dc " dependence of (~J^) on the s i z e m i s f i t parameter, which follows the same general trend as O^-) against Ar. Although stage I I extends over a much wider range of compositions the hardening rate i s an order of magnitude lower compared to that i n stage I . Stage I I merged with stage I I I with a gradual decrease i n 0 p . Y Stage I I I was observed only i n Mg-Al and Mg-Zn a l l o y s . 1.3.2.5. The Temperature Dependence of the S o l u t i o n Strengthening Parameters: The s o l u t i o n hardening curves f o r Mg-Al and Mg-Cd a l l o y s deformed over a range of temperatures are shown i n figS.(16) and (17) respectively. The multistage nature of strengthening p r e v a i l s at a l l temperatures. The extent of stage I increases with decreasing temperature 29 0.1 0.2 0.3 Atomic Fig. 16. The effect curve for of % temperature Mg-Al alloys. 0.4 0.5 Al on the solution hardening 30 r 1 2 3 Atomic Fig. 17. The effect curve for of % temperature Mg-Cd alloys. 4 5 Cd on the solution hardening 31 below 250°K. Above t h i s temperature, however, C_ remains independent of temperature. The temperature dependence of C_ f o r the Mg-Cd and Mg-Al a l l o y s i s shown i n f i g s . (18) and (19) r e s p e c t i v e l y . The v a r i a t i o n of the s o l u t i o n hardening rate with temperature i s shown i n f i g . (20) f o r the Mg-Cd a l l o y s . I t i s observed that between dc 78°K and 140°K (-j-^) ' i s affected very s l i g h t l y "by temperature, whereas a pronounced increase i s apparent between 140 and 260°K. attains a maximum i n the v i c i n i t y of room temperature and s t a r t s to decrease do " thereafter with increasing temperature. (^jjr) » o n t n e o t n e r hand, decreases r a p i d l y from 78°K, reaches a minimum around room temperature and increases thereafter w i t h increasing temperature. the v a r i a t i o n of 0^-) F i g . (21) shows with temperature i n the Mg-Al a l l o y s which i s do " s i m i l a r to that i n the Mg-Cd a l l o y s . However, (^-) was found to be independent of temperature i n the Mg-Al a l l o y s . 1.3.3. The C r i t i c a l T r a n s i t i o n Concentration: The temperature v a r i a t i o n of C^, has already been described earlier. The numerical values of C_ f o r the f i v e a l l o y systems examined at room temperature are l i s t e d i n table I . The t r a n s i t i o n concentration could be r e l a t e d to the s i z e m i s f i t as can be seen from the Ar-C^, p l o t i n f i g . (22). m i s f i t parameter For a large value of Ar, C_ i s small. As the.size Ar i s decreased, C_ increases, i n d i c a t i n g a very large value as Ar approaches zero. a d d i t i o n of a solute with From the C T This i s as expected, f o r the Ar = 0 i . e . magnesium i t s e l f . - Ar r e l a t i o n s h i p i n f i g . (22), the t r a n s i t i o n concentration f o r l i t h i u m as solute turns out to be 0.2 a t . % . s A 32 0.9 - 0.7 " 0.5 0.3 - 0.1 200 100 Temperature Fig. 18. Critical transition to II stage vs. 400 300 °K concentration, temperature for Cd C T from stage solute. 0.13 0.11- 0.09 A 0.07 0.05 100 200 300 Temperature.°K Fig. 19. C^, v s temperature for Al solute. 400 I 33 100 Fig. 20(b). 200 Stage 300 Temperature °K II temperature slope vs 400 for Mg-Cd alloys. 34 F i g . 22. C r i t i c a l t r a n s i t i o n concentration, C^ from stage I to stage I I vs s i z e m i s f i t parameter. 35 direct the experimental present study. been results, Earlier carried verify the out of crystal data 1.3.4. The refers well as a average Cj brittle o^p The of - was brittle found fracture The is brittle size in Mg-Al maximum s t r e s s solute. than from grain transition the temperature of shown in f i g . w i l l to higher alloys u of is is be for of the in plot of that with was the found maximum s t r e s s Mg-Cd a l l o y s pure the "brittle stress, at the maximum for The Mg work. stress to be having an Unlike the solute deformed at as temperature unaffected solute Beyond solute Mg transition transition magnesium. with chapter. in In term containing increasing the Alloying: mode (23). in of hardening. present alloys of and maximum s t r e s s f i g . to later fracture the the a undergo work as single fracture the never support the in from present have the relationship lower.than variation to negative of the (1.4.2.). temperatures in stress increased not in fracture transition 225°K temperature fracture equal in lithium from discussed chapter shown ductile temperature stress (24) Mg d o e s dependence to 65 is of evidence the possible polycrystals Temperature of in not included comes be with outlined onset alloy is concentrations dependence the been however, This temperatures at not Indirect maximum s t r e s s stress series temperature in the low Variation is estimate Mg-Li either. Therefore,at The the alloys. Stress this has estimate, magnesium higher the on temperature stress. to above Maximum at lithium conclusion region of sufficiently on Mg-Li polycrystalline maximum at the The however, since experiments above correctness fracture" verification C^,, by less the concentration. concentration room temperature. 37 F i g . 24. Fracture s t r e s s vs. composition f o r Mg-Cd a l l o y s tested at 295°K. 38 The minimum i n less than 1.3.5. C f i g . disappears T Flow Stress Flow set It that observed strain are of therefore, ° Y P ~ ^ strain case of on of C^, pure the slightly to C T strain fixed terminology with stress shown tested at at higher stresses the Mg-Al figs. and as used strain, a lower than alloys was tested Mg and a figs. (25, 26 and 27). the for is the stage was three stress I any to curves, of stage in II. an containing of T A In large be the excess affected with the increasing to in in curves. observed alloy specified stages effect solutes dependence is to C^,. solute observed alloys that 27) containing at shown increases equal increasing l l Alloying: curves flow here). only solute close increasing (28). stress a shown pure decrease flow strains (not slightly for pronounced the strain the from T solute stress-temperature however, temperature 0.2% in defining and 26 room with in (25, at solute yield to concentration of shown applied temperature f i g . and relationships are of temperatures Temperature the alloys exhibited in to temperature increasing (26)) observed be transition concentration is also concentration stress-temperature shape magnesium strain flow a testing alloys the The alloys the transition (fig. as Mg-Al of at temperature same feature the Relation of w i l l is higher the curves noticeable in which at stress representative is (24) Beyond between Similar 78°K and flow f i g . C a T The solute in At alloying continuous decrease at 0.3 in excess results 423°K. stress (29). with commence containing C^,. in rapidly content. to the have at in % of been Mg-Zn any upto a decrease flow Zn, however, had obtained flow for F i g . 25.. Flow s t r e s s vs.- temperature f o r 65y Mg. 28 100 200 300 400 Temperature °K F i g . 27. Flow s t r e s s vs. temperature f o r Mg + 0.055% AI a l l o y . 500 F i g . 28. T r a n s i t i o n temperature from stage I to stage. I I i n the flow s t r e s s temperature curves of Mg + 0.055 a t . % A l a l l o y vs. s t r a i n . F i g * 29. Flow s t r e s s vs. composition f o r Mg-Zn a l l o y . 44 1.3.6. Ductility: . Percent.elongation extension it was of not specimen 1.3.6.1. the gauge-length practical Alloying at observed that to is reached, alloy content. room strain and the The as reduction against is shown fracture a in based on the measure of ductility, area values ductility in strengthening of at in f i g . uniform because It until further note that Zn, for (30). with order as of the is concentration in solutes Cd solute readily increase the A l , a each and the were In close effective paralleling effects. Dependence the hardening to the concentration decreases increases interesting Temperature work indicate to then is Because to used of duatility It relative negative was obtain temperature the increasing 1.3.6.2. strain Effect: plot examined their true dimensions. A in to or large of Ductility: amount of temperatures strain above the strain to maximum s t r e s s , The effect of temperature series of binary in associated 373°K, it addition with was to the necessary the true strain to fracture. magnesium and Upto approximately slightly of a the l i t t l e with changes testing eff ect dramatically 300°K, in the Mg-Al temperature in the the ductility same range the alloys ductility temperature,alloying on on and upto of strain is to shown magnesium alloying. the magnesium, of concentrations. in is although for f i g . (31). affected Also transition of fracture very irrespective concentration '°YJP Between l n c ^ 300°K e a s and e has s 400°K, c< 7 70 100 200 300 400 Temperature °K F i g . 32. True s t r a i n to f r a c t u r e vs. temperature f o r Mg-Al a l l o y s . 500 47 however, a l l o y i n g additions i n excess of C increasing the d u c t i l i t y . than C T T have a profound e f f e c t i n Magnesium and a l l o y s containing solute l e s s show a progressive increase i n d u c t i l i t y with temperature i n t h i s interval. The higher a l l o y s show maxima and minima i n . d u c t i l i t y i n the temperature i n t e r v a l between 400° and 500°K. The shape and p o s i t i o n of the maxima show a systematic v a r i a t i o n with solute concentration. In constant s t r a i n rate t e s t s , the d u c t i l i t y peak becomes broader and s h i f t s to lower temperatures with increasing aluminum a d d i t i o n . The temperature dependence of the true s t r a i n to maximum stress and that associated w i t h the negative work hardening are shown i n f i g s . (32) and (33) r e s p e c t i v e l y . The s t r a i n associated with the negative work-hardening i s very small below room temperature. Above room temperature, however, the s t r a i n to maximum s t r e s s and that associated with the negative work hardening f o l l o w a trend s i m i l a r to the temperature v a r i a t i o n of the s t r a i n to f r a c t u r e , with the exception that the peaks do not broaden. The maxima i n the case of s t r a i n to maximum s t r e s s were observed at about 450 K, whereas those i n the case of the s t r a i n associated 3 with the negative work hardening are i n the v i c i n i t y of 420°K. D u c t i l i t y maxima s i m i l a r to those i n the present (35) work have been observed e a r l i e r by Greenwood et a l a l l o y and i n Mg-0.8% A l a l l o y by S'tacey^ \ 36 i n Mg-0,2% Pb True s t r a i n to maximum s t r e s s o ho o o p- ho o •P» o O OQ CO ho 0 o <H i-l CO o o • C CD rt CO n> rt •a d i-t C rt n 3 ri> 0 H» 3 fu rt i-t O I o Ul • U) • h O • > > > • •0 O • s o . cn cn > rt C i-l -po o H- 3 C 3 S O o o Co Hi fa OQ • Cn ft) m 3 o i-t e % LO > CD rt i-i &1 1— M 1 CO CO CO O •<! Ul o o CO (e .-e ) % f O Co O o OQ -n CO CO 2 S OQ O H i-( I M C > 7? CD M EJ" CO (B rt H M i-t H U B » O 1 (D ^CO 3 3 H- 3 H- 03 o <o CO rt CD -po o 3 13 CD H CO (U CO OQ H c n CD o Cn O o rt n> m 3 a. 13 n> i-< PJ rt 3* C * CD 3 n> 0Q CJN O O Hi 0) O t rt < CD 8* 49 1.4. DISCUSSIONS In order to understand the mechanism of s o l u t i o n strengthening i n p o i y e r y s t a l l i n e aggregates, i t i s e s s e n t i a l to have a knowledge of the c r y s t a l l o g r a p h i c deformation modes a v a i l a b l e , and t h e i r e f f e c t on the macroscopic.flow and f r a c t u r e c h a r a c t e r i s t i c s of the m a t e r i a l . Keeping t h i s i n mind i t appears l o g i c a l to give a b r i e f review of the e a r l i e r work on the deformation and f r a c t u r e of magnesium followed by a d i s c u s s i o n of the e f f e c t s of solute 1.4.1. on the various flow parameters. Deformation Modes i n Magnesium: (19) In 1928 von Mises f i r s t pointed out that a necessary c o n d i t i o n f o r a p o l y c r y s t a l to be d u c t i l e when i t deforms by c r y s t a l l o g r a p h i c s l i p i n i t s grains i s that the number of independent s l i p systems a v a i l a b l e be f i v e . The t o t a l number of s l i p systems i s given by the crystal structure. Usually there i s one s l i p mode and a number of s l i p systems f o r t h i s mode as determined by the point group symmetry. and K e l l y a n d Groves K o c k s ^ " ^ have examined the number of independent s l i p systems i n various c r y s t a l s t r u c t u r e s , von Mises' f i n d i n g has been used i n the studies of face centred cubic metals i n f i n d i n g the number of (37) s l i p systems found to operate near the g r a i n boundary and also i n t h e o r e t i c a l attempts to deduce the p o i y e r y s t a l l i n e s t r e s s s t r a i n curve (22) from that of s i n g l e c r y s t a l . In many systems, however, other mechanisms such as twinning, g r a i n boundary shear and c e l l s t r u c t u r e formation may occur thereby reducing the number of independent systems required. slip I t i s h e l p f u l to remember that the von Mises c r i t e r i o n i s taken to be a necessary c o n d i t i o n f o r any p o l y c r y s t a l d u c t i l i t y whatsoever, not as one that determined d i f f e r e n t degrees of d u c t i l i t y . 50 1.4.LI. Crystallographic S l i p : Magnesium undergoes s l i p predominantly on the basal system {0001} <1120 > . The shortest s l i p vector which preserves the ABAB basal or close packed plane stacking i s of magnitude a and d i r e c t i o n < 1120> . The t o t a l s t r a i n energy i s lowered by the d i s s o c i a t i o n i n the basal plane of the d i s l o c a t i o n i n t o two p a r t i a l s having the Burgers vector -f- <1010> A stacking f a u l t e x i s t s i n a ribbon between the two p a r t i a l s . Although no d i r e c t way of measuring the f a u l t energy i s a v a i l a b l e f o r magnesium, 2 (39) Seeger estimates i t to be i n the range 200 - 400 ergs/cm . This leads to a predicted separation of the p a r t i a l s at room temperature of the order of an interatomic distance. other than S l i p vectors of the form <1120> have never been observed i n magnesium. Non-basal s l i p vectors of the form <1123> have been observed i n a d d i t i o n to the. — (40 41) basal <1120> vector i n other hexagonal close packed metals l i k e Cd ' (42) (43) Zn and Be , The temperature dependence of the CRSS f o r basal s l i p has been studied by Sheely and Nash^"^ , Conrad and Robertson^^ and (3) by B a s i n s k i Small amounts of non-basal s l i p are seen a f t e r room temperature (14) deformation of pure Mg . I t has been a popular b e l i e f that i f and when non-basal s l i p does occur i t w i l l do so much more r e a d i l y i n systems which have c/a r a t i o equal to or l e s s than.the i d e a l value of 1.633. argument follows from r e l a t i v e close packing considerations. This (44) Seeger has suggested that i n a d d i t i o n to the c/a r a t i o , the stacking f a u l t energy w i l l have a strong influence on the deformation modes in.as much (45) as i t controls the cross s l i p process. hexagonal close packed S t o l o f f and Davies using Zn-Ag a l l o y s of s l i g h t l y varying a x i a l r a t i o s have 51 shown that the e/a r a t i o i s not the only c r i t e r i o n f o r non-basal s l i p . Zirconium and b e r y l l i u m serve as good examples to show that the occurrence of non basal s l i p i s not determined e n t i r e l y by c/a r a t i o and the stacking f a u l t energy of the m a t e r i a l . Although both these metals have approximately the same c/a r a t i o (less than i d e a l ) and have high (47) stacking f a u l t energies, whereas basal s l i p predominates i n b e r y l l i u m Zr deforms mainly by prismatic {1010}<1120> s l i p ^ \ The e a r l i e s t observations of non-basal s l i p i n magnesium were made by S c h m i d ^ ^ who concluded that the became operative at 225°C and above. {101l}<1120> pyramidal system Later work on the compression of (49) t h i n s i n g l e c r y s t a l wafers by Bakarian and Mathewson confirmed the s i g n i f i c a n c e of t h i s temperature and contributed the f i r s t extensive evidence on the waviness of elevated temperature s l i p l i n e s on t h i s system. Burke and H i b b a r d ^ " ^ observed only basal s l i p inhigh p u r i t y s i n g l e c r y s t a l s of magnesium at room temperature except i n the region close to the g r i p where to the g r i p c o n s t r a i n t s . {1011}<1120> system was operative due Thus, up u n t i l 1955 there was an acceptance of 225 C as the temperature below which no s l i p system except G {0001}<1120> would operate i n Mg without the imposition of unusual s t r e s s systems. In 1955, Dorn et a l ^ " ^ began to examine rather c r i t i c a l l y the deformation i n tension of p o i y e r y s t a l l i n e pure magnesium. Small amounts of non-basal s l i p were seen at room temperature and the temperature dependence of non-basal s l i p was found to be.not as simple (12) — — as thought before. Hauser et a l observed prism {1010}<1120> basal {0001} <1120> cross s l i p between 78°K and 298°K at t r i p l e points which are susceptible s i t e s f o r s t r e s s concentration. 52 Reed-H'Ul and Robertson^"^ studied the t e n s i l e deformation of magnesium s i n g l e c r y s t a l s w i t h the stress axis close enough to the basal plane so that basal s l i p and mechanical twinning on suppressed. {1012> were This o r i e n t a t i o n i s of considerable p r a c t i c a l s i g n i f i c a n c e i n the t e n s i l e deformation of p o l y c r y s t a l l i n e sheet and extruded metal because the texture of these materials i s such that the b a s a l plane tends to a l i g n i t s e l f w i t h the d i r e c t i o n of r o l l i n g or extrusion. found that {loTo}<1120> s l i p occurred at 93°K and 298°K. Reed-Hill At low temperatures the s l i p l i n e s had a minimum spacing of l e s s than 5 x 10 ^ cm. Fine prism s l i p l i n e s were seen to be cross slipped by b a s a l s l i p at both these temperatures. The v a r i a t i o n of the c r i t i c a l resolved shear s t r e s s for prismatic s l i p over the temperatures ranging between 78°K and 800?K (9) has been investigated by Ward-Flynn, Mote and Dorn and by Horiuchi (52) and Yoshinaga by . These r e s u l t s are supplementary to the data obtained Reed-Hill and are i n excellent agreement w i t h those of Hauser et a l . F i r s t order pyramidal s l i p {1011}<1120> has been observed i n (51) magnesium s i n g l e c r y s t a l s deformed at elevated temperatures. Reed-Hill found that with the geometry of h i s c r y s t a l s the s l i p l i n e s were so i r r e g u l a r and d i f f u s e that d i r e c t trace a n a l y s i s of t h e i r system was not possible. However, a c a r e f u l study of the asterism i n Laue X-ray photograms made from the deformed c r y s t a l s showed them to be i n t e r p r e t a b l e as the r e s u l t of predominantly discrete {1011}<1120> pyramidal s l i p . Large {1011} pyramidal s l i p bands were also observed on specimens strained i n tension at 298°K w i t h the t e n s i l e axis i n the b a s a l plane and approximately 17° from a {1010} d i r e c t i o n . to f r a c t u r e , the l i m i t e d d u c t i l i t y However,the high loads at 298°K and the apparent r a r i t y of 53 {1011} s l i p bands a l l point to the f a c t that pyramidal s l i p i s not an (53) re There (48) appears to be no c o n f l i c t between these r e s u l t s and those of Schmid important mode of p l a s t i c deformation at room temperature . and B a k a r i a n ^ ^ except that the s i g n i f i c a n c e of the 225°G i s l o s t . Chaudhri et a l ^ ^ ' " ' " ^ have investigated the high temperature deformation of coarse grained p o l y c r y s t a l l i n e magnesium i n t e n s i l e creep at 533°K. From a c a r e f u l trace a n a l y s i s coupled w i t h the waviness of the bands of s l i p l i n e s they concluded that although <1120> d i r e c t i o n was i n v a r i a n t , s l i p occurred with microscopic a l t e r n a t i o n on prism and pyramidal planes. Second order pyramidal {1122} s l i p bands have also, been (53) observed by R e e d - H i l l on s i n g l e c r y s t a l specimens s t r a i n e d i n tension at 83°K with the t e n s i l e axis i n the b a s a l plane and approximately 2° from a <1010> d i r e c t i o n . The asterism found i n a Laue back r e f l e c t i o n photograph and microscopic observation of s l i p l i n e s i n d i c a t e d that the s l i p d i r e c t i o n i s probably {1122} <1123> <1010> . Although Cd, Zn and Be show pyramidal s l i p bands, non basal s l i p vectors have never, been observed i n magnesium. In hexagonal metals the operation of the second order <1123 {1122} >pyramidal s l i p i s a necessary as w e l l as s u f f i c i e n t condition for the a v a i l a b i l i t y of f i v e independent s l i p systems. (56^ by Dorn and M i t c h e l l As reviewed t h i s system i s the only one which can promote extensive deformation p a r a l l e l to the c a x i s . Table I I shows the number of independent systems f o r each of the prominent s l i p systems. 54 Table I I S l i p Systems i n Hexagonal Metals (After D o r n ( 5 6 ) ) No. S l i p Systems Burgers Vector 1 {0001} <1120> a 2 2 UOlo} <1120> a 2 3 { l O l l } <1120> a 4 4 {1122} <1123> c + a 5 5 1 + 2+ 3 a 4 No combination of Number of Ir»depanden Systems {0001} <1120>, {1010}<1120> and {101l}<1120> can provide the f i v e independent systems required. Since the second order pyramidal s l i p of the type {1122}<1123> i s absent i n magnesium, p l a s t i c deformation of the p o i y e r y s t a l l i n e aggregate i s not p o s s i b l e , i n p r i n c i p l e , from s l i p alone. However, considerable p l a s t i c i t y i s observed. This i s due to c e l l formation, twinning, compression banding and g r a i n boundary deformation, which supplement s l i p i n order to s a t i s f y von Mises c r i t e r i o n . 1,4.1.2. P l a s t i c Deformation by Twinning Twinning systems are often not included as p o s s i b l e deformation modes f o r the purpose of s a t i s f y i n g c o m p a t i b i l i t y c o n d i t i o n s , because of the l i m i t e d amount of deformation achieved even when the e n t i r e volume has been twinned. Also twinning can.accommodate e i t h e r c-extension or c- c o n t r a c t i o n but not both. However, the profusion of two or more twinning systems, some leading to an extension and the others leading 55 to a contraction i n the c d i r e c t i o n , can assume the r o l e of independent deformation modes. For instance R e ^ ^ , T i ^ ^ and Z r ^ ^ ' ~ ^ e x h i b i t e s s e n t i a l l y unlimited d u c t i l i t y although i d e n t i f i e d i n any of them. (c + a) s l i p has never been Kocks and Westlake^*^ have a t t r i b u t e d the large d u c t i l i t y i n these materials to the profusion of {112l}<ll26>and {1122} <L123> twinning. The former leads to an extension and the l a t t e r to a contraction i n the c - d i r e c t i o n . The twinning system most common to magnesium i s the {1012} <1011:' type. {1012} twinning r e s u l t s i n an extension i n the c - d i r e c t i o n and i s favoured by compression p a r a l l e l to the basal plane and tension perpendicular to i t . The complete formation of a twin under conditions where the parent c r y s t a l has no r e s t r a i n t to the r e s u l t i n g shear i s a simple case, not usually met i n p r a c t i c e . In general accommodation to the shear.is accomplished by a phenomenon known as accommodation k i n k i n g . of accommodation i s u s u a l l y c a l l e d a bend or a kink plane. may be expected on both {1010} and <1120> planes. The plane Accommodation Non-crystallographic (11) (12) boundary formation has also been observed i n magnesium. Dorn ' found that i n many cases they crossed g r a i n boundaries. He postulated that these boundaries formed because of the bending of the l a t t i c e associated with the non-homogenous deformation of the underlying g r a i n s . The temperature dependence of {1012} twinning has never been studied thoroughly under conditions where the v a r i a b l e s of s t r a i n r a t e and o r i e n t a t i o n were f i x e d . l e s s important Twinning i n p o l y c r y s t a l l i n e magnesium becomes at elevated temperature, but whether t h i s i s i n t r i n s i c to the twinning mechanism or not cannot be s a i d , since the c r i t i c a l s t r e s s 56 for nonbasal s l i p and g r a i n boundary deformation decrease r a p i d l y with increasing temperature. From the studies of deformed p o i y e r y s t a l l i n e specimens Roberts reported the existence of a twinned s t r u c t u r e apparently the habit of [3034}. {3034} . Couling and Roberts on i d e n t i f i e d the habit as This was confirmed on magnesium s i n g l e c r y s t a l s by Reed-Hill The twins are uniquely narrow and they e x i s t i n bands forming interesting arrays at low s t r a i n l e v e l s . These twins are formed when tension i s applied perpendicular to the c a x i s . The r o l l i n g texture of magnesium e f f e c t i v e l y places the grains i n an o r i e n t a t i o n unfavourable {1012} twinning. However to both basal s l i p and {3034} twins are formed when tension i s applied i n the d i r e c t i o n of r o l l i n g . A l s o , since they are responsible f o r b r i t t l e fracture of Mg they have been studied i n somewhat greater d e t a i l than the {1012} twins. The {3034} twinning on the {1011} lamellae are formed as a r e s u l t of a primary plane followed by a second order formed i n the primary twin. {1012} twin Using e l e c t r o n microscope r e p l i c a s Hartt ( 64^ and Reed-Hill have shown that the i r r a t i o n a l habit of these twins i s probably the d i r e c t r e s u l t of a need to accommodate the second order twinning shear. A model has been presented which explains the accommodation r e s u l t i n g i n both an e x t e r n a l shear i n the matrix and an i n t e r n a l shear i n the lamella. Similar twins have been observed by Wonsiewicz and Backofen^"^ i n the complex s t r a i n i n g of magnesium s i n g l e c r y s t a l s at higher temperatures and i n some a l l o y s of Mg by Hosford, J r . et a l at room temperature. The d e t a i l e d understanding (66) of these twins explains the compression banding and the r o l l i n g texture i n magnesiun/^^. However, the established twin systems i n magnesium cannot assume the r o l e of an 57 independent deformation mode mainly because they are formed at places of s p e c i a l s t r e s s concentrations and are incapable of accommodating both expansion and contraction i n the c - d i r e c t i o n . Twinning on .{1013},{1014}. , { 1124} ("62} as on {1121 } , {10l5 } ( 6 3 ) as w e l l have been reported. However, t h e i r existence i s not w e l l established. 1.4.1,3, Grain Boundary Deformation: The operation of grain boundary shearing under tension at room temperature was proved i n the p o l y c r y s t a l l i n e aggregate by Hauser et (11) al . The importance of the process i n the creep of p o l y c r y s t a l l i n e magnesium at elevated temperatures Roberts has been demonstrated by Couling and , They found that the high temperature g r a i n boundary deformation i n p o l y c r y s t a l l i n e magnesium i s a two stage process i n v o l v i n g a l t e r n a t e boundary shearing and migration. Increasing t e s t temperatures and decreasing s t r a i n rates favour l a r g e r contributions to the over a l l s t r a i n from boundary deformation, In the l i m i t i n g case i t appears that a l l the deformation would be l o c a l i z e d at the boundaries. A mechanism which explains the observations i s the a l t e r n a t i o n of a n e l a s t i c boundary shears with the capture of these shears when the boundaries migrate to new p o s i t i o n s , The number of cycles necessary to produce the measured shear has been c a l c u l a t e d and found to agree q u a l i t a t i v e l y with metallographic observations. 58 1.4.1.4. C e l l Formation: C e l l formation r e s u l t s from a stress-accelerated polygonizatipn process caused by non»homogenous d i s t o r t i o n (54 55) ' . Chaudhri et a l (54) have noticed i n the case of Mg ( e s p e c i a l l y coarse grained aggregates) that the breakdown of the metal i n t o c e l l s i s marked i n the g r a i n boundary region. Polygonization can be so pronounced i n the g r a i n boundaries that i t a c t u a l l y leads to r e c r y s t a l l i z a t i o n . Due to the lack of a v a i l a b i l i t y of f i v e independent modes, c e l l formation plays an important r o l e i n the deformation of magnesium. For example, the t r a n s i t i o n i n f r a c t u r e s t r e s s and d u c t i l i t y of magnesium i n the v i c i n i t y of room temperature i s thought to be associated with the onset of c e l l formation and r e c r y s t a l l i z a t i o n (69) . Recently, however, Reed-Hill (64) has associated t h i s t r a n s i t i o n with the operation of {1011}- {1012} double twinning. S u i t e r and W o o d ^ ^ have suggested a mechanism f o r the formation of c e l l s t r u c t u r e s . This depends on the r e l a t i v e movements of the g r a i n boundaries causing rumpling and t w i s t i n g of the s t r u c t u r e . D i s l o c a t i o n movements r e l i e v e the s t r a i n associated w i t h the deformation and lead to the formation of sub-boundaries which develop i n t o the observed c e l l s t r u c t u r e s . (35) C e l l formation has a l s o been observed i n Mg-rPb a l l o y s Mg-Al a l l o y s (36) d e t a i l s of which w i l l be discussed l a t e r . and 59 1.4.2, Fracture of Magnesium P o l y e r y s t a l s : Studies on the flow and f r a c t u r e stress c h a r a c t e r i s t i c s of high p u r i t y magnesium c a r r i e d out by Hauser et a l ^ * ^ and by Toaz and R i p l i n g ^ ^ have revealed that f i n e grained Mg fractures at low but rather constant stress below about 250°K. Above t h i s range, the fracture stress decreases r a p i d l y with increasing temperature and the d u c t i l i t y increases markedly. The temperature at which t h i s change occurs i s regarded by Hauser et a l as the t r a n s i t i o n point from b r i t t l e to d u c t i l e f r a c t u r e , A true t r a n s i t i o n temperature r e f e r s to the s i t u a t i o n where a change from b r i t t l e to d u c t i l e behaviour occurs with no thermal i n s t a b i l i t y of the microstructure and where n e g l i g i b l e deformation occurs p r i o r to f r a c t u r e i n the b r i t t l e range. The use of the term b r i t t l e f r a c t u r e range i s not s t r i c t l y j u s t i f i e d i n the case of magnesium, since a f a i r amount of p l a s t i c deformation precedes f r a c t u r e . However, the c h a r a c t e r i s t i c s of the low temperature f r a c t u r e of magnesium are i n many ways s i m i l a r to those of b r i t t l e f r a c t u r e . For example, the f r a c t u r e stress increases l i n e a r l y with the r e c i p r o c a l of the square root of g r a i n diameter i n accordance with the Hall-Petch r e l a t i o n ^ " ^ , the t r a n s i t i o n temperature increases with increasing grain s i z e and the low temperature f r a c t u r e stress as w e l l as f r a c t u r e s t r a i n are found to be r e l a t i v e l y independent of the s t r a i n r a t e . On the basis of some metallographic studies Toaz and R i p l i n g conclude that the d i s c o n t i n u i t y ( i n the f r a c t u r e stress-temperature r e l a t i o n s h i p ) i n the case of pure magnesium r e s u l t s from the entrance of r e c r y s t a l l i z a t i o n during def o r m a t i o n ^ ^ . I t has been observed by (72) Risebrough that the negative work hardening i n the s t r e s s s t r a i n curves 60 of p o i y e r y s t a l l i n e Zn and Cd i s associated w i t h r e c r y s t a l l i z a t i o n . Metallographic examination of the test samples before and a f t e r the onset of the negative work hardening i n the present work suggests r e c r y s t a l l i z a t i o n to be responsible f o r the work-softening of magnesium. The strain associated with the negative work hardening, which was taken as the s t r a i n to f r a c t u r e l e s s the l i m i t i n g s t r a i n to maximum s t r e s s , was.found to decrease with decreasing temperature, becoming v a n i s h i n g l y low at about 250°K. This observation tends to support the conclusion of Toaz and R i p l i n g on the nature of the t r a n s i t i o n temperature. The f r a c t u r e of Mg and i t s a l l o y s near and below room temperature r e s u l t s p r i m a r i l y from the j o i n i n g of the i n t r a g r a n u l a r cracks by a moderate amount of i n t e r g r a n u l a r cracking. which have been i d e n t i f i e d as planes such as {1014 },{1015} The twinned s t r u c t u r e s t 3034 } twins and the higher order and {1124} are the crack n u c l e a t i o n s i t e s i n i n t r a g r a n u l a r f r a c t u r e . At elevated temperatures, however, the g r a i n boundaries play an important r o l e i n the f r a c t u r e of magnesium and i t s alloys. 1.4.3. This w i l l be considered at a l a t e r stage. S o l u t i o n Hardening: E a r l i e r assessments of s o l u t i o n strengthening i n magnesium a l l o y s have considered the p o s s i b l e e f f e c t s of various solute species on such q u a n t i t i e s as the cohesive strength, surface tension and flow (14) stress . However, such considerations are r a r e l y h e l p f u l i n d e f i n i n g the d e t a i l e d processes involved. Accordingly, i t i s more p r o f i t a b l e to attempt a d i r e c t assessment of the deformation modes and the way i n which solute additions a f f e c t them. 61 As o u t l i n e d i n the l a s t s e c t i o n the deformation of p o l y c r y s t a l l i n e Mg occurs predominantly by s l i p on the basal with a d d i t i o n a l s l i p on the prismatic by a double twinning i n the sequence boundary s l i d i n g . {0001} <1120> {1010}<1120> system system accompanied {1011} - { 1012} and some g r a i n Prism s l i p occurs predominantly at g r a i n corners which are s i t e s of high s t r e s s concentration, and thus acts as a s t r e s s r e l i e f mechanism c o n t r i b u t i n g to increased d u c t i l i t y . Furthermore 5 the y i e l d strength of p o l y c r y s t a l l i n e magnesium w i l l be governed by the CRSS f o r both basal and prismatic s l i p . The most comprehensive data a v a i l a b l e are based on studies on the Mg-Li system by Dorn and h i s (1^ 15 73) colleagues ' ' . These experiments have shown that a d d i t i o n of l i t h i u m to magnesium causes an increase i n the CRSS f o r s l i p on the basal system, but a decrease i n the CRSS f o r s l i p on the prism system. They have also shown t h a t , f o r p o l y e r y s t a l s , the y i e l d s t r e s s of these a l l o y s , v a r i e s with concentration of l i t h i u m roughly i n a manner s i m i l a r to that found i n the present work, and that a s i m i l a r v a r i a t i o n of d u c t i l i t y with conc e n t r a t i o n was a l s o found. Yoshinaga and H o r i u c h i ^ ^ have also investigated the deformation behaviour of Mg-Li p o l y e r y s t a l s as a f u n c t i o n of l i t h i u m concentration. Although both groups of workers found s i m i l a r v a r i a t i o n i n y i e l d s t r e s s with solute concentration, the d u c t i l i t y minimum was observed at 0.4 a t . % L i by Horiuchi ;and Yoshinaga while Dorn et a l found the minimum at 4 at. % L i . The i n t e r p r e t a t i o n offered by Dorn et a l i s that the y i e l d stress of the p o l y c r y s t a l l i n e aggregate i s the combined r e s u l t of the CRSS f o r both basal and prismatic s l i p . The i n i t i a l r a p i d increase was a t t r i b u t e d to the dominant s o l u t i o n hardening f o r basal s l i p , while the 62 subsequent reduced rate of hardening and increased d u c t i l i t y was a t t r i b u t e d to the increasing importance of prismatic s l i p as an a v a i l a b l e deformation mode. Twinning and boundary shear were considered to be of minor importance. P a r a l l e l i n g these conclusions i s the observation that increasing l i t h i u m content r e s u l t s i n a reduction of the c/a r a t i o , and hence the decrease of CRSS f o r prismatic s l i p i s the expected r e s u l t of the decreasing (73) P e i e r l s s t r e s s . The work of Ahmadieh and Dorn has shown P e i e r l s stress to be the r a t e c o n t r o l l i n g mechanism f o r prismatic s l i p at low temperatures. These ideas cannot account adequately f o r the present r e s u l t s . Consider, f i r s t , the dependence of CRSS f o r basal s l i p on concentration. (74) Levine, Sheely and Nash have measured the CRSS f o r basal s l i p i n s i n g l e c r y s t a l s of d i l u t e a l l o y s of magnesium with Zn, A l , Tl, Cd and In and t h e i r r e s u l t s are reproduced i n f i g . (34). These authors conclude that the solute strengthening e f f e c t i s l i n e a r with concentration f o r Zn, A l and T l and that f o r Cd and In there i s no hardening at low concentrations followed by a l i n e a r hardening at higher concentrations. A c l o s e r examination of these data i n d i c a t e s that i f l i n e s of t r u l y best f i t are drawn through the p o i n t s , then i n no case do they extrapolate back to the CRSS f o r pure magnesium. Such l i n e s are drawn i n f i g . (35), and show that f o r a l l solute species, the CRSS f o r basal s l i p i s unaffected by solute a d d i t i o n up to a concentration, approximately C T i n the present work. the same as This conclusion has been confirmed i n Mg-Zn a l l o y s , d e t a i l s of which are discussed i n a l a t e r chapter. C l e a r l y , then the present observation of the very rapid increase i n a v with solute a d d i t i o n from pure Mg to C T cannot be F i g . 35. Revised curves drawn f o r data from r e f . 74. 64 a t t r i b u t e d to a change i n CRSS for basal s l i p . therefore, to conclude that t h i s increase i n I t would appear l o g i c a l must be due to an increase i n the CRSS f o r prismatic s l i p . So f a r , there are no reports i n the l i t e r a t u r e on the : v a r i a t i o n of CRSS f o r prismatic s l i p at very low solute concentrations. Accordingly, such measurements have been c a r r i e d out i n the present work and the r e s u l t s f o r Mg-Zn a l l o y s are shown i n f i g . (93). These confirm the conclusion that the CRSS f o r p r i s m a t i c s l i p does, i n f a c t , increase with increasing solute concentration up to C^. work are discussed i n a l a t e r 1.4.3.1. The V a r i a t i o n of D e t a i l s of t h i s chapter. and D u c t i l i t y with Solute Concentration: i The v a r i a t i o n of both are now more r e a d i l y understandable. and d u c t i l i t y with solute concentration The y i e l d s t r e s s i n p o l y c r y s t a l l i n e m a t e r i a l i s determined by the s t r e s s necessary to a c t i v a t e both basal and prismatic s l i p . The i n i t i a l high rate of s o l u t i o n hardening i s due to the rapid increase i n the CRSS f o r prismatic s l i p , - w h i l e the CRSS for basal s l i p remains unchanged upto C_ (at and above room temperature). Due to s l i p on the basal system, s t r e s s concentrations w i l l a r i s e which may be r e l i e v e d e i t h e r by crack formation or by p l a s t i c flow on the prismatic s l i p system. As the CRSS f o r prismatic s l i p increases from pure magnesium to C-, l e s s p l a s t i c deformation i s p o s s i b l e p r i o r to f r a c t u r e and the d u c t i l i t y i s reduced. 1.4.3.2. da ' The S o l u t i o n Hardening Rate 0^-) : The c r i t i c a l resolved shear s t r e s s f o r basal s l i p i n magnesium i s approximately two orders of magnitude lower than that f o r 65 prismatic s l i p . For example at room temperature the numerical values 2 2 for the two systems are 51 gm/mm and 4600 gm/mm r e s p e c t i v e l y . Thus i t may seem rather u n l i k e l y that prismatic s l i p should operate at the y i e l d stress of the p o l y c r y s t a l l i n e aggregate. However, i n view of the strong r o l l i n g and r e e r y s t a l l i z a t i o n texture of magnesium and i t s a l l o y s the operation of prismatic s l i p i s not at a l l s u r p r i s i n g . These materials have a texture such that the basal plane remains i n c l i n e d to the r o l l i n g or extrusion d i r e c t i o n w i t h i n 10°. The Schmid f a c t o r f o r basal s l i p i n t h i s o r i e n t a t i o n i s about 4-5 times lower than that f o r prism s l i p plane. Thus the deformation behaviour of the p o l y c r y s t a l l i n e aggregate should show a c l o s e r s i m i l a r i t y to that of s i n g l e c r y s t a l s oriented for Prismatic s l i p rather than f o r basal s l i p . Qualitatively, the.stress- s t r a i n curves of the p o l y e r y s t a l s do show a c l o s e r resemblance to the s t r e s s - s t r a i n curves of the s i n g l e c r y s t a l s oriented f o r p r i s m a t i c s l i p . I t would be i n t e r e s t i n g at t h i s juncture to compare the observed i n i t i a l s o l u t i o n hardening rate of the p o l y e r y s t a l s with that of s i n g l e c r y s t a l s i n prism s l i p o r i e n t a t i o n . Single c r y s t a l s and p o l y e r y s t a l s of both Mg-Al and Mg-Zn systems have been deformed at room temperature i n the present work. This i s shown i n Table I I I . For converting the shear s t r e s s to t e n s i l e s t r e s s the f o l l o w i n g r e l a t i o n s h i p a = . 2 r has been used. Table I I I Comparison of S o l u t i o n Hardening Rates i n Single C r y s t a l s With P o l y e r y s t a l s System .da/ . dc" For prismatic s l i p at 295°K ( For p o l y e r y s t a l s at 295°K } l n P S 1 Mg-Zn 3.45 x 10 5 4.74 x 10 5 Mg-Al 5.95 x 1 0 4 6.24 x 1 0 4 I t i s apparent from the table that the s o l u t i o n rate of the p o l y c r y s t a l l i n e aggregatesis 66 strengthening close to.that of s i n g l e c r y s t a l s oriented f o r prism s l i p . No attempt w i l l be made here to compare the e f f e c t of temperature da ' on (-j^-) i n the p o l y e r y s t a l s with that i n s i n g l e c r y s t a l s . The e f f e c t of grain boundary s l i d i n g and c e l l formation i n p o l y c r y s t a l l i n e m a t e r i a l above room temperature (0.31 T ) makes such a comparison d i f f i c u l t . Below room temperature on the other hand i t i s not the prismatic slip system alone which i s affected by the a d d i t i o n of solute up to C_. This amount of solute i s e f f e c t i v e also i n increasing the CRSS f o r basal s l i p below room.temperature. These considerations do not permit a q u a n t i t a t i v e comparison at temperatures below room temperature. 1.4.3.3. Hardening Beyond C^,: For a l l the a l l o y systems considered here the c/a r a t i o increases with increasing solute concentration; that i s , the e f f e c t i s opposite to that f o r Mg-Li system. Yet reference to f i g . (93) shows that f o r increasing concentrations beyond C^,, the CRSS f o r prismatic s l i p decreases. This decrease cannot be accounted f o r , then, i n terms of a.decreasing P e i e r l s s t r e s s r e s u l t i n g from a reduction i n the a x i a l r a t i o , as i n the Mg-Li case. The decreasing CRSS f o r prismatic s l i p can account f o r both the decreased r a t e of s o l u t i o n hardening and the increasing d u c t i l i t y C^. The reduced rate of hardening and increased d u c t i l i t y beyond i n stage I I can, be a t t r i b u t e d to the increasing importance of prismatic s l i p as an operative deformation mode. made s l i g h t l y The operation of prismatic s l i p i n the p o l y e r y s t a l s i s easier due-to the increase i n CRSS f o r basal s l i p i n the a l l o y s containing concentrations of solute 67 i n excess of C^. Thus y i e l d i n these a l l o y s w i l l be achieved by a balance between basal and prismatic s l i p . The i n i t i a l work hardening rate w i l l become lower with increasing solute concentration (beyong C^), because of the increasing ease of s t r e s s r e l i e f by p r i s m a t i c s l i p . This l i n e of argument can be extended f u r t h e r to e x p l a i n . the observed lowering of i n stage I I I . The y i e l d s t r e s s was evaluated at 0.2% p l a s t i c s t r a i n . close to An a l l o y containing solute concentration w i l l have a high i n i t i a l work hardening rate due to the d i f f i c u l t operation of prismatic s l i p . s t r e s s at 0.2% s t r a i n . large excess of This w i l l lead to a large flow On the other.hand an a l l o y containing solute i n w i l l have a lower i n i t i a l work hardening rate and as a r e s u l t , the flow s t r e s s at 0.2% s t r a i n w i l l become smaller than at a lower solute concentration. 1.4.3.4. The T r a n s i t i o n Concentration C^l Above 300°K the CRSS f o r basal s l i p remains unchanged i n stage I of s o l u t i o n strengthening, whereas that f o r p r i s m a t i c s l i p increases. Hence i n p o l y c r y s t a l s the existence of a c r i t i c a l t r a n s i t i o n concentration i s a manifestation of a t r a n s i t i o n i n the CRSS - concentration r e l a t i o n s h i p for prismatic s l i p . This conclusion i s supported by the e q u a l i t y of the t r a n s i t i o n concentration observed i n p o i y e r y s t a l l i n e aggregate at room temperature (0.01 a t . % Zn) to that obtained i n c r y s t a l s oriented f o r p r i s m a t i c s l i p (0.006 a t . % ) . I t should be noted that at a l l temperatures the t r a n s i t i o n concentration i n c r y s t a l s oriented f o r p r i s m a t i c s l i p remains constant. The s i t u a t i o n i s , however, rather complicated temperatures, as discussed e a r l i e r . at low Therefore,the c r i t i c a l t r a n s i t i o n 68 concentration, as obtained from the a of the p o i y e r y s t a l l i n e aggregates tested below room temperature, i s rather a complex quantity which cannot be discussed at the present. 1.4.3.5. The Flow Stress: Toaz and R i p l i n g ^ ^ have found that the t r a n s i t i o n i n the maximum stress-temperature curve r e s u l t s from the entrance of 5 recrystallization. Staceys work on magnesium and i t s a l l o y s containing small amounts of A l has i n d i c a t e d that c e l l formation precedes r e c r y s t a l l i z a t i o n Metallographic studies on pure Mg and Mg-Al a l l o y s deformed between 200 and 300°K up to a s t r a i n of 2%, i n the present work, have f a i l e d to r e v e a l r e c r y s t a l l i z e d g r a i n s , although the t r a n s i t i o n i n the flow s t r e s s from stage I to stage I I occurs i n the same temperature i n t e r v a l . I t i s proposed, therefore, that the onset of c e l l formation (sub grains) i s responsible f o r the t r a n s i t i o n i n the flow s t r e s s " temperature curves. This can be b e t t e r understood as f o l l o w s . When deformation proceeds at a f i x e d s t r a i n rate there i s s t r e s s concentration at the g r a i n corners. This s t r e s s concentration w i l l not be r e l i e v e d by s l i p i n the adjacent g r a i n s , due to von Mises' not being s a t i s f i e d . criterion The operation of p r i s m a t i c s l i p a t the g r a i n corners, s w i l l only p a r t l y r e l i e v e the stresses because basal and p r i s m a t i c s l i p combined cannot provide f i v e independent modes of deformation. At lower temperatures t h i s s t r e s s concentration i s f i n a l l y r e l i e v e d by crack nucleation and subsequent f r a c t u r e , whereas at higher temperatures s t r e s s accelerated polygonization w i l l r e l i e v e the s t r e s s concentration and deformation proceed at a lower flow s t r e s s than at lower temperatures. will 69 This explanation i n v o l v i n g polygonization and c e l l s t r u c t u r e formation i s consistent with the observed s t r a i n s e n s i t i v i t y of the t r a n s i t i o n temperature i n the flow stress-temperature curves f o r 0.055% A l a l l o y ( f i g . (28)). The corresponding t r a n s i t i o n temperature i n pure Mg and Mg - 0.53% A l a l l o y are observed to be l e s s s e n s i t i v e to the s t r a i n at which the flow s t r e s s i s measured. (0„055 at % A l i s close to C T and therefore the CRSS for p r i s m a t i c s l i p i n t h i s a l l o y w i l l , be higher than i n pure Mg or the higher a l l o y s ) . Theref ore^, at a f i x e d s t r a i n rate the extent to which s t r e s s r e l i e f w i l l be achieved by the operation of prismatic s l i p w i l l be s m a l l , thus making c e l l formation an important mechanism. Since c e l l formation i s a s t r e s s accelerated p o l y g o n i z a t i o n process, i t w i l l operate at a lower temperature, the higher the applied s t r a i n , as i s the case with 0.05 at, % A l a l l o y . The strain s e n s i t i v i t y w i l l be lowered with the i n c r e a s i n g ease of p r i s m a t i c s l i p , because more s t r e s s r e l i e f w i l l be achieved through the operation of p r i s m a t i c s l i p ; thereby making c e l l formation a l e s s important process than i n the 0.05 at. % A l a l l o y . 1.4.4. The E f f e c t of Temperature on D u c t i l i t y : The e f f e c t of solute on d u c t i l i t y at constant has been r a t i o n a l i z e d temperature i n terms of the r e l a t i v e ease of p r i s m a t i c s l i p . However, there are two observations which are s t i l l unexplained. 1) They are The increase i n d u c t i l i t y of Mg as w e l l as i t s a l l o y s . w i t h temperature^ above room temperature. 2) The observed maxima and minima i n the d u c t i l i t y - curves of the Mg-Al a l l o y s . temperature 70 The d u c t i l i t y t r a n s i t i o n i n mangesium has been a t t r i b u t e d to the onset of r e c r y s t a l l i z a t i o n ^ ^ . As the temperature increases the CRSS f o r prismatic s l i p decreases and also the ease of polygonization i s enhanced. Both these processes lead to an increased s t r e s s r e l i e f and make longer time a v a i l a b l e f o r r e c r y s t a l l i z a t i o n to proceed. Therefore^ the d u c t i l i t y of magnesium increases continuously with temperature beyond 295°K. The a d d i t i o n of solute up to C T increases the flow s t r e s s f o r prismatic s l i p and t h e r e f o r e t h e d u c t i l i t y of these a l l o y s i s observed p to be s l i g h t l y lower than that of magnesium. At higher solute concentrationsj however, the e f f e c t i v e n s s s of the s t r e s s r e l i e f increases due to the lower flow s t r e s s f o r prismatic s l i p and higher flow s t r e s s f o r basal s l i p leading to an increased d u c t i l i t y i n these a l l o y s . to note that up to 420°K pyramidal s l i p {1011} <1120> I t i s important does not operate . (51) i n magnesium 1.4.4.1. The D u c t i l i t y Maxima: D u c t i l i t y maxima have been observed i n Mg-alloys containing 0.2% (35) Pb and 0.8% A l . Green Wood et a l have found extensive g r a i n boundary c a v i t a t i o n i n the Mg~0.2 % Pb a l l o y i n the temperature i n t e r v a l i n which the loss i n d u c t i l i t y i s encountered. I t was suggested that grain boundary c a v i t a t i o n i s responsible f o r the e a r l y f r a c t u r e . A s h i f t i n the d u c t i l i t y maximum to lower.temperatures was also observed w i t h decreased s t r a i n r a t e , which could be accounted f o r i n terms of the longer time a v a i l a b l e f o r vacancies to d i f f u s e , coalesce and form i n t e r g r a n u l a r voids at a slower s t r a i n r a t e . 71 Stacey reported the occurrence of d u c t i l i t y peaks i n Mg-0.8% A l a l l o y and explained h i s r e s u l t s i n terms of a combined e f f e c t of c a v i t a t i o n and the formation of c e l l s t r u c t u r e adjacent to the grain boundaries. Since the grain boundary movements increase w i t h increasing temperature, the s t r a i n to be accommodated by l a t t i c e bending should accordingly decrease. Thus the formation of c e l l s t r u c t u r e , which according to Stacey i s at l e a s t i n part responsible f o r the d u c t i l i t y peak, may be expected to be w e l l developed at slower s t r a i n rates and at an intermediate temperature range, which i n turn w i l l be determined by the strain rate. The present r e s u l t s on the high temperature d u c t i l i t y of Mg-Al a l l o y s can now be b e t t e r understood. The e f f e c t of a l l o y i n g up to C_ i s to increase the CRSS f o r p r i s m a t i c s l i p . Therefore^in these a l l o y s the attainment of s t r e s s r e l i e f through p r i s m a t i c s l i p i s even l e s s than i n pure magnesium. The s t r a i n rate used i n the present experiments (75%/hr) i s rather high so that there i s n e i t h e r much time a v a i l a b l e f o r r e c r y s t a l l i z a t i o n to proceed, nor can the vacancies coalesce to form i n t e r g r a n u l a r voids. This explains the lower d u c t i l i t y and the absence of maxima i n these a l l o y s . Increasing the a l l o y i n g content i n excess of C^, i s i n e f f e c t equivalent to reducing the s t r a i n rate. understood as f o l l o w s . This equivalence can be The flow s t r e s s f o r prismatic s l i p decreases with i n c r e a s i n g s o l u t e , a d d i t i o n beyond C_. Since p r i s m a t i c s l i p acts as one of the mechanisms causing s t r e s s r e l i e f at the g r a i n corners, the e f f e c t i v e - l e n g t h of time a v a i l a b l e f o r the r e c r y s t a l l i z a t i o n to proceed, therefore, increases at higher solute concentrations. As a 72 r e s u l t , the f i n e grained s t r u c t u r e adjacent to the boundaries i s b e t t e r developed when the solute concentration i s high. This explains the increased d u c t i l i t y with solute concentration. However, the coalescence of vacancies to form i n t e r g r a n u l a r v o i d s , being a time dependent phenomenon, i s also enhanced with i n c r e a s i n g solute content thereby leading to a s h i f t i n the d u c t i l i t y peak to lower temperatures. 1.4.5. Strengthening E f f e c t s i n Multicomponent S o l i d S o l u t i o n s : I t has been frequently noted that the strength of a multicomponent s o l i d s o l u t i o n can be obtained by adding up the strengthening e f f e c t s of the corresponding binary s o l i d s o l u t i o n s . The above conclusion has been e m p i r i c a l l y established f o r face centred cubic alloys. However, even i n the absence of comprehensive data on binary and ternary systems such behaviour should not be expected i n p o l y c r y s t a l l i n e s o l i d s o l u t i o n s having hep s t r u c t u r e . Unlike the p o l y c r y s t a l l i n e aggregates of fee s t r u c t u r e , which deform by the operation of one slip mode (having more than f i v e s l i p systems and hence s a t i s f y i n g von Mises c r i t e r i o n ) , the hep materials undergo p l a s t i c flow by the operation of two or more deformation modes. simultaneous Since the various deformation modes are affected d i f f e r e n t l y by the a d d i t i o n of s o l u t e , the y i e l d s t r e s s of the p o l y c r y s t a l l i n e aggregate represents a balance between these deformation modes and the a d d i t i v e nature of solutes i s u n l i k e l y to be observed i n hep m a t e r i a l s . In the present work t h i s conclusion was v e r i f i e d on a Mg-In-Zn a l l o y tested at room temperature. The strength c a l c u l a t e d from the Mg-In and Mg-Zn b i n a r i e s was found to be much higher than the observed strength of t h i s a l l o y . The Mg-In-Zn ternary was chosen because i t involved the component responsible f o r the maximum strengthening e f f e c t (Zn) and also the one g i v i n g the minimum strengthening e f f e c t ( I n ) , of a l l the solutes examined. The: ternary a l l o y examined had concentration of each solute i n excess of the t r a n s i t i o n concentration f o r the corresponding binary system. A c r i t i c a l examination of the observed strength of t h i s a l l o y suggested that the stage I strengthening i s achieved by one component only and the solute i n excess of C^, f o r t h i s component as w e l l as the t o t a l amount of solute of the other component, have a d d i t i v e e f f e c t i n stage I I . The c a l c u l a t e d value using Mg-In and Mg-Zn b i n a r i e s was found to agree c l o s e l y with the experimental value of a^p of the ternary, i f Zn i s assumed to be the preferred solute responsible f o r stage I strengthening. of t h i s are given i n appendix Details (B) . In order to gain some i n s i g h t , the i n v e s t i g a t i o n of the ternary systems was c a r r i e d f u r t h e r . Two s e r i e s of Mg-Zn-In a l l o y s were prepared containing 0.004 a t . % and 0.007 at»% Zn r e s p e c t i v e l y (both l e s s than C^, f o r Zn) and I n additions up to 1.1 a t . % were made. The r e s u l t s are shown i n f i g s . (36,37). Since Zn concentration i s lower than C , I n should contribute p a r t l y to the stage I strengthening. Experimentally then, a three stage s o l u t i o n strengthening curve i s obtained, as expected. The r e s u l t s show that the stage I slope ( l b i n ternary) i s reduced, the stage I I slope i s increased and the t r a n s i t i o n concentration i s reduced from the corresponding values f o r the Mg-In binary. The i m p l i c a t i o n may be that s o l u t i o n strengthening r e s u l t s from a type of solute atom d i s l o c a t i o n i n t e r a c t i o n with preference f o r prism plane d i s l o c a t i o n s and large s i z e d i f f e r e n c e solutes to be involved. 74 0 0.2 0.4 0.6 Atomic % In 0.8 1.0 75 PART I I 2. 2.1. Solution Hardening In A l l o y Single C r y s t a l s INTRODUCTION AND OBJECTIVES: The study of s i n g l e c r y s t a l s has the advantage of avoiding the d i f f i c u l t problem of dealing with the constraining conditions imposed by the g r a i n boundaries during the deformation of the p o l y c r y s t a l l i n e aggregates. This s i m p l i c i t y , which enables one to obtain a better knowledge of shear s t r e s s conditions on p a r t i c u l a r s l i p planes, has disadvantages due to the poor r e p r o d u c i b i l i t y of the flow s t r e s s values of d i f f e r e n t s i n g l e c r y s t a l s , because of the e f f e c t s of s l i g h t changes i n such f a c t o r s as substructure, impurity concentration, o r i e n t a t i o n and i n i t i a l d i s l o c a t i o n density. A d d i t i o n a l complications a r i s e i n a l l o y s i n g l e c r y s t a l s grown from the melt, due to the solute segregation. Single c r y s t a l s of d i l u t e s o l i d s o l u t i o n s of magnesium containing Zn i n amounts up to 0.45 at % have been studied i n the present i n v e s t i g a t i o n . " The study of the d i l u t e a l l o y s was undertaken because of three main reasons. The s o l u t i o n hardening rate i n the p o l y e r y s t a l s i n Mg d i l u t e s o l u t i o n s i s extremely high. The f i r s t l o g i c a l step i n p u r s u i t of an explanation of the hardening i n p o l y e r y s t a l s i s to study the s o l u t i o n hardening i n s i n g l e c r y s t a l s of low a l l o y s . Another o b j e c t i v e of the d i l u t e s o l u t i o n study was to determine the i n d i r e c t strengthening d i s l o c a t i o n density. e f f e c t of solute a r i s i n g due to a change i n the Strengthening i s p o s s i b l e i n close packed s t r u c t u r e s through an increase i n the d i s l o c a t i o n d e n s i t y , caused by the presence of the s o l u t e . This i n d i r e c t e f f e c t of the solute i s believed to be s i g n i f i c a n t 76 at low concentrations of solute ( 7 5 ) L a s t l y , much of the current theory of s o l u t i o n strengthening assumes e i t h e r an i d e a l or a. regular s o l u t i o n model. Since these models are better d e s c r i p t i o n s at low solute concentrations, they can be tested more exactly i n d i l u t e s o l u t i o n s only. The choice of Zn as solute was made because of i t s strong hardening e f f e c t as observed i n the Mg-Zn p o l y c r y s t a l s . This strong hardening e f f e c t was hoped to make the study of d i l u t e s o l u t i o n s e a s i e r . Zn i s a hexagonal close packed metal which c o n s t i t u t e s a s u b s t i t u t i o n a l solute i n magnesium at the Mg r i c h end of the phase diagram. Additional reasons f o r the choice of Zn are o u t l i n e d i n the s e c t i o n on prismatic s l i p . The experimental procedure f o r specimen preparation 2.2. 2.2.1. i s given e a r l i e r . STRESS-STRAIN RELATIONSHIPS IN BASAL SLIP: The S t r e s s - S t r a i n Curves: I t i s now w e l l recognized that the s t r e s s - s t r a i n curves of a v a r i e t y of c r y s t a l structures show c e r t a i n s i m i l a r i t i e s . stages i n the basic work hardening curve are common to the centred cubic metals and a l l o y s ^ ^ , 7 7 ) ^ ^ t intermetallics e Thus the three face Y\aa.li. h a l i d e s ^ ^ , some & , body centred N i o b i u m ^ ^ and Germanium^"^ . However, the work hardening curve of hexagonal metals c o n s i s t s of two or three stages (3,29,82,83) ' ' ' . The shear stress-vs-shear s t r a i n curves of pure Mg c r y s t a l s deformed at temperatures between 78°K and 423°K at a constant s t r a i n rate are shown i n f i g . (38). I t i s observed that the s t r e s s increases i n a parabolic manner at low s t r a i n s ; a minimum rate of work hardening i s 1400 I 01 I 2 I 3 I 4 Shear S t r a i n I 5 I 6 L 0 1 7 F i g . 38. Resolved shear stress-shear s t r a i n curves f o r Mg s i n g l e c r y s t a l s oriented for Basal s l i p . 78 attained at intermediate s t r a i n s , followed by a region of rapid hardening. A t h i r d stage with a decreasing work hardening rate i s also observed i n c r y s t a l s deformed at and above room temperature. Following the common tendency to break s t r e s s - s t r a i n curves i n t o sections of s i m i l a r work hardening r a t e s , the three stages of deformation w i l l be defined as shown schematically i n f i g . (39). I t i s i n t e r e s t i n g to note that whereas the low i n i t i a l -4 work hardening rate ( 10 -5 -10 G) and an extensive range of easy g l i d e are common to many hexagonal metal c r y s t a l s , the "Sigmoidal Shape" i s a c h a r a c t e r i s t i c feature of magnesium only. The i n i t i a l stage of work hardening becomes sub-divided i n t o two l i n e a r regions i n Z n ^ ^ - and Cd^^ c r y s t a l s deformed at room-temperature, however, t h i s was not observed i n Mg c r y s t a l s i n the present work. These d i f f e r e n c e s i n the work hardening behaviour place Mg i n a category quite d i f f e r e n t from most of the other common hexagonal metals. 2.2.2. The E f f e c t of Substructure on Work Hardening: In order to make a q u a n t i t a t i v e comparison of the work hardening parameters i n d i l u t e a l l o y s p o s s i b l e , i t i s important to keep the e f f e c t of other v a r i a b l e s on these q u a n t i t i e s to a minimum. One such v a r i a b l e i s a low angle boundary running p a r a l l e l to the t e n s i l e a x i s of the c r y s t a l . Ordinary etchants and X-ray back r e f l e c t i o n technique w i l l not detect a s i n g l e sub-boundary i n a large c r y s t a l . However, o p t i c a l micrographs of specimens, e x h i b i t i n g a high rate of work hardening extended only small amounts, show boundaries of twinning and enhanced deformation not observed i n the other specimens. An example of such a boundary i n Mg-0.054 a t . % Zn a l l o y deformed at room temperature i s shown i n f i g . (40). 79 F i g . 40. Sub-boundary running p a r a l l e l to the t e n s i l e - a x i s i n a Mg + 0.054 a t . % Zn a l l o y c r y s t a l deformed i n easy g l i d e at room temperature. 140X 80 (29) I t has been suggested e a r l i e r by Hirsch and L a l l y that t h i s high rate of work hardening i s associated w i t h the said subboundaries. These i n v e s t i g a t o r s have observed that the presence of a s i n g l e sub-boundary of the order of a degree leads to a reduction i n the extent of easy g l i d e by a f a c t o r of f i v e , an increase i n the i n i t i a l work hardening rate by an order of magnitude and a l o s s i n the sigmoidal shape of the s t r e s s - s t r a i n curve. However, the work hardening rate i n stage B remains unaffected by the presence of sub-boundaries. The stress«=strain curves of Mg c r y s t a l s deformed by various workers at room temperature are summarized i n f i g . (41). The inconsistency apparent i n f i g . (41) i s not s u r p r i s i n g i n view of the dramatic e f f e c t of sub-boundaries on work hardening. In most of the e a r l i e r i n v e s t i g a t i o n s the growth rate has been > l " / h r . In the present work, however, i t was observed that l " / h r i s about the l i m i t i n g growth rate beyond which the c r y s t a l s contain many sub-boundaries, as observed by the s p l i t t i n g of the back r e f l e c t i o n spots. Therefore, i n order to obtain good c r y s t a l s a growth rate of 0.4"/hr was used. A l l t e n s i l e test specimens f o r one composition were taken from one s i n g l e c r y s t a l and t e s t s were conducted i n d u p l i c a t e . Repeat t e s t s were considered necessary when the extent of easy g l i d e i n the f i r s t two c r y s t a l s d i f f e r e d by more than 50%. 2.2.3. The S t r e s s - S t r a i n Curves of the Mg-Zn A l l o y s : S t r e s s - s t r a i n curves of a representative set of Mg-Zn a l l o y s are shown as a f u n c t i o n of the test temperature i n f i g s . (42,43). In order to f a c i l i t a t e comparison of the work hardening behaviour as a function of s o l u t e , at a constant temperature, the s t r e s s - s t r a i n curves Shear s t r a i n F i g . 41. Resolved shear stress-shear s t r a i n curves f o r Mg s i n g l e c r y s t a l s deformed by various workers at room temperature. 1400 Shear s t r a i n F i g . 43. Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg + 0.258 a t . % Zn a l l o y single crystals. 84 of a l l o y s containing d i f f e r e n t amounts of solute are grouped together as shown i n f i g s . (44,45, and 46). I t i s observed that the "S" shape of the curves i s retained up to a concentration of solute equal to 0.258 at» % Zn. The sigmoidal shape i s most pronounced i n an intermediate temperature range between 143°K and 295°K. Both above and below t h i s temperature i n t e r v a l the region of easy g l i d e tends to become l i n e a r . The a l l o y containing 0.45 a t . % Zn i s an exception i n that y i e l d points were observed i n t h i s a l l o y at and below room temperature, leading to the absence of the sigmoidal shape of i t s s t r e s s - s t r a i n curves. 2.2.4. Yield Points: Y i e l d points have been observed i n Mg-Zn a l l o y s i n the present work at low temperatures. When tested at 78°K, only a s l i g h t y i e l d point was observed i n 0.054 at* % Zn a l l o y , however, a w e l l defined y i e l d drop became apparent on increasing the solute concentration to 0.45 a t . % . The y i e l d points continued to appear at i n c r e a s i n g l y higher temperatures, as the solute content was increased. For example, the appearance of y i e l d points was l i m i t e d to 78°K only i n the case of 0.054 a t . Zn a l l o y , to temperatures below 200°K i n the case of 0.258 a t . % Zn and i n the case of Mg-0.45 a t . % Zn a l l o y y i e l d points could be seen i n specimens tested at room temperature. In a d d i t i o n to the i n i t i a l y i e l d p o i n t s , m u l t i p l e y i e l d points have been observed i n a l l o y s containing 0.019 a t * % Zn when tested at 423°K. The serrated y i e l d i n g s t a r t s immediately a f t e r the m a t e r i a l undergoes p l a s t i c flow and continues up to a c e r t a i n s t r a i n , which increases with increasing solute a d d i t i o n . Beyond t h i s s t r a i n the s t r e s s - s t r a i n J 0 I 1 F i g . 45. 2 '. L 3 4 5 Shear S t r a i n Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn a l l o y s i n g l e c r y s t a l s deformed at 295 K. Q 0 1 2 3 4 5 Shear S t r a i n F i g . 46„ Resolved shear s t r e s s vs . shear s t r a i n curves f o r Mg-Zn a l l o y s i n g l e c r y s t a l s deformed at 195 K. S 88 curve remains smooth t i l l f r a c t u r e occurs. 2.2.5. The C r i t i c a l Resolved Shear Stress: The CRSS of Mg c r y s t a l s are shown as functions of composition and t e s t i n g temperature i n f i g . (47). Gross p l a s t i c flow was considered to begin at the f i r s t departure from l i n e a r i t y . Sometimes CRSS i s obtained by the e x t r a p o l a t i o n of stage I to zero s t r a i n , however, such a procedure was not p r a c t i c a l because of the "S" shape of the s t r e s s - s t r a i n curves. I t i s c l e a r from f i g . (47) that the CRSS of Mg decreases l i n e a r l y from 74 gm/mm at 78°K to 41 gm/mm at 330°K. 2 2 Beyond 330°K the CRSS remains e s s e n t i a l l y independent of temperature, varying s l i g h t l y due to a change i n shear modulus with temperature. The present trend of the temperature dependence of CRSS i n Mg i s i n agreement w i t h the e a r l i e r f i n d i n g s (6 13 89) ' ' The strengthening e f f e c t of Zn on Mg i s seen to be strongly dependent on temperature. For example, the d i f f e r e n c e i n CRSS between pure Mg and 0.258 at. % Zn c r y s t a l tested at 78°K i s approximately 4-5 times higher than that at room temperature and above. I t i s i n t e r e s t i n g to note that beyond 330°K, the a l l o y s containing Zn i n amounts up to 0.02 at, % have the same CRSS as that of Mg. However, the same a l l o y s when tested at 78°K show a s u b s t a n t i a l increase i n CRSS over that of Mg. The strengthening e f f e c t of Zn as a function of the solute concentration i s shown i n f i g . (48) f o r various t e s t i n g temperatures. The data at 0°K have been obtained by the e x t r a p o l a t i o n of the curves i n f i g . (47) to absolute zero. I t i s apparent from f i g . (48) that the strengthening e f f e c t of the solute on Mg i s not a simple l i n e a r function of the solute 500 Mg-Zn Single Crystols B A S A L SLIP 400- Mg Mg •'0-006 A t . % Z n Mg+0 019 Mg + 0 0 5 4 9 Mg + 0 15 o • Mg + 0 258 o— Mg + 0-45 " o — A— • CM | 300j- co CO o 200 100- 0 100 200 TEMPERATURE 300 9 K F i g . 47. CRSS f o r Basal s l i p vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s . 400 Fig. 48c. S o l u t i o n .strengthening i n basal s l i p vs. concentration .for. Mg-Zn a l l o y s . F i g . 49. Solution strengthening i n basal s l i p vs. square root of the solute, concentration. 91 concentration as reported e a r l i e r by Levine, Sheely and Nash (74) F i g . (49) shows a p l o t of the increase i n CRSS of the a l l o y over that of magnesium against C , where C i s the concentration-of the solute i n a t . % . I t i s c l e a r that the s o l u t i o n hardening occurs i n two l i n e a r stages, I and I I . Stage I continues up to a concentration of solute equal to 0.025 a t . % Zn, followed by stage I I which has a slope approximately 3 times higher than i n stage I . The t r a n s i t i o n concentration from stage I to stage I I i s observed to be independent of temperature. h s o l u t i o n hardening behaviour i n the CRSS-C The occurrence of a two stage p l o t s i m i l a r to that i n the present work has been r e c e n t l y reported i n the d i l u t e Ag-base (face centred (85} cubic) s o l i d solutions containing In solute 2.2.6. The Rate of Solution Strengthening:. The n o n - l i n e a r i t y of s o l u t i o n hardening w i t h respect to z i n c con- centrations makes i t d i f f i c u l t to define a s i n g l e parameter representing the strengthening rate over, a range of compositions. However, s o l u t i o n hardening rate can be conveniently described by the slopes S^ and S ^ of the two l i n e a r parts of the curves i n f i g . (49). I t i s important to note that the s o l u t i o n hardening rate at any solute concentration i s r e l a t e d to the solute conh c e n t r a t i o n and the corresponding slope of the CRSS-C ,9T_ \ 1 8T • S = 3C 2.2.6.1, c curve as f o l l o w s : = loFz ' 3C^ 2C^ (1) The Temperature Dependence of S-j-: The temperature dependence of S^.is shown i n f i g . (50). I t i s apparent that S j decreases l i n e a r l y from 316 gm/mm / ( a t . % ) 2 at 0°K to zero at.330°K. In a l l o y s containing solute up to 0.025 a t . % Zn ( i . e . stage I ) no s o l u t i o n hardening i s observed above 330°K. The c r i t i c a l resolved shear stresses, of Mg and the a l l o y s containing solute i n amounts up to 0.025 a t . % Zn become athermal at 330°K. 92 Q O—I-—o 0 100 200 Temperature.°K 300 400 F i g . 51. The v a r i a t i o n of the s o l u t i o n strengthening parameter S with temperature. T 93 2.2.6.2. The V a r i a t i o n of.S With Temperature: The e f f e c t of temperature on i s shown i n f i g . (51). The 2 s o l u t i o n hardening parameter decreases from 960 gm/mm 1/2 (at.%) at 1/2 2 0°K to 225 gm/mm /(at.%Zn) at 250°K. Beyond 250°K, S decreases very s l i g h t l y with increasing temperature. 2,2.7. Work Hardening: The work hardening parameters have been defined i n an e a r l i e r section. The e f f e c t of solute on these q u a n t i t i e s w i l l be considered here. Because of the inconsistency i n the work hardening parameters of Mg reported e a r l i e r i n the l i t e r a t u r e , i t was considered necessary to i n v e s t i g a t e the s t r a i n hardening behaviour of Mg over a range of temperatures , 2.2.7.1. The Work Hardening Rate i n Stage A, Q : A The work hardening rate during stage A deformation, 9/^, i s shown i n f i g . (52) as a function of composition and temperature. It i s conventional to express the work hardening rate as 9/G where G i s the shear modulus; however, i n the absence of data r e l a t i n g to the concentration dependence of G, 9 i s reported here without taking G i n t o account. I n order to make comparison w i t h other metals p o s s i b l e , 9/G values at a few selected temperatures and compositions are i n d i c a t e d i n f i g . (52). The values of shear modulus f o r t h i s purpose have been taken from the work of Slutsky and Garland and Koster The temperature dependence of 9 ^ f o r Mg i s shown i n f i g . (53). The values of 9 ^ reported in.the l i t e r a t u r e e a r l i e r are also included f o r comparison. The present r e s u l t s i n d i c a t e that 9 ^ decreases r a p i d l y 500 400 - 300 S 00 200 O 0.45 a t . % . Zn ^ 0.258 a t . % Zn Q 0.054 a t . % Zn • 0,019 a t . % Zn (9.5xl0~ ) 5 (3 •H < CD o O 100 - -O -D (0.78X19"" ) 5 100 300 200 400 Temperature °K P i g . 52, The work hardening rate i n stage A vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s , 1200 Temperature Fig» 53. The temperature dependence of the work hardening r a t e i n the easy g l i d e of Magnesium as reported by various workers. 96 with increasing temperature from a value of 6 /G equal to 1.38 x 10~^ at 78°K to 1.07 x 10~ at about 250°K. 5 remains independent of temperature. Beyond 250°K, however, 6 /G A The large s c a t t e r i n d a t a ^ ^ and (QQ\ the high values of 0^ reported e a r l i e r may have been a r e s u l t of the sub-boundaries, which are l i k e l y to be present i n these c r y s t a l s (because of the f a s t rate of growth used by these workers). The existence of a temperature i n s e n s i t i v e 9^ below 200°K as reported by S c h m i d ^ \ Bocek^ ^ 88 89 and C o n r a d ^ i s , however, s u r p r i s i n g . The concentration dependence of 6^ f o r the Mg-Zn a l l o y s i s shown i n f i g . (54) f o r a representative set of temperatures. These curves have been constructed by taking isothermal sections from f i g . (52). I t i s c l e a r that the work hardening rate increases i n a parabolic 1/2 fashion with increasing Zn content. The l i n e a r dependence of 8^ on C i s apparent from f i g . (55). 2.2.7,2. The Extent of Easy G l i d e : The s t r a i n at the end of easy g l i d e , Y ^ . i s shown i n f i g . (56) as a f u n c t i o n of temperature f o r a representative set of Mg-Zn a l l o y s . In pure Mg, y increases from approximately 230% shear s t r a i n at 78°K to 470% at room temperature. increasing temperature. Beyond room temperature y g decreases with Although the e f f e c t of Zn i s to decrease the trend i n the temperature dependence of y D Y B remains the same i n the a a l l o y s as i n Mg. A p l o t of t h e [(t ) B _ M g alloy] a g a i n S t s o l u t e concentration f o r d i f f e r e n t temperatures ( f i g . 57) i n d i c a t e s that the decrease i n the extent of easy g l i d e caused by a l l o y i n g i s independent of temperature between 195° - 373°K. ) 0 0.1 0.2 0.3 0,4 Atomic % Zn F i g . 54. The increase i n work hardening r a t e i n easy g l i d e vs. Zn concentration. Fig.55. The increase i n work hardening rate i n easy g l i d e vs. square root of the Zn concentration. 99 6.0 200 100 400 300 Temperature °K F i g . 56. The extent of easy g l i d e as a f u n c t i o n of temperature for Mg-Zn s i n g l e c r y s t a l s . 0.1 J. 0.2 0.3 0.4 0.5 Atomic % Zn F i g . 57, The decrease i n the extent of easy g l i d e as a function of the solute concentration.' 100 2.2.7.3. Stress at the Onset of Stage B, T : Stage B was considered to begin at a s t r e s s determined by the i n t e r s e c t i o n of the extrapolated l i n e a r stages A and B. However^since stage B was not c l e a r l y defined below room temperature, the values of i B below room temperature are not r e l i a b l e and hence w i l l not be reported here. The v a r i a t i o n of I t i s apparent that x_ with Zn concentration i s shown i n f i g . (58). B x„ increases with i n c r e a s i n g solute concentration. n Also i t i s i n t e r e s t i n g to note that [(x„) - (T„),. ] remains ° B alloy B Mg independent of temperature above 295°K f o r any f i x e d solute concentration. 2.2.7.4. The Work Hardening Rate i n Stage B, 0 : p For most of the crystals tested below room temperature, the work hardening rate i n stage B was found to increase with s t r a i n t i l l f r a c t u r e occurred. Under such circumstances 9 cannot be evaluated accurately. o Therefore, the r e s u l t s of the t e s t s conducted above room.temperature will be presented here. The temperature dependence of 9 f o r Mg and four Mg-Zn a l l o y s i s shown i n f i g . (59). The work hardening r a t e 9^ decreases with increasing temperature. The e f f e c t of a l l o y i n g on 9 i s shown i n f i g . (60). It i s D apparent that the work hardening rate increases i n a near p a r a b o l i c manner with i n c r e a s i n g Zn content and that the e f f e c t i s more pronounced the lower the temperature. F i g . 58. The e f f e c t -of temperature and solute concentration on the stress at the onset of Stage B. 102 Atomic % Zn F i g . 60. The increase i n the work hardening r a t e i n Stage B vs. Zn concentration. 103 2.2.7.5. Deformation i n Stage "C": Stage C immediately follows the stage B, and i s characterised by a decreasing work hardening rate with increasing s t r a i n . Stage C was c l e a r l y observed above room temperature only. The stress corresponding to the f i r s t d e v i a t i o n from l i n e a r i t y at the end of stage B w i l l be termed T^,. The v a r i a t i o n of concentration i s shown i n f i g . (61) f o r 373°K and 423°K. that 2.3. with Zn I t i s observed increases with a l l o y i n g i n a near parabolic manner. THE EFFECT OF SOLUTE ON THE DISLOCATION DENSITIES: I t has been pointed out by Seeger^"^ that s o l u t i o n hardening i s possible i n close packed s t r u c t u r e s , as a r e s u l t of a change i n the d i s l o c a t i o n density through the presence of a s o l u t e . This i n d i r e c t hardening e f f e c t i s thought to be most pronounced at low solute concentrations, e s p e c i a l l y (90 when the d i f f e r e n c e i n s i z e between the solvent and the solute i s large 91) ' Bearing i n mind that the d i f f e r e n c e i n s i z e between Mg and Zn i s large and that the a l l o y s investigated i n t h i s work contain low concentrations of the s o l u t e , an examination of the d i s l o c a t i o n d e n s i t i e s i n these a l l o y s deserves a t t e n t i o n . \ There are two ways possible through which strengthening may achieved due to an increase i n d i s l o c a t i o n density. density may be The g l i d e d i s l o c a t i o n increase leading to an increase i n the long range s t r e s s f i e l d i . e . the athermal component being a f f e c t e d . A l t e r n a t i v e l y ^ o r simultaneously, the f o r e s t d i s l o c a t i o n density may vary thereby changing the short range d i s l o c a t i o n - d i s l o c a t i o n i n t e r a c t i o n leading to a change i n the activated component of the flow s t r e s s . thermally F i g . 61 The s t r e s s at the onset of Stage C vs. Zn concentration. 105 In the face centred cubic structures a knowledge of the density on the g l i d e plane provides information on the forest dislocation dislocation spacing as w e l l , since the g l i d e d i s l o c a t i o n and the forest d i s l o c a t i o n s l i e on c r y s t a l l o g r a p h i c a l l y s i m i l a r planes. However, differences are to be expected i n hexagonal metals, because the two sets of d i s l o c a t i o n s not contained on c r y s t a l l o g r a p h i c a l l y s i m i l a r planes. are Thus i t has been decided to examine the two sets of d i s l o c a t i o n s independently of one another. 2.3.1. The Basal D i s l o c a t i o n Density: Transmission electron microscopy of t h i n f o i l s has been used i n the present i n v e s t i g a t i o n to measure the basal d i s l o c a t i o n density. There e x i s t s considerable controversy i n the l i t e r a t u r e concerning the degree to which d i s l o c a t i o n arrangements observed i n t h i n f o i l s (92-94) are representative of the bulk material degree of rearrangement due . I t i s believed that the to stress r e l a x a t i o n increases^the higher (95) the stacking f a u l t energy. In f a c t , experiments on Al-Ag s o l i d solutions have revealed that more than 60% of the d i s l o c a t i o n s are l o s t during the process of thinning. In the present study the easy g l i d e plane {0001} was kept p a r a l l e l to the f o i l surface, thus lowering che p r o b a b i l i t y of l o s i n g d i s l o c a t i o n s through c r o s s - s l i p . This f o i l o r i e n t a t i o n has been used e a r l i e r by Hirsch (29) and L a l l y i n examining the v a r i a t i o n of d i s l o c a t i o n density as a of deformation i n magnesium. function Through the examination of a c a r e f u l l y chosen set of nonbasal sections, these authors have come to the conclusion that the arrangement and d e n s i t i e s of d i s l o c a t i o n s i n the basal sections are t y p i c a l of the bulk m a t e r i a l . 106 2.3.1.1. F o i l Preparation: Considerable d i f f i c u l t y was encountered i n obtaining f o i l s , free from oxide f i l m , of the Mg-Zn a l l o y s . Therefore,it was decided to study Mg-Al c r y s t a l s instead, at a comparable concentration l e v e l . The choice of A l as solute was mainly due to the large s i z e d i f f e r e n c e between Mg and A l atoms, which i s comparable to that between Mg and The d i s t r i b u t i o n c o e f f i c i e n t s of the two a l l o y systems at low Zn, concentration l e v e l s are also comparable. The f o i l s were prepared by the chemical p o l i s h i n g of c r y s t a l sections p a r a l l e l to the {0001} plane. consisted of 10% n i t r i c a c i d i n water. 0.1" The p o l i s h i n g s o l u t i o n Shallow c a v i t i e s were created on each face of the s l i c e by impinging a j e t of acid-water mixture. The f i n a l thinning was done by immersing the specimen i n the centre of a beaker containing the thinning s o l u t i o n . P e r f o r a t i o n s were seen f i r s t at the c a v i t i e s . The narrow region between two perforations was found most s u i t a b l e f o r the e l e c t r o n microscopy work. 2.3.1.2. Observations: A representative p o r t i o n of the d i s l o c a t i o n s t r u c t u r e i n Mg i s shown i n f i g . (62). A, B and C. The main features are the l o n g . d i s l o c a t i o n dipoles at The presence of u n i d e n t i f i e d dark p a r t i c l e s i n the e l e c t r o n (29) micrographs of Mg have been reported e a r l i e r . In the present work such p a r t i c l e s have been observed i n varying amounts i n a l l specimens ( f i g . (62)) nd are often surrounded by d i s l o c a t i o n loops. a On tilting the specimen the d i s l o c a t i o n s go out of contrast but the dark spots remain i n contrast suggesting was them to be p a r t i c l e s . However, t h e i r s i z e too small f o r i d e n t i f i c a t i o n using selected area d i f f r a c t i o n . A F i g . 62, T y p i c a l d i s l o c a t i o n s t r u c t u r e i n as grown Mg c r y s t a l s - F o i l p a r a l l e l to {0001} Note p a r t i c l e s at D, E, and F, and the high density of dipoles. plane. 108 higher magnification micrograph of such a p a r t i c l e and the sourrounding d i s l o c a t i o n s i s shown i n f i g . (63). Sometimes these p a r t i c l e s have been observed to emit d i s l o c a t i o n s p i r a l s under the heat of the e l e c t r o n beam. T y p i c a l d i s l o c a t i o n structures i n a l l o y s containing 0.18 at. % and 0.36 a t . % A l are shown i n f i g s . (64)and(65) r e s p e c t i v e l y . I t i s observed that the c l o s e l y spaced dipoles become fewer, and the d i s l o c a t i o n s become more evenly d i s t r i b u t e d as the a l l o y i n g content i s increased. 2.3.1.3. The Technique of D i s l o c a t i o n Density Measurement and i t s L i m i t a t i o n s : (97 98) A m o d i f i c a t i o n of the random l i n e i n t e r s e c t i o n method Ham was used i n the present work. ' of The random l i n e s consisted of s i x c i r c l e s with random centres drawn on a transparent template. The observed length of the d i s l o c a t i o n l i n e becomes the a c t u a l length (not a p r o j e c t i o n ) i f i t i s assumed that the d i s l o c a t i o n s run very nearly p a r a l l e l to the basal plane. d i s l o c a t i o n density Under these conditions the p_ w i l l be given by P G = M /(2Lt) (2) where N i s the number of i n t e r s e c t i o n s of the random c i r c l e s with the d i s l o c a t i o n l i n e s . L i s the t o t a l length of the circumference of the c i r c l e s . t i s the thickness of the f o i l i n the region under examination. Much d i f f i c u l t y was encountered i n determining thickness. the f o i l Because s l i p traces cannot be obtained i n b a s a l s e c t i o n s , the f o i l thickness had to be estimated by counting the number of the e x t i n c t i o n 109 F i g . 63. Electron micrograph showing d i s l o c a t i o n s surrounding a p a r t i c l e . F i g . 64. T y p i c a l d i s l o c a t i o n s t r u c t u r e i n an undeformed Mg + 0.18 a t . % A l a l l o y s i n g l e c r y s t a l . Foil s u r f a c e p a r a l l e l to {0001} plane. o Ill F i g . 65. T y p i c a l d i s l o c a t i o n s t r u c t u r e i n an undeformed Mg + 0.38 at. % A l a l l o y single c r y s t a l . F o i l p a r a l l e l to {0001} plane. 112 f r i n g e s from the f o i l edge. In order to obtain an average d i s l o c a t i o n d e n s i t y , counts were made on at l e a s t three d i f f e r e n t areas on each specimen. The random l i n e length used on each specimen was at l e a s t 200 y. total Burgers vectors of kind other than <1120> have never been observed i n magnesium, neither have d i s l o c a t i o n s sharply i n c l i n e d to (29) the basal plane been seen . Thus with the f o i l o r i e n t a t i o n chosen i n the present work, a l l the d i s l o c a t i o n s were i n contrast. This eliminated the need f o r c o r r e c t i n g the measured density f o r d i s l o c a t i o n s out of contrast. The number of short lengths of d i s l o c a t i o n s meeting the surface at c l o s e l y separated points ( i n d i c a t i n g that they are i n c l i n e d to the basal plane) was much smaller than the long segments l y i n g i n the basal plane, hence the measured density may be taken as the b a s a l d i s l o c a t i o n density. 2.3.1.4. The E f f e c t of Solute on the Basal D i s l o c a t i o n Density: 8 2 In pure magnesium a density of 2.4 x 10 lines/cm was observed, 8 (29) which i s close to 2.2 x 10 reported e a r l i e r by Hirsch and L a l l y Tsui (96) , however, has obtained a density of the order of 10 3 -10 6 /cm 2 i n Mg s i n g l e c r y s t a l s . k I t i s seen from a p l o t of p against C in fig. (66) that the d i s l o c a t i o n density increases i n a p a r a b o l i c manner with A l concentrations, Numerically equal to 0.38 p increases by a f a c t o r of three due to an a d d i t i o n of solute at.%. 113 Mg-Al 8 Single Crystols Dislocation Density in Sections Parallel to (OOOI) Plane P * [ 2 - 4 * 8 3 5 \fc ] X I O c 0-2 0-3 JC 0-4 (At.%) 8 lines/cm 05 2 06 172 F i g . 66. Basal d i s l o c a t i o n density vs. square root of s o l u t e concentration f o r Mg-Al a l l o y s . 114 h From the s t r a i g h t l i n e p l o t of C against i n f i g . (66) the following r e l a t i o n s h i p i s obtained. (p ) = [2.4 + 8 . 3 5 ^ ] x 10 l i n e s /cm C 8 (3) 2 G Assuming t h i s r e l a t i o n s h i p holds good up to the l i m i t of s o l i d s o l u b i l i t y (1.6 a t . % ) , the d i s l o c a t i o n density i n the highest a l l o y w i l l be only 5 times higher than i n Mg. findings i n fee This i s i n agreement with the e a r l i e r s o l i d solutions that the d i s l o c a t i o n density i n the a l l o y s i s l e s s than an order of magnitude higher than i n the solvent (2) pure metal 2.3.2. The Forest D i s l o c a t i o n Density: The forest d i s l o c a t i o n s were revealed by an etch p i t t i n g technique, which was developed i n the course of the present i n v e s t i g a t i o n . 2.3.2.1. C r y s t a l Orientation and the P i t C h a r a c t e r i s t i c s : The {0001} plane of magnesium i s the most s u i t a b l e surface for etching, since i t w i l l not reveal the basal d i s l o c a t i o n s , whereas the nonbasal d i s l o c a t i o n s of edge character, which c o n s t i t u t e the f o r e s t d i s l o c a t i o n s can be p r e f e r e n t i a l l y revealed. l o c a t i o n s w i l l be p a r a l l e l to the revealed by etching. {0001} plane and hence w i l l not be C r y s t a l s of Mg and Mg-Zn a l l o y s were spark eroded to obtain 0.1" t h i c k s l i c e s p a r a l l e l to the degrees. A l l screw d i s - {0001} plane within.2 The spark damaged layer was removed by chemical p o l i s h i n g i n 10% HN0~ and the specimen was washed i n ethanol and d r i e d . 115 The etchant consisted of a 20% s o l u t i o n of HNO^ i n water and the etching was c a r r i e d out by dipping the polished specimen f o r about 10 sees, i n warm n i t r i c a c i d s o l u t i o n kept at 30-35°C. The etch p i t s obtained i n t h i s manner were c i r c u l a r i n shape. Hexagon shaped etch p i t s were, however, produced by etching i n a 30% HNO^ s o l u t i o n maintained at room temperature. are c h a r a c t e r i s t i c of the d i s l o c a t i o n etch p i t s . shaped p i t s are shown i n f i g . (67). Such geometric shapes Some of the hexagon For counting the number of d i s - l o c a t i o n s , however, i t was found convenient to use the c i r c u l a r p i t s . The etched surfaces of a representative set of Mg-Zn a l l o y s are shown i n f i g s . (67(a),(b) and ( c ) ) . 2.3.2.2. The Study of Spark Erosion Damage i n Mg Using the D i s l o c a t i o n Etch P i t Method: In order to examine the damaging e f f e c t of spark erosion a sample was etched without removing the e n t i r e damaged l a y e r . micrograph of such a specimen i s shown i n f i g . (68). A I t i s apparent that small twins are formed at the edge of the specimen and the nonbasal edge d i s l o c a t i o n s can be seen at the twin boundaries. On f u r t h e r chemical p o l i s h i n g and subsequent etching the twins disappear, suggesting that they are confined to a narrow surface l a y e r . The etch p i t density decreased t i l l a surface layer 150u i n thickness was removed from the surface. the density remained constant. approximately Below t h i s depth 116 480 x 480 X F i g . 67(a). Hexagonal shape of the etch p i t s , F i g . 67(b). D i s t r i b u t i o n of etch p i t s i n a Mg + 0.019 a t . % Zn c r y s t a l . 84X. 117 F i g . 68. F i g . 69. D i s l o c a t i o n etch p i t s on the {0001} plane of Mg s i n g l e c r y s t a l . Note non-basal edge d i s l o c a t i o n s at the twin boundaries. 75X Etch p i t density vs. Zn concentration. 118 2.3.2.3. V a r i a t i o n of the Etch P i t . Density with A l l o y i n g : The concentration dependence of the number, of etch p i t s per u n i t area i s shown i n f i g . (69). In order to avoid l o c a l d i f f e r e n c e s , counts were made at a magnification such that at l e a s t 800 p i t s were i n the f i e l d of view at one time. each specimen. Three d i f f e r e n t regions were examined on The v a r i a t i o n from specimen to specimen i s shown i n f i g . (69) by the s c a t t e r bars. I t i s apparent that the etch p i t density increases r a p i d l y with a l l o y i n g up to approximately 0.05 a t . % Zn, followed by a very s l i g h t increase up to 0.45 at, % Zn. I t i s i n t e r e s t i n g to note that the etch p i t density i n 4 2 magnesium i s 3.5 x 10 /cm . From a c t i v a t i o n volume measurements on the (4) other hand Conrad 7 10 has a r r i v e d at a f o r e s t density of the order of 8 2 - 10 /cm . Transmission e l e c t r o n microscope studies on non-basal sections (basal plane almost p a r a l l e l to f o i l normal) made by Hirsch (29) and L a l l y , however, i n d i c a t e that the f o r e s t d i s l o c a t i o n density i s 8 2 u n l i k e l y to be as high as 10 /cm . 119 2.4. DISCUSSIONS: Much progress has been made i n the understanding of the s o l i d s o l u t i o n strengthening mechanisms i n metals a f t e r the development of the d i s l o c a t i o n theory. Most of the important mechanisms of i n t e r a c t i o n were proposed w i t h i n a few years a f t e r the study of the behaviour of d i s l o c a t i o n s i n s o l i d s o l u t i o n s had been undertaken. In the past decade, however, the major problem has been the one, of deciding which mechanisms are important i n a given experimental s i t u a t i o n and u n r a v e l l i n g the contributions of the various mechanisms. The r e s u l t s of the present study on Mg-Zn a l l o y s are examined i n the l i g h t of the v a r i o u s strengthening mechanisms, followed by a d i s c u s s i o n of the e f f e c t of solute on the work hardening parameters of magnesium. 2.4,1. The C r i t i c a l Resolved Shear Stress: The CRSS of s i n g l e c r y s t a l s i s perhaps the only s a t i s f a c t o r y parameter which can be used f o r a q u a n t i t a t i v e comparison with the t h e o r e t i c a l p r e d i c t i o n s without any adjustable parameters. In the case of p o l y c r y s t a l l i n e aggregates such adjustable parameters become important, because of the constraining conditions imposed by the grain boundaries. The experimental r e s u l t s can be best viewed against the background of the theory of temperature dependence of the flow s t r e s s as developed by Seeger (38) and F r i e d e l (99^ . According to t h i s theory the applied s t r e s s can be considered as the sum of two components such that T (T) = T G + T * (4) 120 T * i s r e f e r r e d to as the thermal component- of the applied stress and i s associated with short range obstacles which can be overcome with the a i d of thermal energy. T i s the athermal component that a r i s e s due to the long range e l a s t i c i n t e r a c t i o n s such as those between p a r a l l e l g l i d e d i s l o c a t i o n s at distances large compared with b, the Burgers vector. Such obstacles cannot be overcome with the a i d of thermal energy. The consequence of Seeger's postulate i s schematically shown i n f i g . (70), f o r the s i t u a t i o n where the mechanism of y i e l d does not change with temperature. r n v a r i e s with temperature only through a change i n the shear modulus G such that temperature. G/Q T becomes independent of Seeger has modified h i s d e f i n i t i o n of l a t e r to include (92) a short range e l a s t i c i n t e r a c t i o n term The e f f e c t of solute on the two components of the CRSS w i l l now be considered separately. Temperature F i g . 70. The temperature dependence of y i e l d i n terms of the s t r e s s components (after Seeger'^ '). 5 121 2.4.2. Solution Strengthening i n the Athermal Region: The c r i t i c a l resolved shear stresses of magnesium and i t s a l l o y s containing Zn i n amounts up to 0.45 a t . % Zn become athermal above 330°K ( f i g . 47). I t i s apparent from fig.(49) that the a d d i t i o n of Zn i n amounts up to 0.025 a t . % has no e f f e c t on the CRSS of Mg above 330°K ( i . e . S T - 0 ) , however, x increases l i n e a r l y with the square root of Zn concentration above 0.025 a t . % . Another c h a r a c t e r i s i t c feature of the s o l u t i o n hardening i n the athermal region i s the constancy of the strengthening parameter S^j.. As mentioned e a r l i e r x i s the s t r e s s required to overcome the long range obstalces i n the c r y s t a l . The long range s t r e s s f i e l d can be affected by one or more of the f o l l o w i n g i n t e r a c t i o n s i n v o l v i n g the solute and the d i s l o c a t i o n s : 1) A change i n the basal d i s l o c a t i o n density. 2) Elastic interaction. 3) Chemical i n t e r a c t i o n . 4) Short range order. 5) Long range order. 6) F r i c t i o n s t r e s s due to random d i s t r i b u t i o n of s o l u t e . Of these,the change i n d i s l o c a t i o n density i s an i n d i r e c t e f f e c t of solute leading to strengthening. The remaining f i v e a r i s e due to a d i r e c t i n t e r a c t i o n between the solute and the d i s l o c a t i o n . 1 22 2.4.2.1. The Basal D i s l o c a t i o n Density; Seeger^^^ has shown that the long, range s t r e s s f i e l d r e l a t e d to the g l i d e d i s l o c a t i o n density T Q where and = a b G / p x^ i s as f o l l o w s : (5) p a i s a constant, b i s the Burgers v e c t o r , G i s the shear modulus i n the s l i p d i r e c t i o n . The d i s l o c a t i o n density of magnesium has been evaluated as (29) a f u n c t i o n of shear s t r e s s by Hirsch and L a l l y . These authors came to the conclusion that the flow s t r e s s of Mg at room temperature (the thermally a c t i v a t e d component of the flow s t r e s s i s very small at room temperature and hence the CRSS may be taken to be equal to T ^ ) can be r e l a t e d to the d i s l o c a t i o n density by the f o l l o w i n g expression T .= x + 2.7 x 1 0 ~ / p ~ (6) 3 0 where x i s the flow s t r e s s and X 2 i s a constant equal to 40 gm/mm . q I t has been shown e a r l i e r i n t h i s t h e s i s that the basal d i s l o c a t i o n density can be expressed as a f u n c t i o n of A l concentration by the r e l a t i o n p_ - [2.4 + 8.35 /C] x 1 0 cm" where C i s the concentration of s o l u t e . dropped f o r convenience. 8 2 (3) The subscript G has been 123 Combining equations (6) and (3) AT = where AT 40.5 [ 1 - V 1+3.48 C% ] (7) i s the strengthening at a concentration C. The values of A T obtained using equation (7) are p l o t t e d i n f i g . (71) along with the experimental r e s u l t s of Sheely, Levine (74) and Nash on the CRSS of Mg-Al a l l o y s tested at room temperature. I t i s seen that equation (7) gives a constantly i n c r e a s i n g value of x with solute concentration. established that x However, the present r e s u l t s have remains unaffected i n Mg-Zn a l l o y s upto a c e r t a i n minimum concentration of s o l u t e . Also e a r l i e r i n t h i s t h e s i s i t has been shown that t h i s concentration independence of x i s common to a host of Mg-solid s o l u t i o n s i n c l u d i n g the Mg-Al a l l o y s . Thus at low solute concentrations equation (7) i s a poor d e s c r i p t i o n of the e f f e c t of s o l u t e , and i t i s apparent that at higher s o l u t e concentrations the predicted values of x„ are f a r smaller than those observed experimentally. I t should be noted here that p i n equation (6) comprises the grown i n d i s l o c a t i o n s plus those generated due to work hardening, whereas equation (3) describes only the grown i n d i s l o c a t i o n density v a r i a t i o n due to s o l u t i o n e f f e c t . Thus^whereas i n the former case dislocation-dislocation interaction i s a contributing factor, i t i s absent i n the l a t t e r case. In view of t h i s f a c t the combination of equations (6) and (3) to y i e l d equation (7) i s not f u l l y j u s t i f i e d . However, equation (7) w i l l be considered as a close approximation f o r the sake of comparison with the experimental r e s u l t s . 124 0.2 .0.1 0.3 0.4 At. % A l F i g . 71. 400 300 ~ 200 - Comparison of the observed s o l u t i o n strengthening with that expected from the increase i n the basal d i s l o c a t i o n density. 100 2 ,1/2 ,. i n (at. % L i ),1/2 ' F i g . 72. The increase i n CRSS of Mg v s ( L i c o n c e n t r a t i o n ) i n Mg-Li a l l o y s i n g l e c r y s t a l s (Data from Horiuchi and Yoshinaga 125 Therefore,it i s reasonable to conclude that the change i n the basal d i s l o c a t i o n density i s not an important f a c t o r i n s o l u t i o n strengthening of magnesium. S i m i l a r conclusion has been a r r i v e d at by Adams, Vreeland and Wood i n the case of Zn base s o l i d solutions ^ . , A,(118) containing l A 2.4.2.2. E l a s t i c Interaction: The mechanism of e l a s t i c i n t e r a c t i o n was o r i g i n a l l y proposed by C o t t r e l l ^ ^ ^ to explain the y i e l d i n g of Fe-C a l l o y s . Strengthening a r i s e s from the e l a s t i c i n t e r a c t i o n between the stress f i e l d of a d i s l o c a t i o n and the s t r e s s f i e l d due to the l a t t i c e d i s t o r t i o n r e s u l t i n g from the m i s f i t of the solute atom. The problem has been treated by the methods of c l a s s i c a l e l a s t i c i t y by several authors been s u c c e s s f u l l y applied to many cases of i n t e r s t i t i a l 104) ^ a s solutes. An analysis f o r the s u b s t i t u t i o n a l solutions has been given by Suzuki using the concept of. continuously varying composition and l a t t i c e parameter i n the neighbourhood of the d i s l o c a t i o n . As pointed out by Suzuki, the s o l u t i o n hardening i n s u b s t i t u t i o n a l a l l o y s due to t h i s mechanism decreases markedly with temperature by thermal a c t i v a t i o n and becomes p r a c t i c a l l y n e g l i g i b l e at higher temperatures. The present r e s u l t s on Mg-Zn a l l o y s at higher temperatures, however, do not conform to the requirements of t h i s mechanism. The CRSS of Mg-Zn a l l o y s i s almost independent of temperature above about 330°K, yet s o l u t i o n strengthening e f f e c t i s quite pronounced above 330°K ( f i g . 47). Therefore,the e l a s t i c i n t e r a c t i o n theory.cannot be applied to the case of s o l u t i o n hardening i n Mg-Zn a l l o y s tested above room temperature. 126 2.4.2.3. Chemical I n t e r a c t i o n : I t i s now w e l l established that the stacking f a u l t energy can be a function of composition for a l l o y s i n which the d i s l o c a t i o n s are extended. Evidence f o r t h i s has been obtained from X-ray measurements of f a u l t occurrences i n deformed a l l o y s f r o m observations of extended d i s l o c a t i o n s (141 142) rate s e n s i t i v i t y of t J_J_J_ i ' c r y s t a l s having fee s t r u c t u r e . / 1 / nt n e \ stacking d i r e c t electron microscopic and from the temperature and s t r a i n stress s t r a i n curves of s i n g l e As suggested by S u z u k i } this variation i n stacking f a u l t energy with composition should r e s u l t i n a d i f f e r e n c e i n composition between the f a u l t e d area of extended d i s l o c a t i o n s and the bulk m a t e r i a l . also A surface thermodynamic.treatment of the problem has been given by Guard and F i n e ^ ^ ^ . Experimentally, Spreadborough^"'"^"^ has shown that a difference i n the chemical r e a c t i v i t y between the f a u l t e d area and the bulk material e x i s t s which i s evidence that segregation does occur. This segregation has a pinning e f f e c t on the d i s l o c a t i o n s . Suzuki's theory has l a t e r been extended to regular s o l u t i o n s and i n i t s f i n a l form stands as f o l l o w s : R T where T bt 9m* RT A i s the increase i n the c r i t i c a l shear stress of the a l l o y over that of the pure metal, n^r ^ 11 the solvent are . the mole f r a c t i o n s of the solute respectively, V i s the molar volume of the a l l o y , b i s the Burgers vector, t i s the thickness Y i s the stacking f a u l t energy, of the f a u l t e d region, and m and 127 f i s the mole f r a c t i o n of the solute i n the f a u l t e d region, AH i s the i n t e g r a l heat of mixing, R i s the gas T the absolute temperature at which e q u i l i b r i u m i s a t t a i n e d . constant, I t i s seen from equation (8) that a knowledge of the v a r i a t i o n of stacking f a u l t energy with solute concentration i s e s s e n t i a l i n determining particular situation. ( i n the stacking f a u l t ) the a p p l i c a b i l i t y of the equation to a In the case of pure magnesium the stacking f a u l t energy has been estimated, from t h e o r e t i c a l considerations, to be equal (39) 2 to 2 0 0 ergs/cm . Q u a n t i t a t i v e l y , however, t h i s value of never been v e r i f i e d using e l e c t r o n microscopy. Y has Because of the rather long e x t i n c t i o n distance i n magnesium and i t s low shear modulus, i t i s d i f f i c u l t to observe the a l t e r n a t e extension and c o n t r a c t i o n of the nodes i n the hexagonal network formed by the i n t e r a c t i o n - of two sets of (29) screws with d i f f e r e n t basal Burgers vectors . Stacking f a u l t energy can also be estimated by having a knowledge of the stress required to induce cross s l i p . The method has been applied s u c c e s s f u l l y to the case of c r y s t a l s with face centred cubic structure.. However, t h i s method has never been applied to .the hep materials mainly because the stress to induce cross s l i p i s not apparent from the s t r e s s s t r a i n curves of t h i s . group of c r y s t a l s . Bearing i n mind that (4^-f) dm f o r Mg-Zn. a l l o y s i s not A at hand and that the thermodynamic functions of the system are also unknown, an attempt w i l l be made to c a l c u l a t e the extent of Suzuki hardening under c e r t a i n assumptions. F i r s t , we w i l l assume an i d e a l mixing and 3 ^AH 3 therefore -—•—• - 0. Secondly, (^~ \ w i l l be c a l c u l a t e d using the . 3m V 3m,/ A A 2 A f 128 stacking f a u l t energies of pure Zn and pure magnesium. Also assuming the stacking f a u l t to be two atomic layers t h i c k equation (8) reduces to the f o l l o w i n g : T = — 2 ™ S RT V — 3 Q m 2 ( 9 ) where c/a i s the a x i a l r a t i o of the c r y s t a l , and Q = V < *» - ^ 2c T (10) Y the other symbols having t h e i r usual meaning. 2 Y, • = 200 ergs/cm a Me y' = 70 ergs/cm 2 Zn 3 Substituting and V = 14 cm /mole T = 458°K i . e . 0.5 T . m This value i s reasonable i n that the d i f f u s i o n of solute atoms to the stacking f a u l t s w i l l be n e g l i g i b l e below 0.5 T . x f o r 0.45 a t . % Zn a l l o y comes out to be2 21 gm/mm . On the other hand the experimental value of ( O Q ^^rC ^ M g 2 105 gm/mm . = Thus i t i s seen that the chemical hardening mechanism cannot adequately account f o r the observed strengthening. A d d i t i o n a l discrepancy i s encountered i n the composition dependence of s o l u t i o n strengthening. At low solute concentrations (upto 0.45 a t . % Zn) equation (9) p r e d i c t s an almost l i n e a r r e l a t i o n s h i p between x and C whereas the experimental h data f o l l o w a C trend. 2.4.2.4. Short Range Order: The energy of a s o l i d s o l u t i o n v a r i e s l i n e a r l y with the degree of l o c a l order while the entropy v a r i e s roughly l o g a r i t h m i c a l l y ; therefore, unless the i n t e r a c t i o n between l i k e and u n l i k e neighbours i s i d e n t i c a l , the e q u i l i b r i u m state w i l l be one with a non z e r o . l o c a l o r d e r , 129 As pointed out by F i s h e r ^ 0 9 ) t h i s order need not be very great to make a s i g n i f i c a n t c o n t r i b u t i o n to the strengthening. According to F l i n n ^ ^ ^ the short range order i n t e r a c t i o n would lead to a temperature independent f r i c t i o n stress i . e . x should increase with a l l o y i n g i f SRO i n t e r a c t i o n i s present. Applying the t h e o r e t i c a l r e s u l t of F l i n n to the case of basal s l i p i n hep metals, 2 JL ( A B) a kT m m . (11) 2 v 3 where v i s the i n t e r a c t i o n energy f o r l i k e bonds. When the value of v/kT i s s m a l l , v can be c a l c u l a t e d using the f o l l o w i n g approximate formula a v Here kT = ( 1 2 ) i s the l o c a l order parameter which can be determined by X-ray or neutron d i f f r a c t i o n experiments. However, such experiments have not been c a r r i e d out with Mg-Zn a l l o y s . I n the absence of experimentally determined values of the short range order parameter equation (11) cannot be used to c a l c u l a t e the strengthening due to short range order i n the 2 Mg-Zn system. Nevertheless^the f a c t that equation (11) p r e d i c t s a C dependence of the f r i c t i o n s t r e s s speaks against SRO hardening. h present work the observed hardening follows a C I n the relation. L a t e l y i t has been shown by Koppenal^"''^ that neutron i r r a d i a t i o n does not i n f l u e n c e the strength of Cu-14% A l c r y s t a l s upto a dose where r a d i a t i o n induced short range ordering i s already complete. This a l s o i s against the idea that SRO can s t r o n g l y contribute to the long range s t r e s s f i e l d . 130 2,4.2.5. Strengthening.Due to a Random D i s t r i b u t i o n of the Solute: The e a r l i e s t theory of s o l u t i o n strengthening based on a random (102 d i s t r i b u t i o n of the solute was propounded by Mott and Nabarro 112) ' This theory computes the average magnitude of the stress i n the matrix of a d i l u t e s o l i d - s o l u t i o n due to replacing atoms of the matrix by ones that are larger or smaller, Although considering ( i . e . s i z e e f f e c t ) thus s t r a i n i n g the l a t t i c e . s i g n , the average stress on a d i s l o c a t i o n i s zero, r e l a t i v e l y short lengths experience stresses of the order of average stress magnitude and hardening r e s u l t s . The the theory cannot adequately account for the athermal s o l u t i o n strengthening i n general due to two reasons. As pointed out by F l e i s c h e r ^ ^ " ^ the theory of Mott and Nabarro applies only to d i s l o c a t i o n s whose stress f i e l d s have d i l a t i o n associated with them, and hence pure screw d i s l o c a t i o n s are able to move f r e e l y . was the experimental f a i l u r e 1 6 = However, the main objection to the theory ^ Q f the parameter 6 (defined as db " , where b i s the l a t t i c e parameter) to be a proper index of the r e l a t i v e hardening when d i f f e r e n t solute atoms are added to a metal. I t has been observed that the valency of the added element i s a strong factor. F l e i s c h e r has extended the a n a l y s i s further to include i n t e r a c t i o n s responsible for solution s t r e n g t h e n i n g > H 6 ) ^ Q two ng ^ g caused by the hydrostatic component of the stress f i e l d of a d i s l o c a t i o n i n t e r a c t i n g with the volume change produced, by i n s e r t i n g a f o r e i g n atom , ( s i z e or 6 i n t e r a c t i o n ) and the other occurs because the inserted atom represents a small region of d i f f e r e n t e l a s t i c properties from the matrix, so that a d i s l o c a t i o n i n t e r a c t s because i t must do more (or l e s s ) work 131 than usual i n e l a s t i c a l l y shearing the impurity atom (modulus or interaction). n This second i n t e r a c t i o n i s f i r s t order f o r e i t h e r edge or screw d i s l o c a t i o n s since both have shear s t r a i n s . The s i z e i n t e r a c t i o n with a screw d i s l o c a t i o n , however, i s zero to a f i r s t order, since a screw d i s l o c a t i o n has no hydrostatic On the stress according to l i n e a r e l a s t i c i t y . other hand there i s a second order e l a s t i c i n t e r a c t i o n caused by an expansion, which i n essence a r i s e s from the atomic roughness of the planes in a crystal. These planes are forced apart as they are sheared across one another; thus there e x i s t s a hydrostatic screw d i s l o c a t i o n . Taking the 6 and the component of stress around a n i n t e r a c t i o n s i n t o account, the dependence of the room temperature plateau stress on concentration of solute comes out as follows & 3/2 T„ - Z.G.C" . c " G where Z i s a constant calculated by F l e i s c h e r to be equal to 1/760 2 -= n A . I * - . I . (13) J / C for screws, (14) a6 <5 i s already defined. ? n = (15) where x] = G . dC The value of , G being the shear modulus, a l i e s between 3 and 16 f o r i n t e r a c t i o n with screw d i s l o c a t i o n s whereas i t i s greater than or equal to 16 f o r i n t e r a c t i o n with edge dislocations. For p o l y c r y s t a l l i n e Cu-solid solutions a is estimated to be about three implying a screw d i s l o c a t i o n solute atom interaction^"^ . Recently S a x l ^ " ^ has extended F l e i s c h e r ' s calculation of the d i s l o c a t i o n solute i n t e r a c t i o n s t a r t i n g from f i r s t p r i n c i p l e s and gets rather s i m i l a r r e s u l t s . 132 The present r e s u l t s conform to the predicted square-root C dependence of the f r i c t i o n s t r e s s ( f i g . 49). However,in order to make a q u a n t i t a t i v e v e r i f i c a t i o n p o s s i b l e , a knowledge of the concentration dependence of the l a t t i c e parameters and the shear modulus i s necessary. The concentration dependence of the l a t t i c e parameters i n the case of Mg-Zn a l l o y s has been determined by a number of workers (33) •linear s i z e factor of 0.2 as computed by King present c a l c u l a t i o n s . Mg-Zn a l l o y s . The parameter (31 119) ' . The w i l l be used i n the n has never been evaluated f o r However, e l a s t i c constants of some of the Mg-base a l l o y s have been evaluated as a f u n c t i o n of solute concentration i n the case of Ag, In and Sn solutes(1^0)^ p these r e s u l t s i t appears that those elements r o m belonging to group I of the p e r i o d i c table tend to increase the shear modulus of magnesium whereas those belonging to group I I I and IV decrease it. Therefore, since Zn belongs to the same group i n the p e r i o d i c t a b l e as magnesium, i t would be l o g i c a l to conclude that n the case of Mg-Zn a l l o y s . Now i f we neglect w i l l be small i n n i n comparison w i t h dx 6 and s u b s t i t u t e the values of — r , G and e after differentiating dC*! ' screw \, 1 equation (13) with respect to C , Z comes out to be ^-jj > whereas i f 2 E edge ^ S u s e c * then Z becomes ^ \QQ • ^ t ^ s apparent that edge d i s l o c a t i o n solute atom i n t e r a c t i o n does not give a s a t i s f a c t o r y f i t . Z can be improved i f we assume a l i n e a r dependence of on e . c £ g instead of This value of Z would become c l o s e r to (as estimated by F l e i s c h e r ) i f i s p o s i t i v e ; however, t h i s speculation cannot be j u s t i f i e d u n t i l evaluated experimentally. e 3/2 By 3/2 1 Egthe best f i t i s obtained w i t h Z = " J Q Q - substituting 1 T The value of The l i n e a r dependence of on n is E g instead of has,however,been observed i n the case of Ag base s o l i d s o l u t i o n s (121) 133 The only other hexagonal a l l o y system in.which the room temperature plateau has been measured i s the Mg-Li system. Yoshinaga' and H o r i u c h i ^ ^ have a t t r i b u t e d the hardening to the Suzuki chemical strengthening me chani sin. although the experimental data conform to the t h e o r e t i c a l p r e d i c t i o n only upto 6 a t . % L i . Above t h i s concentration of L i the observed hardening i s much smaller than i s required by the Suzuki hardening mechanism. Yoshinaga and HoriU.chi's data has been p l o t t e d by h the present author against C apparent that C as shown i n f i g . (72). It is dependence holds good i n the case of Mg-Li a l l o y s too. Thus i t i s seen that the f r i c t i o n s t r e s s mechanism does e x p l a i n adequately the observed v a r i a t i o n of the room,temperature p l a t e a u — stress with solute concentration i n the Mg-Zn and Mg-Li s o l i d s o l u t i o n s . 2.4.2.6. Strengthening at Low Solute Concentrations: An i n t e r e s t i n g feature of f i g s . (49) and (72) i s that the s t r a i g h t l i n e through the experimental points i n the p l o t does not pass through the o r i g i n . against C The i n t e r s e c t i o n on the C' 2 axis corresponds to a composition equal to 0.025 a t . % i n the Mg-Zn system and 0.29 a t . % i n the case of Mg-Li a l l o y s . A c r i t i c a l examination of R o g a u s c h ' s ^ ^ data reveals that t h i s feature i s common to the Ag-base 2 s o l i d s o l u t i o n s too. Rogauschs data are reproduced i n f i g (73). This e f f e c t has,however,not been explained e a r l i e r . The concentration independence of x^ w i l l be b e t t e r understood i n the l i g h t of a knowledge of the low temperature r a t e c o n t r o l l i n g mechanisms i n the Mg-Zn a l l o y s . This w i l l be discussed i n a l a t e r chapter. 134 2 c F i g . 73. 3 inAt-% T vs concentration f o r Ag s o l i d s o l u t i o n s (af Rogausch (2)). 135 2.4.2.7. Valency E f f e c t : I t has been observed by several i n v e s t i g a t o r s that the r e l a t i v e valency of the solvent and the solute i s an important f a c t o r c o n t r i b u t i n g -u • (114,115,122) • -v. to s o li u t i o n strengthening . „However, since the present fc r e s u l t s are best explained i n terms of the s i z e and modulus i n t e r a c t i o n s , the valency e f f e c t i s of no consequence. Valency e f f e c t i s i n f a c t incorporated i n the modulus i n t e r a c t i o n term. 2.4.2.8. Other Hardening Mechanisms: The only other -hardening mechanism not covered so f a r i s the long range order hardening. This mechanism i s of importance when dealing with the deformation of the super l a t t i c e s only and i s of no consequence i n the present study, which deals with d i l u t e s o l u t i o n s . 1 3 6 2.4.3. S o l u t i o n Strengthening at Low Temperature: Before entering i n t o the d e t a i l e d discussions of the low temperature strengthening mechanismsit i s p r o f i t a b l e to examine the various possible ways i n which the a d d i t i o n of solute. r-T curve can be a l t e r e d by the P r i n c i p a l l y t h i s can happen i n three ways as shown schematically i n f i g . (74). CD CD u 0). -rl >< (a) Temperature E f f e c t of solute on x only . (c) Fig. 74. (b) Temperature E f f e c t of s o l u t i o n on x * only • Temperature Increasing obstacle strength .• The e f f e c t of solute on the x-T curve (Schematic) i a) By increasing b) By increasing the density of the short range obstacles. n which uniformly elevates the x-T curve • done strengthening w i l l be l i m i t e d to temperatures below c) By introducing stronger obstacles. If this i s . This w i l l s h i f t -T to higher temperatures, 137 Experimentally the a l l o y s containing 0.006 and 0.019 a t . % Zn conform to the s i t u a t i o n i n (b). and x increase, however, the At higher Zn concentrations both x x-T curve i s not uniformly elevated. * This i s apparent from f i g . (75), where only temperature for various solute concentrations. by subtracting c o r r e c t i o n to x x x i s p l o t t e d against Here x has been obtained from the measured CRSS (after applying the shear modulus x ). I t i s observed that the temperature s e n s i t i v i t y of increases with increasing solute content. This again suggests that the short range order i s not an important hardening mechanism i n these alloys. Short range hardening i s i n h e r e n t l y athermal, since the energy for nucleating forward s l i p never reaches a maximum value. As a segment of d i s l o c a t i o n bows out the energy continuously increases due p r i n c i p a l l y to the d i s o r d e r i n g that i s induced across the s l i p plane. For t h i s mechanism, therefore, deformation must be induced e x c l u s i v e l y mechanically by the a p p l i c a t i o n of a s u f f i c i e n t l y high s t r e s s to cause disordering. Therefore, i n order that short range ordering i s the 3x * p r i n c i p a l strengthening mechanism, (y^-) at low temperatures should be unaffected by the amount of solute present, which i s d i f f e r e n t from what i s observed experimentally. I t i s recognized that some mechanisms are thermally a e t i v a t a b l e under some conditions and athermal under others. For example, . weak C o t t r e l l atmosphere l o c k i n g of d i s l o c a t i o n s i s thermally a e t i v a t a b l e , but more concentrated and stronger Cottrell-atmosphere l o c k i n g can be athermal. Suzuki l o c k i n g -constitutes a second example: weak Suzuki l o c k i n g of p a r t i a l s having a narrow stacking f a u l t ribbon i s thermally a e t i v a t a b l e , but under otherwise s i m i l a r c o n d i t i o n s , i n a l l o y s that have 138 0 100 200 300 400 Temperature °K * F i g . 75, vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s . 139 low stacking f a u l t energies, the unlocking mechanism i s athermal. The t r a n s i t i o n of C o t t r e l l l o c k i n g from a thermally a c t i v a t a b l e to an athermal mechanism i s p r i n c i p a l l y due to the height of the a c t i v a t i o n energy b a r r i e r , whereas t h i s t r a n s i t i o n for Suzuki looking a r i s e s from the f a c t that high thermal f l u c t u a t i o n s i n energy can only occur over small volumes of the c r y s t a l . The f a c t that the width of the stacking f a u l t i n magnesium i s . r a t h e r narrow (due to high stacking f a u l t energy) makes Suzuki l o c k i n g a p o s s i b i l i t y and secondly the low solute concentrations involved may be taken to include C o t t r e l l l o c k i n g as a possible athermal mechanism i n the Mg-Zn a l l o y s . However, with the help of arguments, s i m i l a r to those described in.connection with the v a r i a t i o n of T _ , i t can be shown that neither i n trend nor q u a n t i t a t i v e l y does Suzuki hardening e x p l a i n the observed low temperature strengthening. Moreover,no s i n g l e mechanism can e x p l a i n the observed break i n the x-C p l o t at 0.025 a t . % Zn. Therefore, at t h i s juncture the i d e n t i f i c a t i o n of the short range obstacles i n Mg and the Mg-Zn a l l o y s may be h e l p f u l i n determining the mechanism of s o l u t i o n strengthening at low temperatures. The j u s t i f i c a t i o n f o r such a procedure comes from the f o l l o w i n g analysis. I t i s now widely accepted that the obstacles g i v i n g r i s e to the short range s t r e s s locations. T * i n close packed metals are the f o r e s t d i s - Therefore, the low temperature strengthening i n Mg can a r i s e from an i n d i r e c t e f f e c t of s o l u t e , namely the change i n the.forest d i s l o c a t i o n density. From the present etch p i t counts i t i s apparent that the.forest d i s l o c a t i o n density increases w i t h increasing amounts of solute. However, experimentally there i s l i t t l e change i n the f o r e s t 140 * spacing beyond 0.04 a t . % Zn, although the observed (g^ ) - ( f i g . 76) continues to increase r a p i d l y even at concentrations beyond 0.04 a t . % Zn. This implies that the change i n the f o r e s t spacing may be the important f a c t o r i n s o l u t i o n strengthening at low solute concentrations, but at higher solute concentrations the short range obstacles must be d i f f e r e n t from the f o r e s t d i s l o c a t i o n s . The rate theory w i l l be used i n an e f f o r t to i d e n t i f y the short range obs-tacles which determine the thermal component of the flow s t r e s s at higher solute concentrations. The p o s s i b l e r o l e of the change i n the f o r e s t d i s l o c a t i o n spacing as a s o l u t i o n strengthening mechanism can also be ascertained by comparing the observed a c t i v a t i o n length with the measured etch p i t spacing. 2.4.3.1. Thermally Activated Deformation: I t has been pointed out e a r l i e r that obstacles are e s s e n t i a l l y of two types, short range obstacles are e f f e c t i v e over distances l e s s than ten atomic diameters and long range obstacles possess s t r e s s f i e l d s of the order of ten atomic diameters or greater. Thermal energy i s able to a s s i s t the applied s t r e s s i n pushing the d i s l o c a t i o n past the short range obstacles, but cannot a i d i n g e t t i n g d i s l o c a t i o n s past the stronger long range obstacles. Above T c a l l thermal b a r r i e r s become transparent and d i s l o c a t i o n s move through the l a t t i c e unimpeded orice the applied s t r e s s has overcome the athermal b a r r i e r s . thermal b a r r i e r s must be overcome Below T , however, c by the assistance of s t r e s s and thermal energy i f an applied s t r a i n - r a t e i s to be maintained. Of the s e v e r a l thermal b a r r i e r s encounted, the strongest determines the r a t e at which d i s l o c a t i o n s can move under given conditions of s t r e s s , s t r a i n rate and temperature. 141 Provided the thermally activated processes occur i n sequence and that the same event i s rate c o n t r o l l i n g throughout the l a t t i c e , the macroscopic s t r a i n rate y may be expressed as - AF/kT Y where Y q V = (16) 6 depends on the number and arrangement of the d i s l o c a t i o n s and t h e i r v i b r a t i o n a l frequency. AF i s the change i n Gibbs' free energy of the system i n surmounting the strongest obstacle. On the other hand, i f the thermally activated processes occur independently and the rate c o n t r o l l i n g step i s not the same throughout the l a t t i c e , then the s t r a i n rate w i l l f o l l o w the relationship^ ^» 24 Z oi Y " - AF/kT (17) e where the subscript " i " r e f e r s to the i * " * kind of mechanism. Under such 1 circumstances the a p p l i c a t i o n of the rate theory f o r the i d e n t i f i c a t i o n of the rate c o n t r o l l i n g mechanism i s not p o s s i b l e , since the e x t r a p o l a t i o n of the macroscopic thermodynamic measurements to a s i n g l e a c t i v a t e d event occurring i n a s p e c i f i c region of the l a t t i c e i s no longer p o s s i b l e . The change i n free energy f o r the thermally a c t i v a t e d event j can be expressed as AH + I |S . I i - AF = 2i 1 - T . 3G G 3T where G i s the shear modulus and („) £ AH i s the a c t i v a t i o n enthalpy, given by AH . . ^ Ho (19) 142 V* i s i d e n t i f i e d as the a c t i v a t i o n volume and i s equal to v* The concept of a c t i v a t i o n volume a r i s e s when one considers the work W done on the system during a n . a c t i v a t i o n event by the e f f e c t i v e s t r e s s T * pushing a d i s l o c a t i o n segment of length 1 a distance d (the a c t i v a t i o n distance) where b i s the Burgers vector of the d i s l o c a t i o n s . The term (b'dl) i s c a l l e d the a c t i v a t i o n volume. The evaluation of the a c t i v a t i o n parameter g * an evaluation of the p a r t i a l d i f f e r e n t i a l s ( . ) y/y AF, AH and V* involves and T din y/y I 12. at T constant density, arrangement and number of mobile d i s l o c a t i o n s . For d i f f e r e n t a l l o y s these f a c t o r s , w i l l be d i f f e r e n t , however, here the constancy r e f e r s to the s i t u a t i o n when one a l l o y i s examined over a range of temperatures. Assuming the y i e l d s t r e s s to be governed by the same thermally activated mechanism over the range of temperatures of i n t e r e s t , one can consider that the structure i s r e l a t i v e l y constant at y i e l d ^^"^ . Hence, on subtracting T from x ( i . e . CRSS) a p l o t of x* against Ax temperature i s obtained ( f i g . (75)) and the slope Og^r) may be taken as ^ In *^ / ° (yj—). The second p a r t i a l — ^ Q i s u s u a l l y evaluated from d i f f e r e n t i a l s t r a i n rate change t e s t s on a s i n g l e specimen during flow at a f i x e d temperature. The flow stress d i f f e r e n c e accompanying instantaneous * changes of s t r a i n rate may be taken as v a r i a t i o n i n e f f e c t i v e s t r e s s with Ax y i f i t i s assumed that the structure remains constant during the i n s t a n t of change. D i f f e r e n t i a l t e s t s corresponding to a s t r a i n rate change by 2 a f a c t o r of 10 were c a r r i e d out by varying the cross head speed on the i n s t r o n from 0.002 to 0.2 ipm and v i c e versa using a push button speed s e l e c t o r . Experiments were performed at temperatures ranging from 143 78 K to 295°K covering the e n t i r e range of temperature s e n i t i v e y i e l d i n g . CJ The d e t a i l s of the s t r a i n rate change tests are described i n appendix (C). 2.4.3.2. The E f f e c t of Solute on the Apparent A c t i v a t i o n Parameters: From the r e l a t i o n s h i p (20) V* = kT a c t i v a t i o n volumes were calculated f o r a s e r i e s of Mg-Zn a l l o y s . The e f f e c t of the applied stress and the solute concentration on the a c t i v a t i o n volume i s shown.in f i g . (77). These tests were, conducted at 78°K and the 3 a c t i v a t i o n volumes are expressed i n terms of b vector of the g l i d e d i s l o c a t i o n s . where b i s the Burgers The measured a c t i v a t i o n volumes have been p l o t t e d against the resolved shear s t r a i n as shown i n f i g . (77) from which the a c t i v a t i o n volume at y i e l d can be obtained by an extrapolation to zero s t r a i n . I t i s observed that i n the case of magnesium the a c t i v a t i o n volume decreases r a p i d l y at low s t r a i n s , but at higher s t r a i n s the rate of decrease i s much smaller. The a l l o y containing .0.019 a t . % Zn e x h i b i t s e s s e n t i a l l y s i m i l a r behaviour as Mg except that the magnitude of V* i s smaller than that of the pure metal at low s t r a i n l e v e l s . The difference i n V* between magnesium and the low a l l o y , however, decreases r a p i d l y so that at s t r a i n s beyond 1.5 the two have the same a c t i v a t i o n volume at a constant s t r a i n l e v e l . The higher a l l o y s containing from 0*15 to 0.45 a t . % Zn, on the other hand, are associated with a c t i v a t i o n volumes which are l e s s s e n s i t i v e to both,stress and s t r a i n . This i s apparent from the fact that whereas i n Mg the a c t i v a t i o n volume 3 3 decreases from 4500 b at y i e l d to 400 b at f r a c t u r e , the corresponding 3 change i n the case of an a l l o y containing to 230 b . 3 0.45 a t . % Zn i s from 320 b V=4500 b Mg-Zn Single Crystals BASAL SLIP 78° K ^ o - o ^ ^ . r — ^ u _ - o - ^ - o ^ ^ ^ ^ ^ o ^ ^ ^ ^ 0 15 Zn 0-45 Zn ^ 0 258 Zn SHEAR STRAIN F i g . 77. A c t i v a t i o n volume vs. shear s t r a i n f o r Mg-Zn s i n g l e c r y s t a l s , OOI9Zn ^ V 145 2.4.3.3. The A c t i v a t i o n Volume at Y i e l d : A d i r e c t measurement of the a c t i v a t i o n volume at y i e l d i s rather d i f f i c u l t because of the uncertainty low s t r a i n s . of V i n measuring Ax at In order to minimize e r r o r , the extrapolated value to zero s t r a i n has been used. The concentration dependence of the * a c t i v a t i o n volume at 78 K i s shown i n f i g . (78). I t i s c l e a r that V 3 decreases dramatically from 4500 b i n pure magnesium to less than 1500 3 b by the addition of as l i t t l e as 0.05 a t . % Zn. Between 0.05 and 0.45 at.% Zn, on the contrary, the a c t i v a t i o n volume decreases very s l i g h t l y . From f i g s . (77) and (78) i t appears that the a l l o y s containing solute i n amounts l e s s than 0.05 a t . % belong to a category d i f f e r e n t from the one which the higher a l l o y s belong t o . The temperature dependence of the a c t i v a t i o n volume at y i e l d i s shown i n f i g . (79). Two compositions were chosen f o r t h i s purpose, Mg being the representative of the group.containing upto 0.05 a t . % solute while 0.45 a t . % Zn a l l o y belonging to the l a t t e r category. The a c t i v a t i o n volume at y i e l d was once again obtained by the method of e x t r a p o l a t i o n to zero s t r a i n . The a c t i v a t i o n volume i s observed to increase r a p i d l y with temperature i n the case of magnesium, whereas the temperature s e n s i t i v i t y of V i n the case of 0.45 a t , % Zn a l l o y i s considerably lower; e s p e c i a l l y at temperatures below 200°K. V P r o f i t a b l e information may be obtained i f i s p l o t t e d against x . This has been done.for Mg and 0.45 a t . % Zn a l l o y as shown i n f i g . (80). The a c t i v a t i o n volume decreases d r a s t i c a l l y with increasing values of x i n the case of magnesium whereas there i s only a moderate decrease i n the case of 0.45 a t . % Zn a l l o y . The values F i g . 79. A c t i v a t i o n volume at y i e l d vs. temperature f o r Mg and Mg + 0.45 a t . % Zn a l l o y s i n g l e c r y s t a l s . 147 18,000 16,000 14,000 - 12,000 cn > e o 10,000 > a o 8,000 •U > O < 6,000 4,000 2,000 100 200 300 * i.n gm//mm2 i * A c t i v a t i o n volume at y i e l d vs. T f o r Mg and Mg + 0.45 at. % Zn a l l o y s i n g l e c r y s t a l s . T N E i g . 80, of V * at 148 * 3 T - 0 f o r Mg comes out to be approximately 16,000 b and that 3 () 5 for 0.45 % Zn a l l o y i s 3,300 b . Conrad, using an i n t e r s e c t i o n model for Mg s i n g l e c r y s t a l s , has shown that the nature of the force-distance curve may vary s l i g h t l y w i t h temperature ( i . e . with x ) due to the influence of s t r e s s on the amount the g l i d i n g dislocatiois bow out on the s l i p plane thereby changing the e f f e c t i v e f o r e s t spacing "1". This decrease i n a c t i v a t i o n volume with s t r a i n has been interpreted by (3) Basinski as a r i s i n g due to an increase i n the forest d i s l o c a t i o n density Therefore, i f the a c t i v a t i o n volume i s to be used i n determining the f o r e s t spacing at y i e l d , then i t i s e s s e n t i a l that the value at x = 0 be chosen. In t h i s connection i t i s worth noting that the temperature v a r i a t i o n of the a c t i v a t i o n volume can be caused by the temperature dependence of the stacking f a u l t energy, which i n turn determines the a c t i v a t i o n distance "d". However, i n materials having high stacking f a u l t energy (e.g. Mg) the distance between the p a r t i a l s i s u n l i k e l y to be a l t e r e d much through changes i n temperature and hence the a c t i v a t i o n distance "d" i s not l i k e l y to be the f a c t o r responsible f o r the temperature dependence of V . 2.4.3.4. Solution E f f e c t on the Apparent A c t i v a t i o n Energy: * S u b s t i t u t i n g f o r AH and V i n equation (18) the a c t i v a t i o n Gibbs free energy becomes AF = -kT 2 | - L IV3T / - ^ • -7T- I (21) 3x* The term \( -r-^; . Gj j i s small and hence w i l l be neglected compared to 9 T • 3 *.\ J> (~~vf X AF can then be approximated to AF : AH : - V* T AH i . e . (|V) • Y/y (22) 149 I t i s important to note that when AH i s s u b s t i t u t e d f o r AF, i t i s AS /fc assumed that the entropy term e term y . This approximation i s incorporated i n the pre-exponential i s v a l i d only when the entropy change does not have s i g n i f i c a n t c o n t r i b u t i o n to the over a l l free energy change. The term AH c a l c u l a t e d using equation ( 1 9 ) does not include the work done by the e f f e c t i v e s t r e s s during thermal a c t i v a t i o n . for t h i s work done the t o t a l a c t i v a t i o n energy (enthalpy) Correcting AH i s then 0 expressed as AH where V T AH 0 + V*T* (23) i s the work done during thermal a c t i v a t i o n . The v a r i a t i o n of AHo with Zn content has been c a l c u l a t e d using equations (19,20) and The term (23) and i s shown i n f i g . (81). AHo should be l a b e l l e d "apparent" a c t i v a t i o n enthalpy, since the e f f e c t i v e s t r e s s before the a c t i v a t i o n event i s unknown. AH o * would be the true a c t i v a t i o n enthalpy only when T = 0 . However, t h i s has.not been done i n the present work. 2.4.3.5. Zinc A l l o y i n g and the Thermally Activated Flow: In s o l i d s o l u t i o n s the mechanism of thermally a c t i v a t e d deformation can be any one of the f o l l o w i n g : 1) I n t e r s e c t i o n of f o r e s t d i s l o c a t i o n s , 2) D i s l o c a t i o n pinning by s i n g l e solute atoms, 3) Tetragonal s t r a i n centres, 4) P e i e r l s , Pseudo P e i e r l s , and Recombination mechanism, 5) Cross s l i p , 6) Cottrell-Lomer D i s s o c i a t i o n , 151 and 7) Fisher l o c k i n g , 8) Suzuki l o c k i n g . Some of these mechanisms have been discussed e a r l i e r . For example Fisher and Suzuki locking mechanisms do not apply to the present case as shown i n the e a r l i e r part of t h i s s e c t i o n . The mechanism of Cottrell-Lomer d i s s o c i a t i o n does not apply to the case of hexagonal structures. Also the case of Tetragonal s t r a i n centres i s i n a p p l i c a b l e since i t applies to i n t e r s t i t i a l i m p u r i t i e s only, while Zn i s a s u b s t i t u t i o n a l solute i n Mg. The remaining four w i l l be discussed i n the f o l l o w i n g pages. 2.4.3.5.1. Cross S l i p : (73) The a c t i v a t i o n volumes associated with the cross s l i p process are of the same order as those f o r i n t e r s e c t i o n , both.being greater than 3 * 100 b . The experimentally determined V i n the Mg-Zn a l l o y s are also 3 greater than 100 b . However, a c t i v a t i o n volume alone cannot be taken to decide between the cross s l i p and the i n t e r s e c t i o n mechanisms. A d d i t i o n a l information may be obtained from the f o l l o w i n g considerations. • In the range of temperature i n v e s t i g a t e d , the only e s t a b l i s h e d cross s l i p planes i n magnesium are the basal {0001} {1010} planes. and the prism The CRSS f o r p r i s m a t i c s l i p i n each of these a l l o y s i s about two orders of magnitude higher than that f o r basal s l i p . Therefore, i t i s u n l i k e l y that cross s l i p would be p o s s i b l e at the onset of p l a s t i c flow. This conclusion i s supported by the absence of cross s l i p markings on the surface of the deformed c r y s t a l s , although the s l i p l i n e observations should not be taken as conclusive when o p t i c a l microscopy i s used f o r t h e i r 152 examination. Cross s l i p does play a s i g n i f i c a n t r o l e i n the work hardening (29) of magnesium i n the stage A of deformation , however, t h i s i s of l i t t l e consequence when CRSS i s the parameter under consideration. Thus i t may be concluded that cross s l i p cannot be the rate c o n t r o l l i n g mechanism i n basal s l i p . 2.4.3.5.2. P e i e r l s , Pseudo-Peierls and Recombination Mechanisms: P e i e r l s mechanism concerns the thermal a c t i v a t i o n of d i s l o c a t i o n motion past l i n e a r obstacles. A rather complete review of t h i s mechanism has been given recently by Guyot and D o r n ^ ^ . 2 The pseudo-Peierls mechanism was o r i g i n a l l y proposed by Dorn to e x p l a i n the thermally a c t i v a t e d flow of Mg-Li a l l o y s . I t i s a s l i g h t m o d i f i c a t i o n of the P e i e r l s mechanism for the case where the two p a r t i a l s are very close together (0.5 to 2b). The stacking f a u l t energy plays a s i g n i f i c a n t r o l e i n the Pseudo P e i e r l s mechanism whereas the Peierls-Nabarro theory does not take t h i s i n t o consideration^"*" ^ . 2 These mechanisms w i l l be discussed i n greater d e t a i l i n connection with prismatic s l i p . Recombination i s thought to be a successful mechanism i n explaining e f f e c t i v e l y the o r i e n t a t i o n dependence and the i n i t i a l rates of s t r a i n hardening i n bcc metals ^ 2 ^. Without going i n t o any further d e t a i l s of the above three mechanisms, i t should be pointed out that the a c t i v a t i o n volume associated 3 with each of these mechanisms i s l e s s than 80 b , whereas the * 3 experimentally determined values of V are greater than 300 b . Therefore, these mechanisms are not a p p l i c a b l e to the present case. 153 2.4.3.5.3. The I n t e r s e c t i o n Model: * I t i s now w e l l recognized that the obstacles determining x i n the basal g l i d e of magnesium are the f o r e s t d i s l o c a t i o n s . I n view of the f a c t that the grown i n d i s l o c a t i o n density does change i n many instances of close packed structures by the a d d i t i o n of s o l u t e , there i s reason to believe that the i n d i r e c t s o l u t i o n strengthening due to such a change can be of importance i f the strengthening due to d i r e c t i n t e r a c t i o n i s r e l a t i v e l y small. Hendrickson and Fine In the past attempt has been made by to e x p l a i n the observed strength of the Ag-Al a l l o y s i n terms of increased grown i n d i s l o c a t i o n d e n s i t i e s . However, 10 -2 such an explanation requires the presence of d i s l o c a t i o n s upto 10 cm i n the as grown c r y s t a l , which i s too high to be met i n p r a c t i c e . The case of Mg-Zn w i l l now be examined i n the l i g h t of the grown i n f o r e s t d i s l o c a t i o n density contribute to r x* (the increase i n basal d i s l o c a t i o n density can only and therefore w i l l not be considered here since i s being dealt with at the present). The a c t i v a t i o n volume at 78°K f o r each of the Mg-Zn a l l o y s 3 tested i s greater than 100 b ( f i g . 78) thus f o r e s t i n t e r s e c t i o n can be the rate c o n t r o l l i n g mechanism i n these a l l o y s . ft ft From f i g . (80) the values of V at x = 0 can be used to c a l c u l a t e the f o r e s t d i s l o c a t i o n density at y i e l d i n Mg and 0.45 a t . % Zn a l l o y using the f o l l o w i n g expression. V* = b . d . l . (24) If a simple assumption i s now made that the a c t i v a t i o n distance "d" can be approximated by the Burgers vector "b" then * V 9 = l> .1 (25) 154 Again, assuming a square array, the f o r e s t d i s l o c a t i o n density Such c a l c u l a t i o n s i n the two cases y i e l d p p= —_ 1 (26) 6 = 3.8 x 10 —2 cm 7 -2 and p„ ,,- „ = 9 x 1 0 cm . A s i m i l a r c a l c u l a t i o n i n Mg by Conrad 0.45 Zn —A (68) -4 yielded 1 = 1.5 x 10 cm i n one set of experiments, ' and 1 = 3.0 x 10 cm o o J i n another ^ \ Conrad has a t t r i b u t e d t h i s inconsistency i n h i s r e s u l t s to the d i f f e r e n c e i n growth c o n d i t i o n s , impurity content and the e f f e c t of recovery treatment on 1 . q The calculated p Mg w =3.8 higher than the etch p i t density. already. 0.45 Zn This discrepancy has been discussed Here we w i l l compare the r a t i o corresponding etch p i t f i g u r e . P x 10^ i s two orders of magnitude Jo =24 M p n y/ a Q P ^ g with the From the a c t i v a t i o n volume measurements whereas the corresponding r a t i o of etch p i t s = 4. M g This implies that e i t h e r the assumption that "d" remains constant i s not true or the basic assumption that the rate c o n t r o l l i n g mechanism i n Mg at<>% Zn a l l o y i s one of i n t e r s e c t i o n i s wrong. of "d" with solute concentration. f a u l t that i s determining Now l e t us consider the v a r i a t i o n I f i t i s the width of the stacking "d'^then "d" cannot decrease to a value l e s s than 0.5 - 2 b, which i s the distance between.the p a r t i a l s i n Mg. the only other p o s s i b i l i t y i s that "d" increases. Therefore, I f i t does then the r a t i o Pallov -p ' becomes even,larger than 24, making the discrepancy worse. Therefore, the f i r s t assumption that the rate c o n t r o l l i n g mechanism i n 0.45 must be wrong. 0.45 a t . % Zn a l l o y i s one of i n t e r s e c t i o n of f o r e s t trees / a) 155 I n t e r s e c t i o n Model at Low Solute Concentrations: The etch p i t density increases rather r a p i d l y by the a d d i t i o n 1/2 of Zn upto 0.04 a t . % and the break i n the C - x p l o t i s at 0.025 a t . % Zn. Therefore, i t i s l i k e l y that the a d d i t i o n of s o l u t e . i n such small q u a n t i t i t e s w i l l not a l t e r the rate c o n t r o l l i n g mechanism of magnesium and hence strengthening could be due to increased f o r e s t density. I n order to put 0 025 Z t h i s suggestion to t e s t l e t us compare '• derived from Mg a c t i v a t i o n volume measurements with the r a t i o of etch p i t s at a comparable * * s i t u a t i o n . In the absence of the value of V f o r 0.025 Zn a l l o y at T = 0, the a c t i v a t i o n volumes at 78°K w i l l be used. This w i l l not be too * erroneous because the temperature e f f e c t on V w i l l be approximately of the P same order i n the two cases. .0»025 Zn Mg evaluated i n t h i s manner i s P equal to 3.2, the corresponding etch p i t r a t i o being 2.5. I n view of the experimental e r r o r involved i n the measurement of the a c t i v a t i o n volume t h i s may be regarded as a good agreement. Hence the thermally a c t i v a t e d mechanism i n Mg and the a l l o y s containing upto 0.025 a t . % Zn i s one of i n t e r s e c t i o n . What remains to be seen i s which of the r a t e c o n t r o l l i n g mechanisms can account f o r the flow i n the higher a l l o y s . The only mechanism not discussed so f a r i s the s i n g l e solute atom d i s l o c a t i o n pinning mechanism. This w i l l be applied to both low and high Zn a l l o y s i n order to see i f i t can provide an a l t e r n a t i v e to the i n t e r s e c t i o n model and to t e s t i t s a p p l i c a b i l i t y at higher concentrations of s o l u t e . 156 2.4.3.5.4. D i s l o c a t i o n Pinning by the Solute Atoms: A model f o r the low temperature short range solute d i s l o c a t i o n i n t e r a c t i o n has been formulated b y ' F r i e d e l ^ ^ ^ . According to t h i s model the d i s l o c a t i o n moves i n a zigzagging fashion from one p o s i t i o n of maximum core i n t e r a c t i o n energy to the next. The s i t u a t i o n i s schematically r e - presented i n f i g . (82). F i g . 82. The s t r e s s D i s l o c a t i o n pinning by solute atoms g i v i n g r i s e to low temperature f r i c t i o n stress (Schematic). x° to do t h i s at T = 0 i s determined by the i n t e r a c t i o n energy and the concentration C of the solute according to the equation: For T= 0: ' x° o bLx = U (27) m In the case of hexagonal close packed metals, 2 b V = bLx = A c t i v a t i o n Volume = — . — , and /3 " 3 i n fee metals bLx = b /Q (note C i s atom f r a c t i o n , not a t . % ) 3 0 T° o = for T>0 (28) C x (T.) •= /3 U =H o Um 4 •c — . (29) " kTlh-(? /Y) , ° (30) 157 At f i n i t e temperatures the f r i c t i o n s t r e s s i s decreased by thermal a c t i v a t i o n expressed i n i t s simplest form i n equation (30). In order to make a comparison between the theory and the experiment we w i l l f i r s t c a l c u l a t e the a c t i v a t i o n volume as a f u n c t i o n of the. solute concentration according to equation (28). Since the measured a c t i v a t i o n volume v a r i e s with temperature i t i s e s s e n t i a l to extrapolate these values to 0 ° K and then compare w i t h the V q obtained from equation (28). This has been done i n f i g . (83). The s o l i d l i n e represents the calculated value whereas the dashed l i n e f o l l o w s the extrapolated values of the a c t i v a t i o n volume to 0 ° K . I t i s apparent that the t h e r o e t i c a l p r e d i c t i o n agrees w i t h the experimental r e s u l t s only at concentrations of solute greater than 0.3 a t . % . There i s marked d e v i a t i o n at low concentrations s p e c i a l l y at concentrations below 0.05 a t . % Zn, implying that the pinning of d i s l o c a t i o n by s i n g l e solute.atoms i s an u n l i k e l y mechanism at low concentrations, although at higher concentrations such a mechanism i s possible. A d d i t i o n a l support f o r the d i s l o c a t i o n pinning by s i n g l e s o l u t e atoms comes from the f a c t that the higher temperature flow s t r e s s i s adequately explained by the f r i c t i o n s t r e s s mechanism i n these a l l o y s , which again involves the concept of s i n g l e solute atoms i n t e r a c t i n g with d i s location lines. Using x° f o r 0.45 a t . % Zn a l l o y and the a c t i v a t i o n volume at 0 ° K the value of U i s found to be 0.48 e.V., which i s much too low m compared to that obtained by the s t r a i n r a t i o change t e s t s at 7 8 ° K . (H Q = 1.237 e.V.). A s i m i l a r discrepancy was encountered by Rogausch^"'''''^ i n the case of Ag-In a l l o y s . ) 2 2000 7000 1 Comparison of Friedel's Model with the Experimental Results. 1600 «M — Extrapolated to 0°K — Calculated using eqn. 6» .c 1200 / 800 02 0-3 ATOMIC% Zn 0-4 05 F i g . 83. Comparison cf the. experimental-results.with, the composition.dependence of a c t i v a t i o n volume as predicted by-. F r i e d e l ^ s model. 400 0 <-> V K * Silver-Al uminium o Silver -Ir dium 2 c in At.-% 4 6 F i g . 84. Concentration dependence of CRSS extrapolated to 0°K f o r Ag-rln and Ag-Al s i n g l e c r y s t a l s (after Haasen^ '). 2 oo 159 F i n a l l y a remark may be made on the predicted l i n e a r i t y of T° on C as represented by equation (30). not.show a l i n e a r r e l a t i o n s h i p with C. Ag-In that The present values of T° do E a r l i e r experiments of Rogausch on and those of Hendrickson and Fine on Ag-Al a l l o y s T° i s a l i n e a r f u n c t i o n of the solute concentration. o of data p l o t t e d together are reproduced i n f i g . (84). reveal The two sets A c l o s e r examination of these data shows that the s t r a i g h t l i n e when extrapolated to zero conc e n t r a t i o n of solute gives T o 2 T f o r Ag = 380 gm/mm whereas the a c t u a l q o / 2 from Rogauschs data comes out to be l e s s than 150 gm/mm . What t h i s o implies i s that x° i s not a l i n e a r f u n c t i o n of C at low solute concentrations. The present experiments were performed on d i l u t e Mg-Zn a l l o y s and t h i s i s why T° i s non-linear with respect to C. The reason f o r such a non l i n e a r i t y being that i n t h i s concentration range there e x i s t s a t r a n s i t i o n from the i n t e r s e c t i o n mechanism to the solute atom d i s l o c a t i o n pinning mechanism. (85) Recent experiments of Hendrickson on Ag s o l i d s o l u t i o n s suggest that the d i s l o c a t i o n density i s not affected much by solute addition. However, t n e s c a t t e r i n the d i s l o c a t i o n density measurements was too high i n Hendricksons experiments to d i s t i n g u i s h the change of density by a f a c t o r of two or three. 2.4.3.6. Strengthening Mechanism i n D i l u t e A l l o y s : The s o l u t i o n strengthening parameter Sj when p l o t t e d against temperature, shows a linear-decrease upto 330°K, above t h i s temperature, however, no s o l u t i o n strengthening is,observed. The most obvious conclusion would be that the a d d i t i o n of solute upto 0.025 a t . % Zn does not contribute to the long range s t r e s s f i e l d . 160 Moreover, since s o l u t i o n strengthening i s observed at low temperatures, i t must be due to some sort of a short range i n t e r a c t i o n process. I t was shown i n a previous section that the rate c o n t r o l l i n g mechanism i n Mg and the low a l l o y s under consideration i s one of i n t e r s e c t i o n of f o r e s t d i s l o c a t i o n s . A l s o , since the experimental r e s u l t s have shown that the f o r e s t d i s l o c a t i o n density does increase r a p i d l y with a l l o y i n g i n the low a l l o y s , i t i s most l i k e l y that s o l u t i o n strengthening i s caused by the presence of a l a r g e r number of f o r e s t dislocations. The constancy of T i n the CRSS-temperature p l o t f u r t h e r £ substantiates the above conclusion. In the presence of a v a i l a b l e data on the extent of increase i n the f o r e s t density with solute concentration, i t i s possible to make a q u a n t i t a t i v e comparison between the observed strength of the a l l o y with that predicted by the higher f o r e s t density. Assuming the f o r e s t d i s l o c a t i o n s to form a regular "square" array,Seeger^^ - has developed an equation which r e l a t e s the s t r e s s 8 required f o r the i n t e r s e c t i o n process to the f o r e s t spacing 1 as f o l l o w s : 2 T where p f = , r ar-d kT pb v " i . . . . I L (31) G I LbT~d"s ~ bT~ds ~M fy J i s the density of the g l i d e d i s l o c a t i o n s j i s the f r a c t i o n of the s l i p plane over which the maximum average amplitude i s T Q T l n v i s the Debye frequency , T i s the average l i n e energy , Y i s the s t r a i n rate d i s .the e f f e c t i v e diameter of the f o r e s t d i s l o c a t i o n s , a i s a strength f a c t o r such that, aT i s the strength of the obstacle, the r e s t of the symbols have t h e i r usual meanings• 161 Moreover, x = therefore , T at T g ard = kT < c In T (32) (33) p b fy where i s the c r i t i c a l temperature above which thermal f l u c t u a t i o n s i n energy greater than ard occur as frequently as i s needed to maintain * the imposed s t r a i n rate even when r = 0. To t h i s approximation the mechanical behaviour f o r c u t t i n g a.simple type of l o c a l i z e d obstacle, the s t r e s s to induce flow at the absolute zero i s given by T o = V + o bl s On the basis of t h i s model the behaviour.of a l l o y s w i l l now be examined. the d i l u t e Mg-Zn I t i s c l e a r from the CRSS-temperature r e l a t i o n s h i p s i n f i g . (47) that the flow s t r e s s of magnesium becomes athermal at 330°K. Also t h i s value of T i s unaffected by solute i n c the 0.006 and 0.019 a t . % Zn a l l o y s . J This constancy of T £ implies that the strength of the obstacles remains unchanged by the a d d i t i o n of solute i.e. T g i s independent of zinc concentration. Under such circumstances the thermally a c t i v a t e d component of flow s t r e s s can be a f f e c t e d only (bearing i n mind here that T through a change i n 1 S i s constant). In (j other words a change i n the f o r e s t d i s l o c a t i o n density i s responsible for s o l u t i o n strengthening at low concentrations. Now equation (34) can be r e w r i t t e n as f o l l o w s : T where A = ^ = T B = ar —— 0 0 . Q = A + f- 2 40 gm/mm , independent of Zn concentration and (35) 162 B w i l l also be taken as independent of Zn concentration since the v a r i a t i o n i n b and the shear modulus with concentration are much smaller than that i n 1 ( T i s a function of the shear modulus). s o T Now expressing T or, where o = T 0 A + B q i n terms of f o r e s t d i s l o c a t i o n density /i7 (36) = A + B /p^T" (37) p i s the f o r e s t d i s l o c a t i o n density, r However, at low solute concentrations p^ = 3.4 x 1 0 4 [ 1 + 5.35 x 10 C] cm 4 (3a) 2 r S u b s t i t u t i n g i n equation (37) the value of p F 4 = A + 184.4 x B (1 + 5.35 x 10 C) 1 x 0 / 2 (38) Using the data f o r pure magnesium, the constants A and B can be determined. A and B come out to be 2 A = 48.8 gm/mm Therefore, (taking G i n t o account) B = 0.196 gm/mm T * 48.8 + 36,2 (1 + 5.35 x 1 0 C ) 4 q 1 / 2 gm/mm (39) 2 The CRSS of 0.006 and 0.019 a t . % Zn a l l o y c a l c u l a t e d using equation (39) are shown i n the table below. TABLE IV Strengthening due to increased f o r e s t density . At. % Zn T ° Extrapolated i n gm/mrn^ T ° Calculated i n gm/mm^ 0.006 106 122 0.019 130 168 163 I t i s seen from the Table IV that the c a l c u l a t e d values come out to be higher than the CRSS extrapolated to 0°K. However, the e x t r a p o l a t i o n i s done over too large a temperature range to be considered accurate. A q u a n t i t a t i v e comparison w i l l be meaningful only when experimental data are a v a i l a b l e close to absolute zero. q u a l i t a t i v e l y the C Nevertheless, . dependence of the CRSS i s i n agreement with the 2 d i c t a t e s of the f o r e s t i n t e r s e c t i o n mechanism. Further evidence i n support of t h i s conclusion comes from the a c t i v a t i o n volume measurements. This has been discussed e a r l i e r . I t i s worth while examining at t h i s juncture the assumptions involved i n the i d e a l i z e d prototype model of Seeger which has been used for c a l c u l a t i n g x . Deviations from the predicted value can occur due to the f o l l o w i n g reasons. 1) the force displacement diagram can d i f f e r from the simple case assumed i n c a l c u l a t i n g equation (35). However, i n the case of magnesium t h i s approximation i s j u s t i f i e d , because i t i s a case of i n t e r s e c t i o n of undissociated basal g l i d e d i s l o c a t i o n s with unreactive f o r e s t d i s l o c a t i o n s . 2.4.3.6.1. Deviations from Square Array: Obstacles never form a regular array as assumed i n formulating equation (35). Enough progress has been made on the s t a t i s t i c a l treatment of the problem to suggest that randomly dispersed obstacles give much lower stresses over the lower temperature range than i s obtained * «.!, (129,130) _ from the square arrays • Over the higher temperature range, A however, the s t r e s s x f o r the random d i s t r i b u t i o n of obstacles l i e s above that predicted f o r a square array model and decreases very slowly with increasing temperature. 164 Whereas i t was assumed that a s i n g l e c u t t i n g would permit 2 the d i s l o c a t i o n s to move only over the average area I i n the square a r r a y , i t has been demonstrated by K o c k s ^ ^ 3 and by the computerized (129) experiments of Foreman and Makin , that a larger area i s swept out. This a r i s e s because once a c u t t i n g has been achieved there i s a c e r t a i n p r o b a b i l i t y the d i s l o c a t i o n can unzip past the next neighbour e t c . In view of these l i m i t a t i o n s inherent i n the t h e o r e t i c a l formulation of equation (35) the observed values of x° may be considered to be i n good agreement with the t h e o r e t i c a l p r e d i c t i o n s . 2.4.4. Work Hardening of Mg S o l i d Solutions: In the past much of the work i n s o l u t i o n strengthening has been concerned with the understanding of the fundamental strengthening mechanisms governing the onset of p l a s t i c flow. However, attempts to c o r r e l a t e the s t r e s s s t r a i n curves of s i n g l e c r y s t a l s to those.of the corresponding p o l y c r y s t a l l i n e aggregates have revealed that r e l a t i o n s h i p s (131-135) do e x i s t between the two sets of work hardening parameters Keeping i n mind that the ultimate objective of the s i n g l e c r y s t a l study i s to lead to an understanding of the macroscopic flow c h a r a c t e r i s t i c s of the p o l y e r y s t a l s , a study of s o l u t i o n strengthening would be incomplete without a d i s c u s s i o n of the work hardening behaviour i n a l l o y s i n g l e crystals. The work hardening c h a r a c t e r i s t i c s of the Mg-Zn a l l o y s i n g l e , c r y s t a l oriented f o r basal s l i p are discussed below. 165 2.4.4.1c The Easy G l i d e i n Magnesium: I t was f i r s t pointed out by Mott that the deformation mechanisms i n face centred cubic c r y s t a l s i n stage I and i n Hexagonal close packed c r y s t a l s i n stage A are s i m i l a r . -4 i n easy g l i d e i s t y p i c a l l y 10 The work hardening rate -5 - 10 G and i n both cases i t appears that the c r y s t a l s deform almost.entirely on one s l i p plane. Two p r i n c i p a l theories have been proposed to e x p l a i n the work hardening i n easy g l i d e : Lally (29) . that of Seeger et a l (137) and of H i r s c h and Hirsch's theory has been extended further by Hazzledine (138) E s s e n t i a l l y both the theories assume that Frank-Read sources are present i n the c r y s t a l and that they emit d i s l o c a t i o n s under applied s t r e s s . In Seeger's model i t i s assumed that a c e r t a i n number of sources remain a c t i v e throughout stage I and emit d i s l o c a t i o n s gradually during deformation. Seeger's model i s a close approximation to the ease of Cu, Zn, Ni-Co a l l o y s (29) etc. On the other hand, s l i p l i n e studies i n Mg i n d i c a t e that only a f r a c t i o n of the sources are a c t i v e i n any small s t r a i n i n t e r v a l , the density of a c t i v e sources i s independent of s t r a i n and d i s l o c a t i o n s are (1 38^ emitted i n bursts from the sources . Hirsch's theory was o r i g i n a l l y , designed f o r the case of Mg and hence w i l l be discussed i n b r i e f . In Hirsch's model the d i s l o c a t i o n s from sources operating simultaneously trap one another and form dipole bands f o r edges and screws; the screws a n n i h i l a t e by cross s l i p leaving edges and an excess of screws of one sign. The flow stress i s c o n t r o l l e d by the i n t e r n a l stress from the excess edge.and screw d i s l o c a t i o n s and from those w i t h non primary basal Burgers v e c t o r s . Since the d i s l o c a t i o n s are paired o f f or a n n i h i l a t e , t h e i r c o n t r i b u t i o n to work hardening i s expected to be low. 166 In t h i s model the d i s l o c a t i o n arrangement i s s t a b i l i z e d by a frictional force of some kind and the prism segments or the jogs are believed to c o n s t i t u t e the Frank-Read sources. The increase i n the hardening rate i n Mg with decreasing temperature could be explained as f o l l o w s . Since the jogs are more d i f f i c u l t to move at lower temperatures, the e f f e c t i v e source length w i l l become smaller as the temperature decreases. The number of p o t e n t i a l sources i s also l i k e l y to increase, because the minimum height of a jog which can serve as anchoring point f o r a source would be smaller (the stable jog height being temperature dependent). Moreover, since the CRSS f o r prismatic s l i p increases r a p i d l y with decreasing temperature, the screws are. l e s s l i k e l y to a n n i h i l a t e and w i l l probably form d i p o l e bands. The increase i n f r i c t i o n s t r e s s due to the presence of j o g s , which are d i f f i c u l t to move, w i l l lead to a s i t u a t i o n where the dipole bands can support a l a r g e r number of excess d i s l o c a t i o n s of one s i g n . (3) Basinski has observed that C o t t r e l l - S t o k e s ' law i s obeyed i n magnesium below 60°K. However, at higher temperatures deviations occur; suggesting the presence of two short-range processes. This observation has been r a t i o n a l i z e d i n the l i g h t of Hirsch's theory as f o l l o w s . The density of the prism segments produced by cross s l i p increases with increasing s t r a i n . I n t e r s e c t i o n of these segments leads to the formation of k i n k s , which i s a thermally a c t i v a t e d process and, therefore, contributes to the decreasing a c t i v a t i o n volume. The o r i g i n of the observed C o t t r e l l — S t o k e s law can be a t t r i b u t e d to the p r o p o r t i o n a l i t y between the prism segments produced by c r o s s . s l i p , and the density of the screw d i s l o c a t i o n s (before a n n i h i l a t i o n ) , when a n n i h i l a t i o n occurs. 167 The present r e s u l t s are i n f a i r l y good agreement with the above theory. 2.4.4.1.2. Easy Glide i n A l l o y C r y s t a l s : I t i s now w e l l established that i n the case of s o l i d s o l u t i o n s having fee s t r u c t u r e , the extent of easy g l i d e increases with solute a d d i t i o n , the work hardening rate i n stage I remains unaffected i n systems showing l i m i t e d s o l i d s o l u b i l i t y , and decreases where the (2 139) s o l u b i l i t y i s extensive ' . In body centred cubic metals the e f f e c t s are i r r e g u l a r , p o s s i b l y because of uncontrolled interstitial impurities ^ . The work hardening behaviour of hexagonal a l l o y s i n g l e c r y s t a l s , however, has not been investigated thoroughly. The e a r l y work of Schmid and co-workers had i n d i c a t e d that the work hardening rate i n Mg increases with solute concentration i n the case of Zn and ( 88) A l solutes . On the other hand Zn e x h i b i t s a lowering i n 0^ with + ^(88,147) increasing impurity content An attempt w i l l be made here to e x p l a i n q u a l i t a t i v e l y the observed dependence of O^on Zn concentration i n the l i g h t of Hirschs theory of work hardening i n Mg^ ^\ 2 The d i s l o c a t i o n sources i n Mg are the prism segments or jogs. The e f f e c t of solute upto 0.025 a t . % Zn i s to increase the f o r e s t d i s l o c a t i o n density. This leads to an increase i n the number of Frank- Read sources r e s u l t i n g i n a larger number of dipole bands being formed, which i n turn increase the long range s t r e s s f i e l d and a more rapid hardening r e s u l t s . Moreover, since the CRSS f o r prismatic s l i p 168 becomes higher, the screws are l e s s l i k e l y to a n n i h i l a t e and w i l l probably form dipole bands, although the c o n t r i b u t i o n from the l a t t e r (29) source would be small as pointed out by Hirsch An increase i n the solute content above 0.025 a t . % Zn r e s u l t s i n a rather r a p i d l y increasing f r i c t i o n stress a r i s i n g from the s i z e and modulus i n t e r a c t i o n s . In the presence of a higher f r i c t i o n stress the dipole c l u s t e r s become d i f f i c u l t to move. In f a c t , the magnitude of the f r i c t i o n stress determines the way i n which the excess d i s l o c a t i o n s d i s t r i b u t e themselves. Thus the presence of solute w i l l lead to a higher work hardening rate through a change i n the f r i c t i o n s t r e s s . 2,4.4.2. The Temperature Dependence of 9^ i n A l l o y C r y s t a l s : The.low temperature work hardening i n the easy g l i d e of a l l o y c r y s t a l s containing upto 0.025 a t . % Zn, can be explained same manner as i n pure. Mg. i n much the As shown e a r l i e r , the rate c o n t r o l l i n g mechanism at,the onset of flow i n Mg and the low a l l o y s i s one of i n t e r s e c t i o n . The increase i n 9^ i n these a l l o y s , however, a r i s e s due to the f o l l o w i n g reason. The presence of a larger number of jogs i n these a l l o y s increases the low temperature f r i c t i o n s t r e s s , enabling the dipole bands to support a l a r g e r number of excess d i s l o c a t i o n s of one s i g n . The s t a b i l i t y of the dipole bands, leads to a more r a p i d l y increasing increased flow stress with s t r a i n . When a d i s l o c a t i o n moves at a low temperature on the basal plane of an a l l o y c r y s t a l , containing solute i n excess of 0.025 a t . % Zn^ the long range f r i c t i o n stress i s overcome (as at higher temperatures) and also the f o r e s t d i s l o c a t i o n s are i n t e r s e c t e d . must also be surmounted. In a d d i t i o n a short range obstacle The f r i c t i o n stress a r i s i n g due to t h i s short 169 range solute d i s l o c a t i o n i n t e r a c t i o n increases with decreasing temperature. Therefore, the work hardening rate 0 A should increase w i t h decreasing temperature as the solute content i s increased. Qualitatively this i s i n agreement with experiment as can be seen from f i g . (54). The parabolic nature of the concentration dependence of 9^ a r i s e s probably due to a C r e l a t i o n s h i p between the increase i n f o r e s t density with solute content at low concentration and that between the f r i c t i o n s t r e s s as the Zn content i s increased. 2.4.4.3. The Extent of Easy.Glide: The face centred cubic metals Cu, N i and A l show a continuous decrease i n Y J J with increasing t e m p e r a t u r e . On the other hand the hexagonal metals C d ^ ^ and Z n ^ ^ 2 4 e x h i b i t an increase i n the extent of easy g l i d e with i n c r e a s i n g temperature. The present r e s u l t s on magnesium i n d i c a t e an increase i n Y with temperature upto 295°K. B Above.this temperature, however, easy g l i d e i s followed by a p a r a b o l i c hardening, which masks stage B. Hence the decrease i n Y-g beyond 295°K as shown i n f i g . (56) should be accepted with r e s e r v a t i o n . The reason f o r the termination of easy g l i d e and the onset of the r a p i d hardening i s not the same i n a l l m a t e r i a l s . For example s l i p on the secondary systems i s known to be responsible f o r the onset of stage I I i n the fee metals and a l l o y s . In hep Zn and Cd, the condensation of vacancies i n t o s e s s i l e loops i s considered responsible f o r the r a p i d uhardening A • d37) 170 No w e l l established theory, however, e x i s t s f o r the case of (29) magnesium. I t has been suggested by Hirsch that the density of d i p o l e bands becomes so large at the end of stage A that they trap the d i s l o c a t i o n s formed. The s t r e s s concentration,therefore,increases leading to twins being nucleated, which subsequently slip lines. new act as b a r r i e r s to the new The p a i r i n g of the newly formed d i s l o c a t i o n s i s l a r g e l y hindered because of the twins. s t r e s s concentration. These d i s l o c a t i o n s p i l e up, leading to a The s t r e s s concentration i s r e l i e v e d by s l i p on the basal plane with non-primary Burgers v e c t o r s , p r i s m a t i c s l i p and f u r t h e r twinning. The observed decrease i n Y-g with a l l o y i n g can be r a t i o n a l i z e d i n terms of an increase i n 9 w i t h a l l o y i n g . Since the work hardening r a t e increases with a l l o y i n g , the s t r e s s to nucleate twins i s reached e a r l i e r i n the a l l o y than i n Mg, provided the shear s t r e s s f o r twin formation remains unaffected by s o l u t e . However, even i f the s t r e s s . required f o r twinning increases with solute content, Yg can still decrease with a l l o y i n g provided the increase i n 9-^ i s s u f f i c i e n t l y large so as to a t t a i n the s t r e s s l e v e l necessary l e s s than Yg to nucleate twins at a s t r a i n i n Mg. The increase i n Yg with temperature i n these a l l o y s can perhaps be r a t i o n a l i z e d i n a s i m i l a r manner considering the high temperature dependence of 9. and a low temperature s e n s i t i v i t y of the twinning s t r e s s . 171 2.4.4.4. Work Hardening i n Stage B: The work hardening rate i n stage I I of fee metals i s -3 t y p i c a l l y 9.^ = 3 x 10 G at room temperature. The work hardening rate 9 f o r Mg at room temperature i s -4 3.7 x 10 G, which i s approximately an order of magnitude lower than i n fee metals. The low work hardening rate i s thought to be due to the high stress necessary to nucleate twins, which can subsequently act as (29) b a r r i e r s to the formation of s l i p l i n e s The v a r i a t i o n of 9 „ with temperature has never been explained a i n the past. However, on the basis of a twin model, such a decrease i s to be expected. Stress r e l i e f at the dipole bands i s attained not only through twinning, but also through slip on the basal plane with non-primary Burgers vectors and by prismatic s l i p . the Between room temperature and 423°K CRSS f o r basal s l i p remains unchanged^therefore^excess s t r e s s r e l i e f at higher temperature i s not expected to be due to s l i p on basal plane with non-primary Burgers vectors. the However, i n t h i s temperature range CRSS f o r prismatic s l i p decreases rather r a p i d l y . Thus the extent of s t r e s s concentration becomes smaller due to the^operation of prism slip. This leads to a slower process of twin nucleation and hence the work hardening rate decreases. The E f f e c t of Solute on 9 : C The CRSS f o r basal s l i p increases with solute content i n a l l o y s containing solute i n excess of 0.025 a t . % Zn, whereas the operation of prismatic s l i p becomes more d i f f i c u l t i n the lower a l l o y s . Both these processes would lead to a higher s t r e s s concentration at the d i p o l e bands 172 than i n Mg. The s t r e s s concentration w i l l r e s u l t i n a l a r g e r number of twins being nucleated and thus the work hardening rate w i l l be higher. 2.4.4.5. The Stage 'C' of Deformation: The stage I I I of work hardening i n face centred cubic s o l i d solutions i s associated w i t h cross s l i p and therefore to c a l c u l a t e the stacking f a u l t energy of the m a t e r i a l ^j_ be.used III (141-142) T T c a n C a n The o r i g i n of stage C i n magnesium, however, i s not w e l l understood. C r y s t a l s deformed i n t o stage C do not show cross s l i p markings when examined under o p t i c a l microscope. The s l i p l i n e s appear i n coarse c l u s t e r s . The exsistence of f i n e cross s l i p markings, however, cannot be ruled out. Replica studies of the s l i p l i n e s may resolve t h i s problem. A d i s c u s s i o n of the e f f e c t of solute on x^, . i n Mg w i l l be premature, u n t i l the reason f o r the dynamic recovery i s e s t a b l i s h e d . 173 2.4,5. The E f f e c t of Solute on the Ease of Prismatic S l i p : 2.4.5.1. Introduction and Objectives: The r o l e of prismatic s l i p i n the deformation of the p o l y c r y s t a l l i n e aggregates of Mg and i t s a l l o y s has been pointed out e a r l i e r i n t h i s thesis. However, the study of s i n g l e c r y s t a l s oriented f o r prismatic s l i p , which should c o n s t i t u t e the ground work f o r the understanding of the macroscopic deformation c h a r a c t e r i s t i c s of Mg p o l y e r y s t a l s has not a t t r a c t e d as much a t t e n t i o n as i t deserved. A rather comprehensive literature i s a v a i l a b l e on the prismatic s l i p of Mg-Li a l l o y s , which e x h i b i t the so c a l l e d " s o l i d s o l u t i o n softening e f f e c t " ^ 16,73)^ ^ has been the 4 conclusion of Dorn and h i s coworkers that only those elements which decrease the c/a r a t i o of magnesium would be e f f e c t i v e i n decreasing the CRSS f o r prismatic s l i p when dissolved i n magnesium. Incidentally,the elements which decrease the a x i a l r a t i o of Mg belong to group I of the periodic table. In contrast to t h i s conclusion the present r e s u l t s on the deformation of the p o l y c r y s t a l l i n e s o l i d s o l u t i o n s of Mg containing solutes which belong to group I I , I I I and IV of the p e r i o d i c table (and hence increase the c/a r a t i o of Mg), suggest that i r r e s p e c t i v e of the type of solute added the CRSS f o r prismatic s l i p decreases with increasing amounts of solute beyond a c r i t i c a l concentration C^,. Thus one of the objectives of the i n v e s t i g a t i o n of prismatic s l i p i n s i n g l e c r y s t a l s was to evaluate the s i g n i f i c a n c e of c/a r a t i o (and hence valency) on the ease of p r i s m a t i c s l i p . The second.objective was to examine the e f f e c t s of a l l o y i n g at very low concentrations, where a rapid rate of s o l u t i o n hardening i s observed i n the p o l y c r y s t a l l i n e a l l o y s . 174 For t h i s purpose the solute chosen, was Zn. The choice of Zn was mainly due to the reason that the p o i y e r y s t a l l i n e a l l o y s of the Mg-Zn system e x h i b i t a l l the three stages of s o l u t i o n hardening d i s t i n c t l y . Also the c/a r a t i o of Mg does not decrease by the a d d i t i o n of Zn. Some a l l o y s containing A l as solute were also i n v e s t i g a t e d . Aluminum belongs to a higher valency group ( I I I ) and increases the c/a r a t i o of Mg. 2.4.5.2. 2.4.5.2.1. Experimental Results: The S t r e s s - S t r a i n Curves: The resolved shear s t r e s s vs shear s t r a i n curves of a representative set of Mg-Zn a l l o y s are shown as a f u n c t i o n of. temperature for various compositions i n f i g s . (85-88). I t i s apparent that the d u c t i l i t y i s considerably lower i n prismatic s l i p than i n basal s l i p . For example pure magnesium undergoes f r a c t u r e at a shear s t r a i n of 580% i n basal s l i p whereas f a i l u r e occurs at a s t r a i n l e s s than 2% i n prism slip. In prismatic s l i p , the shear stress increases i n a p a r a b o l i c manner with s t r a i n at low s t r a i n l e v e l s followed by a l i n e a r hardening at higher strains. In some cases a w e l l defined t h i r d stage with a decreasing work hardening rate followed the l i n e a r hardening. In order to make the e f f e c t of the solute apparent, the s t r e s s s t r a i n -curves of the a l l o y s deformed at f i x e d temperatures are placed together and are shown i n f i g s . (89-90). I t i s observed that at lower temperatures (78-200°K) the s t r e s s - s t r a i n curves of a l l the a l l o y s i n g l e c r y s t a l s f a l l below that of magnesium. But at temperatures above.200°K small additions of solute (up to 0.019 a t . % Zn) l i f t the curves above that of pure magnesium. On increasing the a l l o y i n g content beyond 0.02 a t . % , however, the s t r e s s - s t r a i n curves f a l l below those f o r the lower a l l o y s . 175 0 0.04 0.08 0.12 Shear s t r a i n F i g . 85. Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg s i n g l e c r y s t a l s oriented f o r prismatic s l i p . 176 0 0.04 0.08 0.12 Shear s t r a i n F i g . 86. Resolved shear s t r e s s vs. shear s t r a i n f o r Mg + 0.019 at. % Zn a l l o y s i n g l e c r y s t a l s oriented f o r p r i s m a t i c s l i p . F i g . 87. Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg +0.258 a t . % Zn a l l o y s i n g l e c r y s t a l s oriented f o r p r i s m a t i c s l i p . F i g . 88. Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg + 0.45 a t . % Zn a l l o y s i n g l e c r y s t a l s oriented f o r prismatic s l i p . 179 2 I 0 • I 0.2 I I 0.3 l _ L 0.6 Shear s t r a i n . F i g . 89. Resolved shear s t r e s s vs. shear s t r a i n curves f o r Mg-Zn s i n g l e c r y s t a l s deformed at 423 °K i n prism s l i p orientation. I 0 I 0.04 I 0,08 L_ 0.12 I 0,16 Shear s t r a i n F i g . 90. Resolved,shear stress, vs. shear s t r a i n curves f o r Mg-Zn s i n g l e c r y s t a l s deformed at 78°K i n prism s l i p o r i e n t a t i o n . 181 An i n t e r e s t i n g feature of the c r y s t a l s tested at 423°K i s the large amount of s t r a i n associated with work-softening. S i m i l a r work softening has been observed above room temperature i n the compression of s i n g l e c r y s t a l s of Mg oriented such as to suppress basal s l i p ^ " ^ . Backofen et a l {1012} have a t t r i b u t e d the softening to the onset of {1011} double twinning. However, i n the present t e n s i l e t e s t s at 423°K the c r y s t a l s showed necking, therefore, i t cannot be concluded whether or not twinning i s responsible f o r the loss i n work hardening r a t e . 2.4.5.2.2. Ductility: The shear s t r a i n to f r a c t u r e i s p l o t t e d against the t e s t i n g temperature i n f i g . (91) f o r a l l the Mg-Zn a l l o y s tested i n o r i e n t a t i o n s favourable to prismatic s l i p . I t i s observed that d u c t i l i t y decreases w i t h increasing temperature i n the range 78°-250°K and increases again at higher temperatures. i n pure Mg. A s i m i l a r trend has been observed by Reed-Hill and R o b e r t s o n ^ In s p i t e of the l^rge s c a t t e r i n data i t can be seen that d u c t i l i t y decreases by small additions of solute at temperatures above 250°K, followed by a rapid increase at higher solute concentrations. 2.4.5.2.3. The CRSS f o r Prismatic S l i p : The f i r s t d e v i a t i o n from l i n e a r i t y was once again used as the yield criterion. The temperature and a l l o y dependence of the CRSS for prismatic s l i p i n Mg-Zn a l l o y s i s shown i n f i g . (92). The temperature dependence of the CRSS may be divided roughly i n t o three regions. A r e l a t i v e l y thermal i n s e n s i t i v e region e x i s t s at temperatures between 78°K and 170°K, followed by a strongly temperature dependent stage. The temperature dependent stage merges gradually i n t o a F i g , 91. Shear s t r a i n to f r a c t u r e vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s oriented for prismatic s l i p . 183 region of l e s s e r temperature s e n s i t i v i t y at temperatures i n the v i c i n i t y of 400 K. The numerical values of CRSS f o r Mg obtained i n the present <i (143) work are i n agreement with the values reported i n the l i t e r a t u r e 2.4.5.2.4. The CRSS of Mg-Zn A l l o y s : The composition dependence of CRSS f o r various temperatures i s shown i n f i g . (93). From f i g s . (92 and 93) i t i s c l e a r that at low temperatures the CRSS of magnesium remains unaffected by small additions of solute followed by a r a p i d decrease at higher concentrations. For example at 78°K the CRSS of Mg as w e l l as an a l l o y containing 0.019 a t . % 2 2 Zn a l l o y i s 9.95 kg/mm , whereas that f o r 0.45 a t . % Zn a l l o y i s 6.7 kg/mm . At higher temperatures, on the other hand, the CRSS increases by small additions of Zn, followed by a decrease at higher concentrations. Above approximately 350 K the CRSS of a l l the a l l o y s are higher than that of , Mg. The r e s u l t s of the Mg-Al a l l o y s are shown i n f i g . (94). Higher a l l o y s could not be i n v e s t i g a t e d because of the d i f f i c u l t y encountered i n growing s i n g l e c r y s t a l s containing more than 0.2% A l . composition 1 The trend i n the dependence of CRSS nevertheless i s the same i n both Mg-Al and Mg-Zn a l l o y s . I t i s important to note at t h i s juncture that the i n i t i a l increase i n CRSS f o r prismatic s l i p followed by a decrease at higher concentrations accounts adequately f o r the multistage s o l u t i o n hardening observed i n the p o l y c r y s t a l l i n e m a t e r i a l . S o l i d s o l u t i o n softening has previously been observed i n Mg-Li (73) alloys . However, the study of s i n g l e c r y s t a l s oriented f o r p r i s m a t i c s l i p was confined to concentrations.in excess of 6 a t . % L i . The existence 200 TEMPERATURE °K 300 400 F i g . 92, CRSS f o r prismatic s l i p vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s , ATOMIC % F i g . 93. Zn CRSS f o r prismatic s l i p vs. Zn concentration. F i g . 94. CRSS f o r prismatic s l i p vs. temperature f o r Mg-Al s i n g l e c r y s t a l s . 187 of an i n i t i a l rapid s o l u t i o n strengthening rate i n the p o l y c r y s t a l s of t h i s system, however, suggests an increasing value of CRSS f o r p r i s m a t i c s l i p i n these a l l o y s at low L i concentrations at room temperature. 2.4.5.2.5. The E f f e c t of Solute on the Flow Stress: The process of y i e l d i n g i n s i n g l e c r y s t a l s of Mg oriented f o r prismatic s l i p i s rather gradual. Therefore, the i n t e r p r e t a t i o n s based on the measurements of CRSS, which i s taken as the f i r s t d e v i a t i o n from l i n e a r i t y can be erroneous, e s p e c i a l l y when the d i f f e r e n c e s i n the values of CRSS being examined are small (as i s the case with the d i l u t e a l l o y s ) . In order to avoid t h i s d i f f i c u l t y the flow s t r e s s values at various s t r a i n l e v e l s have been p l o t t e d against solute concentrations for a representative set of temperatures as shown i n f i g s . (95 and 96). F i g . (95) has been constructed f o r c r y s t a l s deformed at 78°K. I t i s observed that the CRSS at low solute concentrations i s much the same as that of Mg, but the flow stresses at higher s t r a i n s decrease r a p i d l y with Zn concentration. At the higher concentrations of solute on the other hand, the flow s t r e s s decreases l e s s r a p i d l y than does the CRSS. The flow s t r e s s concentration r e l a t i o n s h i p at 423°K ( f i g . 96) shows that the shape of the flow curves remains s i m i l a r to that i n the CRSS-concentration plot. The CRSS increases with solute content i n the low a l l o y s followed by a decrease at higher concentrations. These r e s u l t s tend to confirm the v a l i d i t y of the i n t e r p r e t a t i o n s based on the measurements of CRSS. M g - Z n Single Crystals PRISMATIC SLIP 6L 0 1 01 1 — _ 1 02 03 ATOMIC % Zn 1 04 L_ 05 Ftg. 95. Flow s t r e s s f o r prismatic s l i p v s . concentration f o r Mg-Zn s i n g l e c r y s t a l s tested at 78°K. F i g . 96. Flow stress vs. concentration f o r Mg-Zn s i n g l e c r y s t a l s tested at 423°K, 189 2.4,5.3. Discussions: An understanding of the d i s l o c a t i o n mechanisms f o r s l i p i n the pure metal i s often h e l p f u l i n analyzing the nature of the s o l u t e d i s l o c a t i o n i n t e r a c t i o n . With t h i s view i n mind the d i s l o c a t i o n mechanisms responsible f o r prismatic s l i p i n magnesium w i l l be discussed followed by a discussion of the e f f e c t of solute. 2.4.5.3.1. The D i s l o c a t i o n Mechanism f o r Prismatic S l i p : Attempts have been made e a r l i e r to e x p l a i n the d i s l o c a t i o n mechanisms f o r prismatic s l i p i n pure m a g n e s i u m ^ 2 4 . I t has been the conclusion of Ward-Flynn, Mote and D o r n ^ " ^ that the rate c o n t r o l l i n g 4 mechanism i n prismatic s l i p above 450°K i s the thermally a c t i v a t e d cross s l i p p i n g of screw d i s l o c a t i o n s extended i n the basal plane as proposed by Friedel ( 1 0 4 ) . The low temperature rate c o n t r o l l i n g mechanism has never been s y s t e m a t i c a l l y investigated i n the pure metal. (73) of the T - T curve^Dorn suggests However, from the trend that P e i e r l s mechanism must be c o n t r o l l i n g below room temperature. In the present work a l i m i t e d number of s t r a i n rate change tests were conducted to t e s t Dorns p r e d i c t i o n of the mechanism of low temperature prismatic s l i p . The a c t i v a t i o n volumes were measured by changing the s t r a i n rate by a f a c t o r of ten. However, since Mg shows rather l i m i t e d d u c t i l i t y at low temperatures i t was d i f f i c u l t to conduct d i f f e r e n t i a l s t r a i n rate t e s t s . This d i f f i c u l t y was overcome by deforming c r y s t a l s of i d e n t i c a l o r i e n t a t i o n s to f r a c t u r e using two d i f f e r e n t . s t r a i n r a t e s . * The d i f f e r e n c e i n y i e l d stress was then used f o r c a l c u l a t i n g V . 190 Such a procedure has been used i n the past on Mg-Li a l l o y s i n g l e c r y s t a l s (73 The r e s u l t s of such t e s t s on Mg, as w e l l as a s e r i e s of Mg-Zn a l l o y s are shown i n f i g . (97). I t i s seen that i n Mg as w e l l as i t s a l l o y s the 3 a c t i v a t i o n volumes, remain below 80 b at temperatures up to 295°K. This i s consistent with the idea of P e i e r l s mechanism as the r a t e c o n t r o l l i n g step. I t i s important to point out at t h i s juncture that the a c t i v a t i o n 3 volume associated with the c r o s s . s l i p process i s > 100 b . In the a l l o y 3 containing 0.006 a t . % Zn, the a c t i v a t i o n volume was found to be 205 b at room temperature which i s higher than that associated w i t h P e i e r l s mechanism. No explanation, however, could be afforded f o r t h i s exception. A q u a n t i t a t i v e v e r i f i c a t i o n of the P e i e r l s mechanism cannot be made here since magnesium does not show a d i s t i n c t t r a n s i t i o n temperature from the the rmally a c t i v a t e d to an athermal mechanism. : I t i s interesting to note that i n the case of magnesium an athermal region does not e x i s t i . e . The F r i e d e l cross s l i p mechanism, which i s a thermally a c t i v a t e d process, takes over the low temperature P e i e r l s mechanism, which again i s thermally a c t i v a t e d . 2.4.5.3.2. The E f f e c t of Solute: The e f f e c t of solute on the strength of c r y s t a l l i n e s o l i d s i n general i s best understood i f the c o n t r i b u t i o n of the solute to the athermal and the thermally a c t i v a t e d components of the flow s t r e s s are considered separately. The experimental r e s u l t s on s o l i d s o l u t i o n s a v a i l a b l e , t o date i n d i c a t e that the athermal flow s t r e s s never decreases with the a d d i t i o n * of s o l u t e , although T increases or decreases depending on the r a t e F i g . 97. A c t i v a t i o n volume at y i e l d vs. temperature f o r Mg-Zn s i n g l e c r y s t a l s deformed i n prism s l i p o r i e n t a t i o n . 192 c o n t r o l l i n g mechanism operative i n the a l l o y . From the r e s u l t s of (73) the experiments by Ahmadieh and Dorn on Mg-Li.alloys i t i s seen that at s u f f i c i e n t l y high concentrations of l i t h i u m the athermal s t r e s s l e v e l becomes apparent and that i t increases with increasing solute content, as would be expected of the athermal s t r e s s i n r e l a t i o n to s o l u t e . The appearance of the athermal s t r e s s l e v e l deserves a c r i t i c a l ; examination. For the time being the experimental observation that the P e i e r l s s t r e s s decreases with increasing L i content w i l l be taken f o r granted. Since * the athermal s t r e s s increases and the T term decreases with i n c r e a s i n g lithium addition, T (from P e i e r l s to athermal) i s expected to decrease c also with l i t h i u m concentration as i s observed ( f i g . 98). The consequence of such a decrease i n T i s that the thermal.energy a v a i l a b l e at T , i s c c not high enough f o r cross s l i p to occur, therefore, the d i s l o c a t i o n s have to move under the long range s t r e s s f i e l d J.4.5.3.3. (athermal). The Results of the Present Work: The r e s u l t s of the Mg-Zn a l l o y s can be explained i n terms of * an increasing x and a decreasing x . Note that i n the case of Mg-Zh * a l l o y s the increase i n x_ and the decrease i n x are not s u f f i c i e n t n to make the athermal s t r e s s l e v e l appear i n the x -T curve. * temperatures, where the x x term i s dominant over At lower x„, the increase i n i s of l i t t l e importance and therefore the CRSS decreases continuously with Zn concentration. At higher temperatures, however, a peak i n the CRSS-concentration curve appears. Fig. This can be explained b e t t e r w i t h the help of a sketch., (99) i l l u s t r a t e s the s i t u a t i o n schematically. sake of argument that x We w i l l assume f o r the i n the a l l o y s a r i s e s due to a f r i c t i o n s t r e s s 193 0 100 200 300 - F i g . 98. 400 500 600 700 T, °K CRSS f o r prismatic s l i p vs. temperature f o r Mg-Li a l l o y s i n g l e c r y s t a l s (after Ahmadieh and Dorn< >). 73 194 F i g . 99. Schematic representation of the e f f e c t of solute on the various components of flow s t r e s s i n prismatic slip. 195 mechanism i n v o l v i n g s i z e and modulus e f f e c t . dependence of x . This would lead to a C This i s shown,as curve (1). Since x changes.only s l i g h t l y (through a change i n shear modulus) with temperature curve (1) should be v a l i d to a f i r s t approximation at a l l temperatures.. On the * contrary the v a r i a t i o n of dependent f u n c t i o n . on x x with concentration i s a strongly temperature Curves(2) and (3) represent the e f f e c t of solute at a low temperature (T<< Tc) and at a high; temperature (T £S Tc) respectively. The combination of (1) and ( 2 ) and (1) and (3) are shown as curves (4) and (5). Curves (4) and (5) are q u a l i t a t i v e l y i n good agreement with the observed concentration dependence of CRSS at low and high temperatures r e s p e c t i v e l y . A q u a n t i t a t i v e v a r i f i c a t i o n of such a p r o p o s i t i o n , however, i s not possible at the present, because x cannot be separated from x^ i n the absence of a w e l l defined T . The anomalous CRSS-concentration r e l a t i o n s h i p s i n bcc Ta-base . c (144) a l l o y s have a l s o been explained by M i t c h e l l and Raffo manner. 2.4.5.3.4. The O r i g i n of x^ and i n a similar x : In the above explanation there has been no mention of the * o r i g i n of T„ and x and t h e i r v a r i a t i o n with solute concentration. This w i l l be done.in the f o l l o w i n g pages. 2.4.5.3.4.1. The Athermal Stress: The observed athermal s t r e s s .in the Mg-Li alloys.was a t t r i b u t e d (73) by Dorn to the short range ordering in.these a l l o y s . However, a determination of the short range order parameter by Averbach and Herbstein^"^"^ i n these a l l o y s i n d i c a t e s that short range ordering cannot account f o r 196 the observed athermal s t r e s s - A f r i c t i o n s t r e s s mechanism s i m i l a r to the one i n basal s l i p of Mg-Zn a l l o y s could be c o n t r o l l i n g , however, such a guess would, be premature i n the absence of s u f f i c i e n t experimental, data on prismatic s l i p . * 2.4.5.3.4.2. The V a r i a t i o n of x With A l l o y i n g : From the r e s u l t s of the p o l y c r y s t a l l i n e Mg-Li a l l o y s Hauser, (14) Landon and Dorn. proposed that the CRSS f o r p r i s m a t i c s l i p i n these a l l o y s decreases with increasing solute and that t h i s decrease i s a r e s u l t of the decreasing a x i a l r a t i o (c/a) with a l l o y i n g . Subsequently the rate c o n t r o l l i n g mechanism was i d e n t i f i e d i n s i n g l e c r y s t a l s oriented f o r (73) prismatic s l i p by Ahmadieh, M i t c h e l l and Dorn stress. to be one of P e i e r l s However, no explanation was given as to why decreases with l i t h i u m a l l o y i n g . the P e i e r l s s t r e s s Recently Dorn,has modified h i s explanation f u r t h e r , t o e x p l a i n the observed lowering ,of C R S S . This i s the so c a l l e d "Pseudo-Peierls mechanism", which i s an intermediate s i t u a t i o n between P e i e r l s s t r e s s and the F r i e d e l cross s l i p mechanisms. 7 Dorn argues that F r i e d e l s derivations,do not hold good f o r cases where the stacking f a u l t energy i s so high that the distance between the p a r t i a l s i s 0.5 - 2b as i s the case.with Mg. In such s i t u a t i o n s the stacking f a u l t energy must be taken i n t o account. These considerations led Dorn to the conclusion that the stacking f a u l t energy of magnesium increases with the a d d i t i o n of solute I t i s not very c l e a r from h i s theory as to whether i t i s meaningful to t a l k about a higher stacking f a u l t energy when the distance between the p a r t i a l s i s already of the order of 0.5 - 2b, e s p e c i a l l y when the present knowledge of the interatomic forces i s so l i m i t e d . Even i f the 197 theory,is taken f o r granted, c e r t a i n other i n c o n s i s t e n c i e s are encountered. The increase i n the stacking f a u l t energy with l i t h i u m a l l o y i n g i s considered by Dorn to be a r e s u l t of the decreasing e l e c t r o n to atom r a t i o (e/a). Therefore, i n the case of Zn solute where e/a remains constant and A l where e/a increases, there should not be lowering of CRSS with s o l u t e . The present r e s u l t s do not conform to these conclusions. Also i f we take the c/a to be the c r i t e r i o n as (14) proposed e a r l i e r by Hauser and Dorn. was then also the r e s u l t s of Mg-Zn a l l o y s i n which the c/a r a t i o remains constant and the Mg-Al a l l o y s where c/a increases cannot be accounted f o r . L a t e l y , however, i t has been suggested by M i t c h e l l and (144) Raffo that the nucleation of a p a i r of kinks becomes easier i n the presence.of small amounts of (up to 4% Re i n Ta) solute thus.lowering Peierls stress. the The e f f e c t of solute can a l t e r n a t i v e l y be v i s u a l i z e d as. being perturbation of the p e r i o d i c i t y of the P e i e r l s h i l l , thus lowering the e f f e c t i v e value of the height of the b a r r i e r . The acceptance or r e j e c t i o n of t h i s idea w i l l probably depend on whether a l l solutes * decrease T at a l l concentrations of solute or not. S u f f i c i e n t experimental data are not a v a i l a b l e at the present to take such a d e c i s i o n . I t should be borne i n mind here that even i f the CRSS data are a v a i l a b l e , there must be a method of obtaining T from the experimentally measured CRSS. From the r e s u l t s on Mg-solid s o l u t i o n s oriented f o r prismatic s l i p i t appears that the decrease i n P e i e r l s s t r e s s with increasing solute concentration i s not n e c e s s a r i l y associated with a decreasing with the valency of the s o l u t e . c/a r a t i o or The r e s u l t s of the p o i y e r y s t a l l i n e s o l i d s o l u t i o n s i n the present work i n f a c t suggest t h i s to be a general s o l u t i o n e f f e c t i n Mg. 198 3» 1) Summary and Conclusions: I n binary a l l o y p o l y e r y s t a l s of Mg containing Zn,. A l , Pb, Cd or In as s o l u t e , s o l u t i o n hardening occurs i n a two or three stage fashion. I n stage I at the lowest solute concentrations, the hardening i s very high and,linear. Beyond a t r a n s i t i o n concentration, the hardening i s . v e r y much.reduced. 2) A t h i r d stage characterized by a " s o l u t i o n softening" e f f e c t was observed i n the case of Zn and A l solutes. 3) The strengthening observed i s i n the order l i s t e d , and t h i s i s also the order of s i z e mismatch with Zn being the greatest. ductility 4) The decreases f o r solute additions upto C^ and then increases. The t r a n s i t i o n concentration i s a f u n c t i o n of the s i z e d i f f e r e n c e between.the solvent and the solute^being smaller f o r l a r g e r A . r 5) The predominant f a c t o r during stage.I hardening i s the increase i n the.CRSS f o r prismatic s l i p . During stage I I , the CRSS f o r prismatic s l i p decreases with increasing solute a d d i t i o n s . 6) The d i s c o n t i n u i t i e s observed i n the d u c t i l i t y temperature p l o t of the Mg-Al a l l o y s a r i s e due to a combined e f f e c t of r e c r y s t a l l i z a t i o n and g r a i n boundary c a v i t a t i o n , the former being r e l a t e d to the CRSS f o r prismatic s l i p i n the alloy.. 7) The experiments on the ternary Mg-In-Zn a l l o y s suggest that stage I hardening r e s u l t s from a.type of solute atom d i s l o c a t i o n i n t e r a c t i o n , with preference f o r prism plane d i s l o c a t i o n s and large s i z e d i f f e r e n c e solutes to be involved. 199 8) In s i n g l e c r y s t a l s of magnesium-Zn a l l o y s oriented f o r basal s l i p , the athermal component of the CRSS i s independent of Zn concentration upto h 0.025 a t . % beyond which a C 9) Transmission dependence i s obeyed. e l e c t r o n microscopy of t h i n f o i l s of Mg-Al c r y s t a l s shows that the grown i n basal d i s l o c a t i o n density increases i n a parabolic manner with increasing solute content. account f o r the observed v a r i a t i o n of 10) This increase, however, cannot T with solute concentration. The athermal component of the CRSS i n M g s o l i d s o l u t i o n s a r i s e s due to an increase i n the f r i c t i o n s t r e s s with i n c r e a s i n g solute concentration. 11) An etch p i t technique f o r r e v e a l i n g the f o r e s t d i s l o c a t i o n s i n M g has been developed and used to evaluate the increase i n the f o r e s t density with solute concentration. the increase i s high and l i n e a r upto 0.04 The r e s u l t s show that a t . % Zn, beyond which the change i s rather small. 12) The low temperature s o l u t i o n hardening occurs i n two stages, h the two stages being l i n e a r functions of C having d i f f e r e n t slopes, with the t r a n s i t i o n at 0.025 a t . % Zn. 13) Stage I hardening a r i s e s due to an increase i n the f o r e s t d i s l o c a t i o n density with solute concentration whereas i n stage I I a change i n the thermally a c t i v a t e d mechanism occurs from i n t e r s e c t i o n to the s i n g l e solute atom d i s l o c a t i o n pinning mechanism. 14) The e f f e c t s of Zn on the work hardening parameters of Mg s i n g l e c r y s t a l s i n basal s l i p are to increase the stage A and stage B slopes and to decrease the extent of easy g l i d e . 200 15) Tensile t e s t s conducted on oriented s i n g l e c r y s t a l s to suppress basal s l i p and {1012} twinning and to induce prismatic s l i p show that f o r Zn and A l solutes at low temperatures the CRSS f o r prismatic s l i p decreases with increasing solute a d d i t i o n . At high temperatures , however,the CRSS f i r s t increases with solute concentration followed by a decrease. 16) The low temperature rate c o n t r o l l i n g mechanism i n prismatic s l i p i s the overcoming of the P e i e r l s stress b a r r i e r . 17) The observed concentration dependence of the CRSS i n prismatic s l i p can be accounted f o r i n terms of a decreasing P e i e r l s s t r e s s with increasing solute concentration. 18) The decrease i n the P e i e r l s s t r e s s of magnesium with increasing solute a d d i t i o n i s not n e c e s s a r i l y associated with e i t h e r a reduction of the a x i a l r a t i o or the r e l a t i v e valency of the s o l u t e . 201 4. SUGGESTIONS FOR FUTURE WORK: The present study can lead to several l i n e s of i n v e s t i g a t i o n . The ones that deserve immediate a t t e n t i o n include: 1. An extension of the study of the e f f e c t of solute on the ease of prismatic s l i p to include other solute elements and t e s t i n g temperatures down to 4.2°K, i n order to determine the nature of the athermal and the thermally activated components of the flow s t r e s s . 2. A thorough study of the d i l u t e ternary a l l o y s i n g l e c r y s t a l s i n order to gather more information on the p r e f e r e n t i a l nature of s o l u t e d i s l o c a t i o n i n t e r a c t i o n on the prism planes and to determine the s i g n i f i c a n c e of C . T 3. An i n v e s t i g a t i o n of the dependence of the f o r e s t d i s l o c a t i o n . Spacing on p r e - s t r a i n , using the etch p i t t i n g technique developed i n the present work can lead to a b e t t e r understanding of the work hardening behaviour,of magnesium. 4. A systematic study of the y i e l d points and the serrated y i e l d i n g phenomenon i n the Mg-Zn a l l o y s . 5. An i n v e s t i g a t i o n of s o l u t i o n strengthening i n . b a s a l s l i p at higher solute concentrations and lower.temperatures (up to 4.2°K) i n order to supplement the present data and to determine the nature of the solute dislocation interaction. 6. An experimental study of the e f f e c t of a v a r i e t y of solutes on the work hardening parameters of Mg coupled with a thorough s l i p l i n e study and transmission e l e c t r o n microscopy of t h i n f o i l s to determine the m i c r o s t r u c t u r a l aspects.of work-hardening i n the a l l o y s . 202 APPENDIX - A DETERMINATION OF SOLUTE CONCENTRATION IN THE ALLOYS: Much of the present work has been c a r r i e d out on materials containing small amounts of a l l o y i n g elements. Atomic absorption spectrophotometry has been used to determine the concentration of solute. The a t t r i b u t e s which made atomic absorption a t t r a c t i v e are the r e l a t i v e l y few a n a l y t i c a l interferences and the high p r e c i s i o n of the technique. PRINCIPLE OF THE METHOD: In p r i n c i p l e the sample i s d i s s o c i a t e d from i t s chemical bonds ( i n solution) and placed i n t o an unexcited, unionized ground s t a t e . I t i s then capable of absorbing r a d i a t i o n at d i s c r e t e frequencies of narrow band width. D i s s o c i a t i o n i s achieved by burning the sample i n a flame; An e f f e c t i v e burner f o r atomic absorption i s designed with a "premix" system, i n which f u e l , oxidant and the sample are combined i n a mixing chamber before being burned. for Cd, Zn and Pb. A combination of a i r and acetylene was used In the case of A l s o l u t e , however, a s p e c i a l n i t r o u s - oxide acetylene flame was used, since the a i r - a c e t y l e n e mixture does not give a flame hot enough to d i s s o c i a t e aluminum compounds (149) The r a d i a t i o n to be absorbed by the sample i s provided by a hollow cathode lamp, which emits only the spectrum of the desired element, together with that of the f i l l e r gas. In order to screen out the undesired emission, the r a d i a t i o n i s passed through a f i l t e r or monochromator which i s tuned to pass the l i n e of i n t e r e s t but screens out others. 203 INTERFERENCE: For a given design of the burner, o p t i c a l system and the / fuel-oxidant combination, the two most serious e r r o r s i n making a q u a n t i t a t i v e estimate of elements by atomic absorption are brought about by the presence of another i n t e r f e r i n g element i n s o l u t i o n and due to a d i f f e r e n c e i n the v i s c o s i t y of the s o l u t i o n s under examination. The v i s c o s i t y e f f e c t otherwise known as the Bulk or Matrix e f f e c t a r i s e s due to the v a r i a t i o n i n the amount of dissolved m a t e r i a l i n solution. In order to minimize the error due to v i s c o s i t y e f f e c t , the _ concentration of the anion (NO^ i n the present case) and the Mg | | ion were kept constant i n a l l the s o l u t i o n s of each set of unknowns and the corresponding standards. Since the a l l o y s under examination contained only small amounts of a l l o y i n g elements, the change i n the v i s c o s i t y a r i s i n g due to the d i f f e r e n c e i n the amount of the s o l u t e element present i n the samples was considered n e g l i g i b l e . Another type of i n t e r f e r e n c e known as the chemical i n t e r f e r e n c e a r i s e s when the presence of a second i o n i n s o l u t i o n e i t h e r depresses or enhances absorption due to the i o n under examination. E a r l i e r work by B e l l ^ " ' ^ has i n d i c a t e d - t h a t the presence of magnesium does not i n t e r f e r e i n the a n a l y s i s of Zn and Cd. In the presence of aluminum, however, the analysis of Mg is difficult. Although i n the present case A l »as analysed i n Mg matrix, , ++ i t was considered safe to keep the Mg very nearly constant. concentration i n the sample Such matching techniques have been used by e a r l i e r workers i n order to overcome chemical interference. 204 PROCEDURE: Preweighed samples were dissolved in.10% HNO^. _ [ j concentration of NO^ i o n and Mg The were adjusted to a constant value and absorption t e s t s were c a r r i e d out at the f o l l o w i n g Metal wavelengths. Wavelength A Al Cd Pb Zn 0 3093 2288 2170 2138 A t y p i c a l concentration absorbance p l o t f o r Mg-Zn a l l o y s i s shown i n f i g . (100). I t i s seen that absorption i s a l i n e a r f u n c t i o n of the Zn concentration up to approximately 10 ppm. The l i n e a r part of the curve was used f o r determining the composition of the unknown. RESULTS AND LIMITATIONS: Atomic absorption was found to be most s e n s i t i v e i n the case of Zn and Cd where 1 ppm of the element i n s o l u t i o n could be detected easily. I n the case of aluminum, however, the s e n s i t i v i t y was about an order of magnitude lower, which necessitated upgrading of the s o l u t i o n s . The compositions determined using atomic absorption were found to be lower by up to 20% of the nominal composition i n the case of Zn and Cd solutes. This i s to be expected since the vapour.pressure of these solutes i s rather high at the melting temperature of the a l l o y . In the case of Pb and A l s o l u t e s , the determined compositions were w i t h i n - 10% of the nominal compositions . 1.0 0 2 4 6 8 Zn Concentration i n ppm., F i g . 100, -Absorbance vs. Zn concentration. la 12 14 206 APPENDIX - B THE PREFERENTIAL NATURE OF THE SOLUTE-DISLOCATION INTERACTION: A ternary Mg a l l o y containing 0.07 a t . % Zn and 1 a t . % In was tested i n tension at room temperature. The y i e l d stress-composition curves f o r the binary Mg-Zn and Mg-In a l l o y s are shown together i n f i g . (101). I t i s apparent that the concentration of each solute i n the ternary i s higher than C T f o r the corresponding binary system. y i e l d s t r e s s of pure Mg i s 8,500 p s i . From the f i g u r e cfyp The f o r Mg-0.07 a t . % Zn a l l o y i s 12,580 p s i and that f o r Mg-1 at. % In i s equal to 11,430 p s i . Assuming that the strength of a multi-component s o l i d s o l u t i o n can.be obtained by adding up the strengthening e f f e c t s of the corresponding binary s o l u t i o n s , the strength of the Mg-Zn-In binary a l l o y examined should equal 15,510 p s i . Experimentally, however o^p for the ternary a l l o y i s observed to be.12,800 - 200 p s i , suggesting that the strengthening e f f e c t of the various solute:species present simultaneously i n Mg i s non-additive. An a l t e r n a t i v e p o s s i b i l i t y i s the p r e f e r e n t i a l i n t e r a c t i o n of one solute species with d i s l o c a t i o n s g i v i n g r i s e to hardening which i s equivalent to that i n stage I i n the corresponding binary system. The excess of the preferred solute above C^, ( i n the binary) as w e l l as the t o t a l amount of each of the other solute species present i n the ternary w i l l have a d d i t i v e strengthening c o n t r i b u t i o n s equivalent to those i n stage I I of t h e i r corresponding binary systems. In the case of Mg-Zn-In ternary a l l o y whether In or Zn i s the preferred species can be decided as f o l l o w s . Assuming that In atoms are p a r t i c i p a t i n g in.the stage I i n t e r a c t i o n s 207 F i g . 101. S o l u t i o n hardening curves f o r Mg-Zn and Mg-In binary systems. 208 Strength due to In present i n an amount equal to C, (0.25 at.%) = 11,250 p s i (A) 0.75 at„% In w i l l p a r t i c i p a t e i n stage I I i n t e r a c t i o n g i v i n g r i s e to,another 187 p s i (B) 0,07 a t . % Zn w i l l also contribute an equivalent of stage I I of Mg-Zn binary which i s 630 p s i (C) The strength of the ternary a l l o y with In as the preferred species would then be = (A) + (B) + (C) = 11,250 + 187 + 630 p s i =12,067 p s i A s i m i l a r c a l c u l a t i o n taking Zn.to be the preferred species y i e l d s 12,750 p s i to be the strength.of the ternary a l l o y . Keeping in.mind that the r e p r o d u c i b i l i t y of the present r e s u l t s are + w i t h i n - 250 p s i , a comparison of the c a l c u l a t e d strength values with the experimental r e s u l t suggests Zn to be the preferred species i n stage I interaction. This conclusion i s f u r t h e r substantiated by the experiments on a s e r i e s of ternary a l l o y s . I t should, however, be noted here that the a d d i t i v e e f f e c t of solute at concentrations above. C^. i s not s t r i c t l y v a l i d , because at s u f f i c i e n t l y high Zn concentrations s o l u t i o n softening i s to be expected rather than,strengthening, whether or not - the l i m i t i n g con- c e n t r a t i o n above.which softening occurs would be a f f e c t e d by the presence, of In cannot be decided u n t i l f u r t h e r experiments are performed. 209 APPENDIX - C TIE DETERMINATION OF A T FROM STRAIN RATE CHANGE TESTS: The most convenient method of determing the v a r i a t i o n of AT with s t r a i n r a t e i s through instantaneous changes i n strain r a t e during the t e n s i l e t e s t . I t i s , however, important t o remember that the flow s t r e s s d i f f e r e n c e accompanying a change i n s t r a i n rate can be equated to A T only i f i t i s assumed that the d i s l o c a t i o n s t r u c t u r e remains constant during the i n s t a n t of change. In the present work the s t r a i n r a t e was changed by a f a c t o r 2 of 10 (from a cross head.speed of 0,002 to 0=2 ipm) during the t e n s i l e /' t e s t using a push button speed s e l e c t o r . I n p r i n c i p l e both s t r e s s increments and decrements may be taken as A T •„ However, a considerable delay was observed to be associated with the change from high to low strain rate. For t h i s reason, i t was decided that the e r r o r a r i s i n g from y i e l d point phenomenon ( i n the a l l o y s ) would be l e s s than that r e s u l t i n g from the time delay during the decrease i n s t r a i n r a t e . all Therefore, A T values were obtained during an increase i n s t r a i n r a t e . Much of the s t r a i n rate change t e s t s were conducted at 78°K. F i g . (102) i l l u s t r a t e s schematically the flow curves during s t r a i n rate change t e s t s . : Because of the abrupt nature of y i e l d a f t e r a change i n s t r a i n r a t e , i t was r e l a t i v e l y easy to obtain A T i- n t n e case of Mg. However, y i e l d points became apparent as the solute content was increased. In the presence of y i e l d p o i n t s , A T was evaluated as shown i n figure.(102). 210 At temperatures near and above 295°K considerable d i f f i c u l t y was encountered i n obtaining r e l i a b l e values of Ax „ I n the ease of Mg, : the flow curve became parabolic i n nature, thereby making i t . d i f f i c u l t to extrapolate the two l i n e a r stages to obtain A T . In Mg-Zn a l l o y s on the other hand the m u l t i p l e y i e l d - p o i n t e f f e c t made the evaluation of the r e v e r s i b l e change i n flow s t r e s s difficult„ Low s t r a i n High s t r a i n Mg-Zn a l l o y s Fig. 102. The nature of the flow s t r e s s observed during s t r a i n rate change t e s t s i n Mg-Zn s i n g l e c r y s t a l s . (oriented for basal s l i p ) . 211 BIBLIOGRAPHY R.L.. F l e i s c h e r and W. R. Hibbard, J r . ; NPL Symposium No. 15, The Relation between the structure and mechanical properties of metals,,262, (1963). P. 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Solid solution strengthening of magnesium Akhtar, Ainul 1968
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