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Strengthening mechanisms in aluminum alloys Sahoo, Maheswar 1970

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STRENGTHENING MECHANISMS IN ALUMINUM ALLOYS BY MAHESWAR SAHOO B.Sc. (Hons.), Utkal University, India, 1964 E.E., Indian I n s t i t u t e of Science, India, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF , DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept this thesis as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA • December, 1970 In presenting th i s thes i s in pa r t i a l f u l f i lment o f the requirements fo r an advanced degree at the Un ivers i ty of B r i t i s h Columbia, 1 agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes i s fo r scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s f o r f i nanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of Metallurgy  The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date January 15th, 1971 ACKNOWLEDGEMENTS The author wishes to express h i s s i n c e r e g r a t i t u d e , to Dr. J.A. Lund, f o r h i s advice and a s s i s t a n c e , throughout the pr e p a r a t i o n of the t h e s i s . Thanks are a l s o extended to the members of the f a c u l t y and f e l l o w graduate students f o r h e l p f u l d i s c u s s i o n s . The ass i s t a n c e of the t e c h n i c a l s t a f f i s g r e a t l y appreciated. F i n a n c i a l a s s i s t a n c e i n the form of a N a t i o n a l Research Council Scholarship i s g r a t e f u l l y acknowledged. - i i i -ABSTRACT . The substructure of pure aluminum and over-aged Al-4Cu has been v a r i e d by mechanical and thermal treatments. The nature of t h i s substructure and i t s r e s i s t a n c e to annealing has been s t u d i e d , together w i t h the e f f e c t of the substructure on t e n s i l e s t r e n g t h at ambient and elevated temperatures. I t has been found that i n at l e a s t some respects the response of the strength of the over-aged Al-4Cu to mechanical and thermal processing i s very comparable to that of oxide-dispersion-strengthened a l l o y s such as S.A.P. and Ni-ThC^. The over-aged Al-4Cu i s strengthened appreciably by c o l d work. Much of t h i s incremental room-temperature strengthening can be removed by annealing at r e l a t i v e l y low tempera-t u r e s ; i . e . temperatures at which the stre n g t h of c o l d worked pure aluminum i s not lowered. In common w i t h o x i d e - d i s p e r s i o n hardened a l l o y s , the y i e l d s t r e n g t h of cold-worked Al-4Cu at elevated tempera-tures (300°C or 0.62 Tm) i s a c t u a l l y improved by a s t a t i c anneal at 300°C before t e s t i n g . This b e n e f i t increases w i t h i n c r e a s i n g amounts of p r i o r c o l d work. S i m i l a r s t u d i e s have been c a r r i e d out w i t h an S.A.P. extruded a l l o y (10 wt. % A^O^) and comparable r e s u l t s have been obtained. Pure aluminum, Al-4Cu and S.A.P. m a t e r i a l s have been examined by X-ray l i n e p r o f i l e a n a l y s i s to determine the d i s t r i b u t i o n of non-uniform l a t t i c e s t r a i n and the c o h e r e n t l y - d i f f r a c t i n g c r y s t a l l i t e domain s i z e . The X-ray data have been i n t e r p r e t e d i n terms of d i s l o c a t i o n d e n s i t i e s and c o n f i g u r a t i o n s , and compared w i t h d i r e c t observations made - i v -by transmission electron microscopy. An attempt has been made to account semiquantitatively for the strength of the deformed and annealed materials at ordinary and elevated temperatures i n terms of available strengthening mechanisms. The 0.2 pet y i e l d strengths of simple aged Al-4Cu alloys (no substructure) was found to be consistent with the Orowan model of dispersion-strengthen-ing both at R.T. and at 300°C. The room temperature y i e l d strength (ag 2^  °f cold worked and annealed pure aluminum and Al-4Cu alloys was related to the subgrain diameter (£) by the Hall-Petch equation: -1/2 °0 2 = °0 + k ^ where and k are constants. In such cases i t was not believed that there was a contribution to strength from the Orowan mechanism. Sim i l a r l y the 20°C y i e l d strength of the S.A.P. alloy was associated with the fine dislocation substructure produced by thermo-mechanical treatments. The high temperature y i e l d strength of Al-4Cu and S.A.P. was related to the polygonized substructure produced by s t a t i c annealing, which was much finer and more stable i n the case of the oxide dispersion-strengthened alloy. - v -TABLE OF CONTENTS 1. INTRODUCTION 1.2 Scope of the Present Work 2.5.4 Determination of Volume F r a c t i o n of P r e c i p i t a t e s Page 1 1.1 Review of P r i o r Work 7 9 9 10 10 16 17 2. EXPERIMENTAL PROCEDURE 2.1 A l l o y P r e p a r a t i o n 2.2 F a b r i c a t i o n and Heat Treatment 2.2.1 Aluminum-4 Copper and Pure Aluminum 2.2.2 S.A.P 2.3 T e n s i l e T e s t i n g 2.3.1 P r e p a r a t i o n of T e n s i l e Specimens ^ 2.3.2 T e n s i l e Testing Procedure 2.4 X-Ray D i f f r a c t i o n ;  2.4.1 P r i n c i p l e 2.4.2 Specimen P r e p a r a t i o n 2.4.3 X-Ray D i f f r a c t i o n Procedure 2.5 Metallography 2.5.1 O p t i c a l Microscopy 2.5.2 E l e c t r o n Microscopy 2.5.3 Measurement of Grain S i z e and Subgrain S i z e . 18 19 19 19 21 24 24 24 26 2.5.5 C a l c u l a t i o n of I n t e r p a r t i c l e Spacings 28 - v i -Page 3. USE OF X-RAY TECHNIQUES TO ANALYSE DISLOCATION DENSITY AND CONFIGURATION 30 3.1 Basis of X-ray L i n e P r o f i l e A n a l y s i s 30 3.2 Computer A n a l y s i s 35 3.3 Determination of D i s l o c a t i o n D e n s i t i e s and Configurations from X-Ray Data 37 4. RESULTS MD OBSERVATIONS 40 4.1 T e n s i l e Tests 40 4.1.1 Room Temperature Tests 40 4.1.1.1 Aluminum-4 Copper and Pure Aluminum 40 4.1.1.2 S.A.P 51 4.1.2 300°C Tests 53 4.1.2.1 Aluminum-4 Copper and Pure Aluminum 53 4.1.2.2 S.A.P 67 4.2 X-Ray D i f f r a c t i o n 69 4.3 Metallography 78 4.3.1 O p t i c a l Microscopy 78 4.3.2 E l e c t r o n Microscopy 78 4.3.2.1 Pure Aluminum 78 4.3.2.2 Aluminum-4 Copper 89 4.3.2.3 S.A.P 100 5. DISCUSSION 1 0 8 5.1 T e n s i l e P r o p e r t i e s at 20°C 108 5.1.1 Pure Aluminum 108 Page 5.1.2 Aluminum-4 Copper 116 5.1.2.1 Simple Aged A l l o y (no substructure) 116 5.1.2.2 Aged-and-Deformed A l l o y s 120 5.1.2.3 Deformed-and-Aged A l l o y s 129 5.1.3 S.A.P 132 5.2 S t r e s s - S t r a i n Curves and D u c t i l i t y at 20°C 135 5.3 T e n s i l e P r o p e r t i e s at 300°C 141 5.3.1 Pure Aluminum 144 5.3.2 Aluminum-4 Copper 146 5.3.3 S.A.P 152 6. SUMMARY AND CONCLUSIONS 155 APPENDIX 158 BIBLIOGRAPHY 162 - v i i i -LIST OF FIGURES Figure Page 1. Flowsheet f o r f a b r i c a t i o n of A l and Al-4Cu 12 48 2. Phase diagram of Al-4Cu on the aluminum-rich s i d e • 27 3. 20°C Data showing the e f f e c t s of c o l d r o l l i n g on the strength of A l and Al-4Cu (B Seri e s ) 43 4. 20°C Data showing the e f f e c t s of annealing temperature on the y i e l d s t r e n g t h of Al-4Cu (B Se r i e s ) vs. pure aluminum a f t e r 70% CW 45 5. 20°C Data showing the e f f e c t s of annealing temperature on the uniform el o n g a t i o n of Al-4Cu (B Seri e s ) vs. pure aluminum a f t e r 70% C.W 47 6. 20°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (A Se r i e s ) a f t e r 70% C.W 48 7. 20°C Data showing the e f f e c t s of annealing time at 300°C on the y i e l d s t r e n g t h Al-4Cu vs. Pure aluminum a f t e r 70% C.W 49 8. 20°C Data showing the e f f e c t s of annealing time at 300°C on the U.T.S. of Al-4Cu vs. pure aluminum a f t e r 70% C.W 5 0 9. 20°C and 300°C Data showing the e f f e c t s of c o l d r o l l i n g on the stre n g t h of S.A.P 52 10. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (A Seri e s ) a f t e r 70% C.W 5 4 11. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (B. Se r i e s ) a f t e r 70% C.W 5 5 12. 300°C .Data showing the e f f e c t s of annealing time at 300°C on the y i e l d s t r e n g t h of Al-4Cu vs. pure aluminum a f t e r 70% C.W 5 7 13. 300°C Data showing the e f f e c t s of annealing time at 300°C on the U.T.S...of Al-4Cu vs. pure aluminum a f t e r 70% C.W. 53 14. 300°C Data showing the e f f e c t s of annealing time at 300°C on the uniform elongation of Al-4Cu vs. pure aluminum a f t e r 70% C.W 59 - i x -F i g u r e Page 15. 300°C Data showing t h e e f f e c t s o f a n n e a l i n g t i m e a t 300°C on t h e a n n e a l i n g b e h a v i o u r o f A l - 4 C u (B S e r i e s ) a f t e r (a) 30% C.W., (b) 40% C.W., (c) 50% C.W., (d) 60% C.W., and (e) 80% C.W 61-65 16. V a r i a t i o n o f l a t t i c e s t r a i n w i t h l a t t i c e d i s t a n c e f o r A l - 4 C u (B. S e r i e s ) and pur e aluminum i n v a r i o u s t h e r m o - m e c h a n i c a l c o n d i t i o n s 71 17. V a r i a t i o n o f l a t t i c e s t r a i n w i t h l a t t i c e d i s t a n c e f o r S.A.P. i n v a r i o u s t h e r m o - m e c h a n i c a l c o n d i t i o n s .... 71 18. V a r i a t i o n o f domain s i z e c o e f f i c i e n t w i t h l a t t i c e d i s t a n c e f o r A l - 4 C u (B S e r i e s ) and pur e aluminum i n v a r i o u s t h e r m o - m e c h a n i c a l c o n d i t i o n s 72 19. V a r i a t i o n o f domain s i z e c o e f f i c i e n t w i t h l a t t i c e d i s t a n c e f o r S.A.P. i n v a r i o u s t h e r m o - m e c h a n i c a l c o n d i t i o n s 73 20. V a r i a t i o n o f domain s i z e c o e f f i c i e n t w i t h l a t t i c e d i s t -ance f o r A l - 4 C u (B S e r i e s ) a f t e r 50% and 70% C.W 73 21. O p t i c a l m i c r o g r a p h o f ove r - a g e d A l - 4 C u showing g r a i n s i z e and PFZ, 23X . 79 22. O p t i c a l m i c r o g r a p h o f A l - 4 C u (B S e r i e s ) a f t e r 70% C.W. , 23X 79 23. O p t i c a l m i c r o g r a p h o f A l - 4 C u CA S e r i e s ) a f t e r 70% C.W. , 23X 79 24. O p t i c a l m i c r o g r a p h o f A l - 4 C u (B S e r i e s ) c o l d - r o l l e d 70% and a n n e a l e d a t 300°C f o r 8 h r s . , 23X 80 25. O p t i c a l m i c r o g r a p h of A l - 4 C u (A S e r i e s ) c o l d - r o l l e d 70% and a n n e a l e d a t 300°C f o r 8 h r s . , 23X 80 26a-c T r a n s m i s s i o n e l e c t r o n m i c r o g r a p h o f p u r e aluminum a f t e r 70% C.W., (a) 15,000X, (b) 10,000X, (c) 20,000X 82 27a,b T r a n s m i s s i o n e l e c t r o n m i c r o g r a p h o f pur e aluminum a f t e r 60% C.W., 20,000X 83 28a,b T r a n s m i s s i o n e l e c t r o n m i c r o g r a p h o f pur e aluminum a f t e r 80% C.W., 20,000X 84 29. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 300°C f o r 1 h r . , 15.000X 30. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 300°C f o r 6 h r s . , 10,000X 31. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 100°C f o r 1 h r . , 20.000X 32. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 250°C f o r 1 h r . , 15,000X 33. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 400°C f o r 1 h r . , 5.000X 34. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 80% and annealed at 300°C f o r 3 h r s . , 5,000X 35. Chromium shadowed carbon r e p l i c a of over-aged Al-4Cu showing CuAl£ ( 9 ) p r e c i p i t a t e s , 6,000X 36. Transmission e l e c t r o n micrograph of over-aged Al-4Cu showing CUAI2 p r e c i p i t a t e s , 10,000X 37. Transmission e l e c t r o n micrograph of Al-4Cu (B Serie s ) showing the hot-worked m i c r o s t r u c t u r e , 20,000X 38a-c Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) a f t e r 70% C.W., 35,000X 39a,b Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 100°C f o r 1 h r . , a) 30,000X, b) 40,000X 40a,b Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 200°C f o r 1 h r . , 30,000X 41 Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 350°C f o r 1 h r . , 15,000X - x i -Figure Page 42a,b Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 15 mins., 25,000X 96 43a,b Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 30 mins., 23,000X 97 44. Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 2 h r s . , 23,000X 98 45. Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 4 h r s . , 23,000X 98 46a,b Transmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 8 h r s . , a) 20,000X, b) 15,000X 99 47. Transmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 15 h r s . , 15,000X 99 48. Transmission e l e c t r o n micrograph of S.A.P. i n the as received c o n d i t i o n showing the d i s t r i b u t i o n of A 1 2 0 3 p a r t i c l e s , 46,000X 102 49a,b Transmission e l e c t r o n micrograph of S.A.P. showing the hot-worked m i c r o s t r u c t u r e , 23,000X 103 50a-c Transmission e l e c t r o n micrograph of S.A.P. c o l d -r o l l e d 50%, 58,000X 105 51a,b Transmission e l e c t r o n micrograph of S.A.P. c o l d -r o l l e d 50% and annealed at 540°C f o r 24 h r s . , 58,000X 1 ° 6 52. 20°C Y i e l d s t r e n g t h of pure aluminum as a f u n c t i o n of the r e c i p r o c a l of the square root of the sub-g r a i n diameter H 2 53. 20°C and 300°C Y i e l d s t r e n g t h of over-aged Al-4Cu a l l o y s p l o t t e d against Orowan's parameter 54. 20°C Y i e l d strength of Al-4Cu (B S e r i e s ) as a f u n c t i o n of the R e c i p r o c a l of the square root of the subgrain diameter 124 - x i i -Figure Page 55. Comparison of Orowan strengthening and substructure strengthening for various values of £ or Dg 126 56. Transmission electron micrograph of Al-4Cu (C Series) cold-rolled 70% after solution treatment and aged1 at 300°C for 1 hr., (a) showing 6 ' and 9 precipitates, 50,000X (b) showing subgrains,35,000X 131 57. 20°C True stress-true s t r a i n curves for pure aluminum, Al-4Cu (B Series) and S.A.P. i n various thermo-mechanical conditions 136 58. 20°C True stress-true s t r a i n curves for Al-4Cu (B series) cold-rolled 70% and annealed at different temperatures 137 59. 300°C Y i e l d strength of pure aluminum as a function of the subgrain diameter 145 60. Simplified Orowan plot for the 20°C and 300°C y i e l d strength of over-aged Al-4Cu 161 - x i i i -LIST OF TABLES Table Page I Chemical A n a l y s i s of A l and AL-4Cu 10 I I D i s p e r s i o n Parameters f o r Age-Hardened Al-4Cu A l l o y s and the Corresponding Y i e l d Strength Values at R.T. and 300°C 4 1 I I I Room Temperature T e n s i l e Results f o r Cold-Rolled A l and Al-4Cu (B Seri e s ) 4 2 IV Room Temperature T e n s i l e Results f o r Cold-Rolled S.A.P 5 1 V Comparison of 300°C Y i e l d Strength Values f o r Cold-R o l l e d A l and Al-4Cu 60 VI E f f e c t of S t a t i c Annealing on the 300°C Y i e l d Strength of Al-4Cu Cold Worked P r e v i o u s l y by Various Amounts 66 V I I 300°C T e n s i l e Results f o r Cold-Rolled Al-4Cu 67 V I I I 300°C T e n s i l e Results f o r Cold-Rolled S.A.P 68 IX E f f e c t of S t a t i c Annealing on the 300°C T e n s i l e P r o p e r t i e s of 50% Cold-Rolled S.A.P 68 X Domain Si z e and L a t t i c e S t r a i n D i s t r i b u t i o n 74 XI D i s l o c a t i o n D e n s i t i e s and Configurations 75 X I I Room Temperature Mechanical P r o p e r t i e s f o r High-P u r i t y Aluminum 109 X I I I ao and K Values f o r Aluminum i n the H a l l - P e t c h Equation m XIV Room Temperature and 300°C Y i e l d Strengths and the Corresponding Subgrain Diameters f o r Pure Aluminum A f t e r Various Thermo-mechanical Treatments 158 XV Room Temperature Y i e l d Strengths and the Correspond-ing Subgrain Diameters f o r Al-4Cu, B S e r i e s , Annealed a f t e r 70% Cold Work 1 5 9 XVI C a l c u l a t e d Values of 20°C OQ.2 f r o m Orowan and H a l l -Petch Equations f o r Al-4Cu..l 1 6 0 1. INTRODUCTION 1.1. Review of P r i o r Work Dispersion-hardened m a t e r i a l s are defined as those c o n t a i n i n g a d i s p e r s i o n of an incoherent second phase. The second phase d i s p e r s i o n may be introduced by: (a) P r e c i p i t a t i o n from supersaturated s o l i d s o l u t i o n ( i n which case the dispersed phase i s commonly an i n t e r m e t a l l i c compound). (b) Mechanical mixing of a metal w i t h a f i n e l y - d i v i d e d hard phase (commonly an o x i d e ) , t h i s mixing g e n e r a l l y being accomplished by one of s e v e r a l powder - m e t a l l u r g i c a l methods. To produce dense dispersion-hardened a l l o y s of type (b) from powders i t i s necessary to use f a b r i c a t i o n processes i n v o l v i n g l a r g e amounts of p l a s t i c flow; e.g. e x t r u s i o n . The dispersed phase i s present throughout f a b r i c a t i o n and i t can have a marked e f f e c t upon the f i n a l a s - f a b r i c a t e d m i c r o s t r u c t u r e . By c o n t r a s t , type (a) a l l o y s can be f a b r i c a t e d as s i n g l e phase s o l i d s o l u t i o n s , the d i s p e r s i o n being introduced only by subsequent heat treatment Cover-ageing). I t i s p o s s i b l e , but not common, to do some or a l l of the shaping of type (a) m a t e r i a l s a f t e r ageing, i n which case some of the same e f f e c t s of the second phase on the deformed micro-s t r u c t u r e might be expected as i n the case.of type (b) a l l o y s . - 2 -There i s evidence that the type of second phase present has an important e f f e c t on s t r e n g t h , p a r t i c u l a r l y s t r e n g t h at elevated temperatures. The presence of the second phase c o n t r i b u t e s to the development of a unique and g e n e r a l l y favourable d i s l o c a t i o n substructure during thermal and mechanical processing. In a d d i t i o n , these processing b e n e f i t s to the s t r u c t u r e may be r e t a i n e d on heating to unusually high temperatures. The oxide dispersion-hardened a l l o y s seem to e x h i b i t higher strengths at elevated temperatures than over-aged a l l o y s of type (a). However, the r o l e of mechanical and thermal h i s t o r y i s not c l e a r i n t h i s regard s i n c e there i s a l a c k of p r i o r work i n which the two types of a l l o y have been compared a f t e r s i m i l a r f a b r i c a t i o n treatments. Several d i s l o c a t i o n t h e o r i e s have been advanced to e x p l a i n the magnitude of the y i e l d s t r e s s at low or ambient temperatures i n a l l o y s c o n t a i n i n g a f i n e l y d i v i d e d second phase. These have been reviewed and discussed i n d e t a i l by K e l l y and Ni c h o l s o n . ^ In a l l these t h e o r i e s the i n i t i a l y i e l d s t r e s s i s i d e n t i f i e d w i t h the s t r e s s which must be ap p l i e d to a c r y s t a l to move a s i n g l e d i s l o c a t i o n over a distance which i s l a r g e compared to the i n t e r p a r t i c l e spacing. The y i e l d s t r e n g t h of many dispersion-strengthened products c o n t a i n i n g an incoherent second phase has been s a t i s f a c t o r i l y explained by the well-known Orowan 2 model, i n which d i s l o c a t i o n s are forced to bow out between p a r t i c l e s before by-passing them. The model p r e d i c t s that the y i e l d s t r e n g t h should be p r o p o r t i o n a l to the r e c i p r o c a l of the i n t e r p a r t i c l e spacing. Using Nabarro's estimate of the l i n e t e n sion of a curved d i s l o c a t i o n , K e l l y and Nicholson"'" have given the f i n a l form of the Orowan p r e d i c t i o n as , G b / J ^ S , 1 . T = T s + 47" (~2b } (D - 2 r )/2 ( 1 ) s s - 3 -where T and x are shear s t r e s s e s , s x = i n i t i a l flow s t r e s s of the dispersion-hardened a l l o y s , x = i n i t i a l flow s t r e s s of the m a t r i x , s G = shear modulus of the m a t r i x , b = Burger's vector of the d i s l o c a t i o n , (j) = 1/2(1 + J the mean of l i n e tension f a c t o r s . f o r edge and screw d i s l o c a t i o n s , v = Poisson's r a t i o , D g = mean planar i n t e r p a r t i c l e spacing, r g = mean planar p a r t i c l e r a d i u s . For a p o l y c r y s t a l l i n e m a t e r i a l equation (1) may be m u l t i p l e d by a Taylor f a c t o r of 2.24, to convert shear s t r e s s to t e n s i l e s t r e s s . The t e n s i l e y i e l d s t r e s s , a , can then be w r i t t e n as G b V 2 r s 1 o = c s + 2.24 — ^ £ n ( _ ^ ) _ ^ ... ( 2) s s where a i s the t e n s i l e y i e l d s t r e s s of the matrix m a t e r i a l . The s Taylor f a c t o r of 2.24 has p r e v i o u s l y been proposed and used f o r Al-Ag 3 a l l o y s by Gerold and Mayer. 4 A n s e l l and Lenel have proposed an a l t e r n a t i v e d i s l o c a t i o n model to account f o r the y i e l d behaviour of a l l o y s w i t h a f i n e l y dispersed second phase. The c r i t e r i o n f o r y i e l d i n g i n t h i s model i s that the shear s t r e s s due to groups of d i s l o c a t i o n s piled-up against the second phase p a r t i c l e s must be s u f f i c i e n t to fracture or p l a s t i c a l l y deform the p a r t i c l e s , thereby r e l i e v i n g the back s t r e s s on the d i s l o c a t i o n -4-source. Equation derived on the b a s i s of t h i s model p r e d i c t s that the y i e l d s t r e s s v a r i e s as the r e c i p r o c a l square root of the mean fr e e path between dispersed p a r t i c l e s . For a s e r i e s of aluminum powder extrusions (Al-A^O^) A n s e l l and Lenel p l o t t e d the 0.2 pet o f f s e t y i e l d s t r e n g t h values at two temperatures (R.T. and 400°C) vs. the r e c i p r o c a l of the square root of the average A^O^ p a r t i c l e spacing, and claimed a s t r a i g h t l i n e f i t was observed. However, i f these same experimental data are r e p l o t t e d as s t r e n g t h vs. r e c i p r o c a l of the spacing, the f i t of the data to s t r a i g h t l i n e s i s e q u a l l y good. Thus the Orowan model expla i n s the data at l e a s t as w e l l as the A n s e l l - L e n e l model. A n s e l l and Lenel a l s o p r e d i c t that the dispersed p a r t i c l e s should f r a c t u r e or p l a s t i c a l l y deform, yet Hansen"* observed no i n d i c a t i o n of the f r a c t u r e of Al^O^ p a r t i c l e s i n A l - A ^ O ^ using e l e c t r o n microscopy, even a f t e r severe cold working of the a l l o y . Many workers have a p p l i e d the Orowan model to e x p l a i n the y i e l d behaviour of dispersion-strengthened products. P a r t i c u l a r l y , the 6 7 r e s u l t s of Dew-Hughes and Robertson, and of Byrne et a l . f o r over-aged Al-Cu a l l o y s , and of Gregory and Grant,^ and Hansen^'"^ f o r a s e r i e s of a l l o y s of the S.A.P. (Al-A^O^) type tend to support the Orowan r e l a t i o n s h i p . The Al-Cu system i s probably the one most widely used i n s t u d i e s 6 7 1X*~22 of age hardening behaviour. ' ' A good c o r r e l a t i o n e x i s t s i n t h i s system between the appearance of various s t r u c t u r e s obtained by ageing a quenched supersaturated s o l i d s o l u t i o n , and changes i n hardness of the a l l o y s ^'"^ Four d i s t i n c t types of "zones" or p r e c i p i t a t e s may be formed by ageing these a l l o y s ; G u i n i e r - P r e s t o n zones of the f i r s t and - 5 -second k i n d , e', and eCCuA]^), t h e l a s t b e i n g a s t a b l e p r e c i p i t a t e . The G.P. zones and t h e 0' phase a r e s t r u c t u r a l l y c o h e r e n t and p a r t i a l l y c o h e r e n t w i t h t h e m a t r i x r e s p e c t i v e l y , and t h e mechanisms by w h i c h t h e y s t r e n g t h e n t h e m a t r i x a r e q u i t e d i s t i n c t from t h o s e due to t h e i n c o h e r e n t 0 phase p r e c i p i t a t e . Dew-Hughes and R o b e r t s o n ^ and Byrne e t a l . ^ have p r e s e n t e d e v i d e n c e t h a t d i s l o c a t i o n s bow between Q phase p r e c i p i t a t e p a r t i c l e s i n agreement w i t h Orowan's t h e o r y . There i s some q u e s t i o n , however, as t o t h e mechanism o f y i e l d i n g i n t h e p r e s e n c e o f t h e s e m i - c o h e r e n t 0' p r e c i p i t a t e . From some r e p o r t e d r e s u l t s o f d e f o r m a t i o n o f an Al-4Cu a l l o y hardened 7 18—22 by 9' p r e c i p i t a t e s i t has been i n f e r r e d ' t h a t d i s l o c a t i o n s cannot s h e a r t h r o u g h 0* p r e c i p i t a t e s , a t l e a s t d u r i n g t h e i n i t i a l s t a g e o f p l a s t i c d e f o r m a t i o n , and t h a t t h e y e i t h e r bow out between t h e p a r t i c l e s and by-pass them (Orowan's mechanism) o r t h a t they p i l e up a g a i n s t 18 t h e p a r t i c l e s . N i c h o l s o n e t a l . , b ased on t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y o b s e r v a t i o n s , c l a i m e d t h a t d i s l o c a t i o n s d i d s h e a r t h r o u g h 0' p r e c i p i t a t e s , a l t h o u g h they were i n i t i a l l y h e l d up a t t h e i n t e r f a c e s . 22 On t h e o t h e r hand Koda e t a l . p r e d i c t e d from t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y work t h a t t h e Orowan model c o u l d a p p l y a t l e a s t p a r t i a l l y i n the i n i t i a l s t a g e s o f d e f o r m a t i o n . C o n t r a d i c t o r y o p i n i o n s e x i s t r e g a r d i n g t h e work h a r d e n i n g b e h a v i o u r of A l - C u c r y s t a l s c o n t a i n i n g 0* and 0 p r e c i p i t a t e s . Byrne e t a l . ^ argue t h a t d i s l o c a t i o n s undergo c r o s s - s l i p t o a v o i d t h e p a r t i c l e s as 23 e a r l i e r s u g g e s t e d by H i r s c h , and t h a t t h e o c c u r r e n c e o f the maximum i n t h e s t r e s s - s t r a i n c u r v e c o u l d c o r r e s p o n d t o complete r e p l a c e m e n t o f the Orowan mechanism by a c r o s s - s l i p -mechanism. Dew-Hughes and R o b e r t s o n - 6 -i n s t e a d concluded that i n i t i a l work hardening i s due to r e s i d u a l d i s -l o c a t i o n loops remaining around the p a r t i c l e s , i n accordance w i t h the 24 F i s h e r , Hart and Pry theory. The A l - A ^ O ^ (S.A.P.-Type) a l l o y s have been u t i l i z e d e x t e n s i v e l y as model dispersion-strengthened a l l o y s i n both experimental and i • ... 4,5,8-10,25-32 „ t h e o r e t i c a l i n v e s t i g a t i o n s . Hansen has given support f o r the Orowan theory f o r A l - A ^ O ^ products t e s t e d at room temperature and at 400°C. 33-35 Grant and co-workers have claimed that oxide dispersed a l l o y s prepared by e x t r u s i o n from powders owe t h e i r s t r e n g t h to a high l e v e l of " s t o r e d energy". S t r a i n energy i s developed during the high s t r a i n r a t e deformation a s s o c i a t e d w i t h e x t r u s i o n , and the f u n c t i o n of the c l o s e l y spaced, f i n e oxide p a r t i c l e s i s to p i n d i s l o c a t i o n and to impede g r a i n boundary and sub-boundary shear and m i g r a t i o n . White 36 and Carnahan, from t h e i r m i c r o - p l a s t i c i t y s t u d i e s w i t h TD-Ni ( N i - T b ^ ) , found that optimum stre n g t h was associated w i t h a high l e v e l of accumulated stored energy (high d i s l o c a t i o n density) developed by thermo-mechanical treatments. I t was concluded, i n agreement w i t h the review of Grant and co-workers, that the presence of a f i n e d i s p e r s i o n of a second phase was not of i t s e l f s u f f i c i e n t to promote the optimum p r o p e r t i e s which could be developed by s t r a i n and annealing c y c l e s , von Heimendahl 37 and Thomas came to a s i m i l a r c onclusion f o r Ni-TW^ when r e l a t i n g the t e n s i l e p r o p e r t i e s to m i c r o s t r u c t u r e s based on electron-microscope 38 39 s t u d i e s . I t was suggested by B r i m h a l l et a l . ' that the dispersed second phase p a r t i c l e s , besides being b a r r i e r s to d i s l o c a t i o n motion during deformation at ambient temperatures and on annealing, can act as - 7 -sources of d i s l o c a t i o n i n s e v e r a l ways and thereby increase the d i s l o c a t i o n d e n s i t y (stored energy). According to these arguments, the p a r t i c l e s themselves i n the f a b r i c a t e d a l l o y s are not a d i r e c t source of s t r e n g t h , r a t h e r , i t i s a complex network of p a r t i c l e s , d i s l o c a t i o n t a n g l e s , sub-boundaries, and g r a i n boundaries which determine st r e n g t h . The development of such a complex network i n S.A.P. a l l o y s has been 40 stu d i e d i n some d e t a i l by Goodrich and A n s e l l . 1.2 Scope of the Present Work Although much i s known about the p l a s t i c deformation behaviour at low and ambient temperatures of p r e c i p i t a t i o n - h a r d e n e d Al-Cu a l l o y s , s u r p r i s i n g l y l i t t l e i n f o r m a t i o n i s a v a i l a b l e about the ambient or elevated temperature s t r e n g t h of these a l l o y s i n the presence of a d i s l o c a t i o n s ubstructure. 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 c a r r y out a systematic study of the stre n g t h of these m a t e r i a l s at two temperatures, R.T. (0.32 Tm) and 300°C (0.62 Tm) and to c o r r e l a t e the s t r e n g t h w i t h s t r u c t u r e , f o r a range of s t r u c t u r e s produced by thermal and mechanical treatments. I t has been shown that the d e t r i m e n t a l e f f e c t of p r i o r c o l d working on the high temperature y i e l d and flow strength of dispersion-strengthened 41 a l l o y s such as Ni-ThO^, and A.P.M. (aluminum powder metallurgy) 42 products can be recovered, at l e a s t p a r t i a l l y , by s t a t i c annealing at high temperatures. I t i s not known from p r i o r work whether such a, phenomenon can be expected i n a p r e c i p i t a t i o n - h a r d e n e d a l l o y l i k e Al-4Cu where coarsening of 0 p a r t i c l e s can a l s o occur when the cold worked product i s annealed at hig h temperatures. C l a r i f i c a t i o n of t h i s was another o b j e c t i v e of the work. - 8 -The r e l a t i o n between "stored energy" and d i s l o c a t i o n d e n s i t y i n deformed dispersion-strengthened a l l o y s i s f a r from c l e a r on the b a s i s of published work. I t was hoped to provide f u r t h e r i n s i g h t i n t o t h i s question by means of X-ray l i n e p r o f i l e s t u d i e s on m a t e r i a l s w i t h d i f f e r e n t thermal and mechanical h i s t o r i e s . In order to permit d i r e c t comparison between r e s u l t s obtained w i t h an aged Al-Cu a l l o y and those obtainable w i t h oxide dispersion-strengthened aluminum under the same c o n d i t i o n s , i t was decided to i n c l u d e an S.A.P. ( s i n t e r e d aluminum product) a l l o y i n the i n v e s t i g a t i o n . I t was hoped to be able to e s t a b l i s h whether a p r e c i p i t a t e d d i s p e r s i o n i n aluminum could be as e f f e c t i v e as an oxide d i s p e r s i o n i n improving the strength at elevated temperatures. 2. EXPERIMENTAL PROCEDURE 2.1. A l l o y P r e p a r a t i o n Aluminum and Al-4 wt percent Cu m a t e r i a l s were prepared e n t i r e l y i n the l a b o r a t o r y , whereas the S.A.P. a l l o y was obtained i n a f a b r i c a t e d (extruded) form from an e x t e r n a l source. To prepare the Al-4Cu a l l o y , high p u r i t y aluminum ( o r i g i n a l l y 99.99% A l , supplied by Aluminum Company of Canada Ltd.) and copper ( o r i g i n a l l y 99.99% Cu, sup p l i e d by Kock-Light L a b o r a t o r i e s L t d . , England) were used. M e l t i n g was c a r r i e d out i n a gra p h i t e c r u c i b l e at 720°C using an e l e c t r i c r e s i s t o r furance. In producing the a l l o y , aluminum was melted f i r s t f o l l o wed by the a d d i t i o n of elemental copper. The melt was s t i r r e d w i t h a graphite rod u n t i l the copper had d i s s o l v e d completely. The melt was cast i n t o a s p l i t copper mold to produce a slab of dimensions 5" x 2" x 5/8". Some pure aluminum ca s t i n g s were obtained under the same c o n d i t i o n s . The copper content of the a l l o y was determined by Warnuck Hersey (Vancouver) and i m p u r i t i e s present i n both A l and Al-4Cu were determined s p e c t r o s c o p i c a l l y by the courtesy of the Aluminum Company of Canada, Richmond. The analyses of these m a t e r i a l s are given i n Table I. The sources of apparent z i n c contamination i n the a l l o y s could not be es t a b l i s h e d . - 10 -Table I : Chemical A n a l y s i s of A l and Al-4Cu Elements i n Al-4Cu Aluminum weight pet. Cu 3.950 < 0.010 Fe < 0.010 < 0.010 B < 0.001 < 0.001 S i < 0.005 < 0.001 Mg 0.002 0.002 T i 0.004 < 0.001 V 0.002 < 0.001 Zn 0.020 0.013 Cr 0.002 0.002 Mn < 0.001 < 0.001 A l ^96.00 =-99.960 (by d i f f e r e n c e ) The S.A.P. a l l o y was su p p l i e d by the courtesy of the Oak Ridge N a t i o n a l Laboratory, Oak Ridge, Tennessee, i n the form of an extruded c y l i n d r i c a l rod of diameter 61 mm (2.4 i n . ) . The a l l o y was s i m i l a r to commercial S.A.P. 895 i n oxide content. I t was manufactured from b a l l - m i l l e d aluminum powder by co l d compaction, vacuum annealing at 600°C, hot compaction, and hot e x t r u s i o n w i t h a reduction r a t i o of about 43 twenty. The composition of the m a t e r i a l quoted by the s u p p l i e r was 10.3 wt % A 1 2 0 3 , 0.07 wt % i r o n , 0.05 wt % s i l i c o n , 0.3 wt % carbon, and 4 ppm hydrogen. - 11 -2.2 F a b r i c a t i o n and Heat Treatment 2.2.1 Aluminum-4 Copper and Pure Aluminum The general procedures used f o r the hot and co l d working of aluminum and Al-4Cu are shown i n the flow sheet of F i g . 1. In the case of Al-4Cu a l l o y s a b a s i c o b j e c t i v e i n hot r o l l i n g was to r e t a i n a hot-worked m i c r o s t r u c t u r e . The hot r o l l i n g was c a r r i e d out on a l l o y s i n two c o n d i t i o n s ; (a) s i n g l e phase, wherein only the a - s o l i d s o l u t i o n was present, and (b) two-phase, wherein the incoherent CuAl^ (0) p r e c i p i t a t e was present during r o l l i n g . This second type of hot r o l l i n g was of importance to permit comparison of s t r e n g t h and m i c r o s t r u c t u r e between A l - C u A ^ and S.A.P., the l a t t e r m a t e r i a l having been extruded w i t h oxide p a r t i c l e s present. A b r i e f d e s c r i p t i o n of the flow sheet i s given below. Ingots were homogenised at 540°C f o r 36 hours, furnace cooled and then cleaned i n a d i l u t e aqueous s o l u t i o n of NaOH followed by r i n s i n g i n HNO^ and washing i n water. The slabs were then hot r o l l e d at 540°C ( s i n g l e phase i n a l l cases) to a thickness of 0.225 i n . The r e s u l t i n g m a t e r i a l was cut i n t o lengths of about 4 i n . to 6 i n . One end of each le n g t h was tapered to f a c i l i t a t e i t s entry i n t o the r o l l s during subsequent heavy hot r o l l i n g r e d u c t i o n i n a s i n g l e pass. The lengths were again cleaned i n NaOH s o l u t i o n followed by r i n s i n g i n HNO^ and washing i n water. 'B' Series One set of these s t r i p s was s o l u t i o n t r e a t e d at 540°C f o r 5 hours, water quenched, and then aged at 300°C f o r 15 hours to produce the - 12 -c a s t i n g 5" x 2" x 5/8" 4-540°C 36 hrs (homogenisation) 4-Hot r o l l e d to 0.225 i n . at 540°C clean and taper 540°C, 3 hrs 4-water quench I Ageing 300°C, 15 hrs i Cold r o l l i n g 70% Annealing ( S i m i l a r to B S e r i e s ) 540°C, 5 h r s . 4-Hot r o l l e d at 540°C to 0.150 i n . t h i c k i n one pass 4-water quench Cold r o l l i n g 70% i Annealing (Time at 300°C vari e d ) ageing at 300°C f o r 15 hrs 4-Cold r o l l i n g 70% 4-540°C,5 hrs 4-water quench 4-ageing, 300°C, 15 hrs Hot r o l l e d at 300°C to 0.150 i n . t h i c k i n one pass 4-water quench 4-cold r o l l i n g 30-90% 4-annealing Temperature v a r i e d Time at 300°C v a r i e d Annealing (Temperature varied) D DAI A AA1 Figure 1. Flow sheet f o r f a b r i c a t i o n of A l and Al-4Cu. - 13 -incoherent 6 (CuA^) p r e c i p i t a t e . The time elapsed betweeen quenching and t r a n s f e r to the furnace f o r ageing d i d not exceed 2 minutes. The aged s t r i p s were hot r o l l e d at 300°C to a thickness of 0.150 i n . i n one pass, and then water quenched immediately to r e t a i n the hot worked s t r u c t u r e . They were then kept r e f r i g e r a t e d at -20°C to avoid any s t r u c t u r a l m o d i f i c a t i o n before f u r t h e r use. For the 300°C r o l l i n g , s t r i p s were heated i n a n i t r a t e s a l t bath, and r o l l e d at a high r o l l speed (70 fpm p e r i p h e r a l ) to minimize c o o l i n g of the s t r i p s by the r o l l s . Reduction was 33 percent i n a s i n g l e pass g i v i n g a c a l c u l a t e d mean s t r a i n r a t e of 900 min ^. The combination of high s t r a i n and s t r a i n r a t e at 0.62 Tm reasonably approximates the cond i t i o n s which p r e v a i l when oxide dispersion-strengthened a l l o y s are extruded from powder b i l l e t s . The group of specimens hot r o l l e d at 300°C; i . e . w i t h two phases present c o n s t i t u t e the 'B' s e r i e s i n the flow sheet. A f t e r hot r o l l i n g , most s t r i p s were cleaned as before, c o l d r o l l e d 70% and annealed. The annealing treatment consisted of (a) one hour soaking at 8 temperatures ranging from 50°C to 400°C and (b) soaking f o r d i f f e r e n t times at 300°C. An annealing temperature of 300°C was chosen because i t c o i n c i d e d w i t h the previous ageing temperature and thus would not change the volume f r a c t i o n of the second phase present. Other 'B' s e r i e s s t r i p s were co l d r o l l e d to give reductions i n thickness ranging from 30% to 90%. These c o l d worked specimens were annealed f o r d i f f e r e n t times at 300°C. A, C, D Series Another set of the 0.225 i n . t h i c k s t r i p s produced by hot r o l l i n g - 14 -slabs at 540°C was s o l u t i o n t r e a t e d at 540°C f o r 5 hours, again hot r o l l e d at 540°C to a thickness of 0.150 i n . and water quenched d i r e c t l y . The hot r o l l i n g c o n d i t i o n s were s i m i l a r to those used f o r the 'B' s e r i e s except that a higher m e l t i n g - p o i n t s a l t was used i n hea t i n g the s t r i p s p r i o r to r o l l i n g . R o l l i n g at 540°C ( s i n g l e phase) produced some cracks on one surface of the r o l l e d product f o r reasons unknown. However, the cracks closed i n subsequent c o l d r o l l i n g , and no t r a c e of them could be found by microscopy a f t e r c o l d r o l l i n g reductions greater than 50%. In f a c t , a f i n a l c o l d r o l l i n g r e d u c t i o n of 70% was a p p l i e d to a l l hot r o l l e d m a t e r i a l s i n these s e r i e s . A f t e r hot r o l l i n g , the s t r i p s were cleaned and subjected to three types of thermomechanical treatments. 'D' Series In t h i s case, the 540°C hot r o l l e d -and-quenched m a t e r i a l above was aged at 300°C f o r 15 hours to produce the 9 p r e c i p i t a t e . I t was then c o l d r o l l e d 70% and annealed f o r one hour at tmperatures ranging from 50°C to 400°C. 'A' Series In t h i s s e r i e s , the 540°C hot rolled-and-quenched product was s o l u t i o n t r e a t e d at 540°C f o r 3 hours, quenched i n water, aged at 300°C f o r 15 hours to produce the 0 phase, cold r o l l e d 70%, and f i n a l l y annealed. The annealing treatments were s i m i l a r to those of the 'B' s e r i e s . 'C Series For t h i s s e r i e s , the hot rolled-and-quenched product was s o l u t i o n t r e a t e d f o r 3 hours at 540°C, water quenched, c o l d r o l l e d 70%, and - 15 -then heated at 300°C f o r d i f f e r e n t times. In e f f e c t , the f i n a l heat treatment i n t h i s case was an ageing treatment as w e l l as an annealing operation. The four processing s e r i e s of F i g . 1 may be summarised as f o l l o w s . Series M i c r o s t r u c t u r e during f i n a l M i c r o s t r u c t u r e during cold hot working r o l l i n g (to 0.150 i n . ) (20°C) A s i n g l e phase (540°C) B Two phase A l - C u A l 2 (300°C) C Si n g l e phase (540°C) D S i n g l e phase (540°C) Two phase A l - C u A ^ Two phase A l - C u A ^ S i n g l e phase ( s o l u t i o n treated) Two phase Al-CuAl„ Series A and D d i f f e r e d only s l i g h t l y . For Series A there was a f u l l s o l u t i o n treatment c a r r i e d out between hot and c o l d r o l l i n g , whereas quenching from the hot r o l l i n g temperature was taken to c o n s t i t u t e s o l u t i o n treatment i n Se r i e s D. Since some energy of deformation may. have been r e t a i n e d i n Series D, i t was f e l t that the subsequent ageing response might be somewhat d i f f e r e n t f o r the two s e r i e s . Since oxide, dispersion-strengthened a l l o y s are worked i n the two phase c o n d i t i o n at a l l stages of f a b r i c a t i o n , Series B specimens of Al-4Cu may be considered the most comparable to S.A.P. For comparison purposes pure aluminum slabs were given thermo-mechanical treatments s i m i l a r to the A and to the D s e r i e s . These specimens are designated AAL and DAL r e s p e c t i v e l y . I t was e s t a b l i s h e d - 16 -that the g r a i n s i z e of the c o l d r o l l e d pure aluminum specimens was c l o s e l y comparable to that of c o l d - r o l l e d Al-Cu a l l o y specimens; i . e . i n the order of 0.1 mm. Simple Aged A l l o y s In order to e l u c i d a t e the mechanism of dispersion-hardening, i t was necessary i n a separate experiment to vary the d i s p e r s i o n of 6 and/or 9' p r e c i p i t a t e s by the use of s u i t a b l e heat treatments. To achieve t h i s Al-4Cu specimens (0.045 i n . i n thickness) were s o l u t i o n t r e a t e d fo r 3 hours at 540°C, water quenched and then aged at 300°C f o r times ranging from one hour to 62 hours. These specimens were not worked p r i o r to ageing. To produce a very coarse d i s p e r s i o n of 9 p r e c i p i t a t e s , some of the specimens were f i r s t aged at 450°C f o r d i f f e r e n t times (15 to 32 hours) and f i n a l l y aged at 300°C f o r 24 hours to e s t a b l i s h the e q u i l i b r i u m matrix composition of 0.45 wt % Cu. 2.2.2 S.A.P. A l o t of d i f f i c u l t i e s were experienced i n the f u r t h e r f a b r i c a t i o n of a s - s u p p l i e d S.A.P. rod. An attempt to forge the c y l i n d r i c a l rod i n t o a slab shape was unsuccessful s i n c e cracks were produced at the centre of the c i r c u l a r c r o s s - s e c t i o n . Hot r o l l i n g , a p p l i e d to t h i c k rectangular s e c t i o n s machined from the centre of the rod, produced numerous edge cracks. I n c r e a s i n g the hot r o l l i n g temperature to 540°C d i d not produce any improvement. E v e n t u a l l y i t was found that only t h i n s l i c e s cut from the as-extruded rod could s u s t a i n f u r t h e r heavy deformation. S l i c e s i n i t i a l l y 0.3 i n . t h i c k were machined to provide them w i t h smooth s u r f a c e s , the f i n a l t hickness being 0.25 i n . - 17 -Each s l i c e was hot r o l l e d at 540°C, i n many passes, to a thickness of 0.1 i n . During t h i s p r e l i m i n a r y hot r o l l i n g , a r e d u c t i o n i n thickness of only about 0.01 i n . was p o s s i b l e i n each pass, and the s t r i p was reheated to 540°C a f t e r every pass. The r e s u l t i n g s t r i p was then cut i n t o lengths of 4 i n . , tapered on one end, cleaned i n d i l u t e NaOH s o l u t i o n and annealed at 540°C f o r 2.5 hours. The f i n a l hot r o l l i n g was c a r r i e d out at 540°C under the same c o n d i t i o n s as f o r the A, C, and D s e r i e s . In one pass the thickness was reduced by 0.032 i n . which corresponded to 32% r e d u c t i o n and a c a l c u l a t e d mean s t r a i n r a t e of 1200 min The hot r o l l e d product was quenched i n water immediately, and stored at -20°C to avoid p o s s i b l e f u r t h e r s t r u c t u r a l m o d i f i c a t i o n s . A f t e r hot r o l l i n g , most S.A.P. s t r i p s were cleaned i n d i l u t e NaOH s o l u t i o n and co l d r o l l e d 50% to 0.034 i n . t h i c k n e s s . They were then annealed at 300°C or 540°C f o r v a r y i n g times. The reason f o r using two annealing temperatures i n t h i s case i s explained l a t e r i n the t h e s i s . Other hot r o l l e d S.A.P. s t r i p s were given v a r i a b l e reductions i n thickness by co l d r o l l i n g ; 0-70 percent. In the case of Al-4Cu, A l and S.A.P., annealing treatments were performed only a f t e r punching out t e n s i l e specimens as described i n the next s e c t i o n . The specimens were a i r - c o o l e d a f t e r the required annealing treatments. 2.3 T e n s i l e T e s t i n g 2.3.1 P r e p a r a t i o n of T e n s i l e Specimen T e n s i l e specimens were sheared from the co l d r o l l e d s t r i p s by means of a pneumatically operated punch and d i e se t . The t e n s i l e a x i s - 18 -was i n the r o l l i n g d i r e c t i o n . The reduced s e c t i o n of the specimen was 2.75 i n . long and 0.75 i n . wide, and the c e n t r a l 0.8 i n . length of the reduced s e c t i o n was used as the gauge length. In case of Al-4Cu a l l o y s , where the thickness of the s t r i p was more than 0.050 i n . , t e n s i l e specimens of the same gauge length were obtained by m i l l i n g r a t h e r than shearing. T e n s i l e specimens were p o l i s h e d l i g h t l y w i t h f i n e emery paper then chemically p o l i s h e d i n a 10% NaOH s o l u t i o n , and f i n a l l y washed i n d i l u t e HNO^ and i n water. 2.3.2 T e n s i l e T e s t i n g Procedure A l l specimens were test e d on a Fl o o r Model I n s t r o n T e n s i l e Machine -3 -1 at a s t r a i n r a t e of 6.25 x 10 min . The t e s t temperatures were 20°C (0.32 Tm) and 300°C (0.62 Tm). Since the ageing and annealing treatments f o r Al-4Cu a l l o y s were a l l c a r r i e d out at 300°C, the same temperature was chosen as a t e s t temperature. A p o r t a b l e s a l t pot w i t h Draw Temp 275 s a l t was used to heat specimens f o r the high temperature t e s t s . The bath could be r a i s e d to accommodate the specimen and the g r i p s . Temperature of the s a l t bath was held to w i t h i n ± 2°C of the reported value throughout the t e s t by v a r y i n g the input to the e l e c t r i c r e s i s t a n c e h e a t i n g element as requ i r e d . The molten s a l t was s t i r r e d continuously to maintain a constant temperature throughout the bath. Specimen temperature was followed by means of a thermocouple wired to the gauge length. I t was found that the specimen a t t a i n e d 300°C i n approximately two minutes, f o l l o w i n g which the assembly was hel d at t h i s temperature f o r 10 minutes before proceeding with the t e s t . - 19 -Wedge-type g r i p s made of heat t r e a t e d I n c o n e l , w i t h f i l e - f a c e jaw p i e c e s , were used f o r the t e n s i l e t e s t s . The mating surfaces of the g r i p assembly were coated w i t h a s o l u t i o n of molybedunum s u l f i d e on the i n s i d e as were a l l threaded components of the assembly. A smooth load-elongation curve was obtained on the recording chart under these c o n d i t i o n s . 2.4 X-Ray D i f f r a c t i o n 2.4.1 P r i n c i p l e X-ray l i n e p r o f i l e a n a l y s i s was used to determine the nonuniform l a t t i c e s t r a i n and the coherent c r y s t a l l i t e domain s i z e . The t h e o r e t i c a l X-ray i n t e n s i t y of any r e f l e c t i o n (hkl) can be expressed i n the form of a F o u r i e r s e r i e s whose c o e f f i c i e n t s can be obtained from the Fo u r i e r transform i n t e g r a t i o n . The cosine c o e f f i c i e n t s of the F o u r i e r s e r i e s are r e l a t e d to the l a t t i c e s t r a i n and the domain s i z e . By ana l y s i n g two orders of the same r e f l e c t i o n the non-uniform l a t t i c e s t r a i n and the coherently d i f f r a c t i n g domain s i z e can be e a s i l y determined. A review of the t h e o r e t i c a l b a s i s of the X-ray l i n e p r o f i l e a n a l y s i s i s given i n S e c t i o n 3.1. 2.4.2 Specimen P r e p a r a t i o n Specimens of s i z e 1.5 i n long by 1 i n . wide were sheared from r o l l e d s t r i p , the longer dimension being i n the r o l l i n g d i r e c t i o n . Both surfaces of each specimen were p o l i s h e d on a s e r i e s of emery papers w i t h kerosene l u b r i c a t i o n . The surface to be examined was then lapped - 20 -using 5 micron and 1 micron diamond paste. This procedure was followed by e l e c t r o p o l i s h i n g , u n t i l a smooth and b r i g h t surface was obtained. The e l e c t r o p o l i s h i n g i n v o l v e d the removal of about 0.002 i n . from each surface. For aluminum and Al-4Cu a l l o y s the e l e c t r o p o l i s h i n g s o l u t i o n was of the f o l l o w i n g composition: HN0 3 1 part methyl a l c o h o l 1 part HC1 1 cc per 50 cc of the mixture. The S.A.P. specimens were e l e c t r o p o l i s h e d i n a s o l u t i o n of 20 v o l % p e r c h l o r i c a c i d i n e t h y l a l c o h o l . This e l e c t r o l y t e was recommended by 40 44 Goodrich et a l . ' Heating of the e l e c t r o p o l i s h i n g s o l u t i o n was prevented by means of water-cooling c o i l s around the s t a i n l e s s s t e e l beaker which a l s o served as the cathode. To avoid p r e f e r e n t i a l l o c a l i z e d a t t a c k , the s o l u t i o n was s t i r r e d by a magnetic s t i r r e r . For S.A.P. -2 a l l o y s a p o t e n t i a l of 10-15 v o l t s and a current d e n s i t y of 0.04 amp cm were used. For aluminum and Al-4Cu a l l o y s the corresponding values were -2 5 v o l t s and 0.3 amps cm The d i f f e r e n t m a t e r i a l s and treatments examined by X-ray step-scanning are l i s t e d below: i ) Pure aluminum, AAL s e r i e s , cold r o l l e d 70%, i i ) Pure aluminum, AA1 s e r i e s , c o l d r o l l e d 70% and annealed at 300°C f o r 6 hours, i i i ) Al-4Cu, over-aged, i v ) Al-4Cu, B S e r i e s , hot r o l l e d , v) Al-4Cu, B S e r i e s , c o l d r o l l e d , 50% v i ) Al-4Cu, B S e r i e s , c o l d r o l l e d , 50% and annealed at 300°C f o r 4 hours, - 21 -v i i ) Al-4Cu, B S e r i e s , c o l d r o l l e d 70%, v i i i ) Al-4Cu, B S e r i e s , c o l d r o l l e d 70% and annealed at 300°C for 4 hours, i x ) S.A.P., as r e c e i v e d , x) S.A.P., hot r o l l e d , x i ) S.A.P., c o l d r o l l e d 50%, x i i ) S.A.P., co l d r o l l e d 50% and annealed at 540°C f o r 24 hours. 2.4.3 X-Ray D i f f r a c t i o n Procedure A P h i l i p s X-ray set was used, w i t h a step scanning device and a high speed d i g i t a l p r i n t e r f o r the output from the counter and timer. The goniometer divergence s l i t and s c a t t e r s l i t were each set to 2° and the r e c e i v i n g s l i t to 0.2 mm. N i c k e l - f i l t e r e d CuK^ r a d i a t i o n generated at 40 K.V. was used throughout. Tube currents were v a r i e d from 10 to 26 mA, depending on the thermomechanical h i s t o r y of the specimen, i n order to keep the counting i n t e r v a l to a minimum of 1 sec. fo r a f i x e d count of 20,000 pulses. For t h i s counting r a t e the timer e r r o r was 1.01% and f o r a l l counts of 20,000 pulses there was a 96% p r o b a b i l i t y of the e r r o r being w i t h i n 1.4%. In the step-scanning procedure the goniometer was advanced auto-m a t i c a l l y i n steps of 0.02° (20) from the s e l e c t e d s t a r t i n g angle on the low 0 side of the Bragg r e f l e c t i o n peak. To s t a r t w i t h , the X-ray apparatus was c a l i b r a t e d and a l i g n e d using a s i l i c o n standard. The d i f f e r e n t {hkl} r e f l e c t i o n peaks f o r A l were then l o c a t e d using a continuous scan w i t h a goniometer movement of 1° (29) min ^ coupled w i t h a chart speed of 600 mm hr and a time - 22 -constant of 4 sec. These peaks were compared w i t h A.S.T.M. values. For b e t t e r accuracy i t i s a d v i s a b l e to scan a set of p a r a l l e l r e f l e c t i o n s . In t h i s case the (111) and (222) r e f l e c t i o n s could not be scanned because of the l i m i t a t i o n s imposed on the minimum 20 angle by the divergence and s c a t t e r s l i t s . The (220) r e f l e c t i o n s were strong enough to be recorded but the (440) r e f l e c t i o n s could not be recorded on the a v a i l a b l e d i f f r a c t o m e t e r using CuK r a d i a t i o n . The (200) and (400) a r e f l e c t i o n s were found to be the most s u i t a b l e i n terms of i n t e n s i t y and a v a i l a b i l i t y . To determine the lower and upper angular l i m i t s to be used f o r the step scan , the (200) and (400) r e f l e c t i o n s were scanned continuously i n a range of 15° (20) f o r each m a t e r i a l c o n d i t i o n w i t h a goniometer movement of 0.25° (20) min On the b a s i s of observations from the continuous scans, a range of 8° (20) was subsequently step scanned i n steps of 0.02° (20) r e s u l t i n g i n a set of 400 readings f o r each l i n e . At each step the times to count 20,000 pulses were p r i n t e d a u t o m a t i c a l l y , each time being r e l a t e d r e c i p r o c a l l y to d i f f r a c t e d X-ray i n t e n s i t y . In order to remove the e f f e c t s of instru m e n t a l broadening from the convolution of the observed i n t e n s i t i e s , a well-annealed aluminum powder standard, which gave no X-ray l i n e broadening due to l a t t i c e s t r a i n or small domain s i z e , was step scanned i n the same range f o r each r e f l e c t i o n . The 1 micron aluminum powder (99.99% pure) was vacuum sealed i n a pyrex glass tube and annealed at 500°C f o r 80 minutes. In the case of over-aged Al-4Cu c o n t a i n i n g CuAl^ p a r t i c l e s , the (400) r e f l e c t i o n could not d i r e c t l y be recorded because of the presence of cube - 23 -t e x t u r e . On t i l t i n g the specimen from i t s h o r i z o n t a l p o s i t i o n , a broad (400) peak was obtained. The specimen was moved by hand u n t i l the (400) r e f l e c t i o n peak was maximized, and i n t h i s p o s i t i o n a step-scan was c a r r i e d out. This t i l t i n g of the specimen caused a r e d u c t i o n i n the i n t e g r a t e d i n t e n s i t y of the (200) r e f l e c t i o n , but the half-peak width s u f f e r e d no change. An i n i t i a l treatment of the numerical data from the X-ray d i f f r a c t i o n a n a l y s i s was necessary to remove the c o n t r i b u t i o n to i n t e n s i t y of l i n e s and some r e f l e c t i o n s f o r CuAl^ i n the case of most m a t e r i a l s c o n t a i n i n g t h i s phase. In the case of the simple over-aged Al-Cu a l l o y , and of S.A.P. specimens, overlapping r e f l e c t i o n s due to the presence of C u A l 2 and A^O^ r e s p e c t i v e l y were not recorded on the d i f f r a c t o m e t e r . The (200) r e f l e c t i o n s f o r the cold r o l l e d and c o l d rolled-and-annealed Al-4Cu m a t e r i a l s occurred at 26 = 44.74°, and the overlapping r e f l e c t i o n s were i ) K l i n e f o r A l (200) at 29 = 40.25°, i i ) K g l i n e f o r C u A l 2 (202) and (130) at 20 = 42.14°, i i i ) K l i n e f o r CuAl„ (112) at 20 = 42.70°, i v ) K l i n e f o r CuAl„ (202) and (130) doublet at 20 = 47.40° a I and 47.90°. For the Al-Cu (400) l i n e o c c u r r i n g at approximately 20 = 99° the overlapping r e f l e c t i o n s were, i ) l i n e f o r C u A l 2 (134) at 20 = 97.05°, i i ) l i n e f o r C u A l 2 (600) at 20 = 99.75° (barely d i s c e r n i b l e ) . The c o n t r i b u t i o n to i n t e n s i t y from these overlapping r e f l e c t i o n s were removed by simply smoothing out the t r a c e on the d i f f r a c t o m e t e r chart - 24 -recording i n the appropriate regions. Interpolated i n t e n s i t y values so obtained were then inserted as appropriate r e c i p r o c a l s i n place of the corresponding time values i n the set of times for 20,000 counts obtained previously on the p r i n t e r output. A l l other treatment of the X-ray data i s discussed i n Section 3 of the th e s i s . 2.5 Metallography i 2.5.1 O p t i c a l Microscopy Mounted and polished specimens were etched with d i f f e r e n t reagents to reveal grain boundaries and/or second phase p a r t i c l e s . For pure aluminum, a f r e s h l y prepared s o l u t i o n containing 46.2 cc of HF, 46.2 cc of water and 7.6 cc of HC1 was found to be a s a t i s f a c t o r y etchant. Al-4Cu a l l o y s were etched with K e l l e r ' s reagent, the composition of which i s as follows: HF (cone) 1.0 cc HC1 (cone) 1.5 cc HN03 (cone) 2.5 cc water 95.0 cc S.A.P. was e f f e c t i v e l y etched i n a so l u t i o n of 1% HF by volume i n water. 2.5.2 Electron Microscopy Thin f o i l s of aluminum, Al-4Cu and S.A.P. were examined using an Hi t a c h i HU-11A electron microscope operated at 100 K.V. F o i l s suitable for transmission electron microscopy were prepared by - 25 -e l e c t r o p o l i s h i n g using the standard "window method". The e l e c t r o -p o l i s h i n g s o l u t i o n s and c o n d i t i o n s were the same as those already described i n Sectio n 2.4.2. One d i f f i c u l t y was faced i n preparing t h i n f o i l s from over-aged Al-4Cu a l l o y s . Some of the second phase p a r t i c l e s tended to d i s s o l v e p r e f e r e n t i a l l y during e l e c t r o p o l i s h i n g producing holes i n the f o i l s i n place of the p r e c i p i t a t e s . These holes were more numerous near the edge of the f o i l as would be expected. This d i f f i c u l t y was e l i m i n a t e d p a r t i a l l y by i n c r e a s i n g the vo l t a g e from 5 v o l t s to about 10 v o l t s a f t e r p e r f o r a t i o n of the specimen f i r s t occurred during e l e c t r o p o l i s h i n g . A r e p l i c a t i o n technique was adopted to r e v e a l the second phase p a r t i c l e s i n over-aged Al-4Cu a l l o y s . Conventional two-stage carbon r e p l i c a s were used, w i t h chromium shadowing f o r co n t r a s t . 2.5.3 Measurement of Grain S i z e and Subgrain S i z e The l i n e a r i n t e r c e p t method was used to determine the g r a i n s i z e of aluminum and Al-4Cu a l l o y s from o p t i c a l micrographs, and to determine the subgrain s i z e of A l , Al-4Cu and S.A.P. a l l o y s from trans m i s s i o n e l e c t r o n micrographs. The s i z e of elongated grains produced by r o l l i n g can be measured by any of the counting methods. Measurements must be made i n three mutually perpendicular d i r e c t i o n s , which form an orthogonal t r i p l e t . The g r a i n s i z e , expressed as the number of grains per cubic m i l l i m e t e r • 47 (Nv), can be c a l c u l a t e d from e i t h e r of the f o l l o w i n g equations: Nv = 0 . 7[N AU) N A ( t ) N A ( n ) ] 1 / 2 (3) - 26 -Nv = 0.7[NLU) N L ( t ) N L ( n ) ] (4) where N (£)•, N ( t ) , and N (n) are the number of grains per square A. A A. m i l l i m e t e r i n each of the three s e c t i o n a l planes ( l o n g i t u d i n a l , t r a n s -verse, and normal), and N (£), N ( t ) , and N (n) are the number of grains Li J-j Li per u n i t of length i n d i r e c t i o n s £, t , and n, r e s p e c t i v e l y . 2.5.4 Determination of Volume F r a c t i o n of P r e c i p i t a t e s The volume f r a c t i o n , f , of 0 p r e c i p i t a t e s i n over-aged a l l o y s was c a l c u l a b l e from the Al-Cu phase diagram ( F i g . 2), the d e n s i t y of the alpha s o l i d s o l u t i o n , and the den s i t y of the 0 phase. Taking a den s i t y of 4.35 gms per cc f o r CuA^, a den s i t y of 2.73 gms per cc f o r the alpha s o l i d s o l u t i o n , and assuming the s o l i d s o l u t i o n to conta i n the e q u i l i b r i u m concentration of copper, 0.45 wt %, the volume f r a c t i o n , f, was found to be 0.043. For the S.A.P. a l l o y the volume f r a c t i o n of the oxide phase was s i m i l a r l y c a l c u l a t e d from a knowledge of the weight f r a c t i o n (w) and the d e n s i t y (p 2) of the oxide (Al^O^) according t o : wp,* f = ~n—r^r (5) (l-w)p 2+wp 1 where i s the density of the aluminum matrix (2.73 gms per c c ) . The d e n s i t y of the oxide phase, measured on consolidated products by 49 Hansen, was taken as 3.4 gms per cc. The volume f r a c t i o n f o r A^O^ i n S.A.P. was found to be 0.084. - 27 -Figure 2. Phase diagram of Al-4Cu on the aluminum-rich s i d e . (In t h i s f i g u r e the K-phase i s the same as the alpha-phase mentioned i n the t h e s i s ) . - 28 -2.5.5 C a l c u l a t i o n of I n t e r p a r t i c l e Spacings The mean planar p a r t i c l e radius (r ) and the mean planar i n t e r -p a r t i c l e spacing of 6 p r e c i p i t a t e s i n over-aged Al-4Cu a l l o y s were c a l c u l a t e d from r e p l i c a e l e c t r o n micrographs. The method was described by Dew-Hughes and Robertson,^ and assumes a uniform d i s t r i b u t i o n of s p h e r i c a l p r e c i p i t a t e s throughout the matrix (an assumption which i s not p e r f e c t l y v a l i d i n these a l l o y s ) . Assuming that each p a r t i c l e i n the plane of p o l i s h i s associated w i t h a " c i r c l e of i n f l u e n c e " of radius R^, the volume f r a c t i o n , f , ofthe second phase p a r t i c l e i s given by •r 2 f = -^T (6) R c I f i s the number of p a r t i c l e s per u n i t area of planar s e c t i o n , then i t f o l l o w s that N = (7) P TTR 2 c The mean planar i n t e r p a r t i c l e d i s t a n c e , D g, i s approximately equal to 2R c < Thus, knowing the number of p a r t i c l e s i n t e r c e p t e d by the plane per u n i t area, the mean planar i n t e r p a r t i c l e distance and the mean planar p a r t i c l e radius can be c a l c u l a t e d . In the case of S.A.P., the planar mean f r e e path (m) of the oxide p a r t i c l e s was determined from the Fullman"^ r e l a t i o n s h i p : »- " T 1 (8) L - 29 -where N i s the number of p a r t i c l e s per u n i t length i n t e r s e c t i n g a Li random l i n e on a p o l i s h e d s e c t i o n . The average s p h e r i c a l p a r t i c l e diameter (d) was then obtained using a deduction^"'" from Fullman's formula: 3*2 ( 9) 2 ( l - f ) w The mean planar p a r t i c l e spacing (D g) i s an e n t i r e l y d i f f e r e n t q u a n t i t y from the mean f r e e path (m). The former i s the average distance between nearest neighbours on a plane whereas the l a t t e r i s the mean u n i n t e r -rupted path between p a r t i c l e s . The qu a n t i t y was computed from the formula D s = dCl-fWl! (10) 3. USE OF X-RAY TECHNIQUES TO ANALYSE  DISLOCATION DENSITY AND CONFIGURATION 3.1 Basis of X-Ray Line P r o f i l e Analysis Non-uniform l a t t i c e s t r a i n and small coherent c r y s t a l l i t e domain si z e i n metals and allo y s can be determined from the measurement of X-ray d i f f r a c t i o n l i n e broadening. The evaluation i s r e l a t i v e l y s t r a i g h t -forward when these two e f f e c t s occur separately, and standard text 52 53 books ' deal with the appropriate treatments. Usually these two e f f e c t s occur together and t h e i r evaluation becomes more complex. Based on 54-61 41 the e a r l i e r work of many workers, Clegg has reviewed the t h e o r e t i c a l basis of the measurement of non-uniform l a t t i c e s t r a i n and coherent c r y s t a l l i t e domain s i z e i n metals by the X-ray l i n e p r o f i l e technique. Under conditions of non-uniform l a t t i c e s t r a i n and small c r y s t a l l i t e domain siz e the experimentally-measured d i f f r a c t e d X-ray power per unit length of d i f f r a c t i o n l i n e , q'(29), at a given Bragg angle, e, i s given by the following equation, q* (26) = k(6) ^ - EN(t) [COS2TTJ t cos2Trh X(t) - s i n 2 i r j 1t sin2rrh X(t)] Nl t 1 1 ( I D - 31 -where, N = number of c e l l s i n the coherently d i f f r a c t i n g domain and equal to N^N^N^; N^, and being the average number of c e l l s i n the d i r e c t i o n s a_^, a^ and a.^  r e s p e c t i v e l y , = f u n c t i o n of the angle (20), h = order of the r e f l e c t i o n (hOO) X( t ) = f u n c t i o n of the l a t t i c e s t r a i n , = f u n c t i o n of the domain s i z e f o r i n t e g r a l values of the harmonic number ( t ) . To o b t a i n X ( t ) and experimentally they are combined i n the 1 f o l l o w i n g d e f i n i t i o n s , A(t) • = cos2uh X(t) 1 B(t) = sin2uh X ( t ) 1 From equation (11) f u n c t i o n k(0) can be e l i m i n a t e d by an angular c o r r e c t i o n f o r both L b r e n t z - P o l a r i z a t i o n and the Atomic S c a t t e r i n g Factor and the 2(0) v a r i a b l e can be redefined i n terms of the d i s t a n c e x on the (26) a x i s of the experimentally recorded X-ray d i f f r a c t i o n p r o f i l e ; x being i n u n i t s of s i n 0 . In a d d i t i o n , the harmonic number (t) can be r e l a t e d to the true l a t t i c e d i s t a nce (L) measured i n the c r y s t a l i n the d i r e c t i o n perpendicular to the d i f f r a c t i n g planes, as shown by 56 Wagner. Thus the t h e o r e t i c a l X-ray i n t e n s i t y of equation (11) can be expressed i n the form of the f o l l o w i n g equation, q(x) = E [A(L)COS2TTL -f- x + B(L)sin2iTL |- x] (12) - 32 -where X i s the wavelength of X-ray beam. Equation (12) has the form of a F o u r i e r s e r i e s f o r a f u n c t i o n q(x) from which the c o e f f i c e n t s A(L) and B(L) can be obtained from the transform i n t e g r a t i o n . For the summation of X-ray i n t e n s i t y p r o f i l e s an o r i g i n must be 56 chosen on the sin9 or x a x i s . According to Wagner i f the c e n t r o i d of the X-ray r e f l e c t i o n i s chosen as the o r i g i n , the imaginary or s i n e c o e f f i c i e n t s , B ( L ) , of the derived f u n c t i o n q(x) w i l l be small and the r e a l or cosine c o e f f i c i e n t s , A ( L ) , w i l l have only small o s c i l l a t i o n s . Hence from a knowledge of the cosine c o e f f i c i e n t s both the c r y s t a l l i t e domain s i z e and the extent of non-uniform short range e l a s t i c s t r a i n can be determined. By d e f i n i t i o n , A(L) = cos2Trh X(L) By d e f i n i n g ^,9^ as the Domain S i z e C o e f f i c i e n t A^(L) and c o s 2 u h X(L) 1 S as the order dependent S t r a i n C o e f f i c i e n t A ( L , h Q ) , i . e . A(L,h o) = D S A (L) A (L,h ), the f i n a l working expression i s given by the f o l l o w i n g equation, 2 2 2 Hn A(L,h Q) = £nA°(L) - 2TT2 E 1 ( 1 3 ) where e i s the s t r a i n i n a distance L measured i n the a^ d i r e c t i o n , "a* 2 2 2 1/2 i s the f . c . c . l a t t i c e parameter and h Q = (h +k +£ ) From equation (13), using two orders of an (hoo) r e f l e c t i o n , a set of s t r a i g h t l i n e s can be drawn w i t h values of £n A(L,h Q) as 2 ordinates and the values of h as abscissae, each chosen value of L - 33 -2 r e s u l t i n g i n one l i n e of In A(L,h ) vs. h . The slope of each of these - 2 A 2 L 2 ° 2 l i n e s i s equal to ^ > from which values of mean square s t r a i n e a 2 are obtained for a range of values of L. e i s the s t r a i n i n the [hoo] d i r e c t i o n for a cubic l a t t i c e , averaged over the length L, squared, and averaged over the region from which the r e f l e c t i o n comes. The 2 1/2 graph of (e ) vs. L shows the d i s t r i b u t i o n of non-uniform s t r a i n as a function of distance i n the c r y s t a l . 2 2 From the intercepts of £n A(L,ho) vs. h with h =0 axis values of fcn A^(L) are obtained, converted to A^(L), normalized to unity for L = 0, and plotted as function of L. The average domain s i z e comes from this plot of A^(L) vs. L by two c r i t e r i a ; f i r s t l y from twice the area under the curve and secondly from the negative r e c i p r o c a l slope of A°(L) vs. L at a s p e c i f i e d distance from L = 0 equal to 20% of the approximate domain s i z e f i r s t calculated. This distance i s s p e c i f i e d i n order to avoid the negative curvature or otherwise c a l l e d the "hook e f f e c t " i n the region approaching L = 0 i n the p l o t of A°(L) vs. L. This error arises because of inaccuracies i n the measurement of the true background l e v e l of the observed p r o f i l e which re s u l t s i n low values for the measured area under the X-ray peak. The boundary of a domain could be a grain boundary, subgrain boundary, stacking f a u l t or twin boundary across which the misorientation of the two adjacent l a t t i c e s i s such that the Bragg law cannot be s a t i s f i e d by them for a common incident X-ray i n t e n s i t y . In p r a c t i c e , the observed X-ray p r o f i l e i s not described completely by equation (12) but contains i n addition a c e r t a i n degree of i n s t r u -mental broadening which i s due to the X-ray optics and imperfections of - 34 -the apparatus used. To o b t a i n an experimental X-ray r e f l e c t i o n p r o f i l e which i s broadened only by s t r a i n and domain s i z e e f f e c t s , the procedure g e n e r a l l y known as the "Stokes c o r r e c t i o n " i s used. This in v o l v e s the u n f o l d i n g of the observed conv o l u t i o n of i n t e n s i t i e s using a standard p r o f i l e obtained from a s t r a i n - f r e e annealed sample of r e l a t i v e l y coarse g r a i n s i z e . P art of the observed X-ray l i n e broadening, t a k i n g the form of an asymmetry towards higher angles, a r i s e s because of the dual wavelengths of the K /K doublet i f the K r a d i a t i o n i s being used. The K a 2 a a 2 wavelength can be removed at the source using a c r y s t a l monochromator, or a l t e r n a t i v e l y , as was done i n the present study, i t s c o n t r i b u t i o n to the observed X-ray l i n e p r o f i l e can be removed by a stepwise procedure 5 8 known as the Rachinger c o r r e c t i o n . Stacking f a u l t s and twin boundaries a l s o c o n t r i b u t e to the symmetrical l i n e broadening through the Domain Si z e C o e f f i c i e n t . Hence the domain s i z e D must be correc t e d by u t i l i z i n g the f o l l o w i n g expression, where, D = domain s i z e as determined by X-ray data, D = true substructure domain s i z e excluding f a u l t boundaries, F D = domain s i z e due to s t a c k i n g f a u l t s and twins. For the case of (200) and (400) r e f l e c t i o n s i n an f . c . c . u n i t c e l l D i s expressed as D F ( 1 . 5 a + B ) ( 1 5 ) - 35 -where a = s t a c k i n g f a u l t p r o b a b i l i t y , 3 = twin f a u l t p r o b a b i l i t y , a = f . c . c . l a t t i c e parameter. Expressions have been derived by Warren"^ f o r a i n terms of 6 1 displacement of the peak maximum and by Cohen and Wagner f o r 3 i n terms of the peak asymmetry, i . e . the displacement of the peak maximum from the c e n t r o i d . For ( 2 0 0 ) and ( 4 0 0 ) r e f l e c t i o n s i n an f . c . c . l a t t i c e these expressions are „ PM - 4 5 /T A ( 2 6 >(200) " 2 * t a n 9 o ( 1 6 ) , , 1 O ^ P M +22.5 /3 ^ _ A ( 2 6 } ( 4 0 0 ) = 2 a t a n 6 o ( 1 7 ) CC PM ( A s y m . ) ( 2 ( ) 0 ) = ( 2 0 ° ) ( ^ o o ) - ( 2 e ' ) ( 2 ( J 0 ) = - 1 4 . 6 3tan0 o ( 1 8 ) CC P M C A s y m . ) ( 4 0 0 ) = ( 2 6 ° ) ( 4 0 0 ) - ( 2 0 ° ) ( 4 O Q ) = +14.6 3tan0 o ( 1 9 ) The s h i f t s of the peak maxima f o r ( 2 0 0 ) and ( 4 0 0 ) r e f l e c t i o n s must be i n opposite d i r e c t i o n s to prove positively the presence of s t a c k i n g f a u l t s ; otherwise l a t t i c e macro s t r a i n may have caused the s h i f t i n g . S i m i l a r l y , the asymmetries of the ( 2 0 0 ) and ( 4 0 0 ) r e f l e c t i o n s must be of opposite s i g n to prove p o s i t i v e l y the presence of twinning; otherwise the asymmetry may have been due to some instrument or doublet e f f e c t . 3.2 Computer A n a l y s i s 4 1 A modified computer programme w r i t t e n by Clegg i n Fortran IV f o r the IBM 3 6 0 / 7 0 computer was used to ca r r y out the summations to - 36 -o b t a i n the F o u r i e r c o e f f i c i e n t s and then to o b t a i n the cosine c o e f f i c i e n t s of the unfolded X-ray f u n c t i o n by complex d i v i s i o n . The computer programme a l s o c a r r i e d out the f o l l o w i n g operations f o r each m a t e r i a l and c o n d i t i o n : (a) Corrected f o r the angular dependence of X-ray i n t e n s i t y , i n c l u d i n g that of the atomic s c a t t e r i n g f a c t o r . (b) Converted the data i n t o corresponding i n t e n s i t y values at equal i n t e r v a l s of sin9.' (c) Subtracted the corresponding background i n t e n s i t y . (d) A p p l i e d the Rachinger c o r r e c t i o n to remove the i n t e n s i t y c o n t r i b u t i o n from the K component of the K doublet. (e) C a l c u l a t e d the c e n t r o i d of the r e f l e c t i o n and r e s c a l e d the i n t e n s i t y data to the c e n t r o i d as o r i g i n on the sin0 a x i s . (f) C a r r i e d out the i n t e g r a t i o n s and the complex d i v i s i o n s to o b t a i n the F o u r i e r c o e f f i c i e n t s f o r each X-ray r e f l e c t i o n and normalized these values of A(L) to u n i t y f o r L = 0. (g) Used these c o e f f i c i e n t s to c a l c u l a t e the root mean square l a t t i c e s t r a i n as a f u n c t i o n of l a t t i c e d i s t a n c e f o r each m a t e r i a l 2 1/2 D c o n d i t i o n , i . e . (e ) vs. L., and the domain s i z e c o e f f i c i e n t A (L) vs. L, w i t h reference to equation (13). 2 1/2 D (h) P l o t t e d (e ) vs. L and A (L) vs. L as g r a p h i c a l outputs. ( i ) C a l c u l a t e d the coherent c r y s t a l l i t e domain s i z e s from the l a t t e r graphs according to the two c r i t e r i a discussed e a r l i e r . - 37 -3.3 Determination of D i s l o c a t i o n D e n s i t i e s and Co n f i g u r a t i o n s from X-Ray Data The d i s l o c a t i o n d e n s i t y can be deduced from the domain s i z e and the s t r a i n broadening of the X-ray l i n e . To t h i s end, the work of 62 Williamson and Smallman i s u s u a l l y taken as the primary reference. Expressions (20) and (21) below have been derived by these authors to c a l c u l a t e d i s l o c a t i o n d e n s i t y from the domain s i z e and the s t r a i n breadth r e s p e c t i v e l y . p = ^ (20) D a n d p _ 6 I IEA 1 2__ _ ( 2 1 ) Gb F £n(r/ro) where p = d i s l o c a t i o n d e n s i t y , n = number of d i s l o c a t i o n s i n each face of the c r y s t a l l i t e domain, E = Young's modulus, A = a f a c t o r which depends on the shape of the s t r a i n d i s t r i b u t i o n , 5 = breadth of s t r a i n d i s t r i b u t i o n , G = shear modulus, b = Burgers ve c t o r of the d i s l o c a t i o n , F = d i s l o c a t i o n i n t e r a c t i o n f a c t o r , r = radius of the c r y s t a l c o n t a i n i n g the d i s l o c a t i o n , r = d i s l o c a t i o n core r a d i u s , o Williamson and Smallman have shown that the f a c t o r s A and £ can 2 2 be r e l a t e d to the mean square s t r a i n of the l a t t i c e e , i . e . , A£ = 2 e , that E/G i s approximately 2.6, and that Jin (r/ro) has a reasonable - 38 -value of 4. Taking b = 2.85 A f o r A l , equation (21) can be w r i t t e n as, i R 2 i n 1 6  1.5 e x 10 P = =: ( 2 2 > To apply equations(20) and (22) d i r e c t l y a model i s assumed i n which there i s only one d i s l o c a t i o n per domain boundary and a minimum of d i s l o c a t i o n i n t e r a c t i o n . This model gives n = 1, F = 1 and ;the d i s l o c a t i o n d e n s i t i e s are given by the f o l l o w i n g expressions: p p \ 7 ( 2 3 ) and P g = 1.5 e 2 x 1 0 1 6 (24) where and p g are the values c a l c u l a t e d from equations (20) and (22) r e s p e c t i v e l y using n = 1 and F = 1. In equation (23) the domain s i z e D should be corrected f o r the c o n t r i b u t i o n to l i n e broadening of s t a c k i n g f a u l t and twin boundaries. In the present work the d i s l o c a t i o n d e n s i t y was c a l c u l a t e d using equations (23) and (24) and then the d i s l o c a t i o n c o n f i g u r a t i o n was determined according to the f o l l o w i n g c r i t e r i a : p = p f o r random P s p < p f o r p i l e - u p s K p r s p > p f o r p o l y g o n i z a t i o n p s - 39 -A pile-up configuration represents the extreme degree of i n t e r a c t i o n making F greater than unity. In t h i s case F = n so that p = n p ^ = P /F. Then n = ( P s / P p ) 1 / 2 (25) Here n i s the average number of d i s l o c a t i o n s i n a pile-up. The true d i s l o c a t i o n density for th i s model was calculated from the expression: p = (p„ p ) 1 / 2 (26) & p On the other hand polygonization reduces the energy of each d i s l o c a t i o n . Thus F i s less than unity. Williamson and Smallman point out that under such conditions equation (21) should be modified to obtain the true d i s l o c a t i o n density and they show that equation (21) can be reduced to P = P s/F or p = p ftn(10 ^ )/&n (3 x 1 0 ? / p D ) (27) S . 2 ^ This equation i s best solved by t r i a l and error s t a r t i n g with p = p g i n the righthand side u n t i l the r e s u l t s are consistent with polygoniza-t i o n ( i . e . , F < 1). - 40 -4. RESULTS AND OBSERVATIONS 4.1 T e n s i l e Tests For t e n s i l e t e s t s at 20°C and 300°C, the r e s u l t s f o r aluminum and Al-4Cu w i l l be grouped together because these two m a t e r i a l s were subjected to s i m i l a r thermomechanical treatments. Results f o r S.A.P. w i l l be given s e p a r a t e l y . 4.1.1 Room Temperature Tests 4.1.1.1 Aluminum-4 Copper and Pure Aluminum Table I I summarizes the mean planar i n t e r p a r t i c l e spacings and the mean planar p a r t i c l e r adius of Al-4Cu a f t e r v a r i o u s simple ageing treatments ( f o l l o w i n g s o l u t i o n treatment) along w i t h the corresponding 20°C and 300°C y i e l d s t r e n g t h values. These r e s u l t s are f o r m a t e r i a l s which had received no thermomechanical treatment a f t e r s o l u t i o n treatment. As shown i n Table I I I and F i g . 3, the 20°C y i e l d and u l t i m a t e t e n s i l e strengths of the h o t - r o l l e d Al-4Cu a l l o y t Series B, rose r a p i d l y to 37 k s i (> 400%) and 18 k s i ('v 50%) r e s p e c t i v e l y as a r e s u l t of i n c r e a s i n g r e d u c t i o n by co l d r o l l i n g at 20°C. The data are f o r the B S e r i e s , wherein p r i o r hot r o l l i n g had been c a r r i e d out at 300°C on the two-phase (over-aged) m i c r o s t r u c t u r e . Pure aluminum was not studied i n d e t a i l f o r the same r o l l i n g treatments; however, both i t s y i e l d and Table I I : D i s p e r s i o n Parameters f o r Age-Hardened Al-4Cu A l l o y s and the Corresponding Y i e l d Strength Values at R.T. and 300°C. Ageing Treatment mean planar p a r t i c l e spacing, D s(y) mean planar p a r t i c l e r a d i u s , r ( u) D - 2r s s (D c - 2r ) s s X 0.2 % o f f s e t y i e l d s t r e n g t h , OQ,2 (Ksi) (y) D - 2r l o g 1 0 ( S 2b S ) Cy"1) RT 300°C 300°C, 68 mins. 300°C, 3.5 hrs. 300°C, 7.25 hrs. 300°C, 15 hrs. 300°C, 62 hrs. 450°C, 15 h r s . 300°C, 24 hrs. 450°C, 35 h r s . 300°C, 24 h r s . 0.630 0.660 0.705 1.300 1.600 2.760 4.160 0.065 0.068 0.072 0.135 0.165 0.286 0.430 0.500 0.524 0.560 1.030 1.270 2.190 3.30 5.86 5.66 5.34 3.16 2.73 1.64 1.14 19.3 18.7 18.0 13.3 10.9 8.5 7.4 8.3 7.5 7.1 5.9 4.6 3.0 2.3 - 42 -Table III : Room Temperature Tensile Results f o r Cold-Al-4Cu (B Series) •Rolled A l and Material % Reduction by Cold R o l l i n g a0.2 (Ksi) U.T.S. (Ksi) % Elongation Uniform Total 0 13.3 29.8 11.1 16.0 (Solution-treated and aged only) 0 8.5 34.9 13.0 15.0 (After Hot Rolling) V-i <u a. 30 30.1 41.2 3.7 6.4 p< o u 40 28.4 35.4 2.5 9.2 . <t i .num- 50 32.7 36.7 2.0 9.2 •n e 3 60 35.0 40.9 2.7 9.5 < 70 41.1 48.1 2.8 9.4 80 45.3 53.2 2.7 7.6 90 44.6 55.2 2.6 8.2 0* 1.8* 6.8* 46.2* 58.0* e 50 11.7 12.6 0.7 9.4 •H B 60 12.9 13.9 0.7 7.2 <! a) 70 14.5 14.9 0.5 7.1 PL, 80 15.6 16.5 0.5 3.2 data f or f u l l y r e c r y s t a l l i z e d aluminum. - 43 -A l - 4 C u Aluminum U.T.S. A • 0 20 40 60 80 100 % R e d u c t i o n by R o l l i n g a t 20°C. F i g u r e 3. 20°C Data showing t h e e f f e c t s o f c o l d r o l l i n g on the s t r e n g t h o f A l and A l - 4 C u (B S e r i e s ) . - 44 -ul t i m a t e t e n s i l e s t r e n g t h were increased by only 4 K s i as the r e d u c t i o n by r o l l i n g at 20°C was increased from 50% to 80%. There was an anomalous drop i n the y i e l d and u l t i m a t e strengths of the Al-Cu a l l o y a f t e r reductions between 30% and 40%, which shows c l e a r l y i n F i g . 3. I t i s i n t e r e s t i n g to note that the c o l d r o l l e d two-phase a l l o y shows higher d u c t i l i t y than the pure metal a f t e r comparable amounts of deformation beyond about 50% re d u c t i o n . F i g . 4 shows the e f f e c t of annealing at va r i o u s temperatures f o r a f i x e d annealing time of one hour, on the 20°C y i e l d s t r e n g t h of aluminum and of Al-4Cu a l l o y s which were p r e v i o u s l y c o l d - r o l l e d 70%; a l l o y s from the A, B and D s e r i e s are inc l u d e d . Data has also been p l o t t e d f o r two c o l d - r o l l e d aluminum m a t e r i a l s of d i f f e r e n t p r i o r thermomechanical h i s t o r y , but there i s l i t t l e d i f f e r e n c e between t h e i r responses to annealing. F i g . 4 reveals that s e r i e s A, B, and D m a t e r i a l s had comparable 20°C y i e l d strengths a f t e r being c o l d - r o l l e d 70%; i . e . t h e i r p r i o r s t r u c t u r a l and deformation h i s t o r y had l i t t l e e f f e c t on the stre n g t h a t t a i n e d at t h i s stage. Moreover, the responses of the three m a t e r i a l s to annealing a f t e r 70% c o l d work were e s s e n t i a l l y i d e n t i c a l i n terms of y i e l d s t r e n g t h at 20°C a f t e r one hour of annealing. S i m i l a r p l o t s were obtained i f the u l t i m a t e t e n s i l e s t r e n g t h was s u b s t i t u t e d f o r the y i e l d s trength. An i n t e r e s t i n g f e a t u r e of the data of F i g . 4 i s that there i s a steady decrease i n stre n g t h of Al-4Cu w i t h increase i n annealing temperature i n the range 50-250°C, whereas pure aluminum s u f f e r s very l i t t l e change i n stre n g t h up to an annealing temperature of 250°C. Above 250°C, the curves of F i g . 4 are s i m i l a r i n nature, i n d i c a t i n g a - 45 -44 I : Figure 4. 20°C Data showing the e f f e c t s of annealing temperature on the y i e l d strength of Al-4Cu (B Series) vs. pure aluminum af t e r 70% C.W. - 46 -rapid decrease i n strength with increasing annealing temperature up to 350°C. Fi g . 5 shows t y p i c a l 20°C t e n s i l e elongation (uniform) values corresponding to the y i e l d strength data of F i g . 4. In case of pure cold worked aluminum, the elongation remains at a constant low l e v e l a f t e r annealing at temperatures up to and including 250°C. Further increases i n the annealing temperature cause a rapid and large r i s e i n the elongation value. For the c o l d - r o l l e d Al-Cu two-phase a l l o y s , the elongation a c t u a l l y decreased s t e a d i l y as a r e s u l t of annealing at annealing temperatures i n the range of 50-200°C. Annealing at higher temperatures produced a marked increase i n elongation, although the absolute values attained were appreciably lower for the a l l o y than for the pure metal. There was again no s i g n i f i c a n t d i f f e r e n c e i n response among the a l l o y Series A, B, and D; only Series B data are p l o t t e d . Other annealing experiments involved the use of a constant annealing temperature of 300°C, with varying times i n the range 0-20 hours. Results of such experiments are shown i n F i g . 6 for a Series A two-phase Al-4Cu a l l o y which had been reduced 70% by cold r o l l i n g . The form of those curves was s i m i l a r for Series A and B, as well as for pure aluminum. However, there were some quantitative d i f f e r e n c e i n the response of the 20°C strength of the d i f f e r e n t materials to annealing time, as revealed i n F i g . 7 for y i e l d strength and i n F i g . 8 for U.T.S. S p e c i f i c a l l y , there were differences i n the rate of response to annealing at 300°C for the d i f f e r e n t materials, and i n the "end-point" strength values reached i n a l l cases a f t e r about 6 hours of annealing. In the - 47 -i . ' ' ' I I 1 1 50 1 0 0 1.10 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0 A n n e a l i n ) : ' IVmpt . ' ra t u i "e , ° C . Figure 5. 2CTC Data showing the e f f e c t s of annealing temperature on the uniform e l o n g a t i o n of Al-4Cu (B Se r i e s ) vs. pure aluminum a f t e r 70% C.W. Annealing Time at 300°C, hrs. Figure 6. 20°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (A Series) a f t e r 70% C.W. CO 16 18 20 8 10 12 14 Annealing Time at 300°C, hrs. Figure 7. 20°C Data showing the e f f e c t s of annealing time at 300°C on the y i e l d s t r e n g t h of Al-4Cu vs. pure aluminum a f t e r 70% C.W. 22 CO H 15©-10 O B © A • c • AAL -3 -1 e = 6.25 x 10 min ± ± ± ± ± 16 Figure 8. 18 20 2 4 6 8 10 12 14 Annealing Time at 300°C, hrs. 20°C Data showing the e f f e c t s of annealing time at 300°C on the U.T.S. of Al-4Cu vs. pure aluminum a f t e r 70% C.W. - 51 -0.2% flow s t r e s s v a l u e s , there was some d i f f e r e n c e i n the behaviour of Series A and B m a t e r i a l s , i n s p i t e of the apparent s i m i l a r i t i e s of t h e i r thermal and mechanical h i s t o r i e s . The Se r i e s C a l l o y , f o r which annealing at 300°C a f t e r c o l d work a l s o c o n s t i t u t e d an age-hardening step, shows remarkably s i m i l a r behaviour to Se r i e s A and B a l l o y s i n F i g s . 7 and 8. The strength of the Series C a l l o y was higher than that of other Al-Cu m a t e r i a l s a f t e r annealing f o r 6 or more hours at 300°C. 4.1.1.2 S.A.P. Room temperature t e n s i l e data f o r c o l d - r o l l e d S.A.P.'are summarized i n Table IV and i n F i g . 9. A f t e r hot r o l l i n g and before c o l d r o l l i n g Table IV: Room-Temperature T e n s i l e Results f o r Cold-Rol l e d S.A.P. % Cold Work an 9 U.T.S. % Elongation (Ksi) (Ksi) Uniform T o t a l 0 29.5 37.6 4.3 10.3 (A f t e r Hot R o l l i n g ) 10 35.2 41.6 2.2 6.3 20 36.6 42.1 1.8 2.0 30 37.0 42.6 1.4 8.7 40 35.0 42.1 1.8 4.5 50 34.9 42.4 2.0 7.0 60 33.8 40.8 2.9 6.3 70 35.4 42.0 2.0 8.7 - 52 -50 45 R.T O a 9 0.2 U.T.S. -3 -1 e = 6.25 x 10 min •H 25 20 300°C 0.2 © U.T.S. Figure 9. 10 20 70 30 40 50 60 % Reduction by R o l l i n g at 20°C 20°C and 300°C Data showing the e f f e c t s of cold r o l l i n g on the strength of S.A.P. - 53 -S.A.P. had high 20°C stre n g t h and low t e n s i l e e l o n g a t i o n compared to Al-4Cu. However, the response of the stre n g t h of S.A.P. to c o l d r o l l i n g was much smaller than that of the Al-Cu a l l o y m a t e r i a l s , as seen by comparing Tables I I I and IV. Moreover, the absolute values of both y i e l d and u l t i m a t e strengths i n Al-Cu were appreciably higher a f t e r heavy c o l d working than i n S.A.P. a f t e r comparable deformation. Elongation values f o r the two types of a l l o y s were s i m i l a r a f t e r s i m i l a r reductions by co l d r o l l i n g , and were higher than those e x h i b i t e d by pure aluminum. The isothermal annealing behaviour of S.A.P. was very d i f f e r e n t from that of Al-4Cu m a t e r i a l s . An annealing treatment of a few hours at 300°C was s u f f i c i e n t to decrease the y i e l d s trength of 70% co l d worked Al-4Cu by about 50%. In the case of 50% co l d worked S.A.P., however, 72 hours of annealing at 300°C d i d not produce any dete c t a b l e decrease i n y i e l d or u l t i m a t e t e n s i l e s t r e n g t h . In f a c t , when c o l d - r o l l e d S.A.P. was annealed at 540°C f o r 24 hours, the y i e l d s t r e n g t h decreased by only 1400 p s i (from 34,900 p s i to 33,500 p s i ) , the U.T.S. decreased by 2200 p s i (f rom 42,400 p s i to 40,200 p s i ) , and the d u c t i l i t y was not a l t e r e d at a l l . 4.1.2 300°C Tests 4.1.2.1 Aluminur..-4 Copper Pur el-Aluminum F i g s . 10 and 11 show the t y p i c a l response of the high-temperature (300°C) t e n s i l e p r o p e r t i e s of an Al-4Cu a l l o y to s t a t i c annealing a f t e r 70% c o l d work. C o l d - r o l l e d specimens were s t a t i c a l l y annealed at 300°C f o r d i f f e r e n t times and then reheated to 300°C f o r t e n s i l e 0 2 4 6 8 10 12 14 16 18 Annealing Time at 300°C, hrs. Figure 10. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (A Series) a f t e r 70% C.W. _ 2 « I I I I t I I lo 2 4 6 8 10 12 14 16 18 Annealing time at 300°C, hrs. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (B Series) a f t e r 70% C.W. - 56 -t e s t i n g . As seen from the f i g u r e s , s t a t i c annealing caused an in c r e a s e i n the y i e l d s t r e n g t h of the cold-worked product and a decrease i n both the U.T.S. and the uniform e l o n g a t i o n . A f t e r about 6 hours of annealing there was very l i t t l e change i n st r e n g t h and d u c t i l i t y . Quite a d i f f e r e n t response to annealing was observed i n the case of the 300°C p r o p e r t i e s of pure aluminum. This i s revealed by F i g s . 12, 13, and 14, i n which the y i e l d s t r e n g t h , u l t i m a t e s t r e n g t h s , and uniform elongation at 300°C, r e s p e c t i v e l y , are compared f o r Al-Cu m a t e r i a l s and pure aluminum as a f u n c t i o n of s t a t i c annealing time. A l l the m a t e r i a l s had been c o l d r o l l e d 70% before annealing. Several observations are of p a r t i c u l a r i n t e r e s t i n these p l o t s . F i r s t , the y i e l d s t r e n g t h of a s - r o l l e d pure aluminum i s higher at 300°C than that of any of the Al-Cu m a t e r i a l s . The corresponding e l o n g a t i o n of the pure metal i s r e l a t i v e l y very low. A f t e r s t a t i c anneal-ing f o r more than one hour at 300°C, however, the high temperature y i e l d s t r e n g t h of pure aluminum f a l l s f a r below that of the a l l o y s . A f t e r 4 hours or more of annealing, the 300°C elo n g a t i o n of aluminum i s a l s o the highest of t h i s group of m a t e r i a l s . Another observation from F i g s . 12 and 13 i s that the order of the three Al-Cu s e r i e s i n 300°C y i e l d s t r e n g t h i s i d e n t i c a l to that observed i n 20°C t e s t s (see F i g . 7). I t may a l s o be seen i n F i g . 12 that the dependence of 300°C y i e l d s t r e n g t h on annealing time f o r pure aluminum i s i n the opposite d i r e c t i o n from that of the Al-Cu a l l o y s . In Table V the 300°C y i e l d s t r e n g t h of the c o l d worked aluminum and a B Series Al-Cu a l l o y are compared. The high temperature st r e n g t h of the pure metal i s increased by i n c r e a s i n g p r i o r c o l d work, whereas the opposite i s t r u e , f o r the two-phase a l l o y . O B 9 A » c m AAL e = 6.25 x 10 \ i i n CO Figure 12. 10 12 14 Annealing Time at 300°C, hrs. 16 18 20 300°C Data showing the e f f e c t s of annealing time at 300°C on the y i e l d s t r e n g t h of Al-4Cu vs. pure aluminum a f t e r 70% C.W. 10 12 14 Annealing Time at 300°C, h r s . Figure 13. 300°C Data showing the e f f e c t s of annealing time at 300°C on the U.T.S. of Al-4Cu vs. pure aluminum a f t e r 70% C.W. — 60 -Table V: Comparison of 300°C Y i e l d Strength Values f o r Cold-Rol l e d A l and Al-4Cu. % Cold Work °0.2 ( K S ± ) A l Al-4Cu 40 2.30 1.84 50 2.30 1.76 60 2.51 1.77 70 2.63 1.62 80 2.83 1.47 Al-4Cu a l l o y s (from the B S e r i e s ) , which were c o l d worked from 30% to 80% and then annealed at 300°C f o r d i f f e r e n t times, a l l followed the same trends i n 300°C p r o p e r t i e s as e x h i b i t e d i n F i g . 1 ]. Results f o r the d i f f e r e n t amounts of p r i o r deformation are p l o t t e d i n F i g s . 15(a) to (e). The only notable e f f e c t of v a r y i n g the p r i o r c o l d deformation was i n the magnitude of the increase i n y i e l d s t r e n g t h which r e s u l t e d from s t a t i c annealing at 300°C. This i s shown i n Table VI. The percentage increase i n 300°C y i e l d s t r e n g t h due to s t a t i c annealing decreased w i t h a decrease i n the amount of p r i o r c o l d work, w i t h the notable exception of the r e s u l t f o r 30% p r i o r r e d u c t i o n . As noted e a r l i e r i n regard to F i g . 3, the response of the a l l o y to c o l d work behaved anomalously i n the range 30-40% reduction. T e n s i l e r e s u l t s at 300°C f o r Al-4Cu m a t e r i a l s subjected to various amounts of p r i o r c o l d work are summarized i n Table V I I . This t a b l e includes f o r comparison the data obtained f o r over-aged Al-4Cu which had cn G 3 O Uniform Elongation 6 8 10. 12 Annealing Time at 300 C, hrs. 14 16 12 10 a o •H •u ca oo a o w e M o a a> i Figure 15a. 300°C Data showing the effects of annealing time at 300°C on the annealing behaviour of Al-4Cu (B Series) a f t e r 30% C.W. Al-4Cu (B Series) a f t e r 40% C.W. 12 0 °0.2 © U.T.S. £ Uniform Elongation -3 -1 = 6.25 x 10 min 8 10 12 Annealing Time at 300°C, hrs, 14 16 Figure 15c. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour Al-4Cu after 50% C.W. 14 0 °0.2 © U.T.S. £ Uniform Elongation -3 -1 e = 6.25 x 10 min "8" JL _L 6 8 10 12 Annealing Time at 300°C, hrs. 14 16 12 10 ti 8 -S 4-1 ca 60 ti o r-i 6 g o • r l ti ;=> ON 4> Figure 15d. 300°C Data showing the e f f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (B S e r i e s ) a f t e r 60% C.W. O o 0.2 © Uniform Elongation -3 -1 e = 6.25 x 10 min -o - o -a-JL 1 14 16 14 12 10 c o M c o •H W 6 g o •H C r3 0-ON Figure 15e. 2 4 6 8 10 12 Annealing Time at 300°C, hrs. 300°C Data showing the ef f e c t s of annealing time at 300°C on the annealing behaviour of Al-4Cu (B Series) after 80% C.W. - 66 -Table VI: E f f e c t of S t a t i c Annealing on the 300°C Y i e l d Strength of Al-4Cu Cold-Worked P r e v i o u s l y by Various Amounts % °0.2 ° f C ° l d Cold Work Worked M a t e r i a l i n K s i 80 1.47 2.66 81.0 10 70 1.62 2.79 72.8 6 60 1.77 2.42 34.4 2 50 1.76 2.25 27.8 8 40 1.84 2.19 19.0 2 30 1.63 2.55 56.5 4 not been c o l d worked at a l l . Few c o n s i s t e n t trends are observed i n these data f o r the as- c o l d worked a l l o y . The over-aged Al-4Cu a l l o y at 300°C i s r e l a t i v e l y strong but of low d u c t i l i t y . Hot r o l l i n g of the over-aged a l l o y decreased the 300°C y i e l d and u l t i m a t e s t r e n g t h but s u b s t a n t i a l l y increased the el o n g a t i o n . Cold working of the h o t - r o l l e d m a t e r i a l produced a f u r t h e r decrease i n both the 300°C y i e l d and u l t i m a t e s t r e n g t h and a corresponding increase i n elo n g a t i o n . As documented e a r l i e r i n F i g s . 10-12, the 300°C y i e l d s t r e n g t h of the cold worked a l l o y s could be r a i s e d s u b s t a n t i a l l y by s t a t i c annealing, but i t could not be r e s t o r e d to the value of the over-aged a l l o y even a f t e r 15 hours of annealing at 300 C. Maximum A f t e r Annealing (Ksi) % Increase i n a Q 2 due to annealing Annealing Time at 300°C (hrs) Corresponding to max an „ - 67 -Table V I I : 300°C T e n s i l e Results f o r Cold--Rolled Al-4Cu % Cold Work °0.2 U.T.S. % Elongation (Ksi) (Ksi) Uniform T o t a l 0 only 0 ppts. 5.89 6.31 1.60 19.0 0 A f t e r Hot R o l l i n g 2.03 4.97 8.50 -30 1.63 4.26 12.30 55.0 40 1.84 4.14 12.40 44.0 50 1.76 3.63 10.00 58.4 60 1.77 3.55 12.80 51.7 70 1.62 4.20 13.20 59.0 80 1.47 3.65 12.00 58.8 90 1.58 3.51 12.50 -4.1.2.2 S.A.P. The 300°C t e n s i l e r e s u l t s f o r c o l d - r o l l e d S.A.P. are summarized i n Table V I I I and i n F i g . 9. Of i n t e r e s t are the high absolute values of the 300°C stre n g t h p r o p e r t i e s compared to aluminum and Al-4Cu. The 300°C elongation i s correspondingly much lower f o r S.A.P. In common wit h Al-Cu, the stre n g t h of S.A.P. at 300°C i s lowered by p r i o r c o l d work. However, i n the case of S.A.P. there i s a pr o g r e s s i v e e f f e c t of i n c r e a s i n g amounts of p r i o r deformation (see F i g . 9). The e f f e c t of s t a t i c annealing, a f t e r c o l d r o l l i n g , on the 300°C t e n s i l e p r o p e r t i e s of S.A.P. s t r i p which had received 50% p r i o r c o l d r e d u c t i o n i s demonstrated i n Table IX. S t a t i c annealing has r a i s e d the - 68 -Table ' V I I I : 300°C T e n s i l e Results f o r Cold-R o l l e d S.A.P. % Cold Work °0.2 U.T.S. % E l o n g a t i o n (Ksi) (Ksi) Uniform T o t a l 0 12. 6 14.95 2.2 (Af t e r Hot R o l l i n g ) 10 11. 0 13.88 3.4 -20 10.15 13.87 3.4 7.6 30 9. 44 12.96 3.6 7.3 40 9. 51 , 12.90 3.8 7.3 50 9. 57 12.80 3.7 6.7 60 9. 00 12.50 3.4 -70 9. 35 12.80 3.5 8.7 Table IX: E f f e c t of S t a t i c Annealing on the 300°C T e n s i l e P r o p e r t i e s of 50% Cold-Rolled S.A.P • % Cold Annealing °0.2 (Ksi) U.T.S. % Elongation % ', Increase i n Treatment (Ksi) Strength Uniform T o t a l a 0.2 U' T' S-0 None 12.60 14.95 2.2 - -50 None 9.57 12.80 3.7 6.7 -50 300°C, 48 hrs. 11.10 13.30 3.4 5.0 16.0 4.0 50 300°C, 72 h r s . 11.40 13.30 3.0 - 19.0 4.0 50 540°C, 12 hrs. 11.82 13.60 1.2 7.5 23.0 6.0 50 540°C, 24 hrs. 12.42 13.65 1.0 7.0 30.0 6.5 - 69 -300°C y i e l d s t r e n g t h r e s t o r i n g i t a f t e r a 540°C anneal almost to i t s value f o r the hot r o l l e d c o n d i t i o n . The U.T.S. values are a f f e c t e d i n a s i m i l a r manner, but to a smaller degree. This type of behaviour had been observed i n the case of Al-4Cu, except that i n that case s t a t i c annealing had caused a lowering of the 300°C U.T.S. The other notable d i f f e r e n c e between Al-Cu and S.A.P. l i e s i n the magnitude of the percentage increase i n high temperature y i e l d s t r e n g t h due to s t a t i c annealing. S i x to eight hours of heating at 300°C r a i s e d the 300°C y i e l d s t r e n g t h of c o l d - r o l l e d Al-4Cu by 28% and 73% a f t e r c o l d reductions of 50% and 70% r e s p e c t i v e l y . By c o n t r a s t , 72 hours of heating at 300°C r a i s e d the 300°C y i e l d s t r e n g t h of S.A.P. by only 19% f o r a p r i o r c o l d working r e d u c t i o n of 50%. Heating the c o l d - r o l l e d S.A.P. sheet f o r 24 hours at 540°C improved the 300°C y i e l d s t r e n g t h by 30%, i n d i c a t i n g that the higher heating temperature was more e f f e c t i v e i n improving the elevated temperature p r o p e r t i e s of S.A.P. This type of 42 behaviour has p r e v i o u s l y been observed by Towner f o r A.P.M. products. The 300°C uniform elongations of c o l d - r o l l e d and c o l d - r o l l e d - a n d -annealed S.A.P. v a r i e d between 1% and 4%. The corresponding t o t a l e l o n gation never exceeded 10%. By c o n t r a s t , the p r e c i p i t a t i o n hardened Al-4Cu a l l o y s e x h i b i t e d much higher d u c t i l i t y both i n cold-worked and cold-worked-and-annealed c o n d i t i o n s . 4.2 X-Ray D i f f r a c t i o n Graphs of percent l a t t i c e s t r a i n and domain s i z e c o e f f i c i e n t versus l a t t i c e distance were f i r s t p l o t t e d by the computer. R i s i n g regions of the p l o t s at l a r g e values of (L) were disregarded as being a t t r i b u t a b l e - 70 -to i n s t a b i l i t y i n the F o u r i e r components. However, a c o r r e c t i o n f o r the "hook e f f e c t " at low values of (L) was not a p p l i e d before p l o t t i n g the graphs. The r e s u l t s are shown i n F i g s . 16-20 which show the e f f e c t of v a r i o u s thermo-mechanical treatments on the l a t t i c e s t r a i n and domain s i z e f o r each m a t e r i a l . Best estimates of the domain s i z e obtained from the computer a n a l y s i s are given i n Table X. This t a b l e a l s o contains the root mean square s t r a i n expressed as percent s t r a i n f o r o o o distances of 50 A, 100 A and 150 A. In most cases the s t r a i n s quoted o o f o r 50 A are the peak values o c c u r r i n g near to 50 A; however, i n some o cases the peak occurred at distances greater than 150 A (see F i g s . 16 and 17). As discussed e a r l i e r , domain s i z e estimates should be cor r e c t e d where necessary f o r the c o n t r i b u t i o n s from s t a c k i n g f a u l t s and twin f a u l t s . The s t a c k i n g f a u l t p r o b a b i l i t y a was c a l c u l a t e d from equations (16) and (17) and the twin f a u l t p r o b a b i l i t y B from equations (18) and (19). However, i n no case could the presence of s t a c k i n g f a u l t s and twinning be proved positively and hence the domain s i z e estimates were not corr e c t e d . C a l c u l a t i o n s were made of the d i s l o c a t i o n d e n s i t y p derived from P the domain s i z e or p a r t i c l e s i z e [equation (23)] and the d i s l o c a t i o n d e n s i t y p g derived from the mean square l a t t i c e s t r a i n [equation (24)J. From a knowledge of these two values the d i s l o c a t i o n c o n f i g u r a t i o r s were determined from the c r i t e r i a mentioned i n s e c t i o n 3.3. Table XI summarizes the d i s l o c a t i o n d e n s i t i e s and the c o n f i g u r a t i o n s f o r each m a t e r i a l and c o n d i t i o n . E.oom temperature 0.2 pet y i e l d s t r e n g t h f o r each m a t e r i a l and c o n d i t i o n has been included i n t h i s t a b l e to provide a - 71 -0.20 1. A l , 70% C.W. 2. A l , 70% C.W. + Ann. 3. A l - 4 C u , Over-aged 4. A l - 4 C u , Hot R o l l e d 5. A l - 4 C u , 50% C.W. 6. A l - 4 C u , 50% C.W. + Ann. 7. A l - 4 C u , 70% C.W. 8. A l - 4 C u , 70% C.W. + Ann. 1. S . A . P . , As Received 2. S . A . P . , Hot R o l l e d 3. S . A . P . , 50%. C.W. 4. S . A . P . . 50% C.W. + Ann. Figure 16. V a r i a t i o n of l a t t i c e s t r a i n w i t h l a t t i c e d i s t a nce f o r Al-4Cu (B S e r i e s ) and pure aluminum i n various thermo-mechanical c o n d i t i o n s . Figure 17. V a r i a t i o n of l a t t i c e s t r a i n w i t h l a t t i c e d i s t a nce f o r S.A.P. i n various thermo-mechanical c o n d i t i o n s . 200 300 400 500 L a t t i c e Distance A - 72 -Figure 18. V a r i a t i o n of domain s i z e c o e f f i c i e n t with l a t t i c e distance for Al-4Cu (B Series) and pure aluminum i n various thermo-mechanical conditions. . P . , Hot R o l l e d . . P . , 50% C.W. + Annealed S . A . P . , As Received S . A . P . , 50KC.W. J L , 50* C.W. Figure 19. V a r i a t i o n of domain s i z e c o e f f i c i e n t with l a t t i c e distance for S.A.P. i n various thermo-mechanical conditions. Figure 20. V a r i a t i o n of domain s i z e c o e f f i c i e n t w i t h l a t t i c e distance f o r Al-4Cu (B Serie s ) a f t e r 50% and 70% C.W. 300 400 - 74 -Table X: Domain Si z e and L a t t i c e S t r a i n D i s t r i b u t i o n M a t e r i a l C o n d i t i o n Domain % S t r a i n at Distance (L) Siz e D 5 5 5 — i n A SO A 100 A 150 A A l , Cold r o l l e d 70% >1000 0.136 0.09 0.08 A l , Cold r o l l e d 70% and at 300°C f o r 6 h r s . annealed >1000 0 0 0 Al-4Cu, Over-aged >1000 0 0 0 Al-4Cu, Hot r o l l e d >1000 0.12 0.09 0.09 Al-4Cu, Cold r o l l e d 50% 900 0.23 0.14 0.13 Al-4Cu, Cold r o l l e d 50% annealed at 300°C f o r 4 and hr s . >1000 0 0.06 0.08 Al-4Cu, Cold r o l l e d 70% 860 0.13 0.15 0.14 Al-4Cu, Cold r o l l e d 70% annealed at 300°C f o r 4 and hrs. >1000 0 0 0 S.A.P., as rece i v e d 940 0.13 0.12 0.10 S.A.P., Hot r o l l e d 960 0.12 0.11 0.11 S.A.P., Cold r o l l e d 50% 780 0.19 0.14 0.13 S.A.P., Cold r o l l e d 50% and annealed at 540°C f o r 24 h r s . 900 0.16 0.13 0.12 Table XI: D i s l o c a t i o n D e n s i t i e s and Configurations M a t e r i a l C o n d i t i o n D O A -3 (cm,cm ) ( £ >50 A p s x 100 (cm,cm 3) True d i s - D i s l o c a t i o n l o c a t i o n C o n f i g u r a t i o n s d e n s i t y , p , cm, cm - 3 a0.2 a t 20°C ( K s i ) A l , Cold r o l l e d 70% A l , Cold r o l l e d 70% and annealed at 300°C f o r 6 hrs. Al-4Cu, Over-aged Al-4Cu, Hot r o l l e d Al-4Cu, Cold r o l l e d 50% Al-4Cu, Cold r o l l e d 50% and annealed at 300°C f o r 4 h rs. Al-4Cu, Cold r o l l e d 70% Al-4Cu, Cold r o l l e d 70% and annealed at 300°C f o r 4 h r s . S.A.P., As re c e i v e d S.A.P., Hot r o l l e d S.A.P., Cold r o l l e d 50% S.A.P., Cold r o l l e d 50% and annealed at 540°C f o r 24 h r s . >1000 (1470) >1000 >1000 >1000 (1330) 900 >1000 860 >1000 940 960 780 900 1.4x10 10 1.7x10 10 3.7x10 10 4.1x10 10 3.4x10 3.3x10 4.9x10 10 10 10 3.7x10 10 0.136 0 0 0.12 0.23 0 0.15 0 0.13 0.12 0.19 0.16 2.8x10 10 10 2 . 2 x l 0 1 0 7 . 9 x l 0 1 0 3.4x10 10 2.5x10 2.2x10 6.0x10 10 10 10 3.8x10 10 2x10 ^4x10 ^ 1 0 8 2.2x10 7.9x10 ^2x10' 4 x l 0 1 0 - 1 0 n 8 10 10 ^3x10' 4-5x10 4-5x10 5.4x10 10 10 10 4-5x10 10 Pile-up/random 14.5 P o l y g o n i z a t i o n 2.4 P o l y g o n i z a t i o n 13.3 Pile-up/random 8.5 Pile-up/random 32.7 P o l y g o n i z a t i o n 12.9 P o l y g o n i z a t i o n 41.1 P o l y g o n i z a t i o n 15.0 P o l y g o n i z a t i o n 32.0 P o l y g o n i z a t i o n 29.5 Pile-up/random 34.9 Polyg./random 33.5 - 76 -source of rough estimates of the d i s l o c a t i o n d e n s i t i e s of annealed m a t e r i a l s . In the column under " t r u e d i s l o c a t i o n d e n s i t y " , the true d e n s i t y f o r a p i l e - u p c o n f i g u r a t i o n i s given by p = no^. For a polygonized c o n f i g u r a t i o n , t h e true d e n s i t y i s given by p = pg/F> because under c o n d i t i o n s of p o l y g o n i z a t i o n p p > P s a n d the i n t e r a c t i o n f a c t o r F < 1 [see equation ( 2 2 ) ] . Thus, i n equation (27) the l o g a r i t h m i c 1 41 f a c t o r s are equivalent to —. Clegg suggested that under c o n d i t i o n s r of p o l y g o n i z a t i o n the maximum value that p could take would be approximately 5p and th3t p would be not only greater than p but s s also greater than In Table X I , p f o r Al-4Cu, reduced 70% by c o l d r o l l i n g , was 10 -3 estimated to be 4.1x10 cm,cm . The s t r a i n value obtained from X-ray st u d i e s was l e s s than that of 50% c o l d worked Al-4Cu, and comparable to that of S.A.P. In view of the s i m i l a r i t y of domain s i z e s i n these m a t e r i a l s , the y i e l d s t r e n g t h of 70% c o l d worked Al-4Cu i s high. I t may be concluded that the e s t i m a t i o n of l a t t i c e s t r a i n by the X-ray technique i n the h e a v i l y deformed Al-Cu a l l o y i s f o r some reason i n e r r o r . The d i s l o c a t i o n d e n s i t y , p , f o r t h i s m a t e r i a l has been 11 -3 assigned the range 0.4 to 1x10 cm.cm i n Table X I , to attempt to make the true d i s l o c a t i o n d e n s i t y more c o n s i s t e n t w i t h the observed strength. The domain s i z e of. the four S.A.P. m a t e r i a l s was of the order of o 800 to 1000 A. Their s t r a i n d i s t r i b u t i o n s were a l s o very s i m i l a r and the y i e l d s t r e n g t h v a r i e d over the range 29,000 to 35,000 p s i . The t r u e d i s l o c a t i o n density of S.A.P., reduced 50% by cold r o l l i n g , was estimated 10 ~3 to be 5.4x10 cm.cm . Since p > p^ f o r a polygonized c o n f i g u r a t i o n , - 77 -p f o r the other three S.A.P. m a t e r i a l s having a polygonized c o n f i g u r a t i o n 10 -3 can be assumed to be i n the range 4 to 5 xlO cm.cm In the case of annealed aluminum and Al-4Cu a l l o y s , l a t t i c e s t r a i n s o were n e g l i g i b l e , and domain s i z e was greater than 1000 A. Thus accurate determination of or p g was not p o s s i b l e and the d i s l o c a t i o n c o n f i g u r a -t i o n could not be judged from the values of p^ and p g . However, m e t a l l o -graphy i n d i c a t e d a h i g h l y polygonized substructure f o r annealed aluminum and Al-4Cu (see Sectio n 4.3) and t h i s was i n s e r t e d i n Table XI. Although the true d i s l o c a t i o n d e n s i t y of these annealed m a t e r i a l s could not be determined from the X-ray a n a l y s i s , a rough estimate could be made from equation (30) from a knowledge of the experimentally measured 20°C y i e l d strengths and the y value evaluated l a t e r i n the t h e s i s i n Sections 5.1.1 and 5.1.2.2. In the case of annealed Al-4Cu a l l o y s , the c a l c u l a t e d s t r e n g t h c o n t r i b u t i o n s due to Orowan hardening and s o l i d s o l u t i o n hardening were subtracted from the r e s p e c t i v e measured y i e l d strengths to provide a b a s i s f o r determining the true d i s l o c a t i o n d e n s i t y . 62 Judging from s e v e r a l sources tabulated by Williamson and Smallman, 8 —3 the true d i s l o c a t i o n d e n s i t y of as-aged Al-4Cu was placed at 10 cm.cm These estimated values of true d i s l o c a t i o n d e n s i t y (p) f o r pure aluminum, Al-4Cu and S.A.P. are t a b l u l a t e d i n Table XI. - 78 -4.3 Metallography 4.3.1 O p t i c a l Microscopy The microstructures of A l and Al-4Cu a f t e r d i f f e r e n t mechanical and thermal treatments were examined by o p t i c a l microscopy. F i g . 21 i s a t y p i c a l o p t i c a l photomicrograph of an over-aged Al-4Cu a l l o y which was aged at 300°C f o r 15 hours. This micrograph r e v e a l s very l a r g e equiaxed g r a i n s . The average g r a i n s i z e i s about 800 u . P r e c i p i t a t e -f r e e zones (PFZ) are observed adjacent to g r a i n boundaries. The g r a i n boundary p r e c i p i t a t e s and the f i n e nature of the d i s p e r s i o n of the second phase C u A l 2 p a r t i c l e s has been revealed at higher m a g n i f i c a t i o n s . F i g s . 22 to 25 are o p t i c a l micrographs of the Al-4Cu a l l o y c o l d -r o l l e d 70% (F i g s . 22 and 23), and a f t e r s t a t i c annealing at 300°C f o r 8 hours ( F i g s . 24 and 25). For the sake of comparison, micrographs of both the A s e r i e s and B s e r i e s of a l l o y s are inc l u d e d . In both cases deformation bands were observed i n each g r a i n and the gra i n s were elongated i n the d i r e c t i o n of r o l l i n g . In the annealed c o n d i t i o n apparently s t r a i n - f r e e r e c r y s t a l l i z e d grains were found i n the micro-s t r u c t u r e of the s e r i e s A a l l o y ( F i g . 25) and these grains seemed to have been nucleated at the o r i g i n a l g r a i n boundaries. Such r e c r y s t a l l i z e d g rains were not c l e a r l y observable i n the Se r i e s B a l l o y a f t e r 8 hours of annealing at 300°C. 4.3.2 E l e c t r o n Microscopy , 4.3.2.1 Pure Aluminum F i g s . 26 to 34 are tranmission e l e c t r o n micrographs of pure aluminum i n the co l d r o l l e d and cold rolled-and-annealed c o n d i t i o n s . - 79 -Figure 22. O p t i c a l Micrograph of Figure 23. O p t i c a l Micrograph of Al-4Cu (B Series) a f t e r 70% C.W., Al-4Cu (A S e r i e s ) a f t e r 70% C.W., 23X. 23X. Figure 25. Optical micrograph of Al-4Cu (A Series) c o l d - r o l l e d 70% and annealed at 300°C for 8 hrs., 23X. - 81 -F i g s . 26a, 26b and 26c show 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 s i n a specimen c o l d worked 70%. Well-defined c e l l s are present a f t e r t h i s l a r g e degree of deformation; and the c e l l diameter i s about 0.76 u. The c e l l s were both elongated and equiaxed i n shape ( F i g s . 26a and 26b), as commonly observed by other workers. ' The c e l l w a l l s c o n s i s t of dense d i s l o c a t i o n arrays surrounding areas of low d i s l o c a t i o n d e n s i t y . This type of polygonized s u b s t r u c t u r e was not i n d i c a t e d by the X-ray r e s u l t s of Table X I , which suggested i n s t e a d a p i l e - u p c o n f i g -u r a t i o n i n the 70% c o l d worked pure metal. I t i s p o s s i b l e that the computer estimate of domain s i z e was i n e r r o r and that i t might be o c l o s e r to 1000 A than i n d i c a t e d . This would give > p g ; i . e . a polygonized d i s l o c a t i o n arrangement could be expected. Even a f t e r 60% c o l d r o l l i n g r e d u c t i o n the formation of a c e l l s t r u c t u r e seems to be w e l l advanced ( F i g s . 27a and 27b); i . e . the c e l l w a l l s are sharply d e l i n e a t e d i n most cases. The c e l l diameter i s about 0.82 y. More extensive deformation (about 80% r e d u c t i o n by c o l d r o l l i n g ) reduced the c e l l diameter to about 0.7 y; F i g s . 28a and 28b. The tangled nature of the d i s l o c a t i o n s i n the c e l l w a l l s of the deformed pure metal i s c l e a r l y seen i n these e l e c t r o n micrographs. Measurements of c e l l s i z e i n aluminum f o r a great range of p r i o r deformations were not c a r r i e d out i n the present work. Neverthe-l e s s the r e s u l t s from m a t e r i a l deformed 60%, 70% and 80% by c o l d r o l l i n g i n d i c a t e that a l i m i t i n g minimum c e l l s i z e was probably almost reached a f t e r 80% r e d u c t i o n . This i s i n agreement w i t h the f i n d i n g s of 6 3 Swann f o r c o l d - r o l l e d aluminum, whereas i t c o n t r a d i c t s the r e s u l t s of Hansen"' who found that the c e l l s i z e of high p u r i t y aluminum decreased to - 82 -Cc) 20.000X Figure 26a-c. Tranmission e l e c t r o n micrograph of pure aluminum a f t e r 70% C.W. - 83 -- 84 -GO Figure 28a,b. Transmission e l e c t r o n micrograph of pure aluminum a f t e r 80% C.W., 20,000X. - 85 -about 0.4 u a f t e r about 90% red u c t i o n i n area. The absolute magnitude of the c e l l s i z e i n the present work f o r a given degree of cold r o l l i n g does not correspond to that reported by e i t h e r Swann or Hansen. Swann d i d not describe the method by which he c a l c u l a t e d c e l l s i z e from transmission e l e c t r o n micrographs, but h i s values f o r comparable l e v e l s of deformation are at l e a s t twice those.of the present i n v e s t i g a t i o n . Annealing of 70% cold-worked aluminum at 300°C causes a m o d i f i c a t i o n i n the c e l l s t r u c t u r e . The c e l l s grow, increase i n m i s o r i e n t a t i o n and become i d e n t i f i e d as subgrains ( F i g s . 29 and 30). The tangles of d i s l o c a t i o n s i n c e l l w a l l s give way to more ordered a r r a y s . Annealing c o l d worked pure aluminum f o r one hour at 100°C and 250°C has a minor e f f e c t on the appearance of subgrains ( F i g s . 31 and 32). Some subgrains are r e l a t i v e l y d i s l o c a t i o n - f r e e ; others c o n t a i n jogged d i s l o c a t i o n s . Even a f t e r one hour of annealing at 250°C f o l l o w i n g 70% p r i o r cold work, the subgrain diameter was found to be about l y ; i . e . l i t t l e higher than the c e l l s i n the cold-worked metal. However, a two-fold increase i n subgrain s i z e was observed when the annealing temperature was increased from 250°C to 300°C. At more advanced stages of annealing, e.g. 350°C and 400°C, t y p i c a l r e c r y s t a l l i z e d g r a i n s were found. These were r e l a t i v e l y d i s l o c a t i o n -f r e e i n t e r n a l l y and bounded by l a r g e angle boundaries. F i g . 33 shows such a r e c r y s t a l l i z e d s t r u c t u r e i n aluminum annealed at 400°C f o r one hour. S t r u c t u r a l m o d i f i c a t i o n s produced by annealing of the 80% c o l d -worked aluminum were s i m i l a r to those of the 70% cold-worked metal, except that the subgrain s i z e of the former a f t e r a given annealing Figure 30. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 300°C f o r 6 h r s . , 10,000X. - 87 -Figure 32. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 70% and annealed at 250°C f o r 1 h r . , 15,000X. Figure 34. Transmission e l e c t r o n micrograph of pure aluminum c o l d - r o l l e d 80% and annealed at 300°C f o r 3 h r s . , 5,000X. - 89 -treatment was grea t e r . For example, three hours of annealing at 300°C was s u f f i c i e n t to produce r e c r y s t a l l i z e d g r a i n s i n 80% c o l d - r o l l e d aluminum ( F i g . 34). S i m i l a r s t r u c t u r a l developments i n aluminum have been observed by Swann,^ Weismann et a l . ^ and Hansen.^ 4.3.2.2 Aluminum-4 Copper F i g s . 35 and 36 are e l e c t r o n micrographs from a carbon r e p l i c a and a t h i n f o i l of the over-aged Al-4Cu a l l o y , r e s p e c t i v e l y . The coarse p r e c i p i t a t e s are arrayed i n a w e l l - d e f i n e d Widemanstatten p a t t e r n . The mean planar i n t e r p a r t i c l e spacing of the p r e c i p i t a t e s i s about 1.3 y. From the r e s u l t s of Thomas and Nutting"'""' i t can be concluded that the type of ageing treatment used i n the present i n v e s t i g a t i o n (15 hours at 300°C) would produce a mixture of 6* and e ^ u A ^ ) p r e c i p i t a t e s . The 0 p r e c i p i t a t e i s s t r u c t u r a l l y noncoherent, and 6 1 i s p a r t i a l l y coherent w i t h the matrix. An Al-4Cu a l l o y i n the f u l l y over-aged c o n d i t i o n (62 hours at 300°C), co n t a i n i n g mainly 0 p r e c i p i t a t e s , has a 0.2% y i e l d s t r e n g t h of about 11,000 p s i , whereas an ageing treatment of 15 hours at 300°C gives a y i e l d s t r e n g t h of 13,300 p s i . Hence i t can be concluded that the amount of 6* p r e c i p i t a t e s present i n the l a t t e r case i s r e l a t i v e l y s m a l l . This i s al s o supported by the X-ray measurement of non-uniform l a t t i c e s t r a i n ( F i g . 16) i n the as-aged m a t e r i a l which shows a maximum of 0.06% s t r a i n . F i g . 37 represents the hot-worked m i c r o s t r u c t u r e of the over-aged Al-4Cu (Series B). This e l e c t r o n micrograph shows c e l l s or subgrains which are not very w e l l developed. The subgrains are f a i r l y f r e e of d i s l o c a t i o n s although tangled d i s l o c a t i o n s are seen i n some of the c e l l Figure 35. Chromium shadowed carbon r e p l i c a of over-aged Al-4Cu showing C u A l 2 ( 6 ) p r e c i p i t a t e s , 6,000X. Figure 36. Transmission e l e c t r o n micrograph of over-aged Al-4Cu showing CuAl„ p r e c i p i t a t e s , 10,000X. Figure 37. Tranmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) showing the hot-worked Tnicrostructure, 20,000X. - 91 -i n t e r i o r s . The X-ray a n a l y s i s supports t h i s type of d i s l o c a t i o n arrangement. F i g s . 38a, 38b and 38c are r e p r e s e n t a t i v e t r a n s m i s s i o n e l e c t r o n micrographs of 70% c o l d - r o l l e d Al-4Cu (Series B). The main feature of the s e v e r e l y worked a l l o y i s a very high d i s l o c a t i o n d e n s i t y arranged i n a c e l l s t r u c t u r e . The c e l l s are l e s s w e l l - d e f i n e d than i n pure aluminum ( F i g . 26). Such a polygonized c o n f i g u r a t i o n i s a l s o i n d i c a t e d by the X-ray st u d i e s (see Table X I ) . R e l a t i v e l y d i s l o c a t i o n - f r e e areas are observed between some of these i l l - d e f i n e d c e l l w a l l s . The d i s l o c a t i o n d e n s i t y could not be measured from e l e c t r o n micrographs; however, from the X-ray l i n e p r o f i l e a n a l y s i s i t was estimated to be of the order of 4 x 1 0 ^ - 1 0 ^ cm. cm ^. Numerous tangled d i s l o c a t i o n s and d i s l o c a t i o n loops ( F i g . 38a) are f r e q u e n t l y observed. Some d i s -l o c a t i o n s are apparently a r r e s t e d at the p r e c i p i t a t e s (point A i n F i g . 38b). At point B i n F i g . 38c d i s l o c a t i o n s appear to be h e l d up between the p r e c i p i t a t e s . The m i c r o s t r u c t u r a l changes which occurred during annealing of the s e v e r e l y c o l d worked Al-4Cu a l l o y s were not i n h e r e n t l y d i f f e r e n t from those o c c u r r i n g i n d i s p e r s i o n - f r e e m a t e r i a l ( i . e . pure aluminum). On annealing, the deformed s t r u c t u r e was replaced by a recovered s t r u c t u r e , composed of rather well-developed subgrains. However, there were d i f f e r e n c e s i n the ease of subgrain formation and i n the degree of recovery of remaining c e l l s t r u c t u r e i n these d i f f e r e n t m a t e r i a l s . The s t r u c t u r e observed depends upon the annealing temperature as w e l l as the annealing time. F i g s . 39 to 41 i l l u s t r a t e the s t r u c t u r a l - 92 Figure 38a-c. Cc) Transmission e l e c t r o n micrograph of Al-4Cu (B Ser i e s ) a f t e r 70% C.W., 35,000X. - 93 -Figure 39a,b. (b) 40,000X. Transmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) c o l d - r o l l e d 70% and annealed at 100°C f o r 1 hr. - 94 -Figure 41. Transmission e l e c t r o n micrograph of Al-4Cu (B Series) c o l d - r o l l e d 70% and annealed at 350°C f o r 1 h r . , 15,000X. - 95 -changes i n the Al-4Cu a l l o y a f t e r annealing f o r one hour at 100°C, 200°C and 350°C r e s p e c t i v e l y . A f t e r annealing at 100°C, the s t r u c t u r e i s very s i m i l a r to that of the deformed s t a t e , except that some of the tangled d i s l o c a t i o n s appear to have disentangled themselves to form subgrain boundaries ( F i g s . 39a and 39b). The d i s l o c a t i o n d e n s i t y i s s t i l l high and d i s l o c a t i o n s are a l s o p iled-up at the p r e c i p i t a t e s . Increasing the annealing temperature to 200°C has produced w e l l d e l i n e a t e d d i s l o c a t i o n - f r e e s u b g r a i n s ( F i g . 40a) w i t h a subgrain diameter of about 0.3 u. However, c e l l i n t e r i o r s c o n t a i n i n g tangled d i s l o c a t i o n s have been observed i n some cases ( F i g . 40b). Annealing at a very high temperature, e.g. 350°C, has r e s u l t e d i n a s t r a i n f r e e r e c r y s t a l l i z e d .structure ( F i g . 41). Thin f o i l s of m a t e r i a l s given the l a t t e r heat treatment d i d not r e v e a l any subgrains. The shapes of the p r e c i p i t a t e s i n F i g . 41 (compare w i t h those i n F i g . 36) probably i n d i c a t e growth and s p h e r o i d i s a t i o n of the p r e c i p i t a t e p a r t i c l e s upon co l d working and subsequent annealing. The change of shape of the p r e c i p i t a t e s may be a t t r i b u t e d to the shearing of some of the p r e c i p i t a t e a f t e r l a r g e reductions by c o l d r o l l i n g and to the growth of the p a r t i c l e s during subsequent annealing, presumably by enhanced d i f f u s i o n of copper due to the presence of the subgrain boundaries between the p r e c i p i t a t e p a r t i c l e s . This change of shape of the p r e c i p i t a t e s seems to be a common observation i n most of the Al-4Cu a l l o y s annealed a f t e r c o l d working. F i g s . 42 to 47 show e l e c t r o n micrographs f o r Al-Cu a l l o y s heat trea t e d at 300°C, f o r times v a r y i n g from 15 minutes to 15 hours, a f t e r 70% c o l d work. In a l l cases, well-developed subgrains are observed. - 96 -- 97 -(b) Figure 43a,b. Transmission electron micrograph of Al-4Cu (B Series) c o l d - r o l l e d 70% and annealed at 300°C for 30 mins., 23,000X. - 98 -Figure 44. Transmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 2 h r s . , 23,000X. Figure 45. Tranmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 4 h r s . , 23,000X. - 99 -(a) (b) Figure 46a,b. Tranmission e l e c t r o n micrograph of Al-4Cu (B Seri e s ) c o l d r o l l e d 70% and annealed at 300°C f o r 8 h r s . , (a) 20,000X, (b) 15,000X. Figure 47. Tranmission e l e c t r o n micrograph of Al-4Cu (B Se r i e s ) c o l d - r o l l e d 70% and annealed at 300°C f o r 15 h r s . , 15,000X. - 100 -The subgrain diameter v a r i e s from about 0.55 V f o r 15 minutes of annealing to 2 y f o r 15 hours of annealing. The r a t e of subgrain formation i s r a p i d i n i t i a l l y , but decreases g r a d u a l l y w i t h time. Lack of e x c e s s i v e l y l a r g e subgrains even a f t e r long annealing times i n d i c a t e s the very slow r a t e of growth of the subgrains. Some of the migr a t i n g sub-boundaries appear to have been pinned by the p r e c i p i t a t e s . This may be the reason f o r the slow r a t e of growth of the subgrains, s i n c e i t i s u n l i k e l y that a l l the sharp boundaries produced by po l y -g o n i z a t i o n w i l l be capable of m i g r a t i n g . I t has been observed that coarsening of the 6 phase takes place during long recovery anneals before r e c r y s t a l l i z a t i o n , i n agreement 65 66 wi t h the experimental evidence of Doherty and M a r t i n . ' For example, 15 hours of heat treatment at 300°C a f t e r 70% co l d work has increased the mean planar i n t e r p a r t i c l e spacing from 1.3 y to 2.2 y, whereas annealing f o r one hour at 350°C, which produces a r e c r y s t a l l i z e d s t r u c t u r e , increased the spacing to about 2.5 y. During the recovery period the subgrain boundaries are apparently s t i l l attached to the p r e c i p i t a t e s and the subgrain s i z e increases as the d i s p e r s i o n of the second phase coarsens. This f o l l o w s from the experimental observation that the subgrain diameter i s almost equal to the i n t e r p a r t i c l e spacing. Doherty and M a r t i n have a l s o shown that i n the m a t e r i a l a f t e r heavy deformation, but before r e c r y s t a l l i z a t i o n , the 6 phase coarsens much more r a p i d l y than i n the undeformed m a t e r i a l . 4.3.2.3 S.A.P. S.A.P. was received i n the form of an extruded rod. The m i c r o s t r u c t u r e - 101 -of a l o n g i t u d i n a l s e c t i o n of the extruded bar i s shown i n F i g . 48. As seen from the e l e c t r o n micrographs the oxide phase (A^O^) i s nonuniformly d i s t r i b u t e d throughout the aluminum matrix. Although the oxide phase e x i s t s as d i s c r e t e p a r t i c l e s , evidence of agglomeration or " c l u s t e r i n g " of the p a r t i c l e s has al s o been observed i n some cases. The i n d i v i d u a l oxide p a r t i c l e s are disk-shaped, having an average o o diameter of about 1100 A and a thickness of about 100 A. The matrix i s d i v i d e d i n t o subgrains which are probably formed by the combined e f f e c t of high temperatures and a l a r g e p l a s t i c s t r a i n during e x t r u s i o n . The mean planar i n t e r p a r t i c l e spacing of the oxide i s found to be about 0.08 u . Thus, i n comparison w i t h Al-4Cu, S.A.P. has a second phase dispersed on a much f i n e r s c a l e . In n e i t h e r S.A.P. nor Al-4Cu are the p a r t i c l e s s p h e r i c a l i n shape. However, c o n s i d e r i n g the diameter of the equivalent s p h e r i c a l p a r t i c l e which would produce the same i n t e r p a r t i c l e spacing, the A^O^ p a r t i c l e s are much smaller i n s i z e than the CuA^ p a r t i c l e s . Close s i m i l a r i t y e x i s t s between the m i c r o s t r u c t u r e of S.A.P. and Al-4Cu e i t h e r i n the hot-worked, cold-worked or annealed c o n d i t i o n . F i g s . 49a and 49b are r e p r e s e n t a t i v e transmission e l e c t r o n micrographs fo r S.A.P. i n the hot-worked c o n d i t i o n . I t should be noted that the hot-working temperature f o r S.A.P. was 540°C compared to a temperature of 300°C f o r Al-4Cu. The l a r g e p l a s t i c s t r a i n during r o l l i n g at t h i s high temperature has produced a polygonized s u b s t r u c t u r e w i t h sharply defined sub-boundaries s i m i l a r to that of Al-4Cu. The subgrains are equi-axed and the d i s l o c a t i o n d e n s i t y between the sub-boundaries i s low. , This m i c r o s t r u c t u r e i s s i m i l a r to that of an extruded product of lower - 102 -Figure 48. Tranmission e l e c t r o n micrograph of S.A.P. i n the as rec e i v e d c o n d i t i o n showing the d i s t r i b u t i o n of A l ^ p a r t i c l e s , 46,000X. - 103 -Figure 49a,b. Transmission electron micrograph of S.A.P. showing the hot- Worked microstructure, 23,000X. - 104 -32 oxide content observed by Hansen. The d i s l o c a t i o n s t r u c t u r e produced by c o l d r o l l i n g 50% i s shown i n F i g s . 50a, 50b and 50c. The c e l l w a l l s r e t a i n a ragged appearance and are o c c a s i o n a l l y pinned by the oxide p a r t i c l e s . I t w i l l be n o t i c e d that the c e l l i n t e r i o r s c o n t a i n an appreciable d e n s i t y of d i s l o c a t i o n s ; i n c o ntrast w i t h the r e l a t i v e l y d i s l o c a t i o n - f r e e c e l l i n t e r i o r s observed i n single-phase aluminum cold-worked at room temperature. I s o l a t e d d i s l o c a t i o n tangles i n s i d e the c e l l i n t e r i o r s are a l s o observed i n some cases. This type of d i s l o c a t i o n substructure has been 40 observed by Goodrich and A n s e l l f o r c o l d - r o l l e d S.A.P. co n t a i n i n g 2 wt % and 3 wt % oxide and by Hansen"* f o r cold-drawn S.A.P. co n t a i n i n g 0.2 to 4.7 wt % oxide. In both cases the c e l l s i z e decreased w i t h i n c r e a s i n g s t r a i n , a t t a i n i n g a l i m i t i n g c e l l s i z e i n the more seve r e l y deformed c o n d i t i o n s . Goodrich and A n s e l l observed that the l i m i t i n g c e l l s i z e of the S.A.P.-type a l l o y s was considerably l e s s than that of high p u r i t y aluminum and that the deformation needed to produce t h i s minimum c e l l s i z e was appreciably higher f o r the S.A.P.Ttype a l l o y s . The s l u g g i s h attainment of the l i m i t i n g c e l l s i z e and the development of the smaller c e l l s i z e tend to i n d i c a t e that d i s l o c a t i o n m o b i l i t y i s i n h i b i t e d by the i n t r o d u c t i o n of the dispersed second phase. A f t e r 50% c o l d - r o l l i n g the m a t e r i a l was annealed at 540°C f o r d i f f e r e n t times. F i g s . 51a and 51b i l l u s t r a t e s t r u c t u r a l changes a f t e r an annealing p e r i o d of 24 hours. This s t r u c t u r e i s s i m i l a r to that of 70% c o l d r o l l e d Al-4Cu annealed at low temperatures, e.g. 200°C. Annealing has produced a polygonized substructure w i t h a l a r g e r subgrain 105 -Figure 50a-c. (c) Transmission electron micrograph of S.A.P. c o l d - r o l l e d 50%, 58,000X. - 107 -s i z e and low d i s l o c a t i o n d e n s i t y . Agglomerated oxide p a r t i c l e s are seen i n s i d e the subgrainsand at the subboundaries. A good c o r r e l a t i o n was found to e x i s t between the d i s l o c a t i o n arrangement obtained from metallography and that i n d i c a t e d by the X-ray l i n e p r o f i l e a n a l y s i s of S.A.P. i n any thermo-mechanical c o n d i t i o n . 5. DISCUSSION 5.1 T e n s i l e P r o p e r t i e s at 20°C 5.1.1 Pure Aluminum A large body of inform a t i o n about the deformation of p o l y c r y s t a l l i n e aluminum i s now a v a i l a b l e i n the l i t e r a t u r e , i n c l u d i n g d e t a i l s of the s l i p process, substructure formation and growth, and annealing c h a r a c t e r i s t i c s . The mechanical behaviour of aluminum can be g r e a t l y 6 7 i n f l u e n c e d by the presence of i m p u r i t i e s . Carreker and Hibbard have shown that even small concentration of some i m p u r i t i e s can produce important e f f e c t s such as a d i s t i n c t y i e l d p o i n t , and a marked change i n the temperature dependence of the flow s t r e s s . The aluminum used i n the present i n v e s t i g a t i o n had a p u r i t y of 99.96%, which compares favourably w i t h the highest p u r i t y of metal used by most previous i n v e s t i g a t o r s . The t e n s i l e p r o p e r t i e s obtained i n the present work a f t e r various thermal and mechanical treatments a l s o compare very c l o s e l y to some reported i n the l i t e r a t u r e f o r 99.996% aluminum as shown i n Table X I I . The r e s u l t s of the present work are a l s o i n agreement w i t h data reported by Hansen"* f o r c o l d drawn aluminum. Although aluminum i s strengthened considerably by working at 20°C, the absolute strengthening due to any given amount of c o l d working i s 41 much l e s s than f o r most other f . c . c . metals. For example, n i c k e l , - 109 -Table X I I : Room Temperature Mechanical P r o p e r t i e s f o r H i g h - P u r i t y Aluminum. 99.96% aluminum used i n the 99.996 aluminum from Ref. 48 present work M a t e r i a l c o n d i t i o n ^ U.T.S. M a t e r i a l Condition o_ „ U.T.S. K s i K s i K s i K s i 70% reductions by c o l d r o l l i n g 80% reductions by c o l d r o l l i n g 14.5 14.9 15.6 16.5 75% reductions by c o l d r o l l i n g 15.4 16.3 f u l l y annealed 1 a f t e r 70% c o l d work ,8 6.9 f u l l y annealed 1.8 6.9 a f t e r 75% co l d work when c o l d r o l l e d 75%, has a y i e l d strength of about 100,000 p s i . The d i f f e r e n c e i n the absolute values of the strengths of aluminum and n i c k e l may be a t t r i b u t e d to a d i f f e r e n c e i n t h e i r shear modulus values and to t h e i r minimum substructure "domain", s i z e s a f t e r deformation. 41 Clegg has;found a good c o r r e l a t i o n between high str e n g t h and a f i n e domain s i z e (based on X-ray d i f f r a c t i o n s t u d i e s ) f o r N i and a Ni-Cr a l l o y . N i c k e l , when reduced 75% by c o l d r o l l i n g , r e p o r t e d l y had a o c o h e r e n t l y - d i f f r a c t i n g domain s i z e of 400 A. By c o n t r a s t , aluminum o has been found i n the present work to have a domain s i z e of > 1000 A o (about 1500 A) a f t e r 70% co l d work; see Table XI. When some metals ( i n c l u d i n g aluminum) are co l d worked e x t e n s i v e l y , networks of tangled d i s l o c a t i o n s form which i n three dimensions appear to define the w a l l s of c e l l s or subgrains. W i t h i n the c e l l s are few d i s l o c a t i o n s . The c e l l s are t y p i c a l l y i n the order of one micron - 110 -diameter, and examples are c l e a r l y seen i n F i g s . 26a to 26c. The c e l l w a l l s are of high d i s l o c a t i o n d e n s i t y . Upon annealing at high enough temperatures, d i s l o c a t i o n s i n c e l l w a l l s rearrange to assume a lower-energy, l e s s tangled c o n f i g u r a t i o n ( p o l y g o n i z a t i o n ) , and the c e l l w a l l s become sharp and i d e n t i f i a b l e as low angle subgrain boundaries. S t i l l higher annealing temperatures cause subgrain boundaries to migrate, subgrains to grow, and r e c r y s t a l l i z a t i o n to occur. T h e o r e t i c a l l y , t h e c e l l s or subgrains produced by deformation should be i d e n t i f i e d w i t h the aforementioned " c o h e r e n t l y - d i f f r a c t i n g domains" that are measured by X-ray methods i n h e a v i l y deformed metals. However, o metallography gave a c e l l diameter of 0.76 y (7600 A) f o r pure aluminum reduced 70% by c o l d r o l l i n g whereas the domain s i z e obtained o from X-ray a n a l y s i s was found to be about 1500 A. In order to r e c o n c i l e the subgrain s i z e w i t h the domain s i z e , one can assume that minute o domains (1000 to 2000 A diameter) w i t h low angle boundaries, e x i s t i n the c e l l w a l l s , but have not been resolved by e l e c t r o n microscopy. Some supporting evidence may be found i n F i g . 26c i n the broad c e l l w a l l s f o r c o l d r o l l e d pure aluminum, although i t i s at best d i f f i c u l t to i d e n t i f y unambiguously a " c e l l " or "domain" i n such micrographs. 68 69 C o t t r e l l and L i have shown t h e o r e t i c a l l y that c e l l w a l l s or subgrain boundaries can act as b a r r i e r s to moving d i s l o c a t i o n s . Several w o r k e r s ^ ' c l a i m to have shown t h a t , when subgrains are present, ambient-temperature p r o p e r t i e s depend only on the subgrain s i z e and that the y i e l d s t r e n g t h i s r e l a t e d to the subgrain s i z e by the 72 73 H a l l - P e t c h ' equation, °0.2 = °0 + K £ _ 1 / 2 ( 2 8 ) - I l l -where ^ i-s t n e 0.2 pet. o f f s e t y i e l d strength, O Q and K are constants and I i s the mean subgrain diameter. In t h i s equation i s a f r i c t i o n stress r e s i s t i n g d i s l o c a t i o n motion i n the matrix and K i s a measure of the strengthening e f f e c t of the sub-boundary. An attempt was made to v e r i f y the v a l i d i t y of t h i s r e l a t i o n s h i p by p l o t t i n g experimental data from the present work. The 0.2 pet. y i e l d strength of aluminum i s plotted i n F i g . 52 against the r e c i p r o c a l square root of the measured subgrain diameter. The o r i g i n a l data are i n Table XIV of the Appendix. A good l i n e a r c o r r e l a t i o n i s suggested, and a st r a i g h t l i n e has been 74 5 f i t t e d to the points by the method of le a s t squares. B a l l and Hansen have made s i m i l a r plots from t h e i r own experiments. However, the and K values obtained from F i g . 52 do not agree with those of the p r i o r workers. The comparative data are summarized i n Table XIII. Table XIII: aQ and K Values for Aluminum i n the Hall-Petch Equation Material 10 p s i K 10 p s i u Reference 99.96 pet A l 99.998 pet A l 99.5 pet A l 99.994 pet A l 99.5 pet Al (Recrystallized) -7.7 -4.3 +1.0 0 2.3 19.7 13.3 10.3 11.1 5.7 present work Hansen"' Hansen^ ,74 B a l l Hansen 32 - 112 -- 113 -The l a r g e n e g a t i v e v a l u e o f t h e i n t e r c e p t , o^, i n F i g . 52 c a s t s doubt on the v a l i d i t y o f t h e H a l l - P e t c h r e l a t i o n s h i p f o r s u b s t r u c t u r e s t r e n g t h e n i n g . T h e o r e t i c a l l y , i s a f r i c t i o n s t r e s s r e s i s t i n g d i s l o c a t i o n m o t i o n . S i n c e t h e d i s l o c a t i o n d e n s i t y i n t h e i n t e r i o r o f t h e s u b g r a i n s i s s m a l l , s h o u l d a t most be e q u a l t o t h e y i e l d s t r e n g t h of t h e r e c r y s t a l l i z e d m a t e r i a l ; i . e . about 1000 t o 2000 p s i . I t s h o u l d be n o t e d from T a b l e X I I I and the n a t u r e o f t h e H a l l - P e t c h r e l a t i o n t h a t a n e g a t i v e i n t e r c e p t r e s u l t s when t h e K v a l u e ( s l o p e ) o f t h e d a t a i s l a r g e . The n e g a t i v e i n t e r c e p t can be a s s o c i a t e d w i t h i n a c c u r a c y i n t h e d e t e r m i n a t i o n o f s u b g r a i n d i a m e t e r s by m e t a l l o g r a p h y . I t was m e ntioned e a r l i e r t h a t c o h e r e n t l y - d i f f r a c t i n g domains s h o u l d be i d e n t i f i e d w i t h c e l l s o r s u b g r a i n s . The use o f t h e much s m a l l e r X - r a y domain s i z e s f o r £ i n t h e H a l l - P e t c h e x p r e s s i o n i n t h e c a s e o f the more h e a v i l y - d e f o r m e d ( f i n e r s t r u c t u r e ) a l l o y s w o u l d have t h e e f f e c t o f l o w e r i n g t h e s l o p e o f F i g . 52 as w e l l as t e n d i n g t o g i v e a more p o s i t i v e i n t e r c e p t . I t i s perhaps i n t e r e s t i n g t o n o t e i n t h i s 74 r e g a r d t h a t B a l l , who used an X - r a y microbeam t e c h n i q u e t o d e t e r m i n e 3 1/2 c e l l s i z e , f ound K = 11.1 x 10 p s i y and cr^ = 0 f o r p r e s t r a i n e d pure aluminum. Hansen (see T a b l e X I I I ) o b t a i n e d a h i g h K v a l u e and n e g a t i v e O Q v a l u e , u s i n g m e t a l l o g r a p h i c t e c h n i q u e s t o d e t e r m i n e c e l l s i z e . H i s r e s u l t s a r e t h e r e f o r e s u b j e c t t o t h e same c r i t i c i s m as t h o s e of t h e p r e s e n t work w h i c h a r e based on m e t a l l o g r a p h y a l o n e . 1/2 Even i f one a c c e p t s B a l l ' s v a l u e o f K = 11.1 k s i y , t h e s t r e n g t h e n i n g e f f e c t of c e l l b o u n d a r i e s i s a p p a r e n t l y l a r g e compared to t h a t o f h i g h a n g l e b o u n d a r i e s . I f , i n f a c t , c e l l w a l l s can be - 114 -g r e a t e r b a r r i e r s t o moving d i s l o c a t i o n s t h a n a r e l a r g e - a n g l e b o u n d a r i e s , i t seems l i k e l y t h a t s t r e n g t h must be more c l o s e l y r e l a t e d t o t h e s t r u c t u r e of t h e w a l l s t h a n t o t h e s p a c i n g o f t h e w a l l s . T h i s i s s u p p o r t e d by t h e o b s e r v a t i o n t h a t when a H a l l - P e t c h r e l a t i o n s h i p i s assumed f o r aluminum, t h e K v a l u e i s f a r from c o n s t a n t , but v a r i e s w i d e l y w i t h t h e m e c h a n i c a l and t h e r m a l h i s t o r y o f t h e m e t a l . R o b e r t s and J o l l e y , ^ f r o m t h e i r work w i t h p r e s t r a i n e d a n d - c o l d r o l l e d i r o n , have shown t h a t the d i s l o c a t i o n d e n s i t y w i t h i n t h e s u b g r a i n s o r c e l l s i s a t l e a s t an o r d e r o f magnitude l o w e r t h a n i n t h e s u b g r a i n b o u n d a r i e s . They assume t h a t the d i s l o c a t i o n s i n t h e boundary o f f e r a much s t r o n g e r b a r r i e r t o s l i p d i s l o c a t i o n s t h a n do the d i s l o c a t i o n s i n t h e m a t r i x , and t h a t i t i s t h u s o n l y t h e boundary d i s l o c a t i o n s t h a t c o n t r o l t h e f l o w s t r e s s . R o b e r t s and J o l l e y a t t r i b u t e d i f f e r e n t v a l u e s of K t o t h e v a r y i n g c h a r a c t e r o f t h e b o u n d a r i e s f o r d i f f e r e n t c o n d i t i o n s o f c o l d work, r e c o v e r y and c r y s t a l s t r u c t u r e , and t h e y j u s t i f i e d t h i s a p p r oach by n o t i n g t h a t a l l d a t a p l o t s c o u l d be made t o e x t r a p o l a t e -1/2 back t o the y i e l d s t r e n g t h o f a s i n g l e c r y s t a l a t £ = 0 . H u l t g r e n ^ s y s t e m a t i c a l l y i n v e s t i g a t e d t h e i n f l u e n c e o f p o l y g o n i z e d s u b s t r u c t u r e s i z e and m i s o r i e n t a t i o n on t h e m e c h a n i c a l p r o p e r t i e s o f c o m m e r c i a l l y p u r e aluminum. He found t h a t as s u b s t r u c t u r e m i s o r i e n t a t i o n i n c r e a s e d and s u b g r a i n s i z e d e c r e a s e d , t h e f l o w s t r e s s i n c r e a s e d . The i n c r e a s e i n f l o w s t r e s s was p l o t t e d a g a i n s t t h e i n v e r s e s q u a r e r o o t of s u b g r a i n d i a m e t e r t i m e s t h e s q u a r e r o o t o f a v e r a g e m i s o r i e n t a t i o n -1/2 1/2 (£ if> , b e i n g t h e m i s o r i e n t a t i o n ) and s t r a i g h t l i n e s were 69 o b t a i n e d as p r e d i c t e d by t h e o r y . However, t h e i n t e r c e p t s were n o t -1/2 1/2 z e r o a t £ if/ = 0 f o r the v a r i o u s a n n e a l i n g t e m p e r a t u r e s , and f o r - 115 -the highest annealing temperature (370°C) a negative i n t e r c e p t was obtained. According to Hultgren, the discrepancy may be due e i t h e r to some g r a i n boundary strengthening or to the s t r u c t u r e contained w i t h i n the subgrains but not normally a s s o c i a t e d w i t h the subst r u c t u r e . Substructure strengthening may a l t e r n a t i v e l y be described as a simple f u n c t i o n of d i s l o c a t i o n d e n s i t y . The r e l a t i o n s h i p between mean d i s l o c a t i o n d e n s i t y (p) and flow s t r e s s (x) i n shear f o r f . c . c . metal s i n g l e c r y s t a l s i s of the form x = Y G b p 1 / 2 (29) where y has a value between 0.2 and 0.5. For p o l y c r y s t a l l i n e aluminum the 0.2 pet y i e l d s t r e n g t h becomes r e l a t e d to the d i s l o c a t i o n d e n s i t y by the f o l l o w i n g equation: a 0 = 2.24 YGbp 1 / 2 ' (30) o. z 1 In the case of pure aluminum reduced 70% by c o l d r o l l i n g 3 O Q 2 = 14.5 x 10 p s i G = 3.62 x 10 6 p s i b = 2.85 A 10 -3 p = 2 x 10 cm.cm (Table XI) Upon s u b s t i t u t i n g these values i n equation (30) one obtains y = 0.45. The value of y f o r aluminum should be independent of thermomechanical treatments. U n f o r t u n a t e l y , the d i s l o c a t i o n d e n s i t y of pure aluminum i n the annealed c o n d i t i o n could not be determined a c c u r a t e l y from the - 116 -X-ray l i n e p r o f i l e a n a l y s i s because of the i n s i g n i f i c a n t l i n e broadening from t h i s source. Thus there were no data to permit the value of y obtained above to be compared against a standard. 5.1.2.1 Simple Aged A l l o y (No Substructure) This a l l o y was s o l u t i o n t r e a t e d and aged at 300°C (without i n t e r -vening hot or c o l d deformation) to produce a d i s p e r s i o n of 6 and/or 6' p r e c i p i t a t e s i n the aluminum-rich matrix. As seen from the phase diagram ( F i g . 2 ) , the matrix of the two-phase a l l o y contains 0.45 wt % Cu (0.16 at % Cu) i n e q u i l i b r i u m s o l i d s o l u t i o n at t h i s ageing tempera-ture. Much of t h i s may have been r e t a i n e d i n s o l u t i o n on c o o l i n g to 20°C. The strengthening mechanisms which might be considered i n the simple aged p o l y c r y s t a l l i n e a l l o y are: (a) Conventional d i s p e r s i o n hardening (Orowan), (b) S o l i d s o l u t i o n hardening, (c) Grain boundary strengthening. I t should be noted that f u r t h e r p r e c i p i t a t i o n i n the matrix a f t e r c o o l i n g from the ageing temperature was precluded by maintaining the specimen at -20°C a f t e r the ageing treatment and u n t i l t e n s i l e t e s t s were conducted. Subsequent room temperature ageing or s t r a i n - a g e i n g during t e s t i n g i s assumed to be i n s i g n i f i c a n t on the b a s i s of present observations and those reported by previous workers w i t h Al-Cu. The g r a i n s i z e of the aged a l l o y i n the present work was very l a r g e ; about 800 u. Thus, g r a i n boundary strengthening may be assumed to be 5.1.2 - 117 -n e g l i g i b l e . As a t e s t of the Orowan model f o r d i s p e r s i o n hardening the measured 0.2 pet y i e l d s t r e s s was p l o t t e d i n F i g . 53 against the D - 2r s s parameter l o g i r , ( r r )/(D - 2r ) according to equation (2). The 10 ID S S o r i g i n a l data are i n Table I I . A good l i n e a r c o r r e l a t i o n was apparent f o r the room temperature data, and a s t r a i g h t l i n e was f i t t e d to the po i n t s by the method of l e a s t squares. The slope of t h i s l i n e and i t s 3 i n t e r c e p t (o ) w i t h the ordi n a t e a x i s were found to be 2.5 x 10 p s i . y and 4500 p s i r e s p e c t i v e l y . In equation (2) o g i s the y i e l d s t r e s s of the matrix. In the present work the matri x of the two-phase Al-4Cu a l l o y c o n s i s t s of pure 76 aluminum co n t a i n i n g 0.16 at % Cu i n s o l i d s o l u t i o n . Dorn et a l . have experimentally determined the true s t r e s s - t r u e s t r a i n curves f o r aluminum s o l u t i o n hardened by copper i n the concentration range 0.029 to 0.233 at % Cu. From t h e i r p l o t s the 0.2 pet y i e l d s trength of aluminum con t a i n i n g 0.16 at % Cu i n s o l i d s o l u t i o n i s found to be about 2000 p s i . The remaining 2500 p s i of the experimental i n t e r c e p t (o ) can be a t t r i b u t e d to the s t r a i n hardening which occurred i n the t e n s i l e specimens while being s t r a i n e d 0.2 pet, since the i n i t i a l work hardening r a t e of dispersion-hardened a l l o y s i s known to be very high. The experimental r e s u l t s of Dew-Hughes and Robertson on s i n g l e c r y s t a l s of Al-Cu a l l o y s c o n t a i n i n g 6 (CuA^) p r e c i p i t a t e s i n d i c a t e d that the CRSS was a l i n e a r f u n c t i o n of the r e c i p r o c a l mean planar p a r t i c l e spacing i n agreement w i t h the Orowan model. The slope of the l i n e obtained was shown by the authors to be i n q u a n t i t a t i v e agreement w i t h Orowan's theory, i f C o t t r e l l ' s ^ 7 estimate of the l i n e tension of a d i s l o c a t i o n - 118 -- 119 -was used. C o t t r e l l ' s e s t i m a t e o f l i n e t e n s i o n d i f f e r s from t h a t o f o t h e r s by a f a c t o r o f two. K e l l y and N i c h o l s o n ^ r e p l o t t e d t h e CRSS d a t a o f Dew-Hughes and R o b e r t s o n , t a k i n g i n t o a c c o u n t t h e f l o w s t r e s s D - 2r s s o f t h e s o l i d s o l u t i o n , a g a i n s t l o g ^ C — ^ ) / ( D g - 2 r g ) f o l l o w i n g e q u a t i o n ( 1 ) . The d a t a appeared t o s u p p o r t a l i n e a r r e l a t i o n . The 3 s l o p e o f t h e e x p e r i m e n t a l c u r v e was 6.3 x 10 dynes/cm (0.98 p s i . P) 3 and t h e t h e o r e t i c a l v a l u e from e q u a t i o n (1) i s 3.3 x 10 dynes/cm (0.51 p s i . u ) . Thus t h e two d i f f e r by a f a c t o r o f s l i g h t l y l e s s t h a n two. F o r a p o l y c r y s t a l l i n e m a t e r i a l t h e s l o p e and i n t e r c e p t (o ) c a l c u l a t e d from t h e r e p l o t o f t h e s i n g l e c r y s t a l d a t a o f K e l l y and 1 3 N i c h o l s o n a r e found t o be 2.18 x 10 p s i . u and 1000 p s i r e s p e c t i v e l y . These a r e i n good agreement w i t h t h e r e s u l t s o f the p r e s e n t work. A l - 4 C u when aged a t 300°C f o r o n l y a few h o u r s a f t e r t h e s o l u t i o n t r e a t m e n t i s known t o c o n t a i n a d i s p e r s i o n o f 9.' p r e c i p i t a t e s i n t h e a l u m i n u m - r i c h matrix."'""' A f t e r l o n g e r a g e i n g t i m e s 6* p r e c i p i t a t e s p a r t l y t r a n s f o r m i n t o 0 phase,and t h e m a t r i x c o n t a i n s a d i s p e r s i o n o f b o t h 0 ' and 9 p r e c i p i t a t e s . Thus, t h e d a t a p l o t i n F i g . 53 l e n d s s u p p o r t t o t h e argument r a i s e d in t h e e a r l i e r r e v i e w ( S e c t i o n 1.1) t h a t i n t h e p r e s e n c e o f t h e s e m i - c o h e r e n t 6' p r e c i p i t a t e t h e Orowan model can be a p p l i e d , a t l e a s t i n t h e i n i t i a l s t a g e s o f d e f o r m a t i o n . 78 R e c e n t l y McG. T e g a r t has p o i n t e d out t h a t t h e Orowan t h e o r y i s v a l i d f o r u n i f o r m l y d i s p e r s e d s t r o n g p a r t i c l e s , and t h a t measured and c a l c u l a t e d y i e l d s t r e n g t h s may be e x p e c t e d t o agree w i t h i n a f a c t o r o f two. G r e a t e r d i f f e r e n c e s t h a n t h i s can be e x p e c t e d when the p a r t i c l e s a r e n o t s p h e r i c a l o r when the y i e l d s t r e n g t h i s measured a f t e r some - 120 -small p l a s t i c s t r a i n . The nature of the dispersion of the p a r t i c l e s i s also important i n determining the strength. In Al-4Cu a l l o y s the p r e c i p i t a t e s are i r r e g u l a r i n shape, and t h e i r s i z e and d i s t r i b u t i o n are not uniform. In addition, aged Al-4Cu a l l o y s are known to contain grain boundary p r e c i p i t a t e s whose influence on mechanical properties i s 79 not c l e a r l y understood. L i u and Gurland found that i n low carbon steels carbides are located mainly at grain boundaries, and that they appear to exert an important e f f e c t on deformation behaviour. 5.1.2.2 Aged-and-Deformed A l l o y s A s i g n i f i c a n t feature of dispersion-hardened materials i s the high attainable l e v e l of "stored energy of cold work" which was discussed i n Section 1.1. Comparing the strengths of over-aged and c o l d - r o l l e d Al-4Cu a l l o y with those of c o l d - r o l l e d pure aluminum i n Table I I I , i t can be concluded that a high l e v e l of s t r a i n energy can be imparted to the aged a l l o y by cold working, i n support of e a r l i e r 33-37 such suggestions. . That the d i s l o c a t i o n density of cold r o l l e d Al-4Cu i s very high compared to that of c o l d - r o l l e d pure aluminum i s also apparent from the X-ray result's of Table XI. This supports the 38 39 suggestions of Brimhall et a l . ' that dispersed second phase p a r t i c l e s can act as sources of d i s l o c a t i o n s i n several ways, thereby increasing the rate of s t r a i n hardening. Stored energy i s released during annealing, and provides a d r i v i n g force for both recovery and r e c r y s t a l l i z a t i o n processes. In the case of the cold worked Al-4Cu a l l o y , i t was found (Fig. 4) that there was a gradual but large drop i n 20°C strength with increasing annealing - 121 -temperature i n the range 50-250°C. Humphreys and M a r t i n have suggested that a s i m i l a r drop i n hardness upon annealing t h e i r i n t e r n a l l y o x i d i s e d and c o l d r o l l e d Cu-Si a l l o y s may be due to the r e l a x a t i o n of long range s t r e s s e s by s l i g h t d i s l o c a t i o n movements, as w e l l as to the annealing-out of jogs and the a n n i h i l a t i o n of d i s l o c a t i o n d i p o l e s . In the present work metallography and X-ray l i n e p r o f i l e a n a l y s i s have i n d i c a t e d the e xistence of a polygonized substructure i n aged Al-4Cu, a f t e r 70% r e d u c t i o n by c o l d r o l l i n g . Transmission e l e c t r o n micrographs of t h i s a l l o y ( F i g s . 38a to 38c) show numerous tangles of d i s l o c a t i o n s i n the c e l l i n t e r i o r s and around p r e c i p i t a t e s . I t i s suggested that i n the i n i t i a l stages of recovery, i . e . up to an annealing temperature of 250°C, d i s l o c a t i o n s are r e l e a s e d from such tangles and are a t t r a c t e d towards the c e l l w a l l to c o n t r i b u t e to well-developed polygonized subgrain boundaries ( F i g s . 40a and 40b). A decrease i n d i s l o c a t i o n d e n s i t y (and associated l a t t i c e s t r a i n ) thus occurs at r e l a t i v e l y low annealing temperatures, w i t h some attendant decrease i n y i e l d s t r e n g t h . By c o n t r a s t , c o l d r o l l i n g had i t s e l f produced well-developed (polygonized) c e l l w a l l s w i t h d i s l o c a t i o n - f r e e c e l l i n t e r i o r s i n pure aluminum, and the same low-temperature annealing treatments were probably not s u f f i c i e n t to a l t e r s i g n i f i c a n t l y the d i s l o c a t i o n d e n s i t y or c o n f i g u r a t i o n w i t h i n the c e l l w a l l s . Thus the s t r e n g t h of c o l d worked pure aluminum d i d not respond to annealing i n the range of 50 to 250°C. The l a r g e r drops i n 20°C stren g t h a f t e r annealing at higher temperatures ( i n F i g . 4) correspond to a r a p i d decrease i n d i s l o c a t i o n d e n s i t y w i t h growth of subgrains,accompanied by an increase i n i n t e r p a r t i c l e - 122 -spacing. Annealing at the higher temperatures (e.g. 350°C and 400°C) produced a s t r a i n - f r e e r e c r y s t a l l i z e d m i c r o s t r u c t u r e and a s i g n i f i c a n t i ncrease i n the spacing of the 0 p a r t i c l e s i n Al-4Cu. A f t e r annealing at 350°C, the i n t e r p a r t i c l e spacing had increased to 2.5 y. Consider-i n g c o n t r i b u t i o n s due to d i s p e r s i o n hardening and s o l i d s o l u t i o n hardening the y i e l d s t r e n g t h of t h i s m a t e r i a l was c a l c u l a t e d to be about 7000 p s i which i s c l o s e to the measured value of 8300 p s i . An increase i n the annealing time at 300°C l i k e w i s e produced a simultaneous increase i n both i n t e r p a r t i c l e spacing and subgrain s i z e i n Al-4Cu. In a d d i t i o n , the i r r e g u l a r elongated p r e c i p i t a t e s observed i n the as-aged a l l o y became more s p h e r i c a l . The c a l c u l a t e d c o n t r i b u t i o n of Orowan strengthening i n the c o l d worked-and-annealed Al-4Cu i s found to be much l e s s than i n the simple over-aged a l l o y due to t h i s coarsening and s p h e r o i d i s a t i o n of the 0 phase w i t h thermo-mechanical treatments. The appreciably higher st r e n g t h of recovered Al-4Cu a l l o y s compared to that of pure aluminum (Fig s . 4, 7 and 8) f o r any annealing treatment i s an i n d i c a t i o n of the r e t a r d a t i o n of recovery processes, and the r e t e n t i o n of part of the s t r a i n e d m i c r o s t r u c t u r e , due to the presence of the second phase p a r t i c l e s . The e x t r a s t r e n g t h of the recovered a l l o y cannot simply be accounted f o r adequately by the second phase d i s p e r s i o n . For example, the cold-worked Al-4Cu a l l o y , 'B' S e r i e s , when annealed at 300°C f o r 4 hours had a y i e l d strength of 15,000 p s i . The p r e d i c t e d y i e l d s t r e n g t h of t h i s a l l o y due to the combined e f f e c t s of Orowan hardening (t a k i n g i n t o account the observed increase i n i n t e r p a r t i c l e spacing) and s o l i d s o l u t i o n hardening i s found to be about - 123 -9000 p s i . Thus, at l e a s t 6000 p s i of the measured y i e l d s t r e n g t h , and p o s s i b l y a much l a r g e r f r a c t i o n (as i n d i c a t e d below) must be a t t r i b u t a b l e to some form of substructure hardening. Using measured subgrain diameters, a H a l l - P e t c h p l o t was made of the 20°C y i e l d s t r e n g t h data ( F i g . 54). The o r i g i n a l data are contained in- Table XV of the Appendix. When a s t r a i g h t l i n e was f i t t e d to the points by the method of l e a s t squares, (the i n t e r c e p t ) was 1800 p s i , i n agreement w i t h the expected y i e l d s trength of the r e c r y s t a l l i z e d 3 1/2 matrix metal. The slope of the p l o t was 15.9 x 10 p s i y As noted p r e v i o u s l y i n Secti o n 5.1.1, measured subgrain diameters are considerably at variance w i t h domain s i z e s determined by the X-ray technique, the l a t t e r being much sm a l l e r . In the case of aged-and-r o l l e d Al-4Cu, a meaningful value of domain s i z e was obtained from the o X-ray a n a l y s i s ; i . e . about 860 A a f t e r 70% c o l d work. I f t h i s domain s i z e i s taken as the true subgrain s i z e , and an average y i e l d s t r e n g t h of 41,100 p s i i s taken from the t e n s i l e data, the H a l l - P e t c h r e l a t i o n g i v e s ; 41,100 = 1800 + k(0.086) 1 / 2 (31) 1/2 from which k = 11.5 K s i u. •. I t i s i n t e r e s t i n g to note that t h i s value 74 of k i s very c l o s e to that obtained by B a l l f o r pure deformed aluminum (see Table X I I I ) . B a l l ' s X-ray technique f o r the determination of c e l l or subgrain s i z e was a p p l i c a b l e to c e l l diameters w e l l i n o excess of the 1000 A lower l i m i t of the technique used i n the present work, which made i t u s e f u l f o r the pure metal. - 124 -38 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 -1/2 r . ,-1/2 £ , (micron) ' Figure 54. 20°C Y i e l d strength of Al-4Cu (B Series) as a f u n c t i o n of the r e c i p r o c a l of the square root of the subgrain diameter. - 125 -I t i s important to note that i n the previous d e r i v a t i o n of k, i t was assumed that a l l but 1800 p s i . of the y i e l d s t r e n g t h of the worked-and-annealed a l l o y was due to subgrain boundary strengthening. Yet i n the case of simple aged a l l o y s (Section 5.1.2.1) almost a l l observed strengthening was a t t r i b u t e d to the Orowan mechanism. The p o s s i b i l i t i e s must be considered that (a) Orowan and sub-boundary hardening e f f e c t s can be a d d i t i v e , and (b) i n the aged-worked-annealed a l l o y , hardening may be due to one mechanism i n one annealed c o n d i t i o n , but due mainly to another mechanism i n another c o n d i t i o n . There appears to be no j u s t i f i c a t i o n f o r adding Orowan and sub-boundary strengthening i n the same m a t e r i a l . The b a r r i e r s represented by the two mechanisms must be overcome s u c c e s s i v e l y , r a t h e r than simultaneously, by d i s l o c a t i o n s moving i n the s l i p plane; thus the stronger b a r r i e r s should determine the flow s t r e s s . C a l c u l a t e d values of O Q ^ f r o m Orowan and H a l l - P e t c h equations are p l o t t e d against p a r t i c l e spacing and domain (or subgrain) s i z e i n F i g . 55. For the Orowan p l o t , a s i m p l i f i e d v e r s i o n of equation (2) has been used; i . e . , 2 x const. x Gb a0.2 = a s + D ( 3 2 ) When the experimental data f o r the simple aged a l l o y ( Section 5.1.2.1) are p l o t t e d according to t h i s equation (see F i g . 60 i n Appendix), i t i s found that a A „ = 5300 + 8900 D 1 (33) 0.2 s 60 50 40 3 30 20 10 O Orowan E q u a t i o n , an „ = 5300 + 8900 D 0.2 s -1 H a l l - P e t c h E q u a t i o n , a 2 = 1800 + 11500 I -1/2 E x p e r i m e n t a l Range o f D or I E x p e r i m e n t a l Range of D I I I L 1 J L ON 0.8 1.6 2.0 2.8 3.6 I o r D , m i c r o n s s F i g u r e 55. Comparison of Orowan s t r e n g t h e n i n g and s u b s t r u c t u r e s t r e n g t h e n i n g f o r v a r i o u s v a l u e s o f I or D - 127 -The H a l l - P e t c h p l o t of F i g . 55 was based on the value of k determined from equation (31); i . e . o Q 2 = 1800 + 11.5 x 10 3 j f 1 / 2 (34) The e n t i r e experimental range of D g values was 1.3 to 2.2 y. The corresponding range of both measured subgrain s i z e s and X-ray domain s i z e s f o r the cold-worked-and-annealed a l l o y was 0.09 to 2 y. Obser-v a t i o n of F i g . 55 rev e a l s that w i t h i n these ranges, c a l c u l a t e d sub-boundary strengthening i s at l e a s t as great as d i s p e r s i o n strengthening. In f a c t , f o r most of the deformed-annealed m a t e r i a l s , the domain s i z e (or measured a value) was much l e s s than the i n t e r p a r t i c l e spacing, and sub-boundary strengthening can c l e a r l y be expected to dominate. Even a f t e r the heaviest annealing treatment of 15 hours at 300°C, where both D and I (measured) were about 2 microns, c a l c u l a t e d hardening from s the H a l l - P e t c h e f f e c t i s as great as that from the Orowan e f f e c t . I t i s concluded that i n a l l the over-aged Al-4Cu m a t e r i a l s which were subjected to thermo-mechanical treatment,the observed s t r e n g t h i s due almost e n t i r e l y to substructure strengthening, as i n the case of pure aluminum. This i s i n marked con t r a s t to the co n c l u s i o n f o r the simple over-aged a l l o y , where the i n t e r p a r t i c l e spacing was i n a l l cases much l e s s than the g r a i n s i z e , and where no f i n e substructure was present. In a l l cases of cold-worked-and-annealed Ni-ThO^ w i t h domain s i z e s 41 l e s s than d i s p e r s o i d i n t e r p a r t i c l e spacings, Clegg a l s o concluded that sub-boundary strengthening predominated. The strengthening e f f e c t of - 128 -the dispersed second phase p a r t i c l e s i s then i n t e r p r e t e d i n terms of the e f f e c t of the p a r t i c l e s on the operation of m u l t i p l e s l i p systems during p r i o r deformation,the i n h i b i t i o n they provide to dynamic recovery, and t h e i r r e t a r d a t i o n e f f e c t on s t a t i c recovery and r e c r y s t a l l i z a t i o n . I t should be noted that substructures can be described a l t e r n a t i v e l y i n terms of d i s l o c a t i o n d e n s i t y ( s i m i l a r to the e a r l i e r d i s c u s s i o n f o r the case of pure aluminum). In t h i s approach d i s l o c a t i o n s are v i s u a l i z e d as c o n t r i b u t i n g to the "matrix y i e l d s t r e s s " i n the Orowan equation, (2), and thus i t i s perhaps reasonable to add t h e i r c o n t r i b u t i o n to that of the p a r t i c l e s . This i s i n c o n t r a s t to the previous approach, where d i s l o c a t i o n s were considered only i n r e l a t i o n to the c e l l s or subgrains which they bound, and where Orowan strengthening was not considered to be a d d i t i v e to subgrain strengthening. The method of adding these strengthening c o n t r i b u t i o n s has been used by a number of p r i o r workers i n c l u d i n g Dew-Hughes and Robertson"*"7 w i t h Al-Cu a l l o y s 5 32 81 c o n t a i n i n g G.P. zones, Hansen ' w i t h A l - A ^ O ^ products, and Webster w i t h d i s p e r s i o n hardened nichrome (TDNiC). Al-4Cu ('B' Series) a f t e r 70% r e d u c t i o n by c o l d r o l l i n g had a 0.2 pet y i e l d s t r e n g t h of 41,100 p s i . In the over-aged c o n d i t i o n the y i e l d s t r e n g t h of t h i s a l l o y was only 13,300 p s i . Thus, the s t r e n g t h c o n t r i b u t i o n a s sociated w i t h d i s l o c a t i o n d ensity i s 27,800 p s i . The 10 -3 d i s l o c a t i o n d e n s i t y of t h i s a l l o y i s at l e a s t 4 x 10 cm.cm and p o s s i b l y higher by a f a c t o r of two (see Table X I ) . The value of y obtained from equation (30) using these data i s found to be i n the range 0.4 to 0.6, which may be compared w i t h the value of 0.45 f o r pure aluminum. - 129 -5.1.2.3 Deformed-and-Aged A l l o y s I t i s i n t e r e s t i n g to analyse the performance of the 'C' S e r i e s of Al-4Cu. These m a t e r i a l s were co l d r o l l e d 70% immediately a f t e r s o l u t i o n treatment, and were then aged at 300°C f o r v a r i o u s amounts of time. The second phase was thus introduced only a f t e r deformation. By c o n t r a s t , a l l o y s of the A or B Series were c o l d worked e n t i r e l y i n the presence of the second phase. Compared to a l l o y s of the A or B S e r i e s , the ' C1 Series a l l o y s e x h i b i t e d higher strengths both at R.T. and at 300°C f o r any p r i o r thermo-mechanical treatment. In the cold-worked s t a t e the 'C' S e r i e s had an unusually high y i e l d s t r e s s ; about 49,000 p s i , compared to a value of 41,000 p s i f o r Series B. Both a l l o y s i n the h e a v i l y deformed s t a t e are known to conta i n f i n e substructure c e l l s . However, a f t e r a short time at room temperature, there i s a marked increase i n the y i e l d s t r e s s of the m a t e r i a l which was deformed i n the s o l u t i o n - t r e a t e d c o n d i t i o n . K e l l y and Nicholson''" have mentioned the r e s u l t s of Graf, who showed that p l a s t i c deformation of a s i n g l e c r y s t a l of s o l u t i o n - t r e a t e d Al-Cu leads to the formation of G.P. zones at room temperature much more r a p i d l y than would occur i n the absence of p r i o r deformation. Thus the 8000 p s i increment i n y i e l d s t r e n g t h of the 'C1 Series a l l o y i s probably due to the unavoidable p r e c i p i t a t i o n of some G.P. zones at room temperature a f t e r c o l d r o l l i n g and p r i o r to t e n s i l e t e s t i n g . P r e c i p i t a t i o n phenomena are i n f a c t commonly a f f e c t e d by cold work p r i o r to ageing. The nature of the p r e c i p i t a t e s formed and the ra t e of n u c l e a t i o n of p r e c i p i t a t e s are u s u a l l y governed by the amount of p r i o r c o l d work, the ageing temperature,and the time of ageing. These, i n t u r n , determine the ra t e of hardening. - 130 -Generally prior deformation accelerates the whole p r e c i p i t a t i o n 82-84 process. Several workers have shown that cold deformation p r i o r to ageing increases the rate of nucleation of an intermediate precipitate. It i s also accepted that the p a r t i a l l y coherent 6 ' phase i n Al-Cu can nucleate only i n a nearly perfect l a t t i c e , whereas i n a moderately or heavily distorted l a t t i c e the nucleation of the noncoherent e q u i l i -brium 9 phase i s favoured. After 70% r o l l i n g deformation the a l l o y contains regions of high dislocation density ( c e l l walls) and regions of lower d i s l o c t i o n density. Thus p r e c i p i t a t i o n of both 0 and 0 ' may start simultaneously during subsequent ageing at 300°C, 0 nucleating at the regions of high dislocation density and 0 1 at regions nearly free of dislocations. The 0 ' and 9 phases can be distinguished by electron d i f f r a c t i o n , but more eas i l y by their t y p i c a l and different shapes; 85 i.e. 9 ' i s p l a t e l i k e , 9 occurs as more massive p a r t i c l e s . The shape of 9 (CuAl^) p a r t i c l e s depends on the i r mechanism of formation; i n 8 3 deformed alloys they are found to be almost spheres. This i s shown i n Fig. 56a which i s a transmission electron micrograph of Al-4Cu, 'C' Series, reduced 70% by cold r o l l i n g and then aged at 300°C for one hour. After the p r e c i p i t a t i o n of 9' phase, the dislocations rearrange to form sub-boundaries (Fig. 56b). Large 0 ' p a r t i c l e s grow and 84 f i n a l l y transform into 9 phase, while small ones dissolve. At longer ageing times the subgrain size increases, and the misorientation between subgrains increases. These two phenomena are governed by the coarsening of the 9 phase. No X-ray d i f f r a c t i o n studies were carried out on the C Series alloys. Thus, only measured subgrain sizes are available for the interpretation of y i e l d strength i n terms of a Hall-Petch relationship. - 131 -Figure 56. Tranmission e l e c t r o n micrograph of Al-4Cu (C S e r i e s ) c o l d -r o l l e d 70% a f t e r s o l u t i o n treatment and aged at 300°C f o r 1 hr. (a) showing e' and 0 p r e c i p i t a t e s , 50,000X. (b) showing subgrains,35,000X. - 132 -In view of the emphasis placed p r e v i o u s l y on domain s i z e f o r such i n t e r p r e t a t i o n i n Al-Cu a l l o y s , no q u a n t i t a t i v e treatment of the C Series data i s warranted. 5.1.3 S.A.P. o I f i t i s assumed that the domain s i z e of ^ 1000 A revealed by X-ray st u d i e s (Table XI) f o r S.A.P. i s i d e n t i f i a b l e w i t h a true subgrain s i z e , the subgrain strengthening could be a p p r e c i a b l e . According to equation (34), based on Al-Cu data, the y i e l d s t r e n g t h should be about o 38,000 p s i f o r I = 1000 A. This i s only s l i g h t l y higher than the observed st r e n g t h . I t i s s i g n i f i c a n t to note from Table XI that c o l d r o l l e d Al-Cu a l l o y s and S.A.P. a l l o y s ( a l l c o n d i t i o n s ) had comparable X-ray domain s i z e s and comparable strengths. Several workers^' 8 ^ have claimed to show evidence f o r Orowan 9 32 strengthening i n S.A.P.-type a l l o y s . Hansen ' worked w i t h a l l o y s c o n t a i n i n g a wide range of oxide contents. He found that h i s lower Al^O^ m a t e r i a l s could be f u l l y r e c r y s t a l l i z e d by heat treatment, thus e l i m i n a t i n g a c o n t r i b u t i o n from substructure. For such m a t e r i a l s Hansen proposed that s t r e n g t h was due mainly to the Orowan mechanism, w i t h an added c o n t r i b u t i o n from g r a i n boundaries. When these low oxide S.A.P. a l l o y s were c o l d worked and annealed under c o n d i t i o n s which produced a r e s i d u a l s u b s t r u c t u r e , Hansen assumed that the substructure 5 32 hardening ' could be added d i r e c t l y to Orowan hardening. To account f o r the substructure c o n t r i b u t i o n , Hansen used the H a l l - P e t c h r e l a t i o n -ship i n conjunction w i t h measured subgrain s i z e . However, the assumed Orowan c o n t r i b u t i o n to s t r e n g t h , based on the r e s u l t s w i t h r e c r y s t a l l i z e d - 133 -a l l o y s , was so l a r g e that the slope of Hansen's H a l l - P e t c h p l o t s was low; i . e . the substructure c o n t r i b u t i o n to strength was small and r e l a t i v e l y i n s e n s i t i v e to c e l l s i z e . When Hansen"*"^ worked w i t h high oxide content S.A.P. a l l o y s , he found that they could not be r e c r y s t a l l i z e d ; thus he was not able to i s o l a t e d i r e c t l y an Orowan c o n t r i b u t i o n to the stren g t h of these a l l o y s . He used the H a l l - P e t c h p l o t s of h i s str e n g t h data w i t h measured c e l l or subgrain s i z e s , and took the i n t e r c e p t s at £ = oo to be the Orowan c o n t r i b u t i o n . For an a l l o y e s s e n t i a l l y i d e n t i c a l to the S.A.P. used i n the present work, he claimed an i n t e r c e p t of 26,000 p s i , which he argued was a reasonable value f o r Orowan strengthening when h i s r e s u l t s w i t h lower oxide contents ( r e c r y s t a l -l i z e d ) were ex t r a p o l a t e d . o The measured mean planar i n t e r p a r t i c l e spacing, D g, was. about 800 A fo r S.A.P. m a t e r i a l s i n the present work. Applying equation (2) w i t h appropriate constants f o r aluminum, a c a l c u l a t e d y i e l d s t r e s s of ^ 100,00 p s i i s obtained; i . e . s e v e r a l times higher than the observed value. Since the constants i n the Orowan equation f o r aluminum are w e l l t e s t e d by the work of other i n v e s t i g a t o r s , i t must be i n f e r r e d that the metal l o g r a p h i c techniques used to determine D g i n S.A.P. have considerably underestimated the spacing. P a r t of the d i f f i c u l t y a r i s e s from the f a c t that the oxide p a r t i c l e s are c l u s t e r e d ; e.g. see F i g s . 49 and 51. I f c l u s t e r s are i d e n t i f i e d as " p a r t i c l e s " , that i s , i f the spacing of p a r t i c l e s w i t h i n a c l u s t e r i s neglected, the mean planar spacing i s much higher. Assuming that only Orowan-type strengthening i s s i g n i f i c a n t i n the S.A.P. of the present work, equation (2) reveals that the oxide p a r t i c l e - 134 -spacing should be about 0.3 ]i to account f o r the observed flow s t r e s s . In a l l c o n d i t i o n s i n which i t was examined, the S.A.P. of the present work contained a f i n e s u b s t r u c t u r e . I f Hansen's a n a l y s i s were accepted, 26,000 p s i would be a t t r i b u t a b l e to d i r e c t p a r t i c l e (Orowan) strengthening, and 6000-8000 p s i would be due to s u b s t r u c t u r e . There are s e v e r a l reasons why t h i s i n t e r p r e t a t i o n of the r e s u l t s must be r e j ected: (a) In the presence of both subgrain or c e l l boundaries and p a r t i c l e s , there i s no reason to expect the e f f e c t s of each b a r r i e r to be simply a d d i t i v e . (b) I f sub-boundary strengthening i s to be i n c l u d e d , i t s c o n t r i -b u tion should be c o n s i s t e n t w i t h that observed i n pure aluminum and Al-4Cu i n the present work. The very f i n e substructures i n S.A.P. should be capable of c o n t r i b u t i n g s e v e r a l times the 6000-8000 p s i increment noted above (See F i g . 52 f o r pure aluminum, and F i g . 54 f o r Al-4Cu). (c) The extremely complex nature of the m i c r o s t r u c t u r e and sub-s t r u c t u r e of S.A.P. i n a l l c o n d i t i o n s (see F i g s . 49 to 51) makes i t d i f f i c u l t to have any confidence i n values of D g or H determined by metallographic techniques. Thus a l l the observed str e n g t h of S.A.P. a l l o y s can be adequately explained i n terms of substructure strengthening. There i s n e i t h e r a need nor a j u s t i f i c a t i o n f o r i n v o k i n g Orowan strengthening i n t h i s a l l o y . I t i s p o s s i b l e to use the aforementioned a l t e r n a t i v e view of sub-s t r u c t u r e as an array of d i s l o c a t i o n s g i v i n g a strengthening c o n t r i b u t i o n - 135 -a = 2.24 Y G bP • The X-ray data of Table XI show that the stre n g t h of S.A.P. can be explained on t h i s b a s i s when a comparison i s made wi t h cold-worked Al-4Cu (see Se c t i o n 5.1.2.2). Transmission e l e c t r o n micrographs f o r S.A.P. (see F i g s . 49 and 51) show the presence of c l u s t e r s of oxide p a r t i c l e s both i n c e l l i n t e r i o r s and along c e l l w a l l s . A f t e r 50% co l d work (see F i g s . 50a to 50c) most of the c e l l i n t e r i o r s were f r e e of d i s l o c a t i o n s . This would probably i n d i c a t e that a s i g n i f i c a n t f r a c t i o n of the e x t r a d i s l o c a t i o n s produced by c o l d work have been held up between the oxide p a r t i c l e s i n the c l u s t e r s . D i s l o c a t i o n s a r r e s t e d i n such c l u s t e r s are unable to break away upon heating. This i s probably the reason f o r the high d i s l o c a t i o n density and f o r the i n s i g n i f i c a n t decrease i n stre n g t h of cold-worked S.A.P. even a f t e r annealing f o r 24 hours at 540°C; see Table XI. 5.2 S t r e s s - S t r a i n Curves and D u c t i l i t y at 20°C S t r e s s - s t r a i n curves f o r d i f f e r e n t m a t e r i a l s t e s t e d i n the present work are reproduced i n F i g s . 57 and 58, and some i n t e r e s t i n g d i f f e r e n c e s are revealed. I t i s not p o s s i b l e from the curves of F i g . 57 to compare i n i t i a l work-hardening r a t e s , because of the coarse s c a l e of the s t r a i n a x i s i n the p l o t . Thus, f o r example, the low slope of the curve f o r annealed 'B' Series Al-4Cu a l l o y at > 1% s t r a i n i s i n d i c a t i v e only of a low net r a t e of hardening a f t e r very l a r g e s c a l e d i s l o c a t i o n motion has occurred..- The net rate of work hardening i n t h i s m a t e r i a l was i n f a c t high at .small s t r a i n s 0.02% as p a r t i a l l y seen i n F i g . 58. Thus, the curves r e v e a l the e f f e c t s of combined hardening and dynamic recovery - 136 -54 1. M l , 70% C.W. 2. M l , 70% C.W. + annealing at 300°C for 6 hrs 3. Al-4Cu, over-aged 4. Al-4Cu, hot-rolled 5. Al-4Cu, B, C.W. 70% 6. Al-4Cu, B, C.W. 70% + annealed at 300°C for 1 hr. 7. Al-4Cu, B, C.W. 70% + annealed at 300°C for 4 hrs. 8. S.A.P., C.W. 50% 9. S.A.P., C.W. 50% + annealed at 540°C for 24 hrs. 0.02 0.04 0.06 0.08 True Strain 0.1 0.12 0.14 Figure 57. 20°C True stress-true s t r a i n curves for pure aluminum, Al-4Cu (B Series) and S.A.P. i n various thermo-mechanical conditions. - 137 -•H CO CO CO tu CU S-i H 0.01 0.03 0.02 True S t r a i n Figure 58. 20°C True s t r e s s - t r u e s t r a i n curves f o r Al-4Cu (B Se r i e s ) cold-r o l l e d 70% and annealed at d i f f e r e n t temperatures. - 138 -processes, the l a t t e r of which become more important w i t h i n c r e a s i n g s t r a i n . 86 As v i s u a l i z e d by Alden, dynamic recovery i s ass o c i a t e d w i t h two e f f e c t s ; (a) the a n n i h i l a t i o n of i n t e r a c t i n g d i s l o c a t i o n s which acts to lower the average flow s t r e s s , and (b) i n c r e a s i n g heterogeneity of d i s l o c a t i o n d i s t r i b u t i o n ; i . e . subgrain formation which leads to the formation of " s o f t spots" which can y i e l d at s t r e s s e s lower than the average flow s t r e s s . The shapes of the curves of F i g s . 57 and 58 can be explained i n these terms. He a v i l y c o l d worked metals or a l l o y s , or any m a t e r i a l s (e.g. S.A.P.) con t a i n i n g a dense, f i n e d i s l o c a t i o n substructure at the s t a r t of the tension t e s t are u n l i k e l y to undergo much dynamic recovery during the t e s t as a r e s u l t of a change i n d i s l o c a t i o n " d i s p e r s i o n " , i . e . e f f e c t (b) above. Any c e l l s present are already extremely f i n e , and " s o f t spots" which e x i s t are t h e r e f o r e r e l a t i v e l y not-very " s o f t " . However, the d i s l o c a t i o n d e n s i t y i s i n i t i a l l y so high that s m all a d d i t i o n a l s t r a i n i n tension causes a " s a t u r a t i o n l e v e l " of den s i t y to be achieved i n which d i s l o c a t i o n s are a n n i h i l a t e d as f a s t as others are generated. Thus the maximum s t r e s s on such m a t e r i a l s i s a t t a i n e d a f t e r r e l a t i v e l y small uniform s t r a i n (low uniform e l o n g a t i o n v a l u e s ) . This i s true f o r h e a v i l y cold-worked pure aluminum, over-aged Al-4Cu, and S.A.P., as w e l l as f o r "annealed S.A.P." which s t i l l has a dense substructure a f t e r annealing. Although a l l the above m a t e r i a l s e x h i b i t low el o n g a t i o n values f o r the broad reasons noted, i t i s s i g n i f i c a n t that c o l d worked pure aluminum has much l e s s d u c t i l i t y than e i t h e r Al-4Cu or S.A.P. As - 139 -discussed e a r l i e r , i n the presence of a f i n e d i s p e r s o i d , s l i p occurs on more systems w i t h i n each grtain; i . e . more d i s l o c a t i o n s can be " s t o r e d " i n the l a t t i c e than i n the case of a pure metal. Thus 70% c o l d work on pure aluminum has produced polygonized s t r u c t u r e , and f r e s h d i s l o c a t i o n s produced by t e n s i l e s t r a i n are r e a d i l y a n n i h i l a t e d w i t h i n the pre-e x i s t i n g polygonized sub-boundaries. Recovery thus accompanies s t r a i n hardening almost from the outset of the te n s i o n t e s t . By c o n t r a s t , the 70% c o l d worked dispersion-hardened a l l o y s can a s s i m i l a t e more d i s l o c a t i o n s during t e n s i l e s t r a i n i n g before recovery begins to keep pace w i t h s t r a i n hardening. The as-aged Al-Cu a l l o y ( v i r t u a l l y no substructure i n i t i a l l y ) and the hot r o l l e d Al-Cu a l l o y , have i n i t i a l l y low d i s l o c a t i o n d e n s i t i e s but contain a d i s p e r s i o n of a second phase. The second phase p a r t i c l e s c o n t r i b u t e to very r a p i d d i s l o c a t i o n generation when these m a t e r i a l s are f i r s t s t r a i n e d i n te n s i o n . In the e a r l y stages of fl o w , the d i s -l o c a t i o n s are homogeneously d i s t r i b u t e d . With i n c r e a s i n g s t r a i n , however, c e l l s develop; i . e . " s o f t " and "hard" spots are formed. The c e l l s i z e i s i n i t i a l l y l a r g e , and so c e l l i n t e r i o r s are s i g n i f i c a n t l y s o f t e r than c e l l w a l l s . Thus the recovery c o n t r i b u t i o n of e f f e c t (b) i n the Alden theory may be important w h i l e w e l l - d e f i n e d c e l l s or sub-grains are s t i l l forming. Appreciable s t r a i n can be accommodated ( i . e . r e l a t i v e l y high elongation) during the formation of a f i n e substructure. At l a r g e s t r a i n s the high d i s l o c a t i o n d e n s i t y leads to the s a t u r a t i o n e f f e c t described above, when d i s l o c a t i o n a n n i h i l a t i o n e f f e c t s account f o r the attainment of the maximum s t r e s s . The e f f e c t of d i s l o c a t i o n d i s t r i b u t i o n has become pmaller as the c e l l s i z e has decreased w i t h i n c r e a s i n g s t r a i n . - 140 -F i n a l l y , the behaviour of m a t e r i a l s such as annealed pure aluminum and c o l d worked-and-annealed Al-4Cu i n F i g . 57 can be considered. In annealed pure aluminum, there are no second phase p a r t i c l e s to c o n t r i b u t e to r a p i d d i s l o c a t i o n generation or small c e l l formation beyond the very e a r l i e s t s t r a i n r e g i o n . The formation of coarse polygonized c e l l w a l l s leads to an important recovery e f f e c t due to (b) above, but la r g e s t r a i n s can be accommodated i n the process; i . e . the m a t e r i a l e x h i b i t s a high uniform e l o n g a t i o n . A l s o , d i s l o c a t i o n s which s l i p i n t o the sharp subgrain w a l l s (see F i g s . 29 and 30) are probably a n n i h i l a t e d w i t h r e l a t i v e ease. Thus, the slope of the s t r e s s - s t r a i n curve i s g e n e r a l l y low i n F i g . 57. The behaviour of c o l d worked-and-annealed Al-4Cu i s more d i f f i c u l t to i n t e r p r e t . The s t a t i c anneal at 300°C a f t e r heavy c o l d work has produced a polygonized substructure i n which the sub-grain boundaries are extremely w e l l - d e f i n e d yet c l o s e l y spaced (see F i g s . 43 through 45). During subsequent t e n s i l e s t r a i n i n g , i t i s p o s s i b l e t h a t , i n common w i t h pure aluminum, these sharp boundaries are s i n k s f o r many of the freshly-produced d i s l o c a t i o n s , such that d i s l o c a t i o n s are r e a d i l y a n n i h i l a t e d , and s o f t spots are c o n s t a n t l y regenerated. This keeps the net r a t e of work hardening low. However, the generation of d i s l o c a t i o n s at p a r t i c l e s permits a high s t r a i n to be accommodated before the recovery e f f e c t s overcome s t r a i n hardening. I t may be n o t i c e d from F i g . 58 that there i s a gradual decrease i n the uniform elongation of Al-4Cu, Series B, w i t h i n c r e a s i n g annealing temperature up to about 200°C, above which uniform e l o n g a t i o n increases very r a p i d l y . The r a t e of work hardening of these a l l o y s , p a r t i c u l a r l y at low p l a s t i c s t r a i n s , i s seen i n F i g . 58 to increase w i t h p r i o r annealing temperature up to 200°C,beyond which i t decreases considerably. - 141 -When the work hardening r a t e i s hi g h , the u l t i m a t e s t r e n g t h i s reached a f t e r very small p l a s t i c s t r a i n s , thereby producing a decrease i n uniform e l o n g a t i o n . In summary, the observed d i f f e r e n c e s i n s t r e s s - s t r a i n curves and elon g a t i o n values are ass o c i a t e d w i t h d i f f e r e n c e s i n the o r i g i n a l m i c r o s t r u c t u r e , w i t h respect to the den s i t y and d i s t r i b u t i o n of d i s l o c a t i o n s i n the i n i t i a l s u bstructure. Of s p e c i a l i n t e r e s t i s the observation that a f i n e , w e l l - p o l y g o n i z e d substructure i n a d i s p e r s i o n -hardened a l l o y can a c t u a l l y c o n t r i b u t e to a marked r e d u c t i o n i n the ra t e of work-hardening at s t r a i n s >0.2 percent. 5.3 T e n s i l e P r o p e r t i e s at 300°C 87 88 According to Guyot and Ruedl, ' above room temperature (up to _3 350°C), f o r a s t r a i n fo 2 x 10 the movement of d i s l o c a t i o n s i n the r e c r y s t a l l i z e d m a t r i x of Al-4Cu and low-oxide S.A.P. a l l o y s i s c o n t r o l l e d by c r o s s - s l i p and climb, as i n pure aluminum. The high observed a c t i v a t i o n energies f o r deformation of S.A.P. (reaching 10 or more times the s e l f - d i f f u s i o n energy) measured above 350°C suggests that the high temperature deformation mechanisms i n S.A.P. are r a d i c a l l y d i f f e r e n t from those i n pure aluminum. In the pure metal, the climb of d i s l o c a -t i o n s i s the c o n t r o l l i n g process up to the melti n g p o i n t , w i t h a constant a c t i v a t i o n energy c l o s e to that of s e l f - d i f f u s i o n . D i f f e r e n t models such as (a) g r a i n boundary s l i d i n g , (b) d i s l o c a t i o n generation from g r a i n boundaries, (c) p a r t i c l e by-passing by g l i d e , and (d) thermal a c t i v a t i o n of j u n c t i o n r e a c t i o n s , suggested by s e v e r a l workers, have been 88 discussed by Guyot and Ruedl. These various models are each p a r t i a l l y - 142 -s a t i s f a c t o r y and i t i s dou b t f u l that a s i n g l e mechanism can, at high 87 temperatures, uniquely describe the flow mechanism. However, Guyot suggested that the thermal a c t i v a t i o n of d i s l o c a t i o n s pinned i n t h e i r g l i d e plane by j u n c t i o n r e a c t i o n s w i t h a t t r a c t i v e f o r c e s seem to c o n t r o l , perhaps i n p a r a l l e l w i t h climb, the p l a s t i c deformation of S.A.P. 86 In terms of Alden's theory, the rearrangement and a n n i h i l a t i o n processes of recovery can proceed more r e a d i l y at 300°C than at 20°C because of thermal a s s i s t a n c e , and s t r e s s i s no longer necessary i n conjunction w i t h temperature to cause these recovery processes to occur. Dynamic recovery mechanisms f o r hot working c o n d i t i o n s have been 89 discussed by Jonas et a l . Dynamic recovery i n a high temperature t e n s i l e t e s t i s not equivalent to that which would occur i n a s t a t i c anneal at the same temperature without the a p p l i c a t i o n of the a p p l i e d s t r e s s . Jonas et a l . conclude that under dynamic c o n d i t i o n s of deformation and heat treatment ( c h a r a c t e r i s t i c of high temperature t e n s i l e t e s t s ) , the formation of a polygonized d i s l o c a t i o n substructure i s apparently discouraged by the m o b i l i t y of the sub-boundaries under the a c t i o n of the a p p l i e d s t r e s s . By c o n t r a s t , i n a s t a t i c anneal f o l l o w i n g p r i o r c o l d work, recovery processes can lead to the development of a polygonized substructure i n which the d i s l o c a t i o n s have climbed i n t o boundaries to provide a s t a b l e c o n f i g u r a t i o n of lower energy. Another f a c t o r to consider i s the d i r e c t e f f e c t of the dispersed second phase on the high temperature y i e l d s t r e n g t h . Because of the - 143 -ease of c r o s s - s l i p and climb, at a temperature of 300°C (0.62 Tm) the d i s p e r s o i d - d i s l o c a t i o n i n t e r a c t i o n i n v o l v e d i n the Orowan model might be expected to have very l i t t l e e f f e c t on the y i e l d s t r e s s . To check t h i s , the 300°C y i e l d s t r e n g t h of over-aged Al-4Cu a l l o y s ( c o n t a i n i n g e s s e n t i a l l y no substructure) was p l o t t e d against the parameter D - 2r s s l o g . . _ ( — )/(P - 2r ) i n F i g . 53. From the s t r a i g h t l i n e and the 10 2b s s i n t e r c e p t ( a g ) obtained i n t h i s p l o t , one can say that the Orowan theory i s apparently s t i l l a p p l i c a b l e (at l e a s t at s m a l l p l a s t i c 9 10 s t r a i n s ) even at t h i s high temperature. Hansen, ' found that the y i e l d s t r e n g t h of A l - A ^ O ^ products was i n agreement w i t h the Orowan theory 41 at 400°C. On the other, hand Clegg argued that the bowing out of d i s l o c a t i o n s between dispersed p a r t i c l e s should not be considered at high temperatures. Rather he argued that the b a r r i e r s must be s t a b l e and/or continuous to be e f f e c t i v e under the a p p l i e d c o n d i t i o n s of temperature and s t r e s s . The only form of continuous b a r r i e r that can e x i s t i n such m a t e r i a l s i s a substructure d i s l o c a t i o n w a l l or a g r a i n boundary. According to Clegg, the second phase s t a b i l i z e s the sub-g r a i n boundaries, thereby maintaining t h e i r c o n t r i b u t i o n to high strength. From these apparent d i f f e r e n c e s i n opinion one could conclude that i n the r e c r y s t a l l i z e d c o n d i t i o n , the y i e l d s t r e n g t h of d i s p e r s i o n -hardened m a t e r i a l s should be explained on the b a s i s of the s t r e s s necessary to by-pass d i s p e r s o i d p a r t i c l e s , but i n the presence of a d i s l o c a t i o n substructure the sub-boundaries should be considered as the p r i n c i p a l b a r r i e r s to flow. S o l i d s o l u t i o n hardening becomes l e s s e f f e c t i v e at elevated temperatures. The b i n d i n g of a s o l u t e atom to a d i s l o c a t i o n i s short - 144 -range i n nature, and thermal a c t i v a t i o n can a s s i s t a d i s l o c a t i o n to escape from a s o l u t e atom or atmosphere. Thus most of the s o l i d s o l u t i o n increment due to 0.16% at % Cu i n the Al-4Cu a l l o y at 20°C may not be e f f e c t i v e at 300°C. This i s supported by the r e s u l t s of 12 S t a r r et a l . who obtained a 0.5 pet flow s t r e s s of 1500 p s i at 300°C and at a s t r a i n r a t e of 0.118 min ^ f o r a s o l i d s o l u t i o n of aluminum c o n t a i n i n g 0.194 at % Cu. From t h i s we can reasonably assume the 300°C 0.2 pet flow s t r e s s of aluminum c o n t a i n i n g 0.16 at % Cu to -3 -1 be l e s s than 1000 p s i at a s t r a i n r a t e of 6.25 x 10 min . This i s w i t h i n 200 p s i of the y i e l d s t r e n g t h reported f o r r e c r y s t a l l i z e d 6 7 pure aluminum at 300°C. 5.3.1 Pure Aluminum The g e n e r a l l y low stre n g t h of pure aluminum at 300°C (F i g s . 12 and 13) i n d i c a t e s that the sub-boundaries produced by annealing the cold-worked metal are not s t a b l e b a r r i e r s to d i s l o c a t i o n movement under the co n d i t i o n s of a high temperature t e s t . This i s presumably due to the r e l a t i v e l y high m o b i l i t y of the sub-boundaries i n the pure metal under a p p l i e d s t r e s s and temperature. I t was shown i n Sectio n 5.1.1 that the room temperature y i e l d s t r e n g t h of aluminum co n t a i n i n g subgrains could be r e l a t e d to the subgrain diameter by the H a l l - P e t c h r e l a t i o n [equation (28)J. At high temperatures, dynamic growth of subgrains during the t e s t , prevents 89 t h i s r e l a t i o n s h i p from being v a l i d . In f a c t , Jonas et a l . have suggested that a more general r e l a t i o n s h i p should be a p p l i e d at -M elevated temperatures; i . e . a r j 2 = °0 + ' w ^ e r e ^ a n <^ ^' a r e constants. From t h e i r review of the r e s u l t s of various workers, M was - 145 -o t> i CN d D t>0 o Figure 59. I, microns 300°C Y i e l d s t r e n g t h of pure aluminum as a f u n c t i o n of the subgrain diameter. - 146 -found to vary between 1 and 2. The above equation was i n v e s t i g a t e d i n the present work by p l o t t i n g log(aQ 2 ~ ag) vs. l o g I i n F i g . 59. A s t r a i g h t l i n e was f i t t e d by the 6 7 method of l e a s t squares. In order to draw t h i s l o g p l o t , a reported value of OQ = 800 p s i was used. From F i g . 59, values of M = 0.75 and K'~= 1.56 x 10 3 p s i (micron)^'^^ a r e obtained. Thus, the 300°C y i e l d s trength of pure aluminum can be expressed i n the f o l l o w i n g form: o Q 2 = 800 + 1.56 x 103a)"°'75 (35) Uniform e l o n g a t i o n values f o r aluminum at 300°C were found to be l e s s than those at room temperature f o r any annealing treatment. The aforementioned dynamic growth of subgrains i s a form of recovery. At small s t r a i n s , the rate of s o f t e n i n g due to subgrain growth and d i s l o c a -t i o n a n n i h i l a t i o n exceeds the r a t e of hardening due to d i s l o c a t i o n m u l t i p l i c a t i o n ; i . e . the maximum (ultimate) uniform a p p l i e d s t r e s s i s reached a f t e r r e l a t i v e l y s m a l l uniform s t r a i n . 5.3.2 Alumirium-4 Copper From Table V I I i t can be seen that the 300°C y i e l d s t r e n g t h of 12 over-aged Al-4Cu (no substructure) i s 5,900 p s i . S t a r r et a l . a l s o determined the flow s t r e s s of Al-4Cu at such high temperatures. For a volum e t r i c mean f r e e path of 7.8 u between the CuA^ p a r t i c l e s the y i e l d s t r e n g t h was found to be about 3,500 p s i . The i n t e r p a r t i c l e spacing i n the present work was much f i n e r , and a y i e l d s t r e s s of 5,900 p s i i s thus reasonable. In view of the low y i e l d s t r e n g t h of aluminum at 300°C, and the i n s i g n i f i c a n t s t r e n g t h increment due to s o l i d - 147 -s o l u t i o n hardening, t h i s observed y i e l d s t r e n g t h f o r over-aged Al-4Cu apparently i n d i c a t e s that there i s a l a r g e component of strengthening due d i r e c t l y to the presence of the CuA^ p a r t i c l e s . I t was shown i n Section 5.3 that the 300°C y i e l d s t r e n g t h of over-aged Al-4Cu could be explained on the b a s i s of the Orowan model. From the Orowan p l o t i n F i g . 53, a , which corresponds to the y i e l d s t r e n g t h of the base metal, was found to be 800 p s i . The slope of the Orowan p l o t at 300°C i n F i g . 3 3 53 i s 1.24 x 10 p s i . u compared tothe value of 2.5 x 10 p s i . u at room temperature. This low slope may i n d i c a t e that the Orowan model does not apply at high temperatures and that p a r t i c l e s are i n s t e a d by-passed by other mechanisms such as c r o s s - s l i p and climb. Hot r o l l i n g followed by c o l d r o l l i n g d r a s t i c a l l y reduced both the 300°C y i e l d and u l t i m a t e t e n s i l e s t r e n g t h of over-aged Al-4Cu, the former being a f f e c t e d more than the l a t t e r . S t a t i c annealing a f t e r c o l d r o l l i n g increased the 300°C y i e l d s t r e n g t h but decreased the 300°C u l t i m a t e t e n s i l e s t r e n g t h r e l a t i v e to the c o l d r o l l e d c o n d i t i o n . The increase i n 300°C y i e l d s t r e n g t h due to s t a t i c annealing was found to r e l a t e g e n e r a l l y to an i n c r e a s i n g amount of cold-work (Table V I ) . Another i n t e r e s t i n g observation was that i n the c o l d worked condi-t i o n s the 300°C y i e l d s t r e n g t h of pure aluminum was higher than that of Al-4Cu (Table v ) . A l s o , the 300°C y i e l d strength of the pure metal was increased by i n c r e a s i n g amounts of p r i o r c o l d work, i n d i r e c t contrast to the observation f o r the Al-4Cu a l l o y . A l l these observa-t i o n s must be explained by a u n i f i e d argument. 41 42 I t had been shown p r e v i o u s l y by Clegg and by Towner that t h e i r - 148 -cold-worked a l l o y s had high temperature str e n g t h p r o p e r t i e s i n f e r i o r to those of the as r e c e i v e d or extruded a l l o y s and that s t a t i c annealing of the c o l d worked products r e s t o r e d , at l e a s t p a r t i a l l y the s t r e n g t h at elevated temperatures. The low s t r e n g t h of h e a v i l y cold-worked A.P.M. products at elevated temperatures had been q u a l i t a t i v e l y 42 explained by Towner as being due to a high concentration of vacancies f a c i l i t a t i n g d i s l o c a t i o n climb. Heating the c o l d worked m a t e r i a l at elevated temperatures to produce recovery before t e n s i l e t e s t i n g lowered the vacancy c o n c e n t r a t i o n , thus making i t more d i f f i c u l t f o r d i s l o c a t i o n s i n the annealed m a t e r i a l s to climb. However, i t i s known that most of the deformation-induced vacancies i n pure aluminum disappear i n a few minutes at room temperature and t h a t complete annealing-out 90 can occur at about 200°C. Thus, Towner's explanation f o r the i n c r e ase i n high temperature y i e l d s t r e n g t h may not be a p p l i c a b l e to Al-4Cu a l l o y s . 41 Clegg, on the other hand, explained h i s r e s u l t s w i t h Ni-ThO^ i n terms of the development of a s t a b l e polygonized substructure during s t a t i c annealing. In the case of d i s p e r s i o n strengthened m a t e r i a l s , the d i s p e r s o i d p a r t i c l e s are thought to exert a pinning e f f e c t on the boundaries due to c o n s i d e r a t i o n s of i n t e r f a c i a l energies. The r e s u l t i n g s t a b i l i z a t i o n of the substructure has a l s o been observed i n the present study. Sub-boundaries are e f f e c t i v e b a r r i e r s to d i s l o c a t i o n motion and were thus used by Clegg to i n t e r p r e t the remarkable hi g h temperature s t r e n g t h of h i s a l l o y s . From X-ray l i n e p r o f i l e a n a l y s i s and t r a n s m i s s i o n e l e c t r o n microscope observations, annealed aluminum and Al-4Cu a l l o y s are known to co n t a i n a polygonized substructure w i t h w e l l d e l i n e a t e d sub-boundaries. The Al-4Cu a l l o y has a l s o been shown to c o n t a i n a f i n e - 149 -c e l l s t r u c t u r e i n the 70% c o l d - r o l l e d c o n d i t i o n , but the c e l l w a l l s are not sharply defined i n comparison w i t h c o l d - r o l l e d aluminum. We can, then,suggest that the development of a polygonized substructure w i t h w e l l defined sub-boundaries i s r e s p o n s i b l e f o r the increase i n high temperature y i e l d s t r e n g t h a f t e r s t a t i c annealing. In c o n t r a s t , the numerous tangled d i s l o c a t i o n s present i n the c e l l i n t e r i o r s of c o l d -worked Al-4Cu can probably a c c e l e r a t e d i s l o c a t i o n climb and c r o s s - s l i p processes to produce y i e l d i n g at lower s t r e s s l e v e l s . Since c o l d -worked, aluminum contains very sharp c e l l w a l l s w i t h d i s l o c a t i o n - f r e e c e l l i n t e r i o r s , i t s 300°C y i e l d s t r e n g t h i s higher than that of Al-4Cu. A f t e r about one hour of annealing at 300°C, the subgrains i n aluminum become very l a r g e , and are not as e f f e c t i v e as b a r r i e r s to d i s l o c a t i o n motion, thereby g i v i n g a y i e l d s t r e n g t h lower than that of Al-4Cu CFig. 12). Since sub-boundaries are formed by the rearrangement of d i s l o c a t i o n s , d i s l o c a t i o n d e n s i t y i n sub-boundaries a f t e r annealing w i l l probably be higher f o r a m a t e r i a l which has had more p r i o r c o l d work. Such sub-boundaries can be expected to be stronger d i s l o c a t i o n b a r r i e r s . This e x p l a i n s t e n t a t i v e l y the observation that the percentage increase i n 300°C y i e l d s t r e n g t h due to s t a t i c annealing increased w i t h i n c r e a s i n g amounts of p r i o r c o l d work (Table V I ) . I t was a l s o n o t i c e d i n Table V f o r Al-4Cu that the higher was the amount of p r i o r c o l d work, the lower was the 300°C y i e l d s t r e n g t h , the opposite being true f o r pure aluminum. In pure aluminum, s i n c e the sharpness of c e l l w a l l s i s known to increase w i t h i n c r e a s i n g amounts of c o l d work., ^  the 300°C y i e l d strength i s expected to increase i n the same order. However, i n Al-4Cu, reduced 70% by co l d r o l l i n g , sharp - 150 -c e l l w a l l s were not observed (see F i g s . 38a to 38c). The apparent decrease i n 300°C y i e l d s t r e n g t h w i t h i n c r e a s i n g amounts of c o l d work can then be a t t r i b u t e d to the d e n s i t y of tangled or random d i s l o c a t i o n s i n the c e l l w a l l s . This d e n s i t y apparently increases w i t h i n c r e a s i n g amounts of p r i o r deformation and enhances probable d i s l o c a t i o n climb and c r o s s - s l i p processes to give r i s e to a very low y i e l d s t r e n g t h at 300°C. E a r l i e r i n t h i s d i s c u s s i o n the 300°C y i e l d s t r e n g t h of over-aged Al-4Cu (5,900 p s i ) was a t t r i b u t e d t e n t a t i v e l y to Orowan strengthening. Since the 0-phase d i s p e r s i o n i s s t i l l present i n the co l d worked-and-annealed a l l o y s , i t i s e s s e n t i a l to account f o r t h e i r low 300°C y i e l d s t r e n g t h s ; i . e . 1600-2800 p s i . Several p o s s i b l e explanations can be considered: Ca) Orowan strengthening i s not r e s p o n s i b l e f o r the high 300°C st r e n g t h of as-aged Al-4Cu, as p r e v i o u s l y assumed. Cb) The e f f e c t i v e n e s s of 8 p a r t i c l e s as b a r r i e r s to deformation at 300°C i s g r e a t l y reduced by the presence of a d i s l o c a t i o n sub-s t r u c t u r e . Cc) The 6 - p r e c i p i t a t e d i s p e r s i o n i n co l d worked-and-annealed Al-4Cu CB S e r i e s ) i s much d i f f e r e n t than i n the simple aged a l l o y f o r the same ageing treatment of 15 hours at 300°C; i . e . annealing the a l l o y c o n t a i n i n g a dense substructure has caused major changes i n the 0 phase. Explana t i o n Ca) r e q u i r e s that some other source of strengthening be invoked to account f o r the high 300°C st r e n g t h of the as-aged a l l o y . The only p o s s i b l e mechanism not already discussed would appear - 151 -to be g r a i n boundary strengthening. However, the g r a i n s i z e i n aged a l l o y s was l a r g e , and was no smaller than i n pure annealed aluminum. Thus ex p l a n a t i o n (a) must be r e j e c t e d , and Orowan strengthening at 300°C i n the aged a l l o y must be accepted. . Explan a t i o n (b) seems reasonable to account f o r at l e a s t some l o s s of Orowan strengthening i n the presence of a subst r u c t u r e . I t i s a l s o c o n s i s t e n t w i t h the e a r l i e r argument used to e x p l a i n why s t a t i c annealing improved the 300°C y i e l d s t r e n g t h of c o l d r o l l e d Al-4Cu. Considerable support f o r explanation (c) i s provided by comparing F i g s . 42 to 47 (deformed and annealed a l l o y ) w i t h F i g s . 35 and 36 (as-aged a l l o y ) . The p r e c i p i t a t e p a r t i c l e s i n the as-aged a l l o y are elongated, a f a c t which c o n t r i b u t e s to a smaller planar i n t e r p a r t i c l e spacing than would be the case f o r s p h e r i c a l p a r t i c l e s of the same volume. In marked c o n t r a s t , the p a r t i c l e s of 0 i n the deformed-and-annealed a l l o y are much more s p h e r i c a l i n shape. There i s al s o some evidence that the average p a r t i c l e s i z e has been increased by the thermo-mechanical treatment, growth of p a r t i c l e s p o s s i b l y having been f a c i l i t a t e d by d i f f u s i o n along subgrain boundaries (see F i g . 42b). The 300°C uniform e l o n g a t i o n of cold-worked Al-4Cu was much higher than both i t s 20°C uniform e l o n g a t i o n (compare F i g s . 6 and 14) and the 300°C uniform e l o n g a t i o n of pure aluminum. I t was mentioned e a r l i e r that the rearrangement and a n n i h i l a t i o n processes of recovery can proceed at a f a s t e r r a t e at 300°C because of thermal a s s i s t a n c e . However, the second phase p a r t i c l e s c o n t r i b u t e to a high r a t e of d i s l o c a t i o n m u l t i p l i c a t i o n . Thus, there i s perhaps a balance between the r a t e of s o f t e n i n g due to d i s l o c a t i o n a n n i h i l a t i o n and the r a t e of - 152 -hardening due to d i s l o c a t i o n m u l t i p l i c a t i o n and the cold-worked Al-4Cu i s l i k e l y to undergo higher uniform elongation before a t t a i n i n g the maximum s t r e s s . Upon s t a t i c annealing, the 300°C y i e l d strength increases and the 300°C ultimate strength decreases. Thus, the uniform elongation i s expected to decrease i n s p i t e of the fa c t that the previous two opposing processes occur simultaneously. By contrast, the d i s l o c a t i o n density of the as-aged Al^-4Cu (no substructure) i s i n i t i a l l y very low. The dislocations generated during te s t i n g at 300°C are r e a d i l y annihilated due to thermal a c t i v a t i o n . This behaviour i s s i m i l a r to that of pure aluminum at 300°C (Section 5.3.1). As expected, over-aged Al-4Cu shows a very low uniform elonga-tion. 5.3.3 S.A.P. In the case of as-aged Al-4Cu, 300°C y i e l d strength was a t t r i b u t e d to Orowan strengthening. A f t e r cold working, or cold working and annealing the a l l o y , Orowan strengthening was not r e a l i z e d at 300°C because the dispersion had coarsened, and because substructure d i s l o c a -tions f a c i l i t a t e d the by-passing of the p a r t i c l e s at the high temperature. In contrast to over-aged Al-4Cu, the dispersion of second phase i n S.A.P. i s l i t t l e a l t e r e d by thermal or mechanical treatments. Moreover, there was always a f i n e substructure present i n the S.A.P. materials, whereas Al-4Cu i n the as-aged condition contained no s i g n i f i c a n t substructure, and only i n the cold worked condition was the substructure as f i n e as i n S.A.P. It now becomes important to decide whether the high observed 300°C strength of S.A.P. i n the present work (9,000-13,000 psi) i s - 153 -a t t r i b u t a b l e to Orowan strengthening, substructure strengthening, or some compromise mechanism. From a p l o t of measured 300°C y i e l d s t r e n g t h vs. ^— (see F i g . s 60 i n Appendix), the s i m p l i f i e d Orowan equation (32) f o r d i s p e r s i o n hardening of Al-4Cu i s found to be of the form a = 1900 + 3.9 x 10 3D _ 1 (36) s o Using the measured D g value of 800 A f o r S.A.P. i n equation (36) gives a c a l c u l a t e d y i e l d s t r e s s of 50,000 p s i . This i s s e v e r a l times higher than the observed value. Following our previous arguments f o r S.A.P. i n Sectio n 5.1.3, the oxide p a r t i c l e spacing should be about 0.35 y to 0.5 y to account f o r the observed flow s t r e s s i n terms of Orowan-type strengthening. o Since the domain s i z e of about 1000 A obtained from X-ray a n a l y s i s (Table XI) f o r S.A.P. i s i d e n t i f i e d w i t h the subgrain s i z e , subgrain boundary strengthening can be s i g n i f i c a n t at 300°C. Based on pure aluminum data, the 300°C y i e l d s t r e n g t h c a l c u l a t e d from equation (35) o f o r % = 1000 A i s about 10,000 p s i . This compares w e l l w i t h the observed 300°C stre n g t h of S.A.P. (9,000-13,000 p s i ) . Several reasons can be suggested f o r a t t r i b u t i n g the 300°C stren g t h of S.A.P. to subst r u c t u r e . (a) In the presence of both a f i n e substructure and d i s p e r s o i d p a r t i c l e s , there i s again no reason to b e l i e v e that the two types of b a r r i e r give a d d i t i v e strengthening. From the X-ray studies (Table X I ) , the substructure of S.A.P. i s known to be very s t a b l e even a f t e r - 154 -s t a t i c annealing at 540°C f o r 24 hours. Thus, the high s t a b i l i t y of the f i n e substructure of S.A.P. can probably be maintained under the co n d i t i o n s of the high temperature t e n s i l e t e s t . In t h i s case the oxide p a r t i c l e s can be considered to play the i n d i r e c t r o l e of s t a b i l i z i n g the subst r u c t u r e . (b) The c o n t r i b u t i o n from subgrain boundary strengthening i s found to be c o n s i s t e n t w i t h the observations made i n pure aluminum and Al-4Cu i n the present work. I t was shown i n t h i s s e c t i o n that the 300°C y i e l d s t r e n g t h of S.A.P. can be t e n t a t i v e l y explained i n terms of equation (35), based on data f o r pure aluminum. I t i s al s o found that the e f f e c t s of p r i o r c o l d working and cold working and annealing on the 300°C y i e l d s t r e n g t h of S.A.P. can be explained i n terms of the arguments suggested f o r two-phase Al-4Cu a l l o y s ; i . e . the development of a f i n e polygonized substructure w i t h sharp sub-boundaries due to s t a t i c annealing of the cold-worked m a t e r i a l improves the high temperature s t r e n g t h of d i s p e r s i o n - strengthened m a t e r i a l s . In support of t h i s argument, Table IX shows that the highest temperature of h e a t i n g , which produces a w e l l developed polygonized s u b s t r u c t u r e , i s more e f f e c t i v e i n i n c r e a s i n g the 300°C y i e l d s t r e n g t h of cold-worked S.A.P. In c o n c l u s i o n the remarkably high s t r e n g t h of S.A.P. at elevated temperatures can be a t t r i b u t e d to the presence of a f i n e polygonized s u b s t r u c t u r e , s t a b i l i z e d by oxide p a r t i c l e s . By c o n t r a s t , the r e l a t i v e l y coarse polygonized substructure produced as a r e s u l t of coarsening of the CuA^ p a r t i c l e s can be the cause f o r the lower strength of Al-4Cu at h i g h temperatures. 6. SUMMARY AND CONCLUSIONS 1. Substructure i n pure aluminum, over-aged Al-4Cu and S.A.P., produced by s u i t a b l e mechanical and thermal treatments, was st u d i e d by transmission e l e c t r o n microscopy and by X-ray l i n e p r o f i l e a n a l y s i s to determine the r e l a t i o n s h i p between the s t r u c t u r e and the t e n s i l e s trength at two t e s t temperatures, R.T. (0.32 Tm) and 300°C (0.62 Tm). 2. The 0.2 pet y i e l d strengths of simple aged Al-4Cu a l l o y s (no substructure) were found to be c o n s i s t e n t w i t h the Orowan model of dis p e r s i o n - s t r e n g t h e n i n g both at R.T. and at 300°C. 3. A f t e r c o l d working and annealing to produce a su b s t r u c t u r e , the y i e l d strengths of aluminum and over-aged Al-4Cu obeyed the r e l a t i o n s h i p CT0.2 = °0 + k 1 where I i s i d e n t i f i e d as the measured c e l l s i z e (or X-ray domain s i z e ) of the subst r u c t u r e . 4. In the case of Al-4Cu w i t h a c e l l or subgrain s i z e smaller than the 0 phase i n t e r p a r t i c l e spacing, the 20°C y i e l d strength could not be i d e n t i f i e d w i t h the Orowan type mechanism; r a t h e r , the sub-boundaries were found to be strength-determining. - 156 -5. S i m i l a r l y , the observed 20°C y i e l d s t r e n g t h of S.A.P. a l l o y s could be explained only i n terms of substr u c t u r e strengthening. Orowan strengthening was again found to be i n e f f e c t i v e i n these m a t e r i a l s i n the presence of a f i n e s u b s t r u c t u r e . This i s i n d i r e c t c o n t r a d i c t i o n 5 32 of the conclusions r e c e n t l y published by Hansen. ' 6. As an a l t e r n a t i v e view, the 20°C y i e l d s t r e n g t h of pure aluminum, Al-4Cu and S.A.P. i n the presence of a d i s l o c a t i o n substructure could be ass o c i a t e d p a r t i a l l y w i t h the t o t a l d e n s i t y of d i s l o c a t i o n s and not w i t h the subgrain s i z e . Under such c o n d i t i o n s , the y i e l d s t r e n g t h of Al-4Cu and S.A.P. was considered as a s u p e r p o s i t i o n of dis p e r s i o n - s t r e n g t h e n i n g and d i s l o c a t i o n substructure strengthening. 7. The 20°C s t r e s s - s t r a i n curves f o r pure aluminum, Al-4Cu and S.A.P. i n d i f f e r e n t c o n d i t i o n s were explained i n terms of the balance between work-hardening and dynamic recovery processes i n these m a t e r i a l s . 8.. The 300°C y i e l d s t r e n g t h of pure aluminum was reasonably s a t i s f i e d by a r e l a t i o n s h i p of the form CT0.2 " a 0 + K 4 where <JQ and K.' are constants and i i s the measured subgrain diameter. 9. The 300°C y i e l d behaviour of p r e c i p i t a t i o n - h a r d e n e d Al-4Cu c o n t a i n i n g a substructure was comparable to that of oxide d i s p e r s i o n -strengthened m a t e r i a l s such as S.A.P. and N i - T t ^ ; i . e . i t was sub-structure-determined. - 157 -10. S t a t i c annealing at 300 C before t e s t i n g removed the det r i m e n t a l e f f e c t s of p r i o r c o l d work on the 300°C stre n g t h of Al-4Cu and S.A.P. by producing a more s t a b l e , polygonized s u b s t r u c t u r e . 11. The higher 300°C st r e n g t h of S.A.P. compared to Al-4Cu has been i n t e r p r e t e d i n terms of the f i n e r and more s t a b l e substructure i n the former m a t e r i a l . The s t a b i l i t y and f i n e spacing of the oxide p a r t i c l e s i n S.A.P. i s conducive to the formation of a very f i n e domain or subgrain s i z e . By c o n t r a s t , the 9-phase p a r t i c l e s i n Al-Cu undergo growth and s p h e r o i d i s a t i o n as a r e s u l t of work-anneal treatments, and the substructure i s coarser and l e s s s t a b l e . - 158 -APPENDIX Table XIV: Room Temperature and 300°C Y i e l d Strengths and the Corres-ponding Subgrain Diameters f o r Pure Aluminum A f t e r Various Thermo-mechanical Treatments. M a t e r i a l Condition -1/2 Subgrain I Diameter i n microns (micron) 0.2 pet y i e l d If2 s t r e n S t n ^ n K s i R.T. 300°C Cold r o l l e d 60% Cold r o l l e d 70% Cold r o l l e d 80% 0.82 0.76 0.70 1.10 1.15 1.20 12.9 14.6 15.6 2.51 2.63 2.83 Cold r o l l e d annealed at 1 hr. 80% and 300°C f o r 1.90 0.720 1.57 Cold r o l l e d annealed at 30 min. 70% and 300°C f o r 1.33 0.87 10.7 2.40 Cold r o l l e d annealed at 1 hr. 70% and 300°C f o r 1.58 0.80 7.5 2.00 Cold r o l l e d annealed at 2 hrs. 70% and 300°C f o r 2.28 0.66 5.7 1.65 Cold r o l l e d 70% and annealed at 300°C f o r 3.15 0.56 2.4 0.76 6 hrs. Cold r o l l e d 70% and annealed at 100°C f o r 0.85 1.09 14.00 1 hr. Cold r o l l e d 70% and annealed at 250°C f o r 1.00 1.00 12.60 1 hr. - 159 -Table XV: Room Temperature Y i e l d Strengths and the Corresponding Subgrain Diameters f o r Al-4Cu, B S e r i e s , Annealed a f t e r 70% Cold Work. Annealing Treatment Subgrain Diameter, SL, i n microns ,"1/2 0.2 pet y i e l d _ 1< 2 s t r e n g t h at R.T. i n (micron) . i n K s i 1 hr. at 200°C 15 min. at 300°C 30 min. at 300°C 1 hr. at 300°C 2 hrs. at 300°C 4 h r s . at 300°C 8 hrs. at 300°C 0.30 0.55 0.65 0.90 1.08 1.41 1.98 1.82 1.35 1.24 1.05 0.96 0.84 0.71 32.50 31.20 23.10 20.9 18.6 17.4 15.1 13.4 - 160 -Table XVI: C a l c u l a t e d Values of 20°C a from Orowan and H a l l - P e t c h Equations f o r Al-4Cu. I or D i n microns OQ 2 C a l c u l a t e d from H a l l - P e t c h equation (34) i n K s i a n „ C a l c u l a t e d from Orowan equation (33) i n K s i 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 1.6 2.0 2.6 3.0 3.4 38.2 27.6 22.8 20.0 18.0 16.7 14.7 13.3 10.9 9.9 8.9 8.4 8.0 94.30 49.80 35.00 27.50 23.10 20.10 16.40 14.20 10.20 9.75 8.30 7.90 7.60 - 161 -ol I I I I I 1 J _ | 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1 t . ,-1 — — , (micron) s ure 60. 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