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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. E.E.,  (Hons.), U t k a l U n i v e r s i t y , I n d i a , 1964 I n d i a n I n s t i t u t e o f S c i e n c e , I n d i a , 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 t h i s t h e s i s as conforming standards  THE  UNIVERSITY OF BRITISH COLUMBIA • December, 1970  t o the r e q u i r e d  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, the L i b r a r y s h a l l I  make i t f r e e l y a v a i l a b l e  f u r t h e r agree that  permission  for  1 agree  that  r e f e r e n c e and study.  f o r e x t e n s i v e copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department o r by h i s of  this  representatives. thesis  It  is understood that copying o r p u b l i c a t i o n  f o r f i n a n c i a l gain shall  written permission.  Department of  Metallurgy  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Date  Columbia  J a n u a r y 15th, 1971  not be allowed without my  ACKNOWLEDGEMENTS  The a u t h o r w i s h e s t o e x p r e s s h i s s i n c e r e g r a t i t u d e , t o Dr. J.A. Lund, f o r h i s a d v i c e and a s s i s t a n c e , throughout t h e p r e p a r a t i o n o f the t h e s i s .  Thanks a r e a l s o extended t o t h e members o f t h e f a c u l t y  and f e l l o w graduate s t u d e n t s f o r h e l p f u l d i s c u s s i o n s . assistance 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  The  appreciated.  F i n a n c i a l a s s i s t a n c e i n t h e form o f a N a t i o n a l Research Scholarship  i s g r a t e f u l l y acknowledged.  Council  - iii  -  ABSTRACT .  The  s u b s t r u c t u r e o f pure aluminum and over-aged A l - 4 C u has been  v a r i e d by m e c h a n i c a l and t h e r m a l t r e a t m e n t s .  The n a t u r e o f t h i s  s u b s t r u c t u r e and i t s r e s i s t a n c e t o a n n e a l i n g has been s t u d i e d ,  together  w i t h t h e e f f e c t o f the s u b s t r u c t u r e on t e n s i l e s t r e n g t h a t ambient and elevated  temperatures.  I t has been found t h a t i n a t l e a s t some r e s p e c t s t h e response o f the s t r e n g t h o f t h e over-aged Al-4Cu t o m e c h a n i c a l and t h e r m a l p r o c e s s i n g i s v e r y comparable t o t h a t o f o x i d e - d i s p e r s i o n - s t r e n g t h e n e d a l l o y s such as S.A.P. and Ni-ThC^. a p p r e c i a b l y by c o l d work. strengthening  The over-aged A l - 4 C u i s s t r e n g t h e n e d  Much o f t h i s i n c r e m e n t a l  room-temperature  can be removed by a n n e a l i n g a t r e l a t i v e l y low tempera-  t u r e s ; i . e . temperatures a t w h i c h t h e s t r e n g t h of c o l d worked pure aluminum i s n o t lowered.  I n 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 , t h e y i e l d s t r e n g t h o f cold-worked A l - 4 C u a t e l e v a t e d temperat u r e s (300°C o r 0.62 Tm) i s a c t u a l l y improved by a s t a t i c anneal a t 300°C b e f o r e t e s t i n g . of p r i o r c o l d work. extruded  T h i s b e n e f i t i n c r e a s e s w i t h i n c r e a s i n g amounts 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.  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 t o determine the d i s t r i b u t i o n o f nonuniform size.  l a t t i c e s t r a i n and t h e 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 The X-ray d a t a have been i n t e r p r e t e d i n terms o f 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 o b s e r v a t i o n s made  - iv by transmission e l e c t r o n microscopy. An attempt has been made to account s e m i q u a n t i t a t i v e l y f o r the strength of the deformed and annealed materials at ordinary and elevated temperatures i n terms of a v a i l a b l e strengthening mechanisms. The 0.2 pet y i e l d strengths of simple aged Al-4Cu a l l o y s (no substructure) was found to be consistent w i t h the Orowan model of dispersion-strengthening 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 a l l o y s was r e l a t e d 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 c o n t r i b u t i o n to strength from the Orowan mechanism.  S i m i l a r l y the 20°C y i e l d strength of the S.A.P.  a l l o y was associated w i t h the f i n e d i s l o c a t i o n substructure produced by thermo-mechanical treatments.  The high temperature y i e l d strength  of Al-4Cu and S.A.P. was r e l a t e d to the polygonized  substructure  produced by s t a t i c annealing, which was much f i n e r and more stable i n the case of the oxide dispersion-strengthened  alloy.  - v TABLE OF CONTENTS Page  1.  2.  1  INTRODUCTION 1.1  Review of P r i o r Work  1.2  Scope o f the P r e s e n t Work  7  EXPERIMENTAL PROCEDURE  9  2.1  Alloy Preparation  9  2.2  F a b r i c a t i o n and Heat Treatment  10  2.2.1  Aluminum-4 Copper and Pure Aluminum  10  2.2.2  S.A.P  16  2.3  2.4  2.5  17  Tensile Testing 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 T e s t i n g Procedure  X-Ray D i f f r a c t i o n  ^ 18 19  ;  2.4.1  Principle  19  2.4.2  Specimen P r e p a r a t i o n  19  2.4.3  X-Ray D i f f r a c t i o n Procedure  21  Metallography  24  2.5.1  O p t i c a l Microscopy  24  2.5.2  E l e c t r o n Microscopy  2.5.3  Measurement of G r a i n S i z e and S u b g r a i n  2.5.4  Determination Precipitates  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  of Volume F r a c t i o n of  24 Size. 26 28  - v iPage 3.  4.  USE OF X-RAY TECHNIQUES TO ANALYSE DISLOCATION DENSITY AND CONFIGURATION  30  3.1  B a s i s 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  D e t e r m i n a t i o n 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 from X-Ray Data  37  RESULTS M D 4.1  40  T e n s i l e Tests  40  4.1.1  Room Temperature T e s t s  40  4.1.1.1  Aluminum-4 Copper and Pure Aluminum  40  4.1.1.2  S.A.P  51  4.1.2  5.  OBSERVATIONS  300°C T e s t s  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  DISCUSSION  1 0 8  5.1  T e n s i l e P r o p e r t i e s a t 20°C  108  5.1.1  108  Pure Aluminum  Page 5.1.2  5.1.3  6.  Aluminum-4 Copper  116  5.1.2.1  Simple Aged A l l o y (no s u b s t r u c t u r e )  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  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 a t 20°C  135  5.3  Tensile Properties  141  a t 300°C  5.3.1  Pure Aluminum  144  5.3.2  Aluminum-4 Copper  146  5.3.3  S.A.P  152  SUMMARY AND CONCLUSIONS  155  APPENDIX  158  BIBLIOGRAPHY  162  - viii -  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 A l - 4 C u  12  2.  Phase diagram o f A l - 4 C u on t h e a l u m i n u m - r i c h s i d e  •  27  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 t h e 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 )  43  20°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 e m p e r a t u r e on t h e y i e l d s t r e n g t h o f A l - 4 C u (B S e r i e s ) v s . pure aluminum a f t e r 70% CW  45  20°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 e m p e r a t u r e on t h e u n i f o r m e l o n g a t i o n of Al-4Cu (B S e r i e s ) v s . pure aluminum a f t e r 70% C.W  47  20°C Data showing t h e e f f e c t s o f a n n e a l i n g time 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 (A S e r i e s ) a f t e r 70% C.W  48  20°C Data showing t h e e f f e c t s o f a n n e a l i n g time a t 300°C on t h e y i e l d s t r e n g t h A l - 4 C u v s . Pure aluminum a f t e r 70% C.W  49  48  4.  5.  6.  7.  8.  9. 10.  11.  12.  13.  14.  20°C Data showing t h e e f f e c t s o f a n n e a l i n g time a t 300°C on the U.T.S. o f A l - 4 C u v s . pure aluminum a f t e r 70% C.W 20°C and 300°C Data showing t h e e f f e c t s of c o l d r o l l i n g on the s t r e n g t h o f S.A.P 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 time 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 (A S e r i e s ) a f t e r 70% C.W 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 time 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 70% C.W 300°C .Data showing t h e e f f e c t s of a n n e a l i n g time a t 300°C on t h e y i e l d s t r e n g t h o f A l - 4 C u v s . pure aluminum a f t e r 70% C.W  5 0  52  5 4  5 5  5 7  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 time a t 300°C on t h e U.T.S...of A l - 4 C u v s . pure aluminum a f t e r 70% C.W.  53  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 time at 300°C on t h e u n i f o r m e l o n g a t i o n of Al-4Cu v s . pure aluminum a f t e r 70% C.W  59  - i x Figure 15.  16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  Page 300°C D a t a s h o w i n g 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 o n 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 ) 3 0 % C.W., ( b ) 4 0 % C.W., ( c ) 5 0 % C.W., (d) 6 0 % C.W., a n d ( e ) 8 0 % C.W  61-65  V a r i a t i o n of l a t t i c e s t r a i n with l a t t i c e distance f o r A l - 4 C u (B. S e r i e s ) and p u r e aluminum i n v a r i o u s thermo-mechanical c o n d i t i o n s  71  V a r i a t i o n of l a t t i c e s t r a i n with l a t t i c e distance 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  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 ) a n d p u r e a l u m i n u m i n various thermo-mechanical c o n d i t i o n s  72  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 conditions  73  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 a n c e f o r A l - 4 C u (B S e r i e s ) a f t e r 5 0 % a n d 7 0 % C.W O p t i c a l m i c r o g r a p h o f over-aged Al-4Cu showing s i z e a n d P F Z , 23X .  dist73  grain  O p t i c a l micrograph of Al-4Cu C.W. , 23X  (B S e r i e s ) a f t e r 7 0 %  O p t i c a l micrograph of Al-4Cu C.W. , 23X  CA S e r i e s ) a f t e r 7 0 %  79  79  79  O p t i c a l micrograph 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% a n d a n n e a l e d a t 300°C f o r 8 h r s . , 23X  80  O p t i c a l m i c r o g r a p h o f A l - 4 C u (A S e r i e s ) c o l d - r o l l e d 70% a n d 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 pure aluminum a f t e r 7 0 % 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 p u r e a f t e r 6 0 % C.W., 20,000X  aluminum 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 p u r e a f t e r 8 0 % C.W., 2 0 , 0 0 0 X  aluminum 84  29.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 300°C f o r 1 h r . , 15.000X  30.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 300°C f o r 6 h r s . , 10,000X  31.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 100°C f o r 1 h r . , 20.000X  32.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 250°C f o r 1 h r . , 15,000X  33.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 400°C f o r 1 h r . , 5.000X  34.  Transmission e l e c t r o n m i c r o g r a p h o f pure aluminum c o l d - r o l l e d 80% and annealed a t 300°C f o r 3 h r s . , 5,000X  35.  Chromium shadowed carbon r e p l i c a o f over-aged 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 m i c r o g r a p h o f over-aged showing CUAI2 p r e c i p i t a t e s , 10,000X  37.  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 of Al-4Cu (B S e r i e s ) showing t h e 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 m i c r o g r a p h o f Al-4Cu a f t e r 70% C.W., 35,000X  Al-4Cu Al-4Cu  (B S e r i e s )  39a,b Transmission e l e c t r o n m i c r o g r a p h o f Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 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 m i c r o g r a p h o f Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 200°C f o r 1 h r . , 30,000X 41  Transmission e l e c t r o n m i c r o g r a p h o f Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 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 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 annealed a t 300°C f o r 15 mins., 25,000X  96  43a,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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 30 mins., 23,000X  97  44.  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 A l - 4 C u (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 2 h r s . , 23,000X  98  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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 4 h r s . , 23,000X  98  46a,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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 8 h r s . , a) 20,000X, b) 15,000X  99  45.  47.  48.  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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 15 h r s . , 15,000X  99  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 S.A.P. i n t h e as r e c 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 o f A 1 0 p a r t i c l e s , 46,000X  102  49a,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 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 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 S.A.P. c o l d r o l l e d 50%, 58,000X  105  2  51a,b  52.  3  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 S.A.P. c o l d r o l l e d 50% and annealed a t 540°C f o r 24 h r s . , 58,000X 20°C Y i e l d s t r e n g t h o f pure aluminum as a f u n c t i o n of t h e r e c i p r o c a l o f the square r o o t o f t h e subg r a i n diameter  53.  20°C and 300°C Y i e l d s t r e n g t h o f over-aged a l l o y s p l o t t e d a g a i n s t Orowan's parameter  54.  20°C Y i e l d s t r e n g t h o f Al-4Cu (B S e r i e s ) as a f u n c t i o n o f t h e R e c i p r o c a l o f the square r o o t o f the s u b g r a i n diameter  1°  6  H2  Al-4Cu  124  - xii-  Figure 55.  Page Comparison of Orowan strengthening and substructure strengthening f o r various values of £ or D  126  Transmission electron micrograph of Al-4Cu (C Series) 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 h r . , (a) showing 6 ' and 9 p r e c i p i t a t e s , 50,000X (b) showing subgrains,35,000X  131  20°C True stress-true s t r a i n curves f o r pure aluminum, Al-4Cu (B Series) and S.A.P. i n various thermomechanical conditions  136  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 series) c o l d - r o l l e d 70% and annealed at d i f f e r e n t temperatures  137  300°C Y i e l d strength of pure aluminum as a function of the subgrain diameter  145  S i m p l i f i e d Orowan p l o t f o r the 20°C and 300°C y i e l d strength of over-aged Al-4Cu  161  g  56.  1  57.  58.  59. 60.  - xiii LIST OF TABLES Table I II  III  IV V VI  VII VIII IX  X XI XII XIII XIV  XV  XVI  Page Chemical A n a l y s i s o f A l and AL-4Cu  10  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 t h e Corresponding Y i e l d S t r e n g t h V a l u e s a t R.T. and 300°C  4 1  Room Temperature 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 A l and A l - 4 C u (B S e r i e s )  4 2  Room Temperature 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  5 1  Comparison o f 300°C Y i e l d S t r e n g t h V a l u e s f o r C o l d R o l l e d A l and A l - 4 C u  60  E f f e c t o f S t a t i c A n n e a l i n g on t h e 300°C Y i e l d S t r e n g t h o f A l - 4 C u C o l d Worked P r e v i o u s l y by V a r i o u s Amounts  66  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 A l - 4 C u  67  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  68  E f f e c t of S t a t i c Annealing  on t h e 300°C T e n s i l e  P r o p e r t i e s o f 50% C o l d - R o l l e d S.A.P  68  Domain S i 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  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 Room Temperature M e c h a n i c a l P r o p e r t i e s f o r H i g h P u r i t y Aluminum ao and K V a l u e s f o r Aluminum i n t h e H a l l - P e t c h Equation  75  Room Temperature and 300°C Y i e l d S t r e n g t h s and t h e Corresponding S u b g r a i n Diameters f o r Pure Aluminum A f t e r V a r i o u s Thermo-mechanical Treatments Room Temperature Y i e l d S t r e n g t h s and t h e Correspondi n g S u b g r a i n Diameters f o r A l - 4 C u , B S e r i e s , Annealed a f t e r 70% C o l d Work C a l c u l a t e d V a l u e s o f 20°C OQ.2 f Petch Equations f o r Al-4Cu..l  r  o  m  109 m  158  1 5 9  Orowan and H a l l 1  6  0  1. 1.1.  INTRODUCTION  Review o f P r i o r Work D i s p e r s i o n - h a r d e n e d m a t e r i a l s a r e d e f i n e d as those c o n t a i n i n g a  d i s p e r s i o n o f an i n c o h e r e n t second phase.  The second phase d i s p e r s i o n  may be i n t r o d u c e d by: (a) P r e c i p i t a t i o n from s u p e r s a t u r a t e d s o l i d s o l u t i o n ( i n which  case  the d i s p e r s e d phase i s commonly an i n t e r m e t a l l i c compound). (b) M e c h a n i c a l m i x i n g o f a m e t a l w i t h a f i n e l y - d i v i d e d h a r d phase (commonly an o x i d e ) , t h i s m i x i n g g e n e r a l l y b e i n g a c c o m p l i s h e d by one o f 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 d i s p e r s i o n - h a r d e n e d a l l o y s of type (b) from powders i t i s n e c e s s a r y t o use f a b r i c a t i o n p r o c e s s e s i n v o l v i n g l a r g e amounts o f p l a s t i c f l o w ; e.g. e x t r u s i o n .  The d i s p e r s e d phase i s p r e s e n t  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 t h e f i n a l as-fabricated microstructure. 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 , t h e d i s p e r s i o n b e i n g i n t r o d u c e d o n l y by subsequent heat t r e a t m e n t Cover-ageing).  I t i s p o s s i b l e , but n o t common, t o do  some o r a l l o f t h e s h a p i n g o f type (a) m a t e r i a l s a f t e r a g e i n g , i n which case some of t h e same e f f e c t s o f t h e second phase on t h e deformed m i c r o s t r u c t u r e might be expected as i n t h e case.of type (b) a l l o y s .  -  2 -  There i s e v i d e n c e t h a t t h e type o f second phase p r e s e n t 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 a t e l e v a t e d  temperatures.  The presence o f t h e second phase c o n t r i b u t e s t o t h e  development o f a unique and g e n e r a l l y f a v o u r a b l e d i s l o c a t i o n d u r i n g thermal and m e c h a n i c a l p r o c e s s i n g .  substructure  I n a d d i t i o n , these  processing  b e n e f i t s t o t h e s t r u c t u r e may be r e t a i n e d on h e a t i n g t o u n u s u a l l y temperatures.  The o x i d e d i s p e r s i o n - h a r d e n e d  a l l o y s seem t o e x h i b i t  h i g h e r s t r e n g t h s a t e l e v a t e d temperatures than over-aged a l l o y s type  (a).  high  of  However, t h e r o l e o f 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 i s n o t  c l e a r i n t h i s r e g a r d s i n c e t h e r e i s a l a c k o f p r i o r work i n w h i c h t h e two types o f 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.  S e v e r a l d i s l o c a t i o n t h e o r i e s have been advanced t o e x p l a i n t h e magnitude o f t h e y i e l d s t r e s s a t low o r 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  and d i s c u s s e d i n d e t a i l by K e l l y and N i c h o l s o n . ^  reviewed  I n a l l these  theories  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 t h e s t r e s s w h i c h must be a p p l i e d t o a c r y s t a l t o move a s i n g l e d i s l o c a t i o n over a d i s t a n c e w h i c h i s l a r g e compared t o t h e i n t e r p a r t i c l e s p a c i n g . of many d i s p e r s i o n - s t r e n g t h e n e d  products  The y i e l d  strength  c o n t a i n i n g an i n c o h e r e n t  second phase has been s a t i s f a c t o r i l y explained by t h e well-known Orowan 2  model,  i n w h i c h d i s l o c a t i o n s a r e f o r c e d t o 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 t h a t the y i e l d  strength  should be p r o p o r t i o n a l t o t h e r e c i p r o c a l o f t h e i n t e r p a r t i c l e Using Nabarro's e s t i m a t e o f t h e l i n e t e n s i o n o f a curved  spacing.  dislocation,  K e l l y and Nicholson"'" have g i v e n the f i n a l form o f the Orowan p r e d i c t i o n as , G b T  =  T  s  +  47"  (  / J ^ S , 1 } ~2b (D - 2 r )/2  s  s  . (  1  )  -  where T and x x  s  a r e shear  3 -  stresses,  = i n i t i a l flow stress of the dispersion-hardened a l l o y s ,  x  = initial  s  flow s t r e s s of the m a t r i x ,  G  = shear modulus o f t h e m a t r i x ,  b  = Burger's v e c t o r o f the d i s l o c a t i o n ,  (j)  = 1/2(1 +  J t h e mean o f l i n e t e n s i o n  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 r  g  = mean p l a n a r i n t e r p a r t i c l e s p a c i n g ,  g  = mean p l a n a r 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  e q u a t i o n (1) may be m u l t i p l e d  by a  T a y l o r f a c t o r o f 2.24, t o c o n v e r t shear s t r e s s t o 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  o = c  s  + 2.24  G b — ^  V s ( _ ^ ) 2  £  n  1 _^  r  s where a  s  ...  i s t h e t e n s i l e y i e l d s t r e s s of t h e m a t r i x m a t e r i a l .  T a y l o r f a c t o r o f 2.24 has p r e v i o u s l y  ( ) 2  s The  been proposed and used f o r A l - A g  3 a l l o y s by G e r o l d and Mayer. 4 A n s e l l and L e n e l  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 t h e y i e l d b e h a v i o u r o f a l l o y s w i t h a f i n e l y d i s p e r s e d 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 t h a t t h e  shear s t r e s s due t o groups o f d i s l o c a t i o n s p i l e d - u p a g a i n s t t h e second phase p a r t i c l e s must be s u f f i c i e n t t o f r a c t u r e o r p l a s t i c a l l y deform the p a r t i c l e s , t h e r e b y r e l i e v i n g the back s t r e s s on t h e d i s l o c a t i o n  -4-  source.  E q u a t i o n d e r i v e d on the b a s i s of t h i s model p r e d i c t s t h a t  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 r o o t of the mean f r e e p a t h between d i s p e r s e d p a r t i c l e s .  For a s e r i e s of aluminum powder  e x t r u s i o n s ( A l - A ^ O ^ ) A n s e l l and L e n e l p l o t t e d the 0.2 s t r e n g t h v a l u e s a t two temperatures  observed.  yield  (R.T. and 400°C) v s . the r e c i p r o c a l  of the square r o o t of the average A^O^ a s t r a i g h t l i n e f i t was  pet o f f s e t  p a r t i c l e s p a c i n g , and c l a i m e d  However, i f these same e x p e r i m e n t a l  d a t a a r e r e p l o t t e d as s t r e n g t h v s . r e c i p r o c a l of the s p a c i n g , the f i t of the d a t a 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  e x p l a i n s the d a t a a t l e a s t as w e l l as the A n s e l l - L e n e l model.  Ansell  and L e n e l a l s o p r e d i c t t h a t t h e d i s p e r s e d p a r t i c l e s s h o u l d f r a c t u r e or p l a s t i c a l l y deform, y e t 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 ^ u s i n g e l e c t r o n m i c r o s c o p y , even a f t e r  s e v e r e c o l d w o r k i n g of the a l l o y . Many workers have a p p l i e d the Orowan model t o e x p l a i n the y i e l d b e h a v i o u r of d i s p e r s i o n - s t r e n g t h e n e d p r o d u c t s . 6 r e s u l t s of Dew-Hughes and R o b e r t s o n ,  P a r t i c u l a r l y , the 7  and of Byrne e t a l .  f o r over-  aged A l - C u a l l o y s , and of Gregory and G r a n t , ^ and Hansen^'"^ f o r a s e r i e s of a l l o y s of the S.A.P. ( A l - A ^ O ^ ) type tend to s u p p o r t the Orowan r e l a t i o n s h i p . The A l - C u system i s p r o b a b l y the one most w i d e l y used i n s t u d i e s 6 7 1X*~22 of age h a r d e n i n g b e h a v i o u r . ' '  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 v a r i o u s s t r u c t u r e s o b t a i n e d by ageing a quenched s u p e r s a t u r a t e d s o l i d s o l u t i o n , and changes i n hardness the a l l o y s  ^'"^  of  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  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  be  - 5 -  second The  e', a n d 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 .  kind,  G.P. z o n e s  a n d t h e 0' p h a s e 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  coherent 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 strengthen thematrix are quite d i s t i n c t 0 phase  they  f r o m t h o s e d u e to t h e i n c o h e r e n t  precipitate.  Dew-Hughes a n d R o b e r t s o n ^ a n d B y r n e  et al.^  have p r e s e n t e d  t h a t d i s l o c a t i o n s bow b e t w e e n Q p h a s e p r e c i p i t a t e p a r t i c l e s w i t h Orowan's t h e o r y .  evidence  i n agreement  T h e r e i s some q u e s t i o n , h o w e v e r , a s 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 the semi-coherent  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 a n A l - 4 C u 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 h a s b e e n i n f e r r e d  shear through  '  that dislocations  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  cannot  stage of  p l a s t i c d e f o r m a t i o n , a n d t h a t t h e y e i t h e r bow o u t b e t w e e n t h e p a r t i c l e s and b y - p a s s  them (Orowan's m e c h a n i s m ) o r t h a t t h e y p i l e up a g a i n s t  18 the p a r t i c l e s . microscopy  Nicholson et a l . ,  based  on t r a n s m i s s i o n e l e c t r o n  o b s e r v a t i o n s , claimed that d i s l o c a t i o n s d i d shear  0' p r e c i p i t a t e s , a l t h o u g h t h e y w e r e i n i t i a l l y 22 On  t h e o t h e r hand Koda e t a l .  predicted  through  h e l d up a t t h e i n t e r f a c e s .  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 w o r k t h a t t h e Orowan m o d e l 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  stages of deformation.  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 the work h a r d e n i n g of  A l - C u c r y s t a l s c o n t a i n i n g 0* a n d 0 p r e c i p i t a t e s .  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 23  e a r l i e r suggested by H i r s c h , in  Byrne  behaviour  et a l . ^  t o a v o i d t h e p a r t i c l e s as  a n d t h a t t h e o c c u r r e n c e o f t h e maximum  t h e s t r e s s - s t r a i n curve c o u l d correspond t o complete  t h e Orowan m e c h a n i s m b y a c r o s s - s l i p -mechanism.  replacement o f  Dew-Hughes a n d R o b e r t s o n  - 6 -  i n s t e a d concluded  t h a t i n i t i a l work h a r d e n i n g  l o c a t i o n loops remaining  i s due  to r e s i d u a l  dis-  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 , H a r t 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 d i s p e r s i o n - s t r e n g t h e n e d a l l o y s i n b o t h e x p e r i m e n t a l and i • ... 4,5,8-10,25-32 „ theoretical investigations. Hansen has g i v e n support f o r the Orowan t h e o r y f o r A l - A ^ O ^ p r o d u c t s  t e s t e d a t room temperature  and at 400°C. 33-35 Grant and co-workers prepared  have c l a i m e d t h a t o x i d e d i s p e r s e d  by e x t r u s i o n from powders owe  of " s t o r e d energy". rate deformation  alloys  t h e i r s t r e n g t h to a high l e v e l  S t r a i n energy i s developed d u r i n g the h i g h s t r a i n  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  c l o s e l y spaced, f i n e o x i d e p a r t i c l e s i s t o p i n d i s l o c a t i o n and impede g r a i n boundary and sub-boundary shear and m i g r a t i o n .  the to  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  found t h a t optimum s t r e n g t h was s t o r e d energy  s t u d i e s w i t h TD-Ni  a s s o c i a t e d w i t h a h i g h l e v e l of accumulated  ( h i g h d i s l o c a t i o n d e n s i t y ) developed by  mechanical treatments.  I t was  (Ni-Tb^),  concluded,  thermo-  i n agreement w i t h the  review  of Grant and co-workers, t h a t 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 w h i c h c o u l d be developed by s t r a i n and a n n e a l i n g c y c l e s ,  von Heimendahl  37 and Thomas came t o a s i m i l a r c o n c l u s i o n f o r N i - T W ^ 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 t o m i c r o s t r u c t u r e s based on e l e c t r o n - m i c r o s c o p e 38 39 studies.  I t was  suggested by B r i m h a l l et a l .  '  t h a t the  dispersed  second phase p a r t i c l e s , b e s i d e s b e i n g b a r r i e r s to d i s l o c a t i o n m o t i o n during deformation  at ambient temperatures and on a n n e a l i n g , can a c t as  - 7 -  s o u r c e s o f d i s l o c a t i o n i n s e v e r a l ways and t h e r e b y i n c r e a s e t h e d i s l o c a t i o n density (stored energy).  According to these  arguments, t h e  p a r t i c l e s themselves i n t h e f a b r i c a t e d a l l o y s a r e n o t a d i r e c t s o u r c e of s t r e n g t h , r a t h e r , i t i s a complex network o f p a r t i c l e s ,  dislocation  t a n g l e s , s u b - b o u n d a r i e s , and g r a i n b o u n d a r i e s which determine  strength.  The development of such a complex network i n S.A.P. a l l o y s has been 40 s t u d i e d i n some d e t a i l by G o o d r i c h and A n s e l l .  1.2  Scope o f t h e P r e s e n t Work A l t h o u g h much i s known about t h e p l a s t i c d e f o r m a t i o n b e h a v i o u r  at low and ambient  temperatures o f p r e c i p i t a t i o n - h a r d e n e d A l - C u 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 t h e ambient  or elevated  temperature s t r e n g t h o f t h e s e a l l o y s i n t h e p r e s e n c e o f a d i s l o c a t i o n substructure.  One o f t h e o b j e c t i v e s o f the p r e s e n t i n v e s t i g a t i o n was  to c a r r y o u t a s y s t e m a t i c study o f t h e s t r e n g t h o f these m a t e r i a l s a t two t e m p e r a t u r e s , R.T. (0.32 Tm) and 300°C (0.62 Tm) and t o 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 t h e r m a l and m e c h a n i c a l t r e a t m e n t s . I t has been shown t h a t t h e d e t r i m e n t a l e f f e c t o f p r i o r c o l d w o r k i n g on t h e h i g h temperature y i e l d and f l o w s t r e n g t h of d i s p e r s i o n - s t r e n g t h e n e d 41 a l l o y s such as Ni-ThO^,  and A.P.M. (aluminum powder m e t a l l u r g y )  42 products  can be r e c o v e r e d , a t l e a s t p a r t i a l l y , by s t a t i c a n n e a l i n g a t  high temperatures.  I t i s n o t 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  like  Al-4Cu where c o a r s e n i n g o f 0 p a r t i c l e s can a l s o o c c u r when the c o l d worked p r o d u c t i s annealed a t h i g h t e m p e r a t u r e s . was another o b j e c t i v e of the work.  C l a r i f i c a t i o n of t h i s  - 8 -  The r e l a t i o n between " s t o r e d energy" and d i s l o c a t i o n d e n s i t y i n deformed d i s p e r s i o n - s t r e n g t h e n e d of p u b l i s h e d work.  a l l o y s i s f a r from c l e a r on t h e b a s i s  I t was hoped t o p r o v i d e f u r t h e r i n s i g h t i n t o t h i s  q u e s t i o n by means o f 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 m e c h a n i c a l h i s t o r i e s .  I n o r d e r t o p e r m i t d i r e c t comparison between r e s u l t s o b t a i n e d an aged A l - C u a l l o y and those o b t a i n a b l e w i t h o x i d e aluminum under t h e same c o n d i t i o n s , i t was d e c i d e d  with  dispersion-strengthened t o i n c l u d e an  S.A.P. ( s i n t e r e d aluminum p r o d u c t ) a l l o y i n t h e i n v e s t i g a t i o n .  I t was  hoped t o be a b l e t o 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 c o u l d be as e f f e c t i v e as an o x i d e d i s p e r s i o n i n i m p r o v i n g t h e s t r e n g t h at e l e v a t e d  temperatures.  2.  2.1.  EXPERIMENTAL PROCEDURE  Alloy Preparation Aluminum and A l - 4 wt p e r c e n t Cu m a t e r i a l s were p r e p a r e d e n t i r e l y  i n t h e l a b o r a t o r y , whereas t h e S.A.P. a l l o y was o b t a i n e d 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 s o u r c e . To p r e p a r e t h e Al-4Cu a l l o y , h i g h p u r i t y aluminum  (originally  99.99% A l , s u p p l i e d by Aluminum Company o f Canada L t d . ) and copper ( o r i g i n a l l y 99.99% Cu, s u p p l i e d by K o c k - L i g h t 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 o u t i n a g r a p h i t e c r u c i b l e a t  720°C u s i n g an e l e c t r i c r e s i s t o r f u r a n c e .  I n producing the a l l o y ,  aluminum was m e l t e d f i r s t f o l l o w e d by t h e a d d i t i o n o f e l e m e n t a l copper. The melt was s t i r r e d w i t h a g r a p h i t e r o d u n t i l t h e copper had d i s s o l v e d completely.  The m e l t was c a s t i n t o a s p l i t copper mold t o produce a  s l a b o f dimensions 5" x 2" x 5/8".  Some pure aluminum c a s t i n g s were  o b t a i n e d under t h e same c o n d i t i o n s . The copper c o n t e n t o f t h e a l l o y was determined by Warnuck  Hersey  (Vancouver) and i m p u r i t i e s p r e s e n t i n b o t h A l and A l - 4 C u were determined s p e c t r o s c o p i c a l l y by t h e c o u r t e s y o f t h e Aluminum Company o f Canada, Richmond.  The a n a l y s e s o f these m a t e r i a l s a r e g i v e n i n T a b l e I . The  sources o f apparent z i n c c o n t a m i n a t i o n i n t h e a l l o y s c o u l d n o t be established.  - 10 -  Table I :  C h e m i c a l A n a l y s i s o f A l and Al-4Cu  Elements i n weight p e t .  (by  Al-4Cu  Aluminum  Cu  3.950  < 0.010  Fe  < 0.010  < 0.010  B  < 0.001  < 0.001  Si  < 0.005  < 0.001  Mg  0.002  0.002  Ti  0.004  < 0.001  V  0.002  < 0.001  Zn  0.020  0.013  Cr  0.002  0.002  Mn  < 0.001  < 0.001  Al difference)  ^96.00  =-99.960  The S.A.P. a l l o y was s u p p l i e d by the c o u r t e s y o f t h e Oak Ridge N a t i o n a l L a b o r a t o r y , Oak R i d g e , Tennessee, i n t h e form o f an e x t r u d e d c y l i n d r i c a l r o d o f d i a m e t e r 61 mm  (2.4 i n . ) .  to commercial S.A.P. 895 i n o x i d e c o n t e n t .  The a l l o y was s i m i l a r I t was manufactured from  b a l l - m i l l e d aluminum powder by c o l d compaction, vacuum a n n e a l i n g a t 600°C, h o t compaction, and h o t e x t r u s i o n w i t h a r e d u c t i o n r a t i o o f about 43 twenty.  The c o m p o s i t i o n o f t h e m a t e r i a l quoted by t h e s u p p l i e r was  10.3 wt % A 1 0 , 0.07 wt % i r o n , 0.05 wt % s i l i c o n , 0.3 wt % c a r b o n , 2  3  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 g e n e r a l p r o c e d u r e s used f o r t h e h o t and c o l d w o r k i n g o f  aluminum and A l - 4 C u a r e shown i n t h e f l o w sheet o f F i g . 1.  I n the  case o f 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 h o t r o l l i n g was t o r e t a i n a hot-worked m i c r o s t r u c t u r e .  The h o t r o l l i n g was c a r r i e d o u t 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, w h e r e i n o n l y t h e a - s o l i d s o l u t i o n was p r e s e n t ,  (b)  two-phase, w h e r e i n t h e i n c o h e r e n t C u A l ^ (0) p r e c i p i t a t e was  and  present during r o l l i n g . T h i s second t y p e o f h o t r o l l i n g was o f i m p o r t a n c e t o p e r m i t 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., t h e l a t t e r  m a t e r i a l h a v i n g been e x t r u d e d w i t h o x i d e p a r t i c l e s p r e s e n t .  A brief  d e s c r i p t i o n o f t h e f l o w sheet i s g i v e n below. I n g o t s were homogenised  a t 540°C f o r 36 h o u r s , f u r n a c e c o o l e d and  then c l e a n e d i n a d i l u t e aqueous s o l u t i o n o f NaOH f o l l o w e d by r i n s i n g i n HNO^ and washing i n w a t e r .  The s l a b s were then h o t r o l l e d a t 540°C  ( s i n g l e phase i n a l l c a s e s ) t o a t h i c k n e s s o f 0.225 i n . The r e s u l t i n g m a t e r i a l was c u t i n t o l e n g t h s o f about 4 i n . t o 6 i n . One end o f each l e n g t h was t a p e r e d t o f a c i l i t a t e i t s e n t r y i n t o t h e r o l l s d u r i n g subsequent heavy h o t 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 p a s s .  The l e n g t h s  were a g a i n c l e a n e d i n NaOH s o l u t i o n f o l l o w e d by r i n s i n g i n HNO^ and washing i n w a t e r . 'B'  Series One s e t o f t h e s e s t r i p s was s o l u t i o n t r e a t e d a t 540°C f o r 5 h o u r s ,  water quenched, and then aged a t 300°C f o r 15 hours t o produce t h e  - 12 -  casting 5" x 2" x 5/8" 4540°C 36 h r s (homogenisation) 4Hot r o l l e d t o 0.225 i n . a t 540°C c l e a n and t a p e r 4540°C,5 h r s 4water quench 4a g e i n g , 300°C, 15 h r s  540°C, 5 h r s . 4Hot r o l l e d a t 540°C to 0.150 i n . t h i c k i n one pass 4water quench  a g e i n g a t 300°C f o r 15 h r s 4Cold r o l l i n g 70%  540°C, 3 h r s 4water quench  I  Ageing 300°C, 15 h r s  Cold r o l l i n g 70%  Cold r o l l i n g 70%  Annealing (Time a t 300°C varied)  i  Annealing (Similar to B Series)  Temperature varied  i  Annealing (Temperature varied) D DAI  A AA1  F i g u r e 1.  Hot r o l l e d a t 300°C to 0.150 i n . t h i c k i n one pass 4water quench 4cold r o l l i n g 30-90% 4annealing  Flow sheet f o r f a b r i c a t i o n o f A l and Al-4Cu.  Time a t 300°C v a r i e d  - 13 -  incoherent 6 (CuA^) p r e c i p i t a t e .  The time e l a p s e d betweeen quenching  and t r a n s f e r t o t h e f u r n a c e f o r a g e i n g d i d n o t exceed 2 m i n u t e s .  The  aged s t r i p s were h o t r o l l e d a t 300°C t o a t h i c k n e s s o f 0.150 i n . i n one p a s s , and then water quenched i m m e d i a t e l y t o r e t a i n t h e h o t worked structure.  They were then kept r e f r i g e r a t e d a t -20°C t o a v o i d any  s t r u c t u r a l m o d i f i c a t i o n b e f o r e f u r t h e r use. For t h e 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 b a t h , and r o l l e d a t a h i g h r o l l speed of t h e s t r i p s by t h e r o l l s .  (70 fpm p e r i p h e r a l ) t o m i n i m i z e c o o l i n g  R e d u c t i o n was 33 p e r c e n t 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 o f 900 min ^.  The c o m b i n a t i o n o f  h i g h s t r a i n and s t r a i n r a t e a t 0.62 Tm r e a s o n a b l y approximates t h e c o n d i t i o n s which p r e v a i l when o x i d e d i s p e r s i o n - s t r e n g t h e n e d a l l o y s are e x t r u d e d from powder b i l l e t s . The group o f specimens hot r o l l e d a t 300°C; i . e . w i t h two phases p r e s e n t c o n s t i t u t e t h e 'B' s e r i e s i n t h e f l o w s h e e t .  A f t e r hot  r o l l i n g , most s t r i p s were c l e a n e d as b e f o r e , c o l d r o l l e d 70% and annealed.  The a n n e a l i n g treatment c o n s i s t e d o f (a) one hour s o a k i n g  at 8 temperatures r a n g i n g from 50°C t o 400°C and (b) s o a k i n g f o r d i f f e r e n t times a t 300°C.  An a n n e a l i n g temperature o f 300°C was  chosen because i t c o i n c i d e d w i t h t h e p r e v i o u s a g e i n g temperature and thus would n o t change t h e volume f r a c t i o n o f t h e second phase p r e s e n t . Other 'B' s e r i e s s t r i p s were c o l d r o l l e d t o g i v e r e d u c t i o n s i n t h i c k n e s s r a n g i n g from 30% t o 90%.  These c o l d worked specimens were annealed  f o r d i f f e r e n t times a t 300°C. A, C, D S e r i e s Another s e t o f t h e 0.225 i n . t h i c k s t r i p s produced by h o t r o l l i n g  - 14 -  s l a b s a t 540°C was s o l u t i o n t r e a t e d a t 540°C f o r 5 h o u r s , a g a i n h o t r o l l e d at 540°C t o a t h i c k n e s s o f 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 t o those used f o r t h e 'B' s e r i e s except t h a t a h i g h e r m e l t i n g - p o i n t s a l t was used i n h e a t i n g t h e 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 a t 540°C ( s i n g l e phase) produced some c r a c k s  on one s u r f a c e o f t h e r o l l e d p r o d u c t f o r reasons unknown. the c r a c k s c l o s e d i n subsequent  However,  c o l d r o l l i n g , and no t r a c e o f them  c o u l d be found by m i c r o s c o p y a f t e r c o l d r o l l i n g r e d u c t i o n s g r e a t e r than 50%.  I n 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 o f 70% was a p p l i e d  to a l l h o t r o l l e d m a t e r i a l s i n t h e s e s e r i e s . A f t e r h o t r o l l i n g , t h e s t r i p s were c l e a n e d and s u b j e c t e d t o t h r e e types o f thermomechanical  treatments.  'D' S e r i e s In t h i s c a s e , the 540°C h o t r o l l e d -and-quenched m a t e r i a l above was aged a t 300°C f o r 15 hours t o produce t h e 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 a t tmperatures r a n g i n g from 50°C t o 400°C. 'A' S e r i e s I n t h i s s e r i e s , the 540°C h o t r o l l e d - a n d - q u e n c h e d p r o d u c t was s o l u t i o n t r e a t e d a t 540°C f o r 3 h o u r s , quenched i n w a t e r , aged a t 300°C f o r 15 hours t o produce t h e 0 phase, c o l d r o l l e d 70%, and f i n a l l y annealed.  The a n n e a l i n g t r e a t m e n t s were s i m i l a r t o those o f t h e 'B'  series. 'C  Series For t h i s s e r i e s , t h e h o t r o l l e d - a n d - q u e n c h e d p r o d u c t was s o l u t i o n  t r e a t e d f o r 3 hours a t 540°C, water quenched, c o l d r o l l e d 70%, and  - 15 -  then heated a t 300°C f o r d i f f e r e n t t i m e s . treatment i n t h i s  I n e f f e c t , t h e f i n a l heat  case was an a g e i n g t r e a t m e n t as w e l l as an a n n e a l i n g  operation. The  Series  four processing  s e r i e s o f F i g . 1 may be summarised as f o l l o w s .  Microstructure during f i n a l hot w o r k i n g (to 0.150 i n . )  Microstructure during rolling (20°C)  A  s i n g l e phase (540°C)  Two phase A l - C u A ^  B  Two phase A l - C u A l  Two phase A l - C u A ^  C  S i n g l e phase (540°C)  S i n g l e phase ( s o l u t i o n t r e a t e d )  D  S i n g l e phase (540°C)  Two phase Al-CuAl„  2  (300°C)  S e r i e s A and D d i f f e r e d o n l y s l i g h t l y .  F o r S e r i e s A t h e r e was a  f u l l s o l u t i o n treatment c a r r i e d out between h o t and c o l d whereas quenching from t h e h o t r o l l i n g  cold  rolling,  temperature was t a k e n t o  c o n s t i t u t e s o l u t i o n treatment i n S e r i e s D.  S i n c e some energy o f  d e f o r m a t i o n may. have been r e t a i n e d i n S e r i e s D, i t was f e l t  that  the subsequent a g e i n g response might be somewhat d i f f e r e n t f o r t h e two series. S i n c e oxide, d i s p e r s i o n - s t r e n g t h e n e d  a l l o y s a r e worked i n the  two phase c o n d i t i o n a t a l l s t a g e s o f f a b r i c a t i o n , S e r i e s B specimens of Al-4Cu may be c o n s i d e r e d  t h e most comparable t o S.A.P.  For comparison purposes pure aluminum s l a b s were g i v e n m e c h a n i c a l t r e a t m e n t s s i m i l a r t o t h e A and t o t h e D s e r i e s . specimens  are designated  AAL and DAL r e s p e c t i v e l y .  thermoThese  I t was e s t a b l i s h e d  - 16 -  t h a t t h e g r a i n s i z e o f t h e c o l d r o l l e d pure aluminum specimens was c l o s e l y comparable t o t h a t o f c o l d - r o l l e d A l - C u a l l o y specimens; i . e . i n t h e o r d e r o f 0.1 mm. Simple Aged A l l o y s In  o r d e r t o e l u c i d a t e t h e mechanism o f d i s p e r s i o n - h a r d e n i n g , i t  was n e c e s s a r y i n a s e p a r a t e experiment t o v a r y t h e d i s p e r s i o n o f 6 and/or 9' p r e c i p i t a t e s by t h e use o f s u i t a b l e heat t r e a t m e n t s .  To a c h i e v e  t h i s Al-4Cu specimens (0.045 i n . i n t h i c k n e s s ) were s o l u t i o n t r e a t e d for  3 hours a t 540°C, water quenched and t h e n aged a t 300°C f o r times  r a n g i n g from one hour t o 62 h o u r s . p r i o r to ageing.  To produce a v e r y c o a r s e 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 ,  some o f t h e specimens were f i r s t (15  These specimens were n o t worked  aged a t 450°C f o r d i f f e r e n t times  t o 32 h o u r s ) and f i n a l l y aged a t 300°C f o r 24 hours t o e s t a b l i s h t h e  e q u i l i b r i u m m a t r i x c o m p o s i t i o n o f 0.45 wt % Cu.  2.2.2  S.A.P.  A l o t o f d i f f i c u l t i e s were e x p e r i e n c e d i n t h e f u r t h e r of  fabrication  a s - s u p p l i e d S.A.P. r o d . An attempt t o f o r g e t h e c y l i n d r i c a l r o d  i n t o a s l a b shape was u n s u c c e s s f u l s i n c e c r a c k s were produced a t t h e centre of the c i r c u l a r cross-section.  Hot r o l l i n g , a p p l i e d t o t h i c k  r e c t a n g u l a r s e c t i o n s machined from t h e c e n t r e o f t h e r o d , produced numerous edge c r a c k s .  I n c r e a s i n g t h e h o t r o l l i n g temperature t o  540°C d i d n o t produce any improvement.  E v e n t u a l l y i t was found t h a t  o n l y t h i n s l i c e s c u t from t h e a s - e x t r u d e d r o d c o u l d s u s t a i n f u r t h e r heavy d e f o r m a t i o n . 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 t o  p r o v i d e them w i t h smooth s u r f a c e s , t h e f i n a l t h i c k n e s s b e i n g 0.25 i n .  - 17 Each s l i c e was hot r o l l e d a t 540°C, i n many p a s s e s , t o a t h i c k n e s s 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  t h i c k n e s s o f o n l y about 0.01 i n . was p o s s i b l e i n each p a s s , and the s t r i p was r e h e a t e d t o 540°C a f t e r every p a s s .  The r e s u l t i n g s t r i p was  then c u t i n t o l e n g t h s of 4 i n . , t a p e r e d on one end, c l e a n e d i n d i l u t e NaOH s o l u t i o n and annealed a t 540°C f o r 2.5 h o u r s .  The f i n a l h o t r o l l i n g  was c a r r i e d out a t 540°C under t h e same c o n d i t i o n s as f o r t h e A, C, and D s e r i e s .  I n one pass t h e t h i c k n e s s was reduced by 0.032 i n .  which corresponded t o 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 m i n  The h o t r o l l e d p r o d u c t was quenched i n water i m m e d i a t e l y ,  and s t o r e d a t -20°C t o a v o i d p o s s i b l e  further structural modifications.  A f t e r h o t r o l l i n g , most S.A.P. s t r i p s were c l e a n e d i n d i l u t e NaOH s o l u t i o n and c o l d r o l l e d 50% t o 0.034 i n . t h i c k n e s s . annealed a t 300°C o r 540°C f o r v a r y i n g t i m e s .  They were then  The r e a s o n f o r u s i n g  two a n n e a l i n g temperatures i n t h i s case i s e x p l a i n e d l a t e r i n the thesis.  Other h o t r o l l e d S.A.P. s t r i p s were g i v e n v a r i a b l e r e d u c t i o n s  i n t h i c k n e s s by c o l d r o l l i n g ; 0-70 p e r c e n t . I n t h e case o f A l - 4 C u , A l and S.A.P., a n n e a l i n g t r e a t m e n t s were performed o n l y a f t e r punching out t e n s i l e specimens next s e c t i o n .  as d e s c r i b e d i n t h e  The specimens were a i r - c o o l e d a f t e r t h e r e q u i r e d a n n e a l i n g  treatments.  2.3  Tensile Testing  2.3.1  P r e p a r a t i o n o f T e n s i l e Specimen T e n s i l e specimens were sheared from t h e c o l d r o l l e d s t r i p s by  means o f a p n e u m a t i c a l l y o p e r a t e d punch and d i e s e t .  The t e n s i l e  axis  - 18 -  was i n t h e 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 o f t h e specimen  was 2.75 i n . l o n g and 0.75 i n . w i d e , and t h e c e n t r a l 0.8 i n . l e n g t h of t h e reduced s e c t i o n was  used as t h e gauge l e n g t h .  I n case o f  Al-4Cu a l l o y s , where t h e t h i c k n e s s o f t h e s t r i p was more than 0.050 i n . , t e n s i l e specimens o f t h e same gauge l e n g t h were o b t a i n e d by m i l l i n g r a t h e r than s h e a r i n g . 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 c h e m i c a l l y 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 t e s t e d on a F l o o r Model I n s t r o n T e n s i l e Machine -3 at a s t r a i n r a t e o f 6.25 x 10  -1 min  20°C (0.32 Tm) and 300°C (0.62 Tm).  .  The t e s t temperatures were  S i n c e t h e a g e i n g and a n n e a l i n g  t r e a t m e n t s f o r Al-4Cu a l l o y s were a l l c a r r i e d o u t a t 300°C, t h e same temperature was chosen as a t e s t temperature. A p o r t a b l e s a l t p o t w i t h Draw Temp 275 s a l t was used t o heat specimens f o r t h e h i g h temperature t e s t s . accommodate t h e specimen and t h e g r i p s .  The b a t h c o u l d be r a i s e d t o Temperature  of the s a l t  b a t h was h e l d t o w i t h i n ± 2°C o f t h e r e p o r t e d v a l u e throughout t h e t e s t by v a r y i n g t h e i n p u t t o t h e 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 required. constant  The m o l t e n s a l t was s t i r r e d c o n t i n u o u s l y t o m a i n t a i n a temperature throughout t h e b a t h .  Specimen temperature was  f o l l o w e d by means o f a thermocouple w i r e d t o t h e gauge l e n g t h .  I t was  found t h a t t h e specimen a t t a i n e d 300°C i n a p p r o x i m a t e l y two m i n u t e s , f o l l o w i n g which t h e assembly was h e l d a t 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 h e a t t r e a t e d I n c o n e l , w i t h jaw p i e c e s , were used f o r t h e t e n s i l e t e s t s .  file-face  The mating s u r f a c e s o f  the g r i p assembly were c o a t e d 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 t h r e a d e d components of t h e assembly.  A smooth  l o a d - e l o n g a t i o n c u r v e was o b t a i n e d on the r e c o r d i n g c h a r t under these conditions.  2.4  X-Ray D i f f r a c t i o n  2.4.1  Principle X-ray l i n e p r o f i l e a n a l y s i s was used t o determine t h e nonuniform  l a t t i c e s t r a i n and t h e c o h e r e n t 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 ( h k l ) can be e x p r e s s e d i n t h e form o f 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 o b t a i n e d from t h e Fourier transform integration.  The c o s i n e c o e f f i c i e n t s o f t h e F o u r i e r  s e r i e s a r e r e l a t e d t o t h e l a t t i c e s t r a i n and the domain s i z e . a n a l y s i n g two o r d e r s of t h e same r e f l e c t i o n t h e non-uniform  By  lattice  s t r a i n and t h e 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 can be e a s i l y determined. A r e v i e w o f t h e 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  analysis  i s g i v e n i n S e c t i o n 3.1.  2.4.2  Specimen Specimens  Preparation  o f s i z e 1.5 i n l o n g 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  direction.  Both s u r f a c e s o f each specimen were p o l i s h e d on a s e r i e s o f emery papers w i t h kerosene l u b r i c a t i o n .  The s u r f a c e t o be examined was then l a p p e d  - 20 -  u s i n g 5 m i c r o n and 1 m i c r o n diamond p a s t e .  T h i s p r o c e d u r e 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 s u r f a c e was o b t a i n e d . The  electropolishing involved  surface.  F o r aluminum and A l - 4 C u a l l o y s t h e e l e c t r o p o l i s h i n g  was o f t h e f o l l o w i n g HN0  The  t h e removal o f about 0.002 i n . from each solution  composition: 1 part  3  methyl a l c o h o l  1 part  HC1  1 cc p e r 50 c c o f t h e m i x t u r e .  S.A.P. specimens were e l e c t r o p o l i s h e d  perchloric acid i n ethyl alcohol.  i n a s o l u t i o n o f 20 v o l %  T h i s e l e c t r o l y t e was recommended by  40 44 G o o d r i c h et a l .  '  H e a t i n g o f t h e 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  p r e v e n t e d by means o f w a t e r - c o o l i n g c o i l s around t h e s t a i n l e s s s t e e l beaker which a l s o s e r v e d as t h e cathode. attack,  To a v o i d  preferential localized  t h e 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 .  F o r S.A.P.  -2 a l l o y s a p o t e n t i a l o f 10-15 v o l t s and a c u r r e n t d e n s i t y o f 0.04 amp cm were used. F o r aluminum and Al-4Cu a l l o y s t h e c o r r e s p o n d i n g v a l u e s were -2 5 v o l t s and 0.3 amps cm The  different materials  and t r e a t m e n t s examined by X-ray  step-  s c a n n i n g a r e l i s t e d below: i) ii)  Pure aluminum, AAL s e r i e s , c o l d r o l l e d 70%, Pure aluminum, AA1 s e r i e s , c o l d r o l l e d 70% and annealed a t  300°C f o r 6 h o u r s , iii) iv) v) vi) 4 hours,  A l - 4 C u , over-aged, A l - 4 C u , B S e r i e s , hot r o l l e d , A l - 4 C u , B S e r i e s , c o l d r o l l e d , 50% A l - 4 C u , B S e r i e s , c o l d r o l l e d , 50% and annealed a t 300°C f o r  - 21 -  vii) viii) for  A l - 4 C u , B S e r i e s , c o l d r o l l e d 70%, A l - 4 C u , B S e r i e s , c o l d r o l l e d 70% and annealed a t 300°C  4 hours, ix) x) xi) xii)  2.4.3  S.A.P., as r e c e i v e d , S.A.P., hot r o l l e d , S.A.P., c o l d r o l l e d 50%, S.A.P., c o l d r o l l e d 50% and annealed a t 540°C f o r 24 hours.  X-Ray D i f f r a c t i o n  Procedure  A P h i l i p s X-ray s e t was used, w i t h a s t e p s c a n n i n g d e v i c e and a h i g h speed d i g i t a l p r i n t e r f o r t h e output from t h e c o u n t e r and t i m e r . The goniometer d i v e r g e n c e s l i t and s c a t t e r s l i t were each s e t t o 2° and  the r e c e i v i n g s l i t  t o 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 a t 40 K.V. was used throughout.  Tube c u r r e n t s were v a r i e d  from 10 t o 26 mA, depending on t h e thermomechanical  h i s t o r y of the  specimen, i n o r d e r t o keep t h e c o u n t i n g i n t e r v a l t o a minimum o f 1 s e c . for  a f i x e d count o f 20,000 p u l s e s .  For t h i s c o u n t i n g r a t e t h e t i m e r  e r r o r was 1.01% and f o r a l l counts o f 20,000 p u l s e s t h e r e was a 96% p r o b a b i l i t y o f t h e e r r o r b e i n g w i t h i n 1.4%. In  t h e s t e p - s c a n n i n g procedure t h e goniometer was advanced  auto-  m a t i c a l l y i n s t e p s o f 0.02° (20) from t h e s e l e c t e d s t a r t i n g a n g l e on the low 0 s i d e o f t h e Bragg r e f l e c t i o n peak. To s t a r t w i t h , t h e X-ray a p p a r a t u s was c a l i b r a t e d and a l i g n e d u s i n g a s i l i c o n standard.  The d i f f e r e n t  { h k l } 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 u s i n g a c o n t i n u o u s scan w i t h a goniometer movement of  1° (29) min ^ c o u p l e d w i t h a c h a r t speed o f 600 mm  hr  and a time  - 22 -  c o n s t a n t of 4 s e c .  These peaks were compared w i t h A.S.T.M. v a l u e s .  For b e t t e r a c c u r a c y i t i s a d v i s a b l e t o scan a s e t 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 c o u l d not be scanned because of the l i m i t a t i o n s imposed on the minimum 20 a n g l e by the d i v e r g e n c e and s c a t t e r  slits.  The  (220) r e f l e c t i o n s were s t r o n g enough  to be r e c o r d e d but the (440) r e f l e c t i o n s c o u l d not be r e c o r d e d 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 u s i n g CuK  radiation.  The (200) and  (400)  a r e f l e c t i o n s were found t o 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  availability. To determine the l o w e r and upper a n g u l a r l i m i t s t o be used f o r the  s t e p scan , the (200) and (400) r e f l e c t i o n s were scanned i n a range of 15°  continuously  (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 o b s e r v a t i o n s from the  c o n t i n u o u s s c a n s , a range of 8° (20) was s u b s e q u e n t l y s t e p scanned i n s t e p s of 0.02° (20) r e s u l t i n g i n a s e t of 400 r e a d i n g s f o r each l i n e . At each s t e p the times t o count 20,000 p u l s e s were p r i n t e d a u t o m a t i c a l l y , each time b e i n g r e l a t e d  r e c i p r o c a l l y t o d i f f r a c t e d X-ray i n t e n s i t y .  In o r d e r t o remove the e f f e c t s of i n s t r u m e n t a l b r o a d e n i n g from the c o n v o l u t i o n of the o b s e r v e d i n t e n s i t i e s , a w e l l - a n n e a l e d aluminum powder s t a n d a r d , w h i c h gave no X-ray l i n e b r o a d e n i n g due t o l a t t i c e s t r a i n or s m a l l domain s i z e , was s t e p scanned i n the same range f o r each r e f l e c t i o n .  The 1 m i c r o n aluminum powder (99.99% pure) was  vacuum s e a l e d i n a p y r e x g l a s s tube and annealed a t 500°C f o r 80 minutes. I n the case of over-aged A l - 4 C u c o n t a i n i n g C u A l ^ p a r t i c l e s , the (400) r e f l e c t i o n c o u l d not d i r e c t l y be r e c o r d e d because of the p r e s e n c e of cube  - 23 -  texture.  On t i l t i n g  (400) peak was  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  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 s t e p - s c a n was  c a r r i e d out.  T h i s 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 h a l f - p e a k w i d t h s u f f e r e d no change. An i n i t i a l treatment o f the n u m e r i c a l d a t a from the X-ray  diffraction  a n a l y s i s was n e c e s s a r y t o 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 C u A l ^ 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.  I n the case of the s i m p l e over-aged  Al-Cu  a l l o y , and of S.A.P. specimens, o v e r l a p p i n g r e f l e c t i o n s due t o the presence of C u A l diffractometer.  2  and A^O^ The  r e s p e c t i v e l y were not r e c o r d e d on the  (200) r e f l e c t i o n s f o r the c o l d r o l l e d and  r o l l e d - a n d - a n n e a l e d Al-4Cu m a t e r i a l s o c c u r r e d a t 26  cold  = 44.74°, and  the  o v e r l a p p i n g r e f l e c t i o n s were i)  K  ii)  K  iii)  K  iv)  K  g  l i n e f o r A l (200) a t 29  = 40.25°,  line for CuAl  (130) a t 20  2  (202) and  l i n e f o r CuAl„ (112) a t 20 l i n e f o r CuAl„ (202) and a  = 42.14°,  = 42.70°,  (130) d o u b l e t a t 20  = 47.40°  I  and 47.90°. For the A l - C u (400) l i n e o c c u r r i n g a t a p p r o x i m a t e l y 20  = 99°  the  o v e r l a p p i n g r e f l e c t i o n s were, i)  line for CuAl  2  (134) a t 20  = 97.05°,  ii)  line for CuAl  2  (600) a t 20  = 99.75° ( b a r e l y d i s c e r n i b l e ) .  The c o n t r i b u t i o n t o i n t e n s i t y from these o v e r l a p p i n g r e f l e c t i o n s were removed by s i m p l y smoothing out the t r a c e on the d i f f r a c t o m e t e r c h a r t  - 24 -  r e c o r d i n g i n the a p p r o p r i a t e r e g i o n s .  I n t e r p o l a t e d i n t e n s i t y v a l u e s so  o b t a i n e d were then i n s e r t e d as a p p r o p r i a t e r e c i p r o c a l s i n p l a c e of c o r r e s p o n d i n g time v a l u e s i n the s e t of times p r e v i o u s l y on the p r i n t e r A l l other treatment the  f o r 20,000 counts  the  obtained  output. of the X-ray  data i s d i s c u s s e d i n S e c t i o n 3 of  thesis.  2.5  Metallography i  2.5.1  Optical  Microscopy  Mounted and p o l i s h e d specimens were etched w i t h d i f f e r e n t to r e v e a l g r a i n boundaries  and/or second  aluminum, a f r e s h l y prepared 46.2  cc of water and  etchant.  Al-4Cu  7.6  phase p a r t i c l e s .  s o l u t i o n c o n t a i n i n g 46.2  cc of HC1  was  reagents  For pure  cc of  HF,  found t o be a s a t i s f a c t o r y  a l l o y s were etched w i t h K e l l e r ' s reagent,  the  composition  of which i s as f o l l o w s : HF  (cone)  HC1 HN0  (cone) 3  (cone)  water S.A.P. was  1.0  cc  1.5  cc  2.5  cc  95.0  cc  e f f e c t i v e l y etched i n a s o l u t i o n of 1% HF by volume i n  water.  2.5.2  Electron  Microscopy  T h i n f o i l s of aluminum, Al-4Cu  and  an H i t a c h i HU-11A e l e c t r o n microscope  S.A.P. were examined u s i n g  operated at 100  K.V.  F o i l s s u i t a b l e f o r t r a n s m i s s i o n e l e c t r o n microscopy  were prepared  by  - 25 -  e l e c t r o p o l i s h i n g u s i n g t h e s t a n d a r d "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 t h e same as t h o s e a l r e a d y d e s c r i b e d i n S e c t i o n 2.4.2. One d i f f i c u l t y Al-4Cu a l l o y s .  was f a c e d i n p r e p a r i n g t h i n f o i l s from over-aged  Some o f t h e second phase p a r t i c l e s tended t o 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 h o l e s were more numerous near t h e  edge o f t h e f o i l as would be e x p e c t e d .  T h i s 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 t h e v o l t a g e from 5 v o l t s t o about 10 v o l t s a f t e r p e r f o r a t i o n o f t h e specimen f i r s t o c c u r r e d d u r i n g 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 t e c h n i q u e was adopted t o r e v e a l t h e second phase p a r t i c l e s i n over-aged Al-4Cu a l l o y s .  C o n v e n t i o n a l two-stage carbon  r e p l i c a s were used, w i t h chromium shadowing f o r c o n t r a s t .  2.5.3  Measurement o f G r a i n S i z e and S u b g r a i n S i z e The l i n e a r i n t e r c e p t method was used t o determine t h e 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 m i c r o g r a p h s , and t o determine t h e s u b g r a i n s i z e o f A l , Al-4Cu and S.A.P. a l l o y s from transmission e l e c t r o n micrographs. The s i z e o f e l o n g a t e d g r a i n s produced by r o l l i n g by any o f t h e c o u n t i n g methods.  can be measured  Measurements must be made i n t h r e e  m u t u a l l y p e r p e n d i c u l a r d i r e c t i o n s , which form an o r t h o g o n a l t r i p l e t . The g r a i n s i z e , e x p r e s s e d as t h e number o f g r a i n s p e r c u b i c m i l l i m e t e r (Nv),  • 47 can be c a l c u l a t e d from e i t h e r o f t h e f o l l o w i n g e q u a t i o n s : Nv = 0 . 7 [ N U ) N ( t ) N ( n ) ] A  A  A  1 / 2  (3)  - 26 -  Nv = 0.7[N U) N ( t ) N ( n ) ] L  L  (4)  L  where N (£)•, N ( t ) , and N (n) a r e t h e number o f g r a i n s p e r square A. A A. m i l l i m e t e r i n each o f t h e t h r e e s e c t i o n a l p l a n e s v e r s e , and n o r m a l ) ,  (longitudinal, trans-  and N (£), N ( t ) , and N (n) a r e t h e number o f g r a i n s Li  J-j  Li  per u n i t o f l e n g t h 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 The  o f Volume F r a c t i o n o f P r e c i p i t a t e s  volume f r a c t i o n , f , o f 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 t h e A l - C u phase diagram ( F i g . 2 ) , t h e d e n s i t y o f the a l p h a s o l i d s o l u t i o n , and t h e d e n s i t y o f t h e 0 phase.  Taking a  d e n s i t y o f 4.35 gms p e r cc f o r C u A ^ , a d e n s i t y o f 2.73 gms p e r cc f o r the a l p h a 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 t o c o n t a i n t h e e q u i l i b r i u m c o n c e n t r a t i o n o f copper, 0.45 wt %, t h e volume f r a c t i o n , f , was found t o be 0.043. For t h e S.A.P. a l l o y t h e volume f r a c t i o n of the o x i d e phase was s i m i l a r l y c a l c u l a t e d from a knowledge o f t h e weight f r a c t i o n (w) and the d e n s i t y ( p ) o f t h e o x i d e 2  f  =  wp,* ~n—r^r (l-w)p +wp 2  where The  (Al^O^) a c c o r d i n g t o :  (5) 1  i s t h e d e n s i t y o f t h e aluminum m a t r i x  (2.73 gms p e r c c ) .  d e n s i t y o f t h e o x i d e phase, measured on c o n s o l i d a t e d p r o d u c t s  by  49 Hansen,  was taken as 3.4 gms p e r c c . The volume f r a c t i o n f o r A ^ O ^  i n S.A.P. was found t o be 0.084.  - 27 -  F i g u r e 2.  Phase diagram of Al-4Cu on the a l u m i n u m - r i c h s i d e . ( I n t h i s f i g u r e the K-phase i s the same as the a l p h a 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 p l a n a r p a r t i c l e r a d i u s ( r ) and t h e mean p l a n a r  inter-  p a r t i c l e s p a c i n g o f 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 m i c r o g r a p h s . by Dew-Hughes and R o b e r t s o n , ^ spherical  The method was d e s c r i b e d  and assumes a u n i f o r m d i s t r i b u t i o n o f  p r e c i p i t a t e s throughout t h e m a t r i x (an assumption w h i c h 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 t h a t each p a r t i c l e i n  the p l a n e o f p o l i s h i s a s s o c i a t e d w i t h a " c i r c l e o f i n f l u e n c e " o f r a d i u s R^, the volume f r a c t i o n , f , o f t h e second phase p a r t i c l e i s g i v e n by  •r = -^T R c 2  f  If  (6)  i s t h e number o f p a r t i c l e s p e r u n i t a r e a o f p l a n a r s e c t i o n , then  i t follows that  N  =  (7) TTR  P  c  2  The mean p l a n a r i n t e r p a r t i c l e d i s t a n c e , D , i s a p p r o x i m a t e l y g  2R  c<  equal to  Thus, knowing t h e number o f p a r t i c l e s i n t e r c e p t e d by t h e p l a n e  per u n i t a r e a , the mean p l a n a r i n t e r p a r t i c l e d i s t a n c e and t h e mean p l a n a r p a r t i c l e r a d i u s can be c a l c u l a t e d . I n the case o f S.A.P., the p l a n a r mean f r e e p a t h p a r t i c l e s was determined from t h e F u l l m a n " ^  »-  "T  1  L  (m) o f t h e o x i d e  relationship:  (8)  - 29 -  where N  Li  i s t h e number o f p a r t i c l e s p e r u n i t l e n g t h i n t e r s e c t i n g a  random l i n e on a p o l i s h e d s e c t i o n . diameter  The average s p h e r i c a l p a r t i c l e  (d) was then o b t a i n e d u s i n g a deduction^"'" from  Fullman's  formula:  3*2 2(l-f)  ( ) 9  w  The mean p l a n a r p a r t i c l e s p a c i n g ( D ) 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 g  from t h e mean f r e e p a t h (m). The former i s t h e average d i s t a n c e between n e a r e s t neighbours  on a p l a n e whereas t h e l a t t e r i s t h e mean u n i n t e r -  r u p t e d path between p a r t i c l e s .  The q u a n t i t y  was computed from t h e  formula  D  s = dCl-fWl!  (10)  3.  USE OF X-RAY TECHNIQUES TO ANALYSE DISLOCATION DENSITY AND  3.1  CONFIGURATION  B a s i s of X-Ray L i n e P r o f i l e Non-uniform  lattice strain  Analysis  and s m a l l coherent c r y s t a l l i t e domain  s i z e i n metals and a l l o y s can be determined X-ray d i f f r a c t i o n  l i n e broadening.  from the measurement of  The e v a l u a t i o n i s r e l a t i v e l y  straight-  forward when these two e f f e c t s occur s e p a r a t e l y , and s t a n d a r d t e x t books  52 53 ' d e a l w i t h the a p p r o p r i a t e treatments.  occur t o g e t h e r and t h e i r  U s u a l l y these two e f f e c t s  e v a l u a t i o n becomes more complex. 54-61  the e a r l i e r work of many workers, t h e o r e t i c a l b a s i s of the  41 Clegg  has reviewed the  measurement of non-uniform  lattice  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 profile  Based on  strain line  technique.  Under c o n d i t i o n s of non-uniform  lattice strain  domain s i z e the experimentally-measured l e n g t h of d i f f r a c t i o n  diffracted  and s m a l l c r y s t a l l i t e X-ray power p e r u n i t  l i n e , q'(29), a t a g i v e n Bragg a n g l e , e,  i s given  by the f o l l o w i n g e q u a t i o n ,  q* (26) = k(6) ^ l N  EN(t) [COS2TTJ t cos2Trh X ( t ) - s i n 2 i r j t t 1  1  1  sin2rrh X ( t ) ] (ID  -  31  -  where, N = number of c e l l s i n the c o h e r e n t l y d i f f r a c t i n g domain and e q u a l t o N^N^N^; N^,  and  b e i n g 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 a n g l e  (20),  h = o r d e r of the r e f l e c t i o n X ( t ) = f u n c t i o n of the l a t t i c e  (hOO) strain,  = 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 v a l u e s of the harmonic number ( t ) . To o b t a i n X ( t ) and  e x p e r i m e n t a l l y they are combined i n the 1  following  definitions,  A(t) • =  cos2uh  X(t)  1  B(t)  =  sin2uh X(t) 1  From e q u a t i o n  (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 a n g u l a r  correction  f o r b o t h 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 F a c t o r and the 2(0) v a r i a b l e  can be r e d e f i n e d i n terms o f the d i s t a n c e x on  (26) a x i s of the e x p e r i m e n t a l l y r e c o r d e d X-ray d i f f r a c t i o n p r o f i l e ; b e i n g i n u n i t s of s i n 0 .  I n a d d i t i o n , the harmonic number ( t ) can  the x  be  r e l a t e d to the t r u e l a t t i c e d i s t a n c e (L) measured i n the c r y s t a l i n the d i r e c t i o n p e r p e n d i c u l a r to the d i f f r a c t i n g p l a n e s , 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 e q u a t i o n (11)  be expressed  can  i n the form of the f o l l o w i n g e q u a t i o n ,  q(x) = E [A(L)COS2TTL -f- x + B(L)sin2iTL |- x]  (12)  - 32 -  where X i s t h e w a v e l e n g t h of X-ray beam.  (12)  Equation  has t h e 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 w h i c h t h e c o e f f i c e n t s A(L) and B(L) can be o b t a i n e d from t h e t r a n s f o r m  integration.  For t h e 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 s i n 9 o r x a x i s .  A c c o r d i n g t o 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 t h e o r i g i n , the i m a g i n a r y or s i n e c o e f f i c i e n t s , B ( L ) , of t h e d e r i v e d f u n c t i o n q ( x ) w i l l be s m a l l and the r e a l o r c o s i n e c o e f f i c i e n t s , Hence from a knowledge  A ( L ) , w i l l have o n l y s m a l l o s c i l l a t i o n s .  of the c o s i n e c o e f f i c i e n t s b o t h t h e c r y s t a l l i t e  domain s i z e and t h e e x t e n t of n o n - u n i f o r m s h o r t range e l a s t i c can be d e t e r m i n e d . A(L)  By d e f i n i t i o n , cos2Trh  =  By d e f i n i n g ^,9^  X(L)  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  as t h e o r d e r dependent D  strain  S Strain Coefficient A ( L , h ) , i . e . A(L,h ) = Q  o  S  A (L) A (L,h ) , t h e f i n a l w o r k i n g e x p r e s s i o n i s g i v e n by the f o l l o w i n g equation, 2 2 2  Hn A ( L , h ) = £nA°(L) - 2TT  2  E  (  1  Q  1  3  )  where e i s t h e s t r a i n i n a d i s t a n c e L measured i n the a^ d i r e c t i o n , "a* 2 i s the f . c . c . l a t t i c e parameter and h From e q u a t i o n  Q  2  = (h +k +£  2  1/2 )  ( 1 3 ) , u s i n g two o r d e r s of an (hoo) r e f l e c t i o n , a  s e t of s t r a i g h t l i n e s can be drawn w i t h v a l u e s of £n A ( L , h ) as 2 o r d i n a t e s and the v a l u e s of h as a b s c i s s a e , each chosen v a l u e of L Q  - 33 -  2  r e s u l t i n g i n one l i n e of In A(L,h ) v s . h .  -2A L 2  l i n e s i s e q u a l to  °  2  ^  > from which v a l u e s of mean square s t r a i n e  a  are  The s l o p e of each o f t h e s e  o b t a i n e d f o r a range of v a l u e s o f L.  2  e  2  i s the s t r a i n i n the [hoo]  d i r e c t i o n f o r a c u b i c l a t t i c e , averaged over the l e n g t h L, squared, and averaged over the r e g i o n from which the r e f l e c t i o n comes.  The  2 1/2 graph of (e )  v s . 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 f u n c t i o n of d i s t a n c e i n the c r y s t a l .  2 From t h e i n t e r c e p t s of  £n A(L,ho) v s . h  2 with h  =0  axis values  of fcn A ^ ( L ) a r e o b t a i n e d , c o n v e r t e d to A ^ ( L ) , n o r m a l i z e d to u n i t y f o r L = 0, and p l o t t e d as f u n c t i o n of L.  The average domain s i z e comes  from t h i s p l o t o f A^(L) v s . L by two c r i t e r i a ; the  firstly  from twice  a r e a under the curve and s e c o n d l y from the n e g a t i v e r e c i p r o c a l  s l o p e of A°(L) v s . L a t a s p e c i f i e d d i s t a n c e from L = 0 e q u a l to 20% of the approximate domain s i z e f i r s t is  This  distance  s p e c i f i e d i n order t o a v o i d the n e g a t i v e c u r v a t u r e o r o t h e r w i s e  called of  calculated.  the "hook e f f e c t " i n the r e g i o n approaching L = 0 i n the p l o t  A°(L) v s . L.  T h i s e r r o r a r i s e s because o f i n a c c u r a c i e s i n the  measurement o f the t r u e background  l e v e l o f the observed p r o f i l e which  r e s u l t s i n low v a l u e s f o r the measured a r e a under the X-ray peak. boundary  of a domain c o u l d be a g r a i n boundary,  s t a c k i n g f a u l t o r twin boundary two a d j a c e n t l a t t i c e s  s u b g r a i n boundary,  a c r o s s which the m i s o r i e n t a t i o n of the  i s such t h a t the Bragg law cannot be s a t i s f i e d  by them f o r a common i n c i d e n t X-ray In  The  intensity.  p r a c t i c e , the observed X-ray p r o f i l e i s not d e s c r i b e d c o m p l e t e l y  by e q u a t i o n (12) but c o n t a i n s i n a d d i t i o n 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 o p t i c s and i m p e r f e c t i o n s of  - 34 -  the apparatus used. w h i c h i s broadened  To o b t a i n an e x p e r i m e n t a l X-ray r e f l e c t i o n  profile  o n l y 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  i n v o l v e s the u n f o l d i n g of the observed c o n v o l u t i o n of i n t e n s i t i e s u s i n g a s t a n d a r d p r o f i l e o b t a i n e d 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 a r t of the observed X-ray l i n e b r o a d e n i n g , t a k i n g the form of an asymmetry towards h i g h e r angles, a r i s e s because o f the d u a l wavelengths of the K  /K  d o u b l e t i f the K a  r a d i a t i o n i s b e i n g used.  The K a  a  2  2  wavelength can be removed a t the source u s i n g 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 p r e s e n t s t u d y , 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 s t e p w i s e p r o c e d u r e 58  known as the Rachinger c o r r e c t i o n . S t a c k i n g f a u l t s and t w i n b o u n d a r i e s a l s o c o n t r i b u t e to the s y m m e t r i c a l l i n e b r o a d e n i n g through the Domain S i z e C o e f f i c i e n t .  Hence  the domain s i z e D must be c o r r e c t e d by u t i l i z i n g the f o l l o w i n g e x p r e s s i o n ,  where, D  = domain s i z e as determined by X-ray d a t a ,  D  = t r u e s u b s t r u c t u r e domain s i z e e x c l u d i n g f a u l t b o u n d a r i e s , F  D  = domain s i z e due t o 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 e x p r e s s e d as  (1.5a  D  F  +  B)  (  1  5  )  -  where  35  -  a = stacking fault probability, 3 = twin f a u l t  probability,  a = f.c.c. l a t t i c e  parameter.  E x p r e s s i o n s have been d e r i v e d by Warren"^ f o r a i n terms o f 61  d i s p l a c e m e n t o f t h e peak maximum and by Cohen and Wagner of  f o r 3 i n terms  t h e peak asymmetry, i . e . t h e d i s p l a c e m e n t 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 .  lattice  these e x p r e s s i o n s a r e „ PM  ,, A  (  2  1 O  6  "  ^PM }  /T  -45  >(200)  A ( 2 6  *  2  +22.5  (400)  /3  2  =  t a n 9  ^ a  CC  (Asym.)  ( 2 ( ) 0 )  = (20°) ^  CAsym.)  ( 4 0 0 )  = (26°)  (  o o )  t  a  -  n  o  ( 1 6 )  _ 6  o  ( 1 7 )  PM  (2e')  ( 2 ( J 0 )  PM  CC  ( 4 0 0 )  - (20°)  ( 4 O Q )  3tan0  o  (18)  = +14.6 3tan0  o  (19)  = -14.6  The s h i f t s o f 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 o p p o s i t e d i r e c t i o n s t o prove p o s i t i v e l y  t h e presence of s t a c k i n g  f a u l t s ; o t h e r w i s e 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 , t h e asymmetries of  o f the ( 2 0 0 ) and ( 4 0 0 ) r e f l e c t i o n s must be  o p p o s i t e s i g n t o prove p o s i t i v e l y the presence o f t w i n n i n g ; o t h e r w i s e  the asymmetry may have been due t o some i n s t r u m e n t o r d o u b l e t e f f e c t .  3.2  Computer A n a l y s i s 41  A m o d i f i e d computer programme w r i t t e n by Clegg for  the IBM  360/70  i n F o r t r a n IV  computer was used t o c a r r y out the summations t o  - 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 u n f o l d e d X-ray f u n c t i o n by complex d i v i s i o n . computer programme a l s o c a r r i e d out m a t e r i a l and (a)  The  the f o l l o w i n g o p e r a t i o n s f o r each  condition:  C o r r e c t e d f o r the a n g u l a r dependence of X-ray i n t e n s i t y ,  i n c l u d i n g t h a t of the atomic s c a t t e r i n g f a c t o r . (b)  Converted the d a t a i n t o c o r r e s p o n d i n g i n t e n s i t y v a l u e s a t  e q u a l i n t e r v a l s of sin9.' (c) S u b t r a c t e d the c o r r e s p o n d i n g background i n t e n s i t y . (d)  Applied  the R a c h i n g e r 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 (e)  component of the K  doublet.  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  i n t e n s i t y d a t a to the c e n t r o i d as o r i g i n on the s i n 0 (f)  C a r r i e d out  the i n t e g r a t i o n s and  rescaled  axis.  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 these v a l u e s of A(L) (g)  to u n i t y f o r L =  the  normalized  0.  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 r o o t 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 2 1/2 c o n d i t i o n , i . e . (e )  v s . L.,  and  v s . L, w i t h r e f e r e n c e to e q u a t i o n 2 1/2 (e )  (h)  Plotted  (i)  Calculated  f o r each m a t e r i a l  the domain s i z e c o e f f i c i e n t A  (L)  (13).  D v s . L and A (L) v s . L as g r a p h i c a l  outputs.  the coherent c r y s t a l l i t e domain s i z e s from  l a t t e r graphs a c c o r d i n g to the two  D  c r i t e r i a discussed  earlier.  the  - 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 C o 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 t h e domain s i z e and  the s t r a i n b r o a d e n i n g o f t h e X-ray l i n e .  To t h i s end, t h e work o f  62 W i l l i a m s o n and Smallman  i susually  t a k e n as t h e p r i m a r y r e f e r e n c e .  E x p r e s s i o n s (20) and (21) below have been d e r i v e d by these a u t h o r s t o 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 t h e domain s i z e and t h e s t r a i n breadth  respectively.  p  = ^  (20)  D  a n d  p  _  6 EA __ 2  II  1  _  ( 2 1 )  Gb F £n(r/ro) where p  = dislocation  density,  n  = number o f d i s l o c a t i o n s  E  = Young's modulus,  A  = a f a c t o r w h i c h depends on t h e shape o f t h e 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 v e c t o r o f t h e d i s l o c a t i o n ,  F  = dislocation interaction  r  = radius of the c r y s t a l containing the d i s l o c a t i o n ,  r  o  = d i s l o c a t i o n core  W i l l i a m s o n and Smallman  i n each f a c e o f t h e c r y s t a l l i t e  factor,  radius, have shown t h a t t h e f a c t o r s A and £ can 2  be r e l a t e d  domain,  t o t h e mean square s t r a i n o f t h e l a t t i c e e , i . e . , A£  2 =  2 e , t h a t E/G i s a p p r o x i m a t e l y 2.6, and t h a t Jin ( r / r o ) has a r e a s o n a b l e  - 38 -  v a l u e o f 4.  Taking b = 2.85 A f o r A l , e q u a t i o n  i R e 1.5  n x i10  2  P =  1  (21) can be w r i t t e n a s ,  6  ( >  =:  To a p p l y e q u a t i o n s ( 2 0 )  22  and (22) d i r e c t l y a model i s assumed i n w h i c h  t h e r e i s o n l y one d i s l o c a t i o n per domain boundary and a minimum o f dislocation interaction.  T h i s model g i v e s n = 1, F = 1 a n d t h e ;  d i s l o c a t i o n d e n s i t i e s a r e g i v e n by the f o l l o w i n g e x p r e s s i o n s :  p  p  and  \7 = 1.5 e  P g  and p  where  (23)  g  2  x 10  (24)  1 6  a r e t h e v a l u e s c a l c u l a t e d from e q u a t i o n s  (20) and (22)  r e s p e c t i v e l y u s i n g n = 1 and F = 1. In equation  (23) the domain s i z e D s h o u l d be c o r r e c t e d f o r the  c o n t r i b u t i o n t o l i n e broadening  o f s t a c k i n g f a u l t and t w i n  boundaries.  I n t h e p r e s e n t work t h e 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 u s i n g equations  (23) and (24) and then t h e 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 a c c o r d i n g to the f o l l o w i n g c r i t e r i a :  p  P  =  p p  <  p  >  K  p  p  s  p s  r  f o r random  for pile-ups  p for polygonization s  - 39 -  A pile-up c o n f i g u r a t i o n represents making F g r e a t e r P /F.  than u n i t y .  the extreme degree o f i n t e r a c t i o n  In t h i s case F = n so t h a t p =  np^ =  Then  n  = (P /P ) s  (25)  1 / 2  p  Here n i s the average number o f d i s l o c a t i o n s i n a p i l e - u p .  The t r u e  d i s l o c a t i o n d e n s i t y f o r t h i s model was c a l c u l a t e d from the e x p r e s s i o n :  p = (p„ &  p  )  1  p  /  (26)  2  On the o t h e r hand p o l y g o n i z a t i o n reduces the energy of each dislocation. point out  Thus F i s l e s s than u n i t y .  Williamson  t h a t under such c o n d i t i o n s e q u a t i o n  and Smallman  (21) should  be m o d i f i e d  to o b t a i n the t r u e d i s l o c a t i o n d e n s i t y and they show t h a t (21)  equation  can be reduced to  P = P /F s  or  p  =  ftn(  p  This equation  ^  )/&n (3 x  side u n t i l  (i.e. , F < 1).  (27)  10 /pD) ?  ^  i s b e s t s o l v e d by t r i a l  i n the r i g h t h a n d tion  10  .2  S  and e r r o r s t a r t i n g w i t h  the r e s u l t s a r e c o n s i s t e n t w i t h  p = p  g  polygoniza-  - 40 -  4.  4.1  RESULTS AND OBSERVATIONS  T e n s i l e Tests For t e n s i l e t e s t s a t 20°C and 300°C, t h e r e s u l t s f o r aluminum  and Al-4Cu w i l l be grouped t o g e t h e r because t h e s e two m a t e r i a l s were s u b j e c t e d t o s i m i l a r thermomechanical  treatments.  R e s u l t s f o r S.A.P.  w i l l be g i v e n s e p a r a t e l y .  4.1.1  Room Temperature T e s t s  4.1.1.1  Aluminum-4 Copper and Pure Aluminum  T a b l e I I summarizes t h e mean p l a n a r i n t e r p a r t i c l e s p a c i n g s and t h e mean p l a n a r p a r t i c l e r a d i u s o f Al-4Cu a f t e r v a r i o u s s i m p l e a g e i n g 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 v a l u e s .  These r e s u l t s a r e f o r m a t e r i a l s  which had r e c e i v e d no thermomechanical  treatment a f t e r s o l u t i o n  treatment.  As shown i n T a b l e I I I and F i g . 3, t h e 20°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 s o f t h e h o t - r o l l e d Al-4Cu a l l o y  t  S e r i e s B, r o s e  r a p i d l y t o 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 c o l d r o l l i n g a t 20°C.  The d a t a a r e f o r the  B S e r i e s , w h e r e i n p r i o r h o t r o l l i n g had been c a r r i e d o u t a t 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 n o t s t u d i e d  i n d e t a i l f o r t h e same r o l l i n g t r e a t m e n t s ; however, b o t h i t s y i e l d and  T a b l e 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 t h e C o r r e s p o n d i n g Y i e l d S t r e n g t h V a l u e s  at R.T. and 300°C. mean p l a n a r particle spacing, Ageing  mean p l a n a r particle radius,  D  s  - 2r  s  (D - 2r ) s s D  Treatment l o g  D (y) s  r  ( ) u  X  c  10  (  S  0.2 % o f f s e t y i e l d strength, OQ,2 (Ksi)  - 2r 2b  (y)  Cy" )  S )  RT  300°C  1  300°C, 68 mins.  0.630  0.065  0.500  5.86  19.3  8.3  300°C, 3.5 h r s .  0.660  0.068  0.524  5.66  18.7  7.5  300°C, 7.25 h r s .  0.705  0.072  0.560  5.34  18.0  7.1  300°C, 15 h r s .  1.300  0.135  1.030  3.16  13.3  5.9  300°C, 62 h r s .  1.600  0.165  1.270  2.73  10.9  4.6  450°C, 15 h r s . 300°C, 24 h r s .  2.760  0.286  2.190  1.64  8.5  3.0  450°C, 35 h r s . 300°C, 24 h r s .  4.160  0.430  3.30  1.14  7.4  2.3  - 42 -  Table I I I :  Room Temperature T e n s i l e R e s u l t s (B  Series) a0.2  U.T.S.  (Ksi)  (Ksi)  13.3  29.8  11.1  16.0  8.5  34.9  13.0  15.0  30  30.1  41.2  3.7  6.4  40  28.4  35.4  2.5  9.2 .  .num-  Al-4Cu  f o r Cold-•Rolled A l and  50  32.7  36.7  2.0  9.2  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  46.2*  58.0*  Material  % Reduction by Cold R o l l i n g  0 (Solution-treated and aged o n l y ) 0 ( A f t e r Hot  %  Elongation  Uniform  Total  Rolling)  V-i  <u  a. p< o u <t i  •n  <  0* e  1.8*  6.8*  50  11.7  12.6  0.7  9.4  B  60  12.9  13.9  0.7  7.2  <! a)  70  14.5  14.9  0.5  7.1  80  15.6  16.5  0.5  3.2  •H  PL,  data f o r f u l l y r e c r y s t a l l i z e d  aluminum.  - 43 -  Al-4Cu U.T.S.  0  20  A  Aluminum •  40  60  80  100  % R e d u c t i o n b y R o l l i n g a t 20°C. Figure  3.  20°C D a t a s h o w i n g t h e e f f e c t s o f c o l d o f A l and A l - 4 C u  (B S e r i e s ) .  rolling  on t h e s t r e n g t h  - 44 -  u l t i m a t e t e n s i l e s t r e n g t h were i n c r e a s e d by o n l y 4 K s i as t h e r e d u c t i o n by r o l l i n g a t 20°C was i n c r e a s e d from 50% t o 80%.  There was an anomalous  drop i n t h e y i e l d and u l t i m a t e s t r e n g t h s o f t h e A l - C u a l l o y  after  r e d u c t i o n s between 30% and 40%, w h i c h shows c l e a r l y i n F i g . 3.  It is  i n t e r e s t i n g t o n o t e t h a t t h e c o l d r o l l e d two-phase a l l o y shows h i g h e r d u c t i l i t y than t h e pure m e t a l a f t e r comparable amounts o f  deformation  beyond about 50% r e d u c t i o n . F i g . 4 shows t h e e f f e c t o f a n n e a l i n g a t v a r i o u s t e m p e r a t u r e s f o r a f i x e d a n n e a l i n g time o f one hour, on t h e 20°C y i e l d s t r e n g t h o f aluminum and o f A l - 4 C u a l l o y s w h i c h 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 t h e A, B and D s e r i e s a r e i n c l u d e d . plotted  Data has a l s o been  f o r two c o l d - r o l l e d aluminum m a t e r i a l s o f d i f f e r e n t  prior  thermomechanical h i s t o r y , b u t t h e r e 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 t o a n n e a l i n g . F i g . 4 r e v e a l s t h a t 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 s t r e n g t h s a f t e r b e i n g 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 d e f o r m a t i o n a t t a i n e d a t t h i s stage.  h i s t o r y had l i t t l e e f f e c t on t h e s t r e n g t h  Moreover, t h e responses o f t h e t h r e e m a t e r i a l s  to a n n e a l i n g 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 o f y i e l d s t r e n g t h a t 20°C a f t e r one hour o f a n n e a l i n g .  S i m i l a r p l o t s were  o b t a i n e d i f t h e 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 t h e y i e l d strength.  An i n t e r e s t i n g f e a t u r e o f t h e d a t a o f F i g . 4 i s t h a t t h e r e  i s a steady d e c r e a s e i n s t r e n g t h o f Al-4Cu w i t h i n c r e a s e i n a n n e a l i n g temperature i n t h e range 50-250°C, whereas pure aluminum s u f f e r s  very  l i t t l e change i n s t r e n g t h up t o an a n n e a l i n g temperature o f 250°C. Above 250°C, t h e curves o f F i g . 4 a r e s i m i l a r i n n a t u r e , i n d i c a t i n g a  - 45 44  I  F i g u r e 4.  :  20°C Data showing the e f f e c t s of a n n e a l i n g temperature on the y i e l d s t r e n g t h of Al-4Cu (B S e r i e s ) v s . pure aluminum a f t e r 70% C.W.  - 46 -  r a p i d decrease i n s t r e n g t h w i t h i n c r e a s i n g a n n e a l i n g temperature up to 350°C. F i g . 5 shows t y p i c a l 20°C t e n s i l e e l o n g a t i o n (uniform) v a l u e s c o r r e s p o n d i n g to the y i e l d s t r e n g t h d a t a of F i g . 4.  In case of pure  worked aluminum, the e l o n g a t i o n remains at a c o n s t a n t low l e v e l a n n e a l i n g a t temperatures up to and i n c l u d i n g 250°C. i n the a n n e a l i n g temperature  cold  after  Further increases  cause a r a p i d and l a r g e r i s e i n the  e l o n g a t i o n v a l u e . For the c o l d - r o l l e d A l - C u two-phase a l l o y s ,  the  e l o n g a t i o n 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 a n n e a l i n g at a n n e a l i n g temperatures temperatures produced  i n the range of 50-200°C.  A n n e a l i n g at h i g h e r  a marked i n c r e a s e i n e l o n g a t i o n , a l t h o u g h the  a b s o l u t e v a l u e s a t t a i n e d were a p p r e c i a b l y lower f o r the a l l o y than f o r the pure m e t a l .  There was  a g a i n 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 S e r i e s A, B, and D; o n l y S e r i e s B d a t a are p l o t t e d . Other a n n e a l i n g experiments a n n e a l i n g temperature hours.  i n v o l v e d the use of a c o n s t a n t  of 300°C, w i t h v a r y i n g times i n the range  0-20  R e s u l t s of such experiments are shown i n F i g . 6 f o r a S e r i e s  A two-phase Al-4Cu a l l o y which had been reduced 70% by c o l d The form of those curves was f o r pure aluminum.  rolling.  s i m i l a r f o r S e r i e s A and B, as w e l l as  However, t h e r e were some q u a n t i t a t i v e d i f f e r e n c e i n  the response of the 20°C s t r e n g t h of the d i f f e r e n t m a t e r i a l s to a n n e a l i n g time, as r e v e a l e d i n F i g . 7 f o r y i e l d s t r e n g t h and i n F i g . 8 f o r U.T.S. S p e c i f i c a l l y , t h e r e were d i f f e r e n c e s i n the r a t e of response to a n n e a l i n g at 300°C f o r the d i f f e r e n t m a t e r i a l s , and i n the " e n d - p o i n t " s t r e n g t h v a l u e s reached i n a l l cases a f t e r about 6 hours of a n n e a l i n g .  In the  - 47 -  i 50  .  ' 100  ' 1.10  ' 200  I 250  A n n e a l i n ) : 'IVmpt.'rat ui"e ,  F i g u r e 5.  I  1  300  350  1 400  °C.  2CTC Data showing t h e e f f e c t s o f a n n e a l i n g  temperature on  the u n i f o r m e l o n g a t i o n o f Al-4Cu (B S e r i e s ) v s . pure aluminum a f t e r 70% C.W.  Annealing F i g u r e 6.  Time a t 300°C, h r s .  20°C Data showing t h e e f f e c t s o f a n n e a l i n g time 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 (A S e r i e s ) a f t e r 70% C.W.  CO  8 10 12 14 A n n e a l i n g Time a t 300°C, h r s . F i g u r e 7.  20°C Data showing t h e e f f e c t s of a n n e a l i n g aluminum a f t e r 70% C.W.  time a t 300°C on the y i e l d  16  18  20  s t r e n g t h o f A l - 4 C u v s . pure  22  CO  H  15©-  10  O  B  ©  A  •  c  •  AAL -3  e = 6.25 x 10  ±  2  F i g u r e 8.  ± 4  6  8  ± 10  ±  -1 min  12 14 A n n e a l i n g Time a t 300°C, h r s .  16  18  ±  20  20°C Data showing the e f f e c t s o f a n n e a l i n g time a t 300°C on the U.T.S. o f A l - 4 C u v s . pure aluminum a f t e r 70% C.W.  - 51 -  0.2%  f l o w s t r e s s v a l u e s , t h e r e was some d i f f e r e n c e i n t h e b e h a v i o u r  of S e r i e s A and B m a t e r i a l s , i n s p i t e o f t h e apparent of t h e i r t h e r m a l and m e c h a n i c a l h i s t o r i e s . annealing  similarities  The S e r i e s C a l l o y , f o r w h i c h  a t 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  s t e p , shows remarkably s i m i l a r b e h a v i o u r t o S e r i e s A and B a l l o y s i n F i g s . 7 and 8.  The s t r e n g t h o f t h e S e r i e s C a l l o y was h i g h e r  that of other Al-Cu m a t e r i a l s a f t e r annealing  than  f o r 6 o r more hours a t  300°C.  4.1.1.2  S.A.P.  Room temperature t e n s i l e d a t a f o r c o l d - r o l l e d S.A.P.'are summarized i n T a b l e IV and i n F i g . 9.  T a b l e IV:  A f t e r h o t r o l l i n g and b e f o r e  cold  Room-Temperature 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  % Cold Work  a  n  9  U.T.S.  (Ksi)  (Ksi)  29.5  10  rolling  S.A.P.  % Elongation Uniform  Total  37.6  4.3  10.3  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  0 ( A f t e r Hot R o l l i n g )  - 52 -  R.T  O a  50  0.2  9 U.T.S. e  -3 -1 = 6.25 x 10 min  45  300°C  25 •H  0.2 ©  20  10 F i g u r e 9.  U.T.S.  20  30 40 50 60 % R e d u c t i o n by R o l l i n g a t 20°C  70  20°C and 300°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 S.A.P.  - 53 -  S.A.P. had h i g h 20°C s t r e n g t h and low t e n s i l e e l o n g a t i o n compared t o Al-4Cu.  However, t h e response o f t h e s t r e n g t h o f S.A.P. t o c o l d  r o l l i n g was much s m a l l e r than t h a t o f t h e A l - C u a l l o y m a t e r i a l s , as seen by comparing T a b l e s I I I and IV. Moreover,  the absolute values of  b o t h y i e l d and u l t i m a t e s t r e n g t h s i n A l - C u were a p p r e c i a b l y h i g h e r a f t e r heavy c o l d w o r k i n g than i n S.A.P. a f t e r comparable  deformation.  E l o n g a t i o n v a l u e s f o r t h e two types o f a l l o y s were s i m i l a r  after  s i m i l a r r e d u c t i o n s by c o l d r o l l i n g , and were h i g h e r than those e x h i b i t e d by pure aluminum. The i s o t h e r m a l a n n e a l i n g b e h a v i o u r o f S.A.P. was v e r y d i f f e r e n t from t h a t o f Al-4Cu m a t e r i a l s .  An a n n e a l i n g t r e a t m e n t o f a few hours  at 300°C was s u f f i c i e n t t o d e c r e a s e t h e y i e l d s t r e n g t h o f 70% c o l d worked Al-4Cu by about 50%.  I n t h e case o f 50% c o l d worked S.A.P.,  however, 72 hours o f a n n e a l i n g a t 300°C d i d n o t produce any d e t e c t a b l e decrease i n y i e l d o r u l t i m a t e t e n s i l e s t r e n g t h .  I n f a c t , when c o l d - r o l l e d  S.A.P. was annealed a t 540°C f o r 24 h o u r s , t h e y i e l d s t r e n g t h d e c r e a s e d by o n l y 1400 p s i (from 34,900 p s i t o 33,500 p s i ) , t h e U.T.S. decreased by 2200 p s i (f rom 42,400 p s i t o 40,200 p s i ) , and t h e d u c t i l i t y was n o t a l t e r e d at a l l .  4.1.2  300°C T e s t s  4.1.2.1  Aluminur..-4 Copper Pur el-Aluminum  F i g s . 10 and 11 show t h e t y p i c a l response o f t h e h i g h - t e m p e r a t u r e (300°C) t e n s i l e p r o p e r t i e s o f an Al-4Cu a l l o y t o s t a t i c a n n e a l i n g 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 r e h e a t e d t o 300°C f o r t e n s i l e  0 F i g u r e 10.  2  4  6 8 10 12 14 16 18 A n n e a l i n g Time a t 300°C, h r s . 300°C Data showing the e f f e c t s o f a n n e a l i n g time 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 (A S e r i e s ) a f t e r 70% C.W.  _  « 2  I 4  I 6  I  I t 8 10 12 A n n e a l i n g time a t 300°C, h r s .  I  I  14  16  2  lo 18  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 time 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 70% C.W.  - 56 -  testing.  As seen from t h e f i g u r e s , s t a t i c a n n e a l i n g caused an i n c r e a s e  i n t h e y i e l d s t r e n g t h o f t h e cold-worked p r o d u c t and a decrease i n b o t h the U.T.S. and t h e u n i f o r m e l o n g a t i o n .  A f t e r about 6 hours o f a n n e a l i n g  t h e r e was v e r y l i t t l e change i n s t r e n g t h and d u c t i l i t y . Q u i t e a d i f f e r e n t response t o a n n e a l i n g was observed of t h e 300°C p r o p e r t i e s o f pure aluminum. 12, 13, and 14, i n w h i c h  i n t h e case  T h i s i s r e v e a l e d by F i g s .  t h e 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  u n i f o r m e l o n g a t i o n a t 300°C, r e s p e c t i v e l y , a r e compared f o r A l - C u m a t e r i a l s and pure aluminum as a f u n c t i o n o f s t a t i c a n n e a l i n g A l l t h e m a t e r i a l s had been c o l d r o l l e d 70% b e f o r e  time.  annealing.  S e v e r a l o b s e r v a t i o n s a r e o f p a r t i c u l a r i n t e r e s t i n these  plots.  F i r s t , t h e y i e l d s t r e n g t h o f a s - r o l l e d pure aluminum i s h i g h e r a t 300°C than t h a t o f any o f the A l - C u m a t e r i a l s .  The c o r r e s p o n d i n g  e l o n g a t i o n o f t h e pure m e t a l i s r e l a t i v e l y v e r y low. A f t e r s t a t i c  anneal-  i n g f o r more than one hour a t 300°C, however, t h e h i g h temperature y i e l d s t r e n g t h o f pure aluminum f a l l s f a r below t h a t o f t h e a l l o y s .  After 4  hours o r more o f a n n e a l i n g , t h e 300°C e l o n g a t i o n o f aluminum i s a l s o t h e h i g h e s t o f t h i s group o f m a t e r i a l s .  Another o b s e r v a t i o n from F i g s . 12  and 13 i s t h a t the o r d e r o f the t h r e e A l - C u 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 t o t h a t 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 t h a t t h e dependence o f 300°C y i e l d s t r e n g t h on a n n e a l i n g time f o r pure aluminum i s i n the o p p o s i t e d i r e c t i o n from t h a t o f the A l - C u  alloys.  I n Table V t h e 300°C y i e l d s t r e n g t h o f t h e c o l d worked aluminum and a B S e r i e s A l - C u a l l o y a r e compared.  The h i g h temperature s t r e n g t h o f  the pure m e t a l i s i n c r e a s e d by i n c r e a s i n g p r i o r c o l d work, whereas t h e o p p o s i t e i s t r u e , f o r t h e two-phase a l l o y .  O  B  9  A  »  c  m  AAL  e =  6.25 x 10 \ i i n  CO  10 12 14 A n n e a l i n g Time a t 300°C, h r s . F i g u r e 12.  16  18  20  300°C Data showing the e f f e c t s o f a n n e a l i n g time a t 300°C on t h e y i e l d s t r e n g t h o f A l - 4 C u v s . pure aluminum a f t e r 70% C.W.  F i g u r e 13.  10 12 14 A n n e a l i n g Time a t 300°C, h r s . 300°C Data showing the e f f e c t s o f a n n e a l i n g time a t 300°C on t h e U.T.S. o f A l - 4 C u v s . pure aluminum a f t e r 70% C.W.  — 60 -  T a b l e V:  Comparison o f 300°C Y i e l d S t r e n g t h V a l u e s f o r C o l d - R o l l e d A l and Al-4Cu. % C o l d Work  °0.2 Al  ( K S ± )  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 t h e B S e r i e s ) , w h i c h were c o l d worked from  30% t o 80% and then annealed a t 300°C f o r d i f f e r e n t t i m e s , a l l f o l l o w e d the same t r e n d s 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 ] . R e s u l t s f o r t h e d i f f e r e n t amounts o f p r i o r d e f o r m a t i o n 15(a)  to (e).  deformation  are plotted i n Figs.  The o n l y n o t a b l e e f f e c t o f v a r y i n g t h e p r i o r c o l d  was i n the magnitude o f the i n c r e a s e i n y i e l d s t r e n g t h w h i c h  r e s u l t e d from s t a t i c a n n e a l i n g a t 300°C.  T h i s i s shown i n T a b l e V I .  The p e r c e n t a g e i n c r e a s e i n 300°C y i e l d s t r e n g t h due t o s t a t i c  annealing  decreased w i t h a d e c r e a s e i n t h e amount o f p r i o r c o l d work, w i t h t h e n o t a b l e e x c e p t i o n o f t h e 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 n o t e d  e a r l i e r i n r e g a r d t o F i g . 3, t h e response o f t h e a l l o y t o c o l d work behaved anomalously i n t h e range 30-40% r e d u c t i o n . T e n s i l e r e s u l t s a t 300°C f o r A l - 4 C u m a t e r i a l s s u b j e c t e d t o v a r i o u s amounts o f p r i o r c o l d work a r e summarized i n T a b l e V I I .  This t a b l e  i n c l u d e s f o r comparison t h e d a t a o b t a i n e d f o r over-aged A l - 4 C u which had  12  O  Uniform  10  Elongation  a o •u ca oo a o  •H  w e M o  cn G  i  3  a a>  6 Annealing Figure  15a.  300°C Data showing (B S e r i e s ) a f t e r  the e f f e c t s  30%  C.W.  8 10. 12 Time at 300 C, h r s .  of a n n e a l i n g  14  16  time at 300°C on the a n n e a l i n g  b e h a v i o u r o f Al-4Cu  A l - 4 C u (B S e r i e s ) a f t e r 40% C.W.  12  0  °0.2  ©  U.T.S.  £  Uniform E l o n g a t i o n = 6.25  x 10  -3  min  -1  8 10 12 A n n e a l i n g Time at 300°C, h r s , F i g u r e 15c.  14  16  300°C Data showing the e f f e c t s of a n n e a l i n g time at 300°C on the a n n e a l i n g b e h a v i o u r Al-4Cu a f t e r 50% C.W.  14  0  °0.2  12  ©  U.T.S.  £  Uniform E l o n g a t i o n  -3 -1 e = 6.25 x 10 min  10  ti 8 -S  ON  4>  4-1  ca 60  ti o  r-i 6  g o •rl  ti  ;=>  "8"  JL  6 Annealing F i g u r e 15d.  _L 8 10 12 Time a t 300°C, h r s .  14  16  300°C Data showing the e f f e c t s o f a n n e a l i n g time 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 (B S e r i e s ) a f t e r 60% C.W.  o f Al-4Cu  14  O  o  0.2 12  ©  Uniform  e = 6.25  Elongation  x 10  -3  min  -1  10  c o M  c  o  •H W 6  -o  g o  -o  •H  C  r3  -a-  JL  Figure  15e.  1  8 10 12 16 14 Annealing Time at 300°C, h r s . 300°C Data showing the e f f e c t s of a n n e a l i n g time a t 300°C on the a n n e a l i n g (B S e r i e s ) a f t e r 80% C.W. 2  4  6  0b e h a v i o u r of Al-4Cu  ON  - 66 -  Table VI:  E f f e c t of S t a t i c Annealing  on t h e 300°C Y i e l d  of A l - 4 C u Cold-Worked P r e v i o u s l y by V a r i o u s % °0.2 ° ° Cold Work Worked M a t e r i a l in Ksi f  C  l  d  Maximum A f t e r Annealing (Ksi)  Strength  Amounts  % I n c r e a s e i n A n n e a l i n g Time at 300°C ( h r s ) a due t o Corresponding annealing to max a „ Q  2  n  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 a t a l l .  Few c o n s i s t e n t t r e n d s a r e observed i n  these d a t a f o r t h e a s - c o l d worked a l l o y .  The over-aged A l - 4 C u a l l o y  a t 300°C i s r e l a t i v e l y s t r o n g b u t o f low d u c t i l i t y .  Hot r o l l i n g o f  the over-aged a l l o y d e c r e a s e d t h e 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 e l 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 d e c r e a s e i n b o t h t h e 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 c o r r e s p o n d i n g  increase i n elongation.  As documented e a r l i e r i n F i g s . 10-12, t h e 300°C y i e l d s t r e n g t h o f the c o l d worked a l l o y s c o u l d 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 a n n e a l i n g , b u t i t c o u l d n o t be r e s t o r e d t o t h e v a l u e o f t h e over-aged a l l o y even a f t e r 15 hours o f a n n e a l i n g a t 300 C.  - 67 T a b l e V I I : 300°C T e n s i l e R e s u l t s f o r Cold-- R o l l e d A l - 4 C u % Cold Work  °0.2 (Ksi)  U.T.S. (Ksi)  % Elongation Uniform  Total 19.0  0 only 0 ppts.  5.89  6.31  1.60  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. a r e summarized i n T a b l e V I I I and i n F i g . 9.  Of i n t e r e s t a r e t h e h i g h a b s o l u t e v a l u e s  of t h e 300°C s t r e n g t h p r o p e r t i e s compared t o aluminum and Al-4Cu. 300°C e l o n g a t i o n i s c o r r e s p o n d i n g l y much lower f o r S.A.P.  The  I n common  w i t h A l - C u , t h e s t r e n g t h o f S.A.P. a t 300°C i s lowered by p r i o r c o l d work.  However, i n t h e case o f S.A.P. t h e r e i s a p r o g r e s s i v e e f f e c t o f  i n c r e a s i n g amounts o f p r i o r d e f o r m a t i o n  (see F i g . 9 ) .  The e f f e c t o f s t a t i c a n n e a l i n g , a f t e r c o l d r o l l i n g , on t h e 300°C t e n s i l e p r o p e r t i e s o f S.A.P. s t r i p w h i c h had r e c e i v e d 50% p r i o r c o l d r e d u c t i o n i s demonstrated i n T a b l e I X .  S t a t i c a n n e a l i n g has r a i s e d t h e  - 68 -  T a b l e 'V I I I :  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.  % Cold Work  U.T.S.  °0.2 (Ksi)  (Ksi)  % Elongation Uniform  Total  12. 6  14.95  2.2  10  11. 0  13.88  3.4  -  20  10.15  13.87  3.4  7.6  0 ( A f t e r Hot R o l l i n g )  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  T a b l e IX:  E f f e c t o f S t a t i c A n n e a l i n g on t h e 300°C T e n s i l e P r o p e r t i e s of 50% C o l d - R o l l e d S.A.P •  % Cold  Annealing Treatment  °0.2 (Ksi)  12.60  U.T.S.  % Elongation  (Ksi)  %', I n c r e a s e i n Strength  Uniform  Total  a  14.95  2.2  -  -  12.80  3.7  6.7  -  0.2  U  ' ' T  S  0  None  50  None  50  300°C, 48 h r s .  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 h r s .  11.82  13.60  1.2  7.5  23.0  6.0  50  540°C, 24 h r s .  12.42  13.65  1.0  7.0  30.0  6.5  9.57  - 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 a n n e a l almost t o i t s value f o r the hot r o l l e d condition.  The U.T.S. v a l u e s a r e a f f e c t e d i n  a s i m i l a r manner, b u t t o a s m a l l e r degree.  T h i s type o f b e h a v i o u r  had been observed i n t h e case o f A l - 4 C u , except t h a t i n t h a t case s t a t i c a n n e a l i n g had caused a l o w e r i n g o f t h e 300°C U.T.S.  The o t h e r n o t a b l e  d i f f e r e n c e between A l - C u and S.A.P. l i e s i n t h e magnitude o f t h e percentage i n c r e a s e i n h i g h temperature y i e l d s t r e n g t h due t o s t a t i c annealing.  S i x t o e i g h t hours o f h e a t i n g a t 300°C r a i s e d t h e 300°C  y i e l d s t r e n g t h o f c o l d - r o l l e d A l - 4 C u by 28% and 73% a f t e r c o l d r e d u c t i o n s 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 o f h e a t i n g a t  300°C r a i s e d t h e 300°C y i e l d s t r e n g t h of S.A.P. by o n l y 19% f o r a p r i o r c o l d w o r k i n g r e d u c t i o n o f 50%. H e a t i n g t h e c o l d - r o l l e d S.A.P. sheet f o r 24 hours a t 540°C improved t h e 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 t h a t t h e h i g h e r h e a t i n g temperature was more e f f e c t i v e i n i m p r o v i n g t h e e l e v a t e d temperature p r o p e r t i e s o f S.A.P.  T h i s type o f  42 b e h a v i o u r has p r e v i o u s l y been observed by Towner  f o r A.P.M. p r o d u c t s .  The 300°C u n i f o r m e l o n g a t i o n s o f 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%. e l o n g a t i o n never exceeded 10%.  The c o r r e s p o n d i n g t o t a l  By c o n t r a s t , t h e 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 h i g h e r d u c t i l i t y b o t h i n cold-worked and cold-worked-and-annealed 4.2  conditions.  X-Ray D i f f r a c t i o n Graphs o f p e r c e n t 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 v e r s u s  l a t t i c e d i s t a n c e were f i r s t p l o t t e d by t h e computer.  R i s i n g regions of  the p l o t s a t l a r g e v a l u e s o f (L) were d i s r e g a r d e d as b e i n g a t t r i b u t a b l e  - 70 -  t o i n s t a b i l i t y i n t h e F o u r i e r components. "hook e f f e c t " a t low v a l u e s the graphs.  However, a c o r r e c t i o n f o r t h e  o f (L) was n o t a p p l i e d b e f o r e p l o t t i n g  The r e s u l t s a r e shown i n F i g s . 16-20 w h i c h show t h e e f f e c t  of v a r i o u s thermo-mechanical t r e a t m e n t s on t h e 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 e s t i m a t e s  o f t h e domain s i z e  from t h e computer a n a l y s i s a r e g i v e n i n T a b l e X. contains  obtained  This table also  t h e r o o t mean square s t r a i n e x p r e s s e d as p e r c e n t s t r a i n f o r o  o  o  d i s t a n c e s o f 50 A, 100 A and 150 A.  I n most cases t h e s t r a i n s quoted  o  o  f o r 50 A a r e t h e peak v a l u e s  occurring  near t o 50 A; however, i n some o  cases t h e peak o c c u r r e d  a t d i s t a n c e s g r e a t e r than 150 A (see F i g s . 16 and  17). As d i s c u s s e d  e a r l i e r , domain s i z e e s t i m a t e s  should be c o r r e c t e d where  n e c e s s a r y f o r t h e 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 t w i n  faults.  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 e q u a t i o n s (16) and  (17) and t h e t w i n f a u l t p r o b a b i l i t y B from e q u a t i o n s (18) and ( 1 9 ) .  However, i n no case c o u l d t h e presence o f s t a c k i n g f a u l t s and t w i n n i n g be p r o v e d p o s i t i v e l y  and hence the domain s i z e e s t i m a t e s  were n o t  corrected. C a l c u l a t i o n s were made o f t h e d i s l o c a t i o n d e n s i t y p d e r i v e d P the domain s i z e o r p a r t i c l e s i z e [ e q u a t i o n density p  g  (23)] and t h e d i s l o c a t i o n  d e r i v e d from t h e mean square l a t t i c e s t r a i n [ e q u a t i o n  From a knowledge o f t h e s e two v a l u e s  from  (24)J.  t h e 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 t h e c r i t e r i a mentioned i n s e c t i o n 3.3.  Table XI  summarizes t h e d i s l o c a t i o n d e n s i t i e s and t h e 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 p e t 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 i n c l u d e d i n t h i s t a b l e t o p r o v i d e a  - 71 -  0.20  1.  A l , 70% C.W.  2.  A l , 70% C.W. + A n n .  3.  Al-4Cu,  Over-aged  4.  Al-4Cu,  Hot R o l l e d  5.  Al-4Cu,  50% C.W.  6.  Al-4Cu,  50% C.W. + A n n .  7.  Al-4Cu,  70% C.W.  8.  Al-4Cu,  70% C.W. + A n n .  F i g u r e 16. V a r i a t i o n o f l a t t i c e  strain  w i t h l a t t i c e d i s t a n c e f o r Al-4Cu (B S e r i e s ) and pure aluminum i n v a r i o u s thermo-mechanical c o n d i t i o n s .  1.  S.A.P.,  As R e c e i v e d  2.  S.A.P.,  Hot  Rolled  3.  S.A.P.,  50%.  C.W.  4.  S.A.P..  50% C.W. + A n n .  F i g u r e 17. V a r i a t i o n o f l a t t i c e  strain  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 thermo-mechanical c o n d i t i o n s .  200  300 Lattice  Distance  400  500 A  - 72 -  F i g u r e 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  lattice  distance  f o r Al-4Cu (B S e r i e s ) and pure aluminum i n v a r i o u s thermomechanical c o n d i t i o n s .  F i g u r e 19. .P.,  Hot  ..P.,  50% C.W. +  V a r i a t i o n o f domain s i z e  coefficient  Rolled  with l a t t i c e  distance  Annealed  for  S.A.P. i n v a r i o u s thermo-  mechanical c o n d i t i o n s . S.A.P.,  As Received  S.A.P.,  50KC.W.  J  , 50*  C.W.  L  F i g u r e 20. V a r i a t i o n  o f domain s i z e  coefficient with l a t t i c e  distance  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. 300  400  - 74 -  T a b l e X:  Domain S i 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  Material Condition  Domain Size D in A  % S t r a i n a t D i s t a n c e (L) 5 5 5— SO A 100 A 150 A  A l , C o l d r o l l e d 70%  >1000  0.136  0.09  0.08  A l , C o l d r o l l e d 70% and annealed a t 300°C f o r 6 h r s .  >1000  0  0  0  A l - 4 C u , Over-aged  >1000  0  0  0  A l - 4 C u , Hot r o l l e d  >1000  0.12  0.09  0.09  900  0.23  0.14  0.13  0  0.06  0.08  0.13  0.15  0.14  0  0  0  A l - 4 C u , C o l d r o l l e d 50% A l - 4 C u , Cold r o l l e d 50% and annealed a t 300°C f o r 4 h r s . A l - 4 C u , C o l d r o l l e d 70% A l - 4 C u , C o l d r o l l e d 70% and annealed a t 300°C f o r 4 h r s .  >1000 860 >1000  S.A.P., as r e c e 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., C o l d r o l l e d 50%  780  0.19  0.14  0.13  S.A.P., C o l d r o l l e d 50% and annealed a t 540°C f o r 24 h r s .  900  0.16  0.13  0.12  T a b l e X I : 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 Material  Condition  D O  A  ( £  -3 (cm,cm )  >50 A  x 100  s (cm,cm 3) p  True d i s location density,p, cm, cm 3  Dislocation Configurations  0.2 20°C ( K s i )  a  a  t  -  A l , C o l d r o l l e d 70%  >1000 (1470)  10  1.4x10  0.136  2.8x10  10  2x10  A l , Cold r o l l e d 70% and annealed a t 300°C f o r 6hrs.  >1000  0  ^4x10  A l - 4 C u , Over-aged  >1000  0  ^10  A l - 4 C u , Hot r o l l e d A l - 4 C u , C o l d r o l l e d 50% A l - 4 C u , C o l d r o l l e d 50% and a n n e a l e d a t 300°C for 4 hrs. A l - 4 C u , C o l d r o l l e d 70% A l - 4 C u , C o l d r o l l e d 70% and a n n e a l e d a t 300°C for 4 h r s . S.A.P., As r e c e i v e d S.A.P., Hot r o l l e d  >1000 (1330) 900  10  1.7x10  10  3.7x10  960  7.9xl0  1 0  8  2.2x10 10  14.5  Polygonization  2.4  Polygonization  13.3  Pile-up/random  8.5  7.9x10  10  Pile-up/random  32.7  Polygonization  12.9  Polygonization  41.1  Polygonization  15.0  Polygonization  32.0  Polygonization  29.5  Pile-up/random  34.9  Polyg./random  33.5  0.23 ^2x10' 0 4.1x10  10  3.4x10  10  4xl0  1 0  -10  n  0.15 ^3x10'  >1000 940  1 0  8  Pile-up/random  0.12  >1000 860  2.2xl0  10  0 3.4x10 3.3x10  S.A.P., C o l d r o l l e d 50%  780  4.9x10  S.A.P., C o l d r o l l e d 50% and annealed a t 540°C f o r 24 h r s .  900  3.7x10  10 10 10 10  0.13  2.5x10  0.12  2.2x10  0.19  6.0x10  0.16  3.8x10  10 10 10 10  4-5x10 4-5x10 5.4x10 4-5x10  10 10 10 10  - 76 -  source of rough e s t i m a t e s materials.  of the d i s l o c a t i o n d e n s i t i e s of annealed  I n 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  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 g i v e n by p = no^. polygonized  For g  f a c t o r F < 1 [see e q u a t i o n  (22)].  1 f a c t o r s are e q u i v a l e n t to —. r  p  > P  a n s  Thus, i n e q u a t i o n  Clegg  41  d  the i n t e r a c t i o n (27) the l o g a r i t h m i c  suggested t h a t 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 the maximum v a l u e t h a t p c o u l d take would approximately  5p  also greater  than  s  t o be 4.1x10  but  s  f o r A l - 4 C u , reduced 70% by c o l d r o l l i n g , 10  was  -3 cm,cm  .  The  s t r a i n value obtained  l e s s than t h a t of 50% c o l d worked A l - 4 C u , and  to t h a t of S.A.P.  be  t h 3 t p would be not o n l y g r e a t e r than p  and  In Table X I , p  s t u d i e s was  a  c o n f i g u r a t i o n , t h e t r u e d e n s i t y i s g i v e n by p = p /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  estimated  true  from X-ray  comparable  I n view of the s i m i l a r i t y of domain s i z e s i n t h e s e  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 A l - 4 C u i s h i g h . may  It  be concluded t h a t 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 error.  i n the h e a v i l y deformed A l - C u a l l o y i s f o r some r e a s o n i n  The  assigned  dislocation density, p 11  the range 0.4  to 1x10  , f o r t h i s m a t e r i a l has -3  cm.cm  been  i n T a b l e X I , t o attempt to  make the t r u e 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 f o u r S.A.P. m a t e r i a l s was  of the o r d e r  of  o  800 to 1000 A. T h e i r s t r a i n d i s t r i b u t i o n s were a l s o v e r y 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 d e n s i t y of S.A.P., reduced 50% by c o l d r o l l i n g , was 10 to be 5.4x10  estimated  ~3 cm.cm  .  S i n c e p > p^  f o r a polygonized  configuration,  - 77 -  p f o r t h e o t h e r t h r e e S.A.P. m a t e r i a l s h a v i n g  a polygonized  configuration  10 -3 can be assumed t o be i n t h e range 4 t o 5 x l O cm.cm I n t h e case o f annealed aluminum and A l - 4 C u 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 g r e a t e r than 1000 A. determination  of  or p  g  Thus  accurate  was n o t p o s s i b l e and t h e d i s l o c a t i o n c o n f i g u r a -  t i o n c o u l d n o t be judged from the v a l u e s o f p^ and p . g  graphy i n d i c a t e d a h i g h l y p o l y g o n i z e d  However,  metallo-  s u b s t r u c t u r e f o r annealed  aluminum and A l - 4 C u (see S e c t i o n 4.3) and t h i s was i n s e r t e d i n T a b l e X I . A l t h o u g h t h e t r u e d i s l o c a t i o n d e n s i t y o f these annealed m a t e r i a l s c o u l d n o t be determined from t h e X-ray a n a l y s i s , a rough e s t i m a t e be made from e q u a t i o n  could  (30) from a knowledge o f t h e e x p e r i m e n t a l l y  measured 20°C y i e l d s t r e n g t h s and t h e y v a l u e e v a l u a t e d t h e s i s i n S e c t i o n s 5.1.1 and 5.1.2.2.  l a t e r i n the  I n t h e case o f annealed A l - 4 C u  a l l o y s , t h e 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 t o Orowan h a r d e n i n g and s o l i d s o l u t i o n h a r d e n i n g were s u b t r a c t e d from t h e r e s p e c t i v e measured y i e l d s t r e n g t h s t o p r o v i d e a b a s i s f o r d e t e r m i n i n g  the true  dislocation density. J u d g i n g from s e v e r a l s o u r c e s t a b u l a t e d by W i l l i a m s o n  62 and Smallman, 8 —3  the t r u e d i s l o c a t i o n d e n s i t y o f as-aged Al-4Cu was p l a c e d a t 10  cm.cm  These e s t i m a t e d v a l u e s o f t r u e d i s l o c a t i o n d e n s i t y (p) f o r pure aluminum, A l - 4 C u and S.A.P. a r e t a b l u l a t e d i n T a b l e X I .  - 78 -  4.3  Metallography  4.3.1  O p t i c a l Microscopy The m i c r o s t r u c t u r e s of A l and Al-4Cu a f t e r d i f f e r e n t m e c h a n i c a l  and t h e r m a l t r e a t m e n t s were examined by o p t i c a l m i c r o s c o p y .  F i g . 21  i s a t y p i c a l o p t i c a l p h o t o m i c r o g r a p h o f an over-aged Al-4Cu a l l o y which was aged a t 300°C f o r 15 h o u r s . equiaxed g r a i n s .  This micrograph reveals very l a r g e  The average g r a i n s i z e i s about 800 . u  Precipitate-  f r e e zones (PFZ) a r e observed a d j a c e n t t o g r a i n b o u n d a r i e s .  The g r a i n  boundary p r e c i p i t a t e s and t h e f i n e n a t u r e o f t h e d i s p e r s i o n o f t h e second phase C u A l  2  p a r t i c l e s has been r e v e a l e d a t h i g h e r m a g n i f i c a t i o n s .  F i g s . 22 t o 25 a r e o p t i c a l m i c r o g r a p h s o f the A l - 4 C u a l l o y  cold-  r o l l e d 70% ( F i g s . 22 and 2 3 ) , and a f t e r s t a t i c a n n e a l i n g a t 300°C f o r 8 hours ( F i g s . 24 and 25).  F o r t h e sake o f comparison, m i c r o g r a p h s o f  b o t h t h e A s e r i e s and B s e r i e s o f a l l o y s a r e i n c l u d e d .  I n b o t h cases  d e f o r m a t i o n bands were observed i n each g r a i n and t h e g r a i n s were e l o n g a t e d i n the d i r e c t i o n o f r o l l i n g . I n t h e annealed c o n d i t i o n a p p a r e n t l y s t r a i n - f r e e r e c r y s t a l l i z e d g r a i n s were found i n t h e m i c r o s t r u c t u r e o f t h e s e r i e s A a l l o y ( F i g . 25) and these g r a i n s seemed t o have been n u c l e a t e d a t t h e o r i g i n a l g r a i n b o u n d a r i e s .  Such r e c r y s t a l l i z e d  g r a i n s were n o t c l e a r l y o b s e r v a b l e i n t h e S e r i e s B a l l o y a f t e r 8 hours of a n n e a l i n g a t 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 t o 34 a r e t r a n m i s s i o n e l e c t r o n micrographs o f pure aluminum i n t h e c o l d r o l l e d and c o l d r o l l e d - a n d - a n n e a l e d c o n d i t i o n s .  - 79 -  F i g u r e 22.  O p t i c a l M i c r o g r a p h of  Al-4Cu (B S e r i e s ) a f t e r 70% C.W., 23X.  F i g u r e 23. Al-4Cu 23X.  O p t i c a l M i c r o g r a p h of  (A S e r i e s ) a f t e r 70%  C.W.,  F i g u r e 25.  O p t i c a l micrograph o f Al-4Cu  (A S e r i e s )  cold-rolled  70% and annealed at 300°C f o r 8 h r s . , 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%.  W e l l - d e f i n e d c e l l s are present a f t e r  this  l a r g e degree of d e f o r m a t i o n ; and the c e l l d i a m e t e r i s about 0.76  u.  The c e l l s were b o t h e l o n g a t e d and e q u i a x e d i n shape ( F i g s . 26a and as commonly observed by o t h e r w o r k e r s . of  '  The c e l l w a l l s  26b),  consist  dense d i s l o c a t i o n a r r a y s s u r r o u n d i n g a r e a s of low d i s l o c a t i o n  density.  T h i s type of p o l y g o n i z e d 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 T a b l e X I , w h i c h suggested i n s t e a d a p i l e - u p u r a t i o n i n the 70% c o l d worked pure m e t a l . computer e s t i m a t e of domain s i z e was  config-  I t i s p o s s i b l e t h a t the  i n e r r o r and t h a t i t might  be  o  c l o s e r t o 1000 A than i n d i c a t e d .  T h i s would g i v e  > p ; g  i.e. a  p o l y g o n i z e d d i s l o c a t i o n arrangement c o u l d be e x p e c t e d . 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 f o r m a t i o n 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  w a l l s a r e s h a r p l y d e l i n e a t e d i n most c a s e s . about 0.82  y.  cell  The c e l l d i a m e t e r i s  More e x t e n s i v e d e f o r m a t i o n (about 80% r e d u c t i o n by  r o l l i n g ) reduced the c e l l d i a m e t e r to about 0.7 y; F i g s . 28a and  cold 28b.  The t a n g l e d n a t u r e 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 m e t a l i s c l e a r l y seen i n these e l e c t r o n m i c r o g r a p h s . Measurements o f c e l l s i z e i n aluminum f o r a g r e a t range of p r i o r d e f o r m a t i o n s were not c a r r i e d out i n the p r e s e n t 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 i n d i c a t e t h a t a l i m i t i n g minimum c e l l s i z e was p r o b a b l y almost a f t e r 80% r e d u c t i o n .  rolling  reached  T h i s i s i n agreement w i t h the f i n d i n g s of  63 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 t h a t the c e l l s i z e of h i g h p u r i t y aluminum decreased t o  - 82  -  Cc) 20.000X F i g u r e 26a-c.  T r a n 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 of pure aluminum 70%  C.W.  after  - 83 -  - 84 -  GO F i g u r e 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 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% r e d u c t i o n i n a r e a .  The a b s o l u t e magnitude  of the c e l l s i z e i n t h e p r e s e n t work f o r a g i v e n degree o f c o l d does n o t c o r r e s p o n d  rolling  t o t h a t r e p o r t e d by e i t h e r Swann o r Hansen.  Swann d i d n o t d e s c r i b e t h e method by w h i c h 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,  b u t h i s v a l u e s f o r comparable l e v e l s  of d e f o r m a t i o n a r e a t l e a s t t w i c e t h o s e . o f t h e p r e s e n t A n n e a l i n g o f 70% cold-worked i n the c e l l s t r u c t u r e .  investigation.  aluminum a t 300°C causes a m o d i f i c a t i o n  The c e l l s grow, i n c r e a s e 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 s u b g r a i n s  ( F i g s . 29 and 3 0 ) . The t a n g l e s o f  d i s l o c a t i o n s i n c e l l w a l l s g i v e way t o more o r d e r e d a r r a y s .  Annealing  c o l d worked pure aluminum f o r one hour a t 100°C and 250°C has a minor e f f e c t on t h e appearance o f s u b g r a i n s  ( F i g s . 31 and 3 2 ) . Some s u b g r a i n s  a r e 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 ; o t h e r s c o n t a i n jogged  dislocations.  Even a f t e r one hour o f a n n e a l i n g a t 250°C f o l l o w i n g 70% p r i o r c o l d work, the s u b g r a i n diameter was found t o be about l y ; i . e . l i t t l e than t h e c e l l s i n t h e cold-worked  metal.  higher  However, a t w o - f o l d i n c r e a s e  i n s u b g r a i n s i z e was observed when t h e a n n e a l i n g temperature  was  i n c r e a s e d from 250°C t o 300°C. At more advanced s t a g e s o f a n n e a l i n g , 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  f r e e i n t e r n a l l y and bounded by l a r g e angle b o u n d a r i e s . 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  dislocationF i g . 33 shows  a t 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 a n n e a l i n g o f the 80% c o l d worked aluminum were s i m i l a r t o those o f the 70% cold-worked  metal,  except t h a t the s u b g r a i n s i z e o f the former a f t e r a g i v e n a n n e a l i n g  F i g u r e 30.  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 pure aluminum c o l d - r o l l e d 70% and annealed a t 300°C f o r 6 h r s . , 10,000X.  - 87 -  F i g u r e 32.  T r a n s m i s s i o n e l e c t r o n micrograph o f pure aluminum c o l d - r o l l e d 70% and annealed a t 250°C f o r 1 h r . , 15,000X.  F i g u r e 34.  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 of pure aluminum c o l d - r o l l e d 80% and annealed a t 300°C f o r 3 h r s . , 5,000X.  - 89 -  t r e a t m e n t was g r e a t e r .  F o r example, t h r e e hours o f a n n e a l i n g a t 300°C  was s u f f i c i e n t t o 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 . 3 4 ) . S i m i l a r s t r u c t u r a l developments S w a n n , ^ Weismann e t a l . ^  4.3.2.2  i n aluminum have been o b s e r v e d by  and Hansen.^  Aluminum-4 Copper  F i g s . 35 and 36 a r e e l e c t r o n m i c r o g r a p h s from a carbon r e p l i c a and a t h i n f o i l o f t h e over-aged A l - 4 C u a l l o y , r e s p e c t i v e l y .  The c o a r s e  p r e c i p i t a t e s a r e a r r a y e d i n a w e l l - d e f i n e d Widemanstatten p a t t e r n .  The  mean p l a n a r i n t e r p a r t i c l e s p a c i n g o f t h e p r e c i p i t a t e s i s about 1.3 y. From t h e r e s u l t s o f Thomas and Nutting"'""' i t can be c o n c l u d e d t h a t t h e type o f a g e i n g t r e a t m e n t used i n t h e p r e s e n t i n v e s t i g a t i o n (15 hours at 300°C) would produce a m i x t u r e o f 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 n o n c o h e r e n t , and 6 coherent w i t h the m a t r i x .  1  An A l - 4 C u a l l o y i n t h e f u l l y  i s partially over-aged  c o n d i t i o n (62 hours a t 300°C), c o n t a i n i n g m a i n l y 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 o f about 11,000 p s i , whereas an a g e i n g t r e a t m e n t of 15 hours a t 300°C g i v e s a y i e l d s t r e n g t h o f 13,300 p s i .  Hence i t  can be c o n c l u d e d t h a t the amount o f 6* p r e c i p i t a t e s p r e s e n t i n t h e l a t t e r case i s r e l a t i v e l y s m a l l .  T h i s i s a l s o s u p p o r t e d by t h e X-ray  measurement o f n o n - u n i f o r m l a t t i c e s t r a i n ( F i g . 16) i n t h e as-aged m a t e r i a l w h i c h shows a maximum o f 0.06% s t r a i n . F i g . 37 r e p r e s e n t s t h e hot-worked m i c r o s t r u c t u r e o f t h e over-aged A l - 4 C u ( S e r i e s B ) . T h i s e l e c t r o n m i c r o g r a p h shows c e l l s o r s u b g r a i n s which are not very w e l l developed.  The s u b g r a i n s a r e f a i r l y f r e e o f  d i s l o c a t i o n s a l t h o u g h t a n g l e d d i s l o c a t i o n s a r e seen i n some o f t h e c e l l  F i g u r e 35.  Chromium shadowed  F i g u r e 36.  Transmission electron  carbon r e p l i c a o f over-aged  m i c r o g r a p h of over-aged Al-4Cu  Al-4Cu showing C u A l ( 6 )  showing CuAl„ p r e c i p i t a t e s ,  precipitates,  10,000X.  2  F i g u r e 37.  6,000X.  T r a n 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 A l - 4 C u (B S e r i e s ) showing t h e hot-worked T n i c r o s t r u c t u r e , 20,000X.  - 91 -  interiors.  The  X-ray a n a l y s i s s u p p o r t s 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  transmission  m i c r o g r a p h s of 70% c o l d - r o l l e d A l - 4 C u ( S e r i e s B).  The  main  electron feature  of the s e v e r e l y worked a l l o y i s a v e r y h i g h d i s l o c a t i o n d e n s i t y in a c e l l structure.  The  c e l l s are l e s s w e l l - d e f i n e d  aluminum ( F i g . 26).  Such a p o l y g o n i z e d  by the X-ray s t u d i e s  (see T a b l e X I ) .  arranged  than i n pure  configuration i s also indicated 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 t h e s e 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 c o u l d not be measured from e l e c t r o n m i c r o g r a p h s ; 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 of the o r d e r of 4 x 1 0 ^ - 1 0 ^ cm. cm ^. and  d i s l o c a t i o n l o o p s ( F i g . 38a)  l o c a t i o n s are a p p a r e n t l y 38b).  e s t i m a t e d to  Numerous t a n g l e d  are f r e q u e n t l y o b s e r v e d .  be  dislocations Some d i s -  a r r e s t e d at the p r e c i p i t a t e s ( p o i n t A i n F i g .  At p o i n t 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 w h i c h o c c u r r e d d u r i n g a n n e a l i n g  of  the s e v e r e l y c o l d worked A l - 4 C u 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 annealing,  the deformed s t r u c t u r e was  ( i . e . pure aluminum).  On  r e p l a c e d by a r e c o v e r e d s t r u c t u r e ,  composed of r a t h e r w e l l - d e v e l o p e d s u b g r a i n s .  However, t h e r e were  d i f f e r e n c e s i n the ease of s u b g r a i n  and  formation  i n the degree of  r e c o v e r y of r e m a i n i n g c e l l s t r u c t u r e i n t h e s e 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 a n n e a l i n g  w e l l as the a n n e a l i n g  time.  temperature as  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  -  Cc) F i g u r e 38a-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 of A l - 4 C u (B S e r i e s ) a f t e r 70% C.W.,  35,000X.  - 93  -  (b) 40,000X. F i g u r e 39a,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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 100°C f o r 1 h r .  - 94  F i g u r e 41.  -  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 of A l - 4 C u (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 350°C f o r 1 h r . , 15,000X.  - 95 -  changes i n t h e A l - 4 C u a l l o y a f t e r a n n e a l i n g f o r one hour a t 100°C, 200°C and 350°C r e s p e c t i v e l y .  A f t e r a n n e a l i n g a t 100°C,  the s t r u c t u r e  i s v e r y s i m i l a r t o t h a t o f t h e deformed s t a t e , e x c e p t t h a t some o f the t a n g l e d d i s l o c a t i o n s appear t o have d i s e n t a n g l e d themselves t o form s u b g r a i n b o u n d a r i e s ( 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 h i g h and d i s l o c a t i o n s a r e a l s o p i l e d - u p a t t h e p r e c i p i t a t e s . Increasing  t h e a n n e a l i n g temperature t o 200°C has produced w e l l  delineated  dislocation-free subgrains(Fig.  diameter o f about 0.3 u.  40a) w i t h a s u b g r a i n  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 . 4 0 b ) . A n n e a l i n g at a v e r y h i g h t e m p e r a t u r e , e.g. 350°C, has r e s u l t e d i n a s t r a i n r e c r y s t a l l i z e d .structure  (Fig. 41). Thin f o i l s of materials  free  given  the l a t t e r heat treatment d i d n o t r e v e a l any s u b g r a i n s . The Fig.  shapes o f t h e p r e c i p i t a t e s i n F i g . 41 (compare w i t h  36) p r o b a b l y 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  those i n  o f the  p r e c i p i t a t e p a r t i c l e s upon c o l d w o r k i n g and subsequent a n n e a l i n g .  The  change o f shape o f 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 t o t h e s h e a r i n g of some o f the p r e c i p i t a t e a f t e r l a r g e r e d u c t i o n s by c o l d r o l l i n g and to t h e growth o f the p a r t i c l e s d u r i n g subsequent a n n e a l i n g , presumably by enhanced d i f f u s i o n o f copper due t o t h e presence o f the s u b g r a i n b o u n d a r i e s between the p r e c i p i t a t e p a r t i c l e s .  T h i s change o f  shape o f t h e p r e c i p i t a t e s seems t o be a common o b s e r v a t i o n i n most o f the A l - 4 C u a l l o y s annealed a f t e r c o l d w o r k i n g . F i g s . 42 t o 47 show e l e c t r o n m i c r o g r a p h s f o r A l - C u a l l o y s heat t r e a t e d a t 300°C, f o r times v a r y i n g 70%  c o l d work.  from 15 minutes t o 15 h o u r s , a f t e r  I n a l l cases, well-developed subgrains are observed.  - 96 -  - 97 -  (b) F i g u r e 43a,b.  T r a n s m i s s i o n e l e c t r o n micrograph o f Al-4Cu cold-rolled 23,000X.  (B S e r i e s )  70% and annealed at 300°C f o r 30 mins.,  - 98 -  F i g u r e 44.  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 Al-4Cu (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 2 h r s . , 23,000X.  F i g u r e 45.  T r a n 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 A l - 4 C u (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 4 h r s . , 23,000X.  - 99 -  (a) F i g u r e 46a,b.  (b)  T r a n 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 Al-4Cu (B S e r i e s ) c o l d r o l l e d 70% and annealed a t 300°C f o r 8 h r s . , (a) 20,000X, (b) 15,000X.  F i g u r e 47.  T r a n 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 A l - 4 C u (B S e r i e s ) c o l d - r o l l e d 70% and annealed a t 300°C f o r 15 h r s . , 15,000X.  - 100 The s u b g r a i n diameter v a r i e s from about 0.55 V f o r 15 minutes o f a n n e a l i n g t o 2 y f o r 15 hours o f a n n e a l i n g . f o r m a t i o n i s r a p i d i n i t i a l l y , b u t decreases  The r a t e o f s u b g r a i n g r a d u a l l y w i t h time.  of e x c e s s i v e l y l a r g e s u b g r a i n s even a f t e r l o n g a n n e a l i n g  times  i n d i c a t e s t h e v e r y slow r a t e o f growth o f t h e s u b g r a i n s . m i g r a t i n g sub-boundaries  Lack  Some o f t h e  appear t o have been pinned by t h e p r e c i p i t a t e s .  T h i s may be t h e r e a s o n f o r t h e slow r a t e o f growth o f t h e s u b g r a i n s , s i n c e i t i s u n l i k e l y t h a t a l l t h e sharp b o u n d a r i e s  produced by p o l y -  g o n i z a t i o n w i l l be capable o f m i g r a t i n g . I t has been observed  t h a t c o a r s e n i n g o f t h e 6 phase takes p l a c e  d u r i n g l o n g r e c o v e r y anneals b e f o r e r e c r y s t a l l i z a t i o n , i n agreement 65 66 w i t h t h e e x p e r i m e n t a l evidence o f Doherty and M a r t i n . 15 hours o f heat treatment  '  For example,  a t 300°C a f t e r 70% c o l d work has i n c r e a s e d  the mean p l a n a r i n t e r p a r t i c l e s p a c i n g from 1.3 y t o 2.2 y, whereas a n n e a l i n g f o r one hour a t 350°C, w h i c h 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 , i n c r e a s e d t h e s p a c i n g t o about 2.5 y. p e r i o d t h e s u b g r a i n boundaries  During the recovery  are apparently s t i l l attached to the  p r e c i p i t a t e s and t h e s u b g r a i n s i z e i n c r e a s e s as t h e d i s p e r s i o n o f t h e second phase c o a r s e n s .  T h i s f o l l o w s from t h e e x p e r i m e n t a l o b s e r v a t i o n  t h a t t h e s u b g r a i n diameter i s almost e q u a l t o the i n t e r p a r t i c l e s p a c i n g . Doherty and M a r t i n have a l s o shown t h a t i n t h e m a t e r i a l a f t e r heavy d e f o r m a t i o n , b u t b e f o r e r e c r y s t a l l i z a t i o n , t h e 6 phase coarsens much more r a p i d l y than i n t h e undeformed m a t e r i a l . 4.3.2.3  S.A.P.  S.A.P. was r e c e i v e d i n t h e form o f an e x t r u d e d r o d .  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 o f t h e e x t r u d e d b a r i s shown i n F i g . 48. As seen from t h e e l e c t r o n m i c r o g r a p h s t h e o x i d e phase ( A ^ O ^ ) i s n o n u n i f o r m l y d i s t r i b u t e d throughout the aluminum m a t r i x .  Although  the o x i d e 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 , e v i d e n c e o f a g g l o m e r a t i o n or " c l u s t e r i n g " o f t h e p a r t i c l e s has a l s o been observed i n some c a s e s . The i n d i v i d u a l o x i d e p a r t i c l e s a r e d i s k - s h a p e d , h a v i n g an average o  o  diameter o f about 1100 A and a t h i c k n e s s o f about 100 A.  The m a t r i x  i s d i v i d e d i n t o s u b g r a i n s w h i c h a r e p r o b a b l y formed by t h e combined e f f e c t o f h i g h temperatures and a l a r g e p l a s t i c s t r a i n d u r i n g e x t r u s i o n . The mean p l a n a r i n t e r p a r t i c l e s p a c i n g o f t h e o x i d e i s found t o be about 0.08  u.  Thus, i n comparison w i t h A l - 4 C u , S.A.P. has a second  phase d i s p e r s e d on a much f i n e r s c a l e . are t h e p a r t i c l e s s p h e r i c a l i n shape.  I n n e i t h e r S.A.P. n o r Al-4Cu However, c o n s i d e r i n g the  d i a m e t e r o f t h e e q u i v a l e n t s p h e r i c a l p a r t i c l e w h i c h would produce t h e same i n t e r p a r t i c l e s p a c i n g , t h e A ^ O ^ p a r t i c l e s a r e much s m a l l e r i n s i z e than t h e C u A ^ p a r t i c l e s . C l o s e s i m i l a r i t y e x i s t s between t h e m i c r o s t r u c t u r e o f S.A.P. and Al-4Cu e i t h e r i n t h e hot-worked, cold-worked o r annealed  condition.  F i g s . 49a and 49b a r e 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 m i c r o g r a p h s f o r S.A.P. i n t h e hot-worked  condition.  I t s h o u l d be n o t e d t h a t t h e  h o t - w o r k i n g temperature f o r S.A.P. was 540°C compared t o a temperature of 300°C f o r A l - 4 C u .  The l a r g e p l a s t i c s t r a i n d u r i n g r o l l i n g a t t h i s  h i g h temperature has produced a p o l y g o n i z e d s u b s t r u c t u r e w i t h s h a r p l y d e f i n e d sub-boundaries s i m i l a r t o t h a t o f A l - 4 C u . The s u b g r a i n s a r e e q u i axed and t h e d i s l o c a t i o n d e n s i t y between t h e sub-boundaries i s low. , T h i s m i c r o s t r u c t u r e i s s i m i l a r t o t h a t o f an e x t r u d e d p r o d u c t o f l o w e r  - 102 -  F i g u r e 48.  T r a n 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 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 l ^ p a r t i c l e s , 46,000X.  - 103 -  F i g u r e 49a,b.  Transmission hot- orked W  e l e c t r o n micrograph of S.A.P. showing  m i c r o s t r u c t u r e , 23,000X.  the  - 104 32 o x i d e c o n t e n t o b s e r v e d by Hansen. The in Figs.  dislocation structure  produced by c o l d r o l l i n g 50% i s shown  50a, 50b and 50c. The c e l l w a l l s  and are o c c a s i o n a l l y  r e t a i n a ragged appearance  p i n n e d by t h e o x i d e p a r t i c l e s .  I t w i l l be n o t i c e d  t h a t t h e c e l l i n t e r i o r s c o n t a i n an a p p r e c i a b l e d e n s i t y o f d i s l o c a t i o n s ; i n contrast with 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  cell interiors  observed i n s i n g l e - p h a s e aluminum cold-worked a t room t e m p e r a t u r e . Isolated  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 also  o b s e r v e d i n some c a s e s .  T h i s t y p e o f d i s l o c a t i o n s u b s t r u c t u r e has been 40  observed by G o o d r i c h and A n s e l l  f o r c o l d - r o l l e d S.A.P. c o n t a i n i n g  2 wt % and 3 wt % o x i d e and by Hansen"* f o r cold-drawn S.A.P. c o n t a i n i n g 0.2 t o 4.7 wt % o x i d e . increasing  I n b o t h cases t h e c e l l s i z e d e c r e a s e d w i t h  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 t h e more s e v e r e l y  deformed c o n d i t i o n s .  G o o d r i c h and A n s e l l o b s e r v e d t h a t t h e l i m i t i n g  c e l l s i z e o f t h e S.A.P.-type a l l o y s was c o n s i d e r a b l y l e s s than t h a t o f h i g h p u r i t y aluminum and t h a t t h e d e f o r m a t i o n needed t o produce t h i s minimum c e l l s i z e was a p p r e c i a b l y h i g h e r f o r t h e S.A.P.Ttype a l l o y s . The  sluggish  a t t a i n m e n t o f the l i m i t i n g c e l l s i z e and t h e development  of t h e s m a l l e r c e l l s i z e tend t o i n d i c a t e t h a t d i s l o c a t i o n i s i n h i b i t e d by t h e i n t r o d u c t i o n  o f t h e d i s p e r s e d second phase.  A f t e r 50% c o l d - r o l l i n g t h e m a t e r i a l d i f f e r e n t times.  Figs.  was annealed a t 540°C f o r  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 a n n e a l i n g p e r i o d o f 24 h o u r s . 70%  mobility  This structure  i s s i m i l a r to that of  c o l d r o l l e d A l - 4 C u annealed a t low t e m p e r a t u r e s , e.g. 200°C.  A n n e a l i n g has produced a p o l y g o n i z e d s u b s t r u c t u r e w i t h a l a r g e r  subgrain  105  -  (c)  F i g u r e 50a-c.  Transmission electron 50%,  58,000X.  m i c r o g r a p h of S.A.P. c o l d - r o l l e d  - 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 o x i d e p a r t i c l e s a r e  seen i n s i d e the s u b g r a i n s a n d a t the s u b b o u n d a r i e s . A good c o r r e l a t i o n was found t o e x i s t between t h e d i s l o c a t i o n arrangement o b t a i n e d from m e t a l l o g r a p h y and t h a t i n d i c a t e d line p r o f i l e analysis  of S.A.P. i n any thermo-mechanical  by t h e X-ray condition.  5.  DISCUSSION  5.1  T e n s i l e P r o p e r t i e s a t 20°C  5.1.1  Pure Aluminum A l a r g e body of i n f o r m a t i o n about the d e f o r m a t i o n o f 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 t h e 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 o f the s l i p p r o c e s s , s u b s t r u c t u r e f o r m a t i o n and growth, and a n n e a l i n g characteristics.  The m e c h a n i c a l  b e h a v i o u r of aluminum can be g r e a t l y 67  i n f l u e n c e d by t h e presence  of i m p u r i t i e s .  C a r r e k e r and H i b b a r d  have shown t h a t even s m a l l c o n c e n t r a t i o n of some i m p u r i t i e s can produce i m p o r t a n t 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 t h e temperature  dependence of the f l o w s t r e s s .  The aluminum  used i n t h e p r e s e n t i n v e s t i g a t i o n had a p u r i t y o f 99.96%, w h i c h compares f a v o u r a b l y w i t h t h e h i g h e s t p u r i t y of m e t a l used by most p r e v i o u s investigators.  The t e n s i l e p r o p e r t i e s o b t a i n e d i n the p r e s e n t work  a f t e r v a r i o u s t h e r m a l and m e c h a n i c a l  t r e a t m e n t s a l s o compare v e r y  c l o s e l y t o some r e p o r t e d i n the l i t e r a t u r e f o r 99.996% aluminum shown i n T a b l e X I I .  as  The r e s u l t s of t h e p r e s e n t work a r e a l s o i n  agreement w i t h d a t a r e p o r t e d by Hansen"* f o r c o l d drawn aluminum. A l t h o u g h aluminum i s s t r e n g t h e n e d  c o n s i d e r a b l y by w o r k i n g  a t 20°C,  the a b s o l u t e s t r e n g t h e n i n g due t o any g i v e n amount o f c o l d w o r k i n g i s 41 much l e s s than f o r most o t h e r f . c . c . m e t a l s . For example, n i c k e l ,  - 109 Table X I I :  Room Temperature M e c h a n i c a l P r o p e r t i e s  f o r High-Purity  Aluminum. 99.96% aluminum used i n t h e p r e s e n t work  99.996 aluminum from R e f . 48  Material condition  M a t e r i a l Condition  ^  U.T.S.  Ksi  Ksi  70% r e d u c t i o n s by c o l d r o l l i n g  14.5  14.9  80% r e d u c t i o n s by c o l d r o l l i n g  15.6  16.5  1 ,8  6.9  f u l l y annealed a f t e r 70% c o l d work  75% r e d u c t i o n s by c o l d r o l l i n g  difference  Ksi  15.4  16.3  1.8  6.9  o f about 100,000 p s i .  The  i n t h e a b s o l u t e v a l u e s o f t h e s t r e n g t h s o f aluminum and  n i c k e l may be a t t r i b u t e d t o a d i f f e r e n c e and  Ksi  f u l l y annealed a f t e r 75% c o l d work  when c o l d r o l l e d 75%, has a y i e l d s t r e n g t h  U.T.S.  o_ „  i n t h e i r shear modulus v a l u e s  t o t h e i r minimum s u b s t r u c t u r e "domain", s i z e s a f t e r d e f o r m a t i o n . 41  Clegg  has;found a good c o r r e l a t i o n between h i g h s t r e n g t h  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 ) alloy.  and a f i n e  f o r N i and a N i - C r  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 t h e p r e s e n t work t o have a domain s i z e o f > 1000 A o  (about 1500 A) a f t e r 70% c o l d work; see T a b l e X I . When some m e t a l s ( i n c l u d i n g aluminum) a r e c o l d worked  extensively,  networks o f t a n g l e d d i s l o c a t i o n s form w h i c h i n t h r e e dimensions appear to d e f i n e  t h e w a l l s of c e l l s o r s u b g r a i n s .  dislocations.  W i t h i n t h e c e l l s a r e few  The c e l l s a r e t y p i c a l l y i n t h e o r d e r o f one m i c r o n  - 110 -  d i a m e t e r , and examples are c l e a r l y seen i n F i g s . 26a to 26c. w a l l s a r e of h i g h d i s l o c a t i o n d e n s i t y .  The  cell  Upon a n n e a l i n g a t h i g h enough  t e m p e r a t u r e s , d i s l o c a t i o n s i n c e l l w a l l s r e a r r a n g e to assume a l o w e r energy, l e s s t a n g l e d 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 a n g l e s u b g r a i n b o u n d a r i e s . h i g h e r a n n e a l i n g temperatures  Still  cause s u b g r a i n b o u n d a r i e s to m i g r a t e ,  s u b g r a i n s to grow, and r e c r y s t a l l i z a t i o n t o o c c u r . T h e o r e t i c a l l y , t h e c e l l s or s u b g r a i n s produced by d e f o r m a t i o n s h o u l d 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"  t h a t a r e measured by X-ray methods i n h e a v i l y deformed m e t a l s .  However,  o  m e t a l l o g r a p h y 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 o b t a i n e d o  from X-ray a n a l y s i s was  found t o be about 1500 A.  I n o r d e r to r e c o n c i l e  the s u b g r a i n s i z e w i t h the domain s i z e , one can assume t h a t minute o  domains (1000 to 2000 A d i a m e t e r ) w i t h low a n g l e b o u n d a r i e s , e x i s t i n the c e l l w a l l s , but have not been r e s o l v e d by e l e c t r o n Some s u p p o r t i n g e v i d e n c e may  microscopy.  be found i n F i g . 26c i n the broad  w a l l s f o r c o l d r o l l e d pure aluminum, a l t h o u g h i t i s a t b e s t to i d e n t i f y unambiguously 68 Cottrell  cell  difficult  a " c e l l " or "domain" i n such m i c r o g r a p h s .  69 and L i  have shown t h e o r e t i c a l l y t h a t c e l l w a l l s or  s u b g r a i n b o u n d a r i e s can a c t as b a r r i e r s to moving d i s l o c a t i o n s . S e v e r a l w o r k e r s ^ ' c l a i m to have shown t h a t , when s u b g r a i n s a r e p r e s e n t , ambient-temperature  p r o p e r t i e s depend o n l y on the s u b g r a i n  s i z e and t h a t 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 s u b g r a i n s i z e by the 72 Hall-Petch  73 '  equation, °0.2 °0 =  +  K  £ _ 1 / 2  ( 2 8 )  - Ill-  where  ^ i-  st  n  e  0.2 pet. o f f s e t y i e l d s t r e n g t h , O Q and K a r e c o n s t a n t s  and I i s the mean s u b g r a i n diameter. stress of  resisting dislocation  In t h i s e q u a t i o n  motion i n the m a t r i x and K i s a measure  the s t r e n g t h e n i n g e f f e c t o f the sub-boundary.  to v e r i f y the v a l i d i t y o f t h i s r e l a t i o n s h i p from the p r e s e n t work. plotted  An attempt  by p l o t t i n g  was made  experimental  data  The 0.2 p e t . y i e l d s t r e n g t h o f aluminum i s  i n F i g . 52 a g a i n s t the r e c i p r o c a l  s u b g r a i n diameter.  i s a friction  square  r o o t o f the measured  The o r i g i n a l d a t a a r e i n T a b l e 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 s t r a i g h t  l i n e has been 74  fitted  t o the p o i n t s by the method o f l e a s t  have made s i m i l a r p l o t s  squares.  from t h e i r own experiments.  Ball  5 and Hansen  However, the  and K v a l u e s o b t a i n e d from F i g . 52 do not agree w i t h those o f the p r i o r workers.  The comparative  Table X I I I :  a  Q  d a t a a r e summarized i n T a b l e X I I I .  and K Values f o r Aluminum i n the H a l l - P e t c h E q u a t i o n  Material  K  10 p s i  10  Reference  psi u  99.96 pet A l  -7.7  19.7  p r e s e n t work  99.998 pet A l  -4.3  13.3  Hansen"'  99.5  +1.0  10.3  Hansen^  99.994 pet A l  0  11.1  ,74 Ball  99.5 p e t A l (Recrystallized)  2.3  pet A l  5.7  Hansen  32  - 112 -  - 113 The d o u b t on  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^, the v a l i d i t y  strengthening.  the subgrains  of the H a l l - P e t c h r e l a t i o n s h i p  Theoretically,  d i s l o c a t i o n motion.  i n F i g . 52  is a friction  for substructure  stress resisting  Since the d i s l o c a t i o n d e n s i t y i n the i n t e r i o r  i s small,  s h o u l d a t m o s t be  equal  to the  s t r e n g t h o f 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 . a b o u t 1000 It  s h o u l d be n o t e d  casts  from Table  X I I I and t h e n a t u r e  of  yield t o 2000 p s i .  of the 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  (slope)  of the data 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 c a n be  a s s o c i a t e d w i t h inaccuracy i n the  determination of subgrain diameters mentioned e a r l i e r  by m e t a l l o g r a p h y .  It  was  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  identified with cells  or subgrains.  The  use  be  o f t h e much s m a l l e r  X-ray domain s i z e s f o r £ i n the H a l l - P e t c h e x p r e s s i o n i n the case the more h e a v i l y - d e f o r m e d effect  (finer  s t r u c t u r e ) a l l o y s would have  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  more p o s i t i v e  intercept.  of  the  tending to give  I t i s perhaps i n t e r e s t i n g  to note  in  a  this  74 regard that B a l l ,  cell  size,  found  pure aluminum. negative cell as  size.  who  u s e d an X - r a y m i c r o b e a m t e c h n i q u e 3 1/2  K = 11.1 Hansen  x 10  psi y  (see T a b l e  His r e s u l t s  XIII) obtained a high K value to  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  B a l l ' s v a l u e o f K = 11.1  s t r e n g t h e n i n g e f f e c t of c e l l boundaries that of high angle boundaries.  ksi y  and  determine criticism  t h o s e o f t h e p r e s e n t w o r k w h i c h a r e b a s e d on m e t a l l o g r a p h y 1/2 accepts  determine  cr^ = 0 f o r p r e s t r a i n e d  OQ value, using metallographic techniques  E v e n i f one  to  and  to  alone.  , the  i s a p p a r e n t l y l a r g e compared  I f , in fact,  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 to moving d i s l o c a t i o n s than are l a r g e - a n g l e it  seems l i k e l y  t h a t s t r e n g t h m u s t be more c l o s e l y  s t r u c t u r e of  the w a l l s than to the spacing  supported  the o b s e r v a t i o n  by  w i d e l y w i t h t h e m e c h a n i c a l and  rolled  Jolley,^  i s at l e a s t  boundaries.  an  the  This  thermal  h i s t o r y of the  but  is  varies  metal.  from t h e i r work w i t h p r e s t r a i n e d  order  and-cold  d e n s i t y w i t h i n the  of magnitude lower  than i n the  subgrains  subgrain  They assume t h a t t h e d i s l o c a t i o n s i n t h e b o u n d a r y o f f e r  much s t r o n g e r b a r r i e r t o s l i p the m a t r i x , control  the w a l l s .  i s f a r from constant,  i r o n , h a v e shown t h a t t h e d i s l o c a t i o n  or c e l l s  r e l a t e d to  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  R o b e r t s and  of  boundaries,  and  d i s l o c a t i o n s t h a n do  dislocations in  that i t i s thus only the boundary d i s l o c a t i o n s t h a t  the f l o w s t r e s s .  R o b e r t s and  of K t o the v a r y i n g c h a r a c t e r of of c o l d work, recovery a p p r o a c h by  the  a  and  Jolley  attribute  different  the boundaries f o r d i f f e r e n t  c r y s t a l s t r u c t u r e , and  they  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 b e made t o  values  conditions  justified  this  extrapolate  -1/2 back to the y i e l d Hultgren^  s t r e n g t h of a s i n g l e c r y s t a l at £  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 the  substructure  s i z e and  commercially  p u r e aluminum.  increased  and  m i s o r i e n t a t i o n on  subgrain  -1/2 (£  diameter times  i n f l u e n c e of  polygonized  the mechanical p r o p e r t i e s  f o u n d t h a t as  s i z e decreased, the  i n c r e a s e i n f l o w s t r e s s was subgrain  He  =0.  plotted against  of  substructure misorientation  flow stress increased. the  The  inverse square root  of  the square root of average m i s o r i e n t a t i o n  1/2 if>  ,  being  t h e m i s o r i e n t a t i o n ) and  straight lines  were  69 obtained  as p r e d i c t e d by -1/2  zero at £  theory.  However, the  i n t e r c e p t s were  not  1/2 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  for  - 115 -  the h i g h e s t a n n e a l i n g temperature (370°C) a n e g a t i v e i n t e r c e p t was obtained.  A c c o r d i n g t o H u l t g r e n , t h e d i s c r e p a n c y may be due e i t h e r  to some g r a i n boundary s t r e n g t h e n i n g o r t o t h e s t r u c t u r e c o n t a i n e d w i t h i n t h e s u b g r a i n s but n o t n o r m a l l y a s s o c i a t e d w i t h t h e s u b s t r u c t u r e . 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 may a l t e r n a t i v e l y be d e s c r i b e d as a s i m p l e 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 f l o w s t r e s s (x) i n shear f o r f . c . c . m e t a l s i n g l e c r y s t a l s i s o f t h e form  x  =  Y  Gbp  (29)  1 / 2  where y has a v a l u e between 0.2 and 0.5.  F o r p o l y c r y s t a l l i n e aluminum  the 0.2 p e t y i e l d s t r e n g t h becomes r e l a t e d t o t h e d i s l o c a t i o n d e n s i t y by t h e f o l l o w i n g e q u a t i o n :  a  = 2.24 Gbp  o. z 0  1 / 2  1 Y  '  (30)  I n t h e case o f pure aluminum reduced 70% by c o l d r o l l i n g 3 OQ  2  =  14.5 x 10 p s i  G  = 3.62 x 1 0 p s i  b  = 2.85 A  p  = 2 x 10  6  10  -3 cm.cm (Table X I )  Upon s u b s t i t u t i n g these v a l u e s i n e q u a t i o n  (30) one o b t a i n s y = 0.45.  The v a l u e of y f o r aluminum s h o u l d be independent of thermomechanical treatments.  U n f o r t u n a t e l y , t h e d i s l o c a t i o n d e n s i t y o f pure aluminum  i n t h e annealed  c o n d i t i o n c o u l d n o t be determined a c c u r a t e l y from t h e  - 116  -  X-ray l i n e p r o f i l e a n a l y s i s because o f the i n s i g n i f i c a n t l i n e from t h i s s o u r c e .  broadening  Thus t h e r e were no d a t a to p e r m i t the v a l u e of y  o b t a i n e d above t o be compared a g a i n s t a s t a n d a r d .  5.1.2 5.1.2.1  Simple Aged A l l o y  T h i s a l l o y was  (No  Substructure)  s o l u t i o n t r e a t e d and aged a t 300°C ( w i t h o u t i n t e r -  v e n i n g hot or c o l d d e f o r m a t i o n )  t o 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 m a t r i x o f the two-phase a l l o y c o n t a i n s 0.45  wt  %  Cu (0.16 a t % 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 a g e i n g temperature.  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 t o  20°C. The s t r e n g t h e n i n g mechanisms which might be c o n s i d e r e d i n the s i m p l e aged p o l y c r y s t a l l i n e a l l o y a r e : (a)  Conventional d i s p e r s i o n hardening  (b)  Solid solution  (c)  G r a i n boundary s t r e n g t h e n i n g .  (Orowan),  hardening,  I t s h o u l d be noted t h a t f u r t h e r p r e c i p i t a t i o n i n the m a t r i x a f t e r c o o l i n g from t h e a g e i n g temperature  was  p r e c l u d e d by m a i n t a i n i n g t h e  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 were conducted.  Subsequent room temperature  tests  a g e i n g or s t r a i n - a g e i n g  d u r i n g t e s t i n g i s assumed t o be i n s i g n i f i c a n t on the b a s i s of p r e s e n t o b s e r v a t i o n s and those r e p o r t e d by p r e v i o u s workers w i t h A l - C u . The g r a i n s i z e of the aged a l l o y i n the p r e s e n t work was about 800 u.  Thus, g r a i n boundary s t r e n g t h e n i n g may  very  large;  be assumed t o be  - 117 -  negligible. As a t e s t o f the Orowan model  f o r d i s p e r s i o n h a r d e n i n g the  measured 0.2 p e t 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 a g a i n s t t h e D - 2r s s parameter l o g , ( rr )/(D - 2r ) a c c o r d i n g t o e q u a t i o n ( 2 ) . The i r  10  S  ID  o r i g i n a l d a t a a r e i n Table I I . f o r t h e room temperature  S  A good l i n e a r c o r r e l a t i o n was  apparent  d a t a , and a s t r a i g h t l i n e was f i t t e d t o the  p o i n t s by t h e method o f l e a s t squares.  The s l o p e o f 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 o r d i n a t e a x i s were found t o be 2.5 x 10  psi. y  and 4500 p s i r e s p e c t i v e l y . I n e q u a t i o n (2) o  g  i s the y i e l d s t r e s s o f the m a t r i x .  I n the  p r e s e n t work the m a t r i x o f the two-phase Al-4Cu a l l o y c o n s i s t s of pure 76 aluminum c o n t a i n i n g 0.16 a t % Cu i n s o l i d s o l u t i o n . e x p e r i m e n t a l l y determined  Dorn e t a l .  have  the t r u e 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 t h e c o n c e n t r a t i o n range 0.029 t o 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 t r e n g t h o f aluminum  c o n t a i n i n g 0.16 a t % Cu i n s o l i d s o l u t i o n i s found t o be about 2000 p s i . The r e m a i n i n g 2500 p s i of the e x p e r i m e n t a l i n t e r c e p t (o ) can be a t t r i b u t e d t o the s t r a i n h a r d e n i n g w h i c h o c c u r r e d i n t h e t e n s i l e specimens w h i l e b e i n g s t r a i n e d 0.2 p e t , s i n c e the i n i t i a l work  hardening  r a t e of d i s p e r s i o n - h a r d e n e d a l l o y s i s known t o be v e r y h i g h . The e x p e r i m e n t a l r e s u l t s o f 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 o f the r e c i p r o c a l mean p l a n a r p a r t i c l e s p a c i n g i n agreement w i t h the Orowan model.  The s l o p e o f the l i n e  was shown by t h e a u t h o r s to be i n q u a n t i t a t i v e agreement w i t h theory, i f C o t t r e l l ' s ^  7  obtained  Orowan's  e s t i m a t e o f the l i n e t e n s i o n of a d i s l o c a t i o n  - 118 -  - 119 -  was u s e d .  C o t t r e l l ' s estimate of l i n e  o t h e r s by a f a c t o r o f two.  tension  d i f f e r s from that o f  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 a n d 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 of 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 - 2 r ) f o l l o w i n g g  equation  (1).  g  The d a t a a p p e a r e d t o s u p p o r t a l i n e a r r e l a t i o n .  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  3  dynes/cm  The  ( 0 . 9 8 p s i . P) 3  and  t h e t h e o r e t i c a l value from equation  (0.51  psi. u).  ( 1 ) i s 3.3 x 10  dynes/cm  T h u s t h e two d i f f e r b y a f a c t o r o f s l i g h t l y  less  than  two. For  a polycrystalline material  calculated Nicholson  1  from t h e r e p l o t  t h e s l o p e and i n t e r c e p t  (o )  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  a r e f o u n d t o b e 2.18 x 10  These a r e i n good agreement w i t h  3  p s i . u and 1000 p s i r e s p e c t i v e l y .  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 a g e d a t 300°C f o r o n l y a f e w 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 l u m i n u m - r i c h matrix."'""' partly  After  o f 9.' p r e c i p i t a t e s  l o n g e r a g e i n g t i m e s 6*  i nthe  precipitates  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  both 0'  and 9 p r e c i p i t a t e s .  s u p p o r t t o t h e argument that  a dispersion  Thus, t h e data p l o t  of  i n F i g . 53 l e n d s  r a i s e d inthe e a r l i e r review  (Section  1.1)  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 c a n be a p p l i e d ,  at least i n the i n i t i a l  stages of deformation.  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 and of are  calculated two.  y i e l d s t r e n g t h s may b e e x p e c t e d  Greater differences  not spherical  measured  t o agree w i t h i n  a  factor  t h a n t h i s c a n b e e x p e c t e d when t h e p a r t i c l e s  o r when t h e 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 n a t u r e of the d i s p e r s i o n of the p a r t i c l e s i s  a l s o important i n d e t e r m i n i n g the s t r e n g t h .  In Al-4Cu a l l o y s  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 are not uniform.  the  distribution  In a d d i t i o n , aged Al-4Cu a l l o y s are known to c o n t a i n  g r a i n boundary p r e c i p i t a t e s whose i n f l u e n c e on m e c h a n i c a l p r o p e r t i e s i s 79 not c l e a r l y understood.  L i u and Gurland  found t h a t i n low  carbon  s t e e l s c a r b i d e s are l o c a t e d mainly at g r a i n b o u n d a r i e s , and t h a t appear 5.1.2.2  they  to e x e r t an important e f f e c t on d e f o r m a t i o n b e h a v i o u r . Aged-and-Deformed A l l o y s  A significant  f e a t u r e of d i s p e r s i o n - h a r d e n e d m a t e r i a l s i s the  h i g h a t t a i n a b l e l e v e l of " s t o r e d energy d i s c u s s e d i n S e c t i o n 1.1.  of c o l d work" which  was  Comparing the s t r e n g t h s of over-aged  and  c o l d - r o l l e d Al-4Cu a l l o y w i t h those of c o l d - r o l l e d pure aluminum i n T a b l e I I I , i t can be concluded that a h i g h l e v e l of s t r a i n can be imparted to the aged a l l o y by c o l d working,  energy  i n support of  earlier  33-37 such s u g g e s t i o n s .  .  That the d i s l o c a t i o n d e n s i t y of c o l d  rolled  Al-4Cu i s v e r y h i g h compared to t h a t of c o l d - r o l l e d pure aluminum i s a l s o apparent  from the X-ray result's of T a b l e XI. 38 39  s u g g e s t i o n s of B r i m h a l l et a l .  '  T h i s supports the  t h a t d i s p e r s e d 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 s e v e r a l ways, thereby i n c r e a s i n g the r a t e of s t r a i n Stored energy  hardening.  i s r e l e a s e d d u r i n g a n n e a l i n g , and p r o v i d e s a d r i v i n g  f o r c e f o r both r e c o v e r y and r e c r y s t a l l i z a t i o n p r o c e s s e s . of the c o l d worked Al-4Cu a l l o y , i t was  found  In the case  ( F i g . 4) t h a t t h e r e was  a g r a d u a l but l a r g e drop i n 20°C s t r e n g t h w i t h i n c r e a s i n g a n n e a l i n g  - 121  -  temperature i n the range 50-250°C.  Humphreys and M a r t i n  have  suggested t h a t a s i m i l a r drop i n hardness upon a n n e a l i n g 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 C u - S i a l l o y s may  r e l a x a t i o n of l o n g range s t r e s s e s  to  the  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 a n n e a l i n g - o u t of j o g s and dipoles.  be due  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  I n the p r e s e n t work m e t a l l o g r a p h y 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 x i s t e n c e of a p o l y g o n i z e d s u b s t r u c t u r e i n aged A l - 4 C u , a f t e r 70%  reduction  by c o l d r o l l i n g .  e l e c t r o n m i c r o g r a p h s of t h i s a l l o y ( F i g s . 38a  to 38c)  t a n g l e s 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  Transmission show numerous  around p r e c i p i t a t e s .  I t i s suggested t h a t i n the i n i t i a l s t a g e s of r e c o v e r y , i . e . up a n n e a l i n g 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 t a n g l e s and  A decrease i n d i s l o c a t i o n d e n s i t y  (and  associated  an  from such  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  w e l l - d e v e l o p e d p o l y g o n i z e d s u b g r a i n b o u n d a r i e s ( F i g s . 40a  to  and  to 40b).  l a t t i c e s t r a i n ) thus  o c c u r s at r e l a t i v e l y low a n n e a l i n g t e m p e r a t u r e s , w i t h some a t t e n d a n t decrease i n y i e l d strength.  By c o n t r a s t ,  c o l d r o l l i n g had  itself  well-developed (polygonized) c e l l w a l l s with d i s l o c a t i o n - f r e e i n t e r i o r s i n pure aluminum, and  produced  cell  the same low-temperature a n n e a l i n g  t r e a t m e n t s were p r o b a b l y 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 density strength  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 .  of c o l d worked pure aluminum d i d not  Thus the  respond to a n n e a l i n g  i n the range of 50 to 250°C. The  l a r g e r drops i n 20°C s t r e n g t h  temperatures ( i n F i g . 4) correspond  a f t e r a n n e a l i n g at h i g h e r  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 i n c r e a s e  in interparticle  - 122 -  spacing.  A n n e a l i n g a t t h e h i g h e r 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 n c r e a s e i n t h e s p a c i n g o f t h e 0 p a r t i c l e s i n Al-4Cu.  After annealing  at 350°C, t h e i n t e r p a r t i c l e s p a c i n g had i n c r e a s e d t o 2.5 y.  Consider-  i n g c o n t r i b u t i o n s due t o d i s p e r s i o n h a r d e n i n g and s o l i d s o l u t i o n h a r d e n i n g the y i e l d s t r e n g t h o f t h i s m a t e r i a l was c a l c u l a t e d t o be about 7000 p s i which i s c l o s e t o t h e measured v a l u e of 8300 p s i . An i n c r e a s e i n t h e a n n e a l i n g time a t 300°C l i k e w i s e produced a s i m u l t a n e o u s i n c r e a s e i n b o t h i n t e r p a r t i c l e s p a c i n g and s u b g r a i n s i z e i n Al-4Cu.  I n a d d i t i o n , t h e i r r e g u l a r e l o n g a t e d p r e c i p i t a t e s observed  i n t h e 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  of Orowan s t r e n g t h e n i n g i n t h e c o l d worked-and-annealed  contribution  Al-4Cu i s  found t o be much l e s s than i n the s i m p l e over-aged a l l o y due t o t h i s c o a r s e n i n g and s p h e r o i d i s a t i o n o f t h e 0 phase w i t h  thermo-mechanical  treatments. The a p p r e c i a b l y h i g h e r s t r e n g t h o f r e c o v e r e d Al-4Cu a l l o y s compared t o t h a t of pure aluminum ( F i g s . 4, 7 and 8) f o r any a n n e a l i n g treatment i s an i n d i c a t i o n o f the r e t a r d a t i o n o f r e c o v e r y p r o c e s s e s , and the r e t e n t i o n of p a r t 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 t o t h e presence of t h e 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 t h e r e c o v e r e d  a l l o y cannot s i m p l y be accounted f o r a d e q u a t e l y by t h e second phase dispersion.  F o r example, t h e cold-worked Al-4Cu a l l o y , 'B' S e r i e s ,  when annealed a t 300°C f o r 4 hours had a y i e l d s t r e n g t h 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 o f t h i s a l l o y due t o t h e combined e f f e c t s of Orowan h a r d e n i n g ( t a k i n g i n t o account t h e observed i n c r e a s e i n i n t e r p a r t i c l e s p a c i n g ) and s o l i d s o l u t i o n h a r d e n i n g i s found t o be about  - 123 9000 p s i .  Thus, a t l e a s t 6000 p s i o f t h e 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 o f s u b s t r u c t u r e h a r d e n i n g . U s i n g measured s u b g r a i n d i a m e t e r s , a H a l l - P e t c h p l o t was made o f the 20°C y i e l d s t r e n g t h d a t a ( F i g . 5 4 ) . The o r i g i n a l d a t a a r e c o n t a i n e d in- T a b l e XV o f t h e Appendix.  When a s t r a i g h t l i n e was f i t t e d t o t h e  p o i n t s by t h e method o f l e a s t s q u a r e s ,  (the i n t e r c e p t ) was 1800 p s i ,  i n agreement w i t h t h e expected y i e l d s t r e n g t h o f t h e r e c r y s t a l l i z e d 3 matrix metal.  The s l o p e o f t h e p l o t was 15.9 x 10  1/2 psi y  As noted p r e v i o u s l y i n S e c t i o n 5.1.1, measured s u b g r a i n are c o n s i d e r a b l y a t v a r i a n c e w i t h domain s i z e s determined t e c h n i q u e , t h e l a t t e r b e i n g much s m a l l e r .  diameters  by t h e X-ray  I n t h e case o f aged-and-  r o l l e d A l - 4 C u , a m e a n i n g f u l v a l u e o f domain s i z e was o b t a i n e d from t h e 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 t h e t r u e s u b g r a i n 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 t a k e n from t h e t e n s i l e d a t a , t h e H a l l - P e t c h r e l a t i o n gives; 41,100  =  1800  +  k(0.086)  1/2 from w h i c h k = 11.5 K s i u. •.  1  /  I t i s i n t e r e s t i n g t o note t h a t t h i s v a l u e 74  of k i s v e r y c l o s e t o t h a t o b t a i n e d by B a l l aluminum (see T a b l e X I I I ) .  (31)  2  f o r pure deformed  B a l l ' s X-ray t e c h n i q u e f o r t h e d e t e r m i n a t i o n  of c e l l o r s u b g r a i n s i z e was a p p l i c a b l e t o c e l l d i a m e t e r s w e l l i n o  excess o f t h e 1000 A lower l i m i t o f t h e t e c h n i q u e used i n t h e p r e s e n t work, w h i c h made i t u s e f u l f o r t h e pure m e t a l .  - 124 -  38  0  0.4  0.8  1.2 1.6 -1/2 . ,-1/2 £ , (micron) '  2.0  2.4  r  F i g u r e 54.  20°C Y i e l d s t r e n g t h 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 r o o t of the s u b g r a i n d i a m e t e r .  2.8  - 125 -  I t i s i m p o r t a n t t o n o t e t h a t i n the p r e v i o u s d e r i v a t i o n of k, i t was  assumed t h a t 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 s u b g r a i n boundary s t r e n g t h e n i n g .  the case of s i m p l e aged a l l o y s s t r e n g t h e n i n g was  ( S e c t i o n 5.1.2.1) almost a l l observed  a t t r i b u t e d to the Orowan mechanism.  The  possibilities  must be c o n s i d e r e d t h a t (a) Orowan and sub-boundary h a r d e n i n g can be a d d i t i v e , and may  Yet i n  (b) i n the aged-worked-annealed a l l o y ,  effects  hardening  be due t o one mechanism i n one annealed c o n d i t i o n , but due  to another mechanism i n another  mainly  condition.  There appears to be no j u s t i f i c a t i o n f o r adding Orowan and boundary s t r e n g t h e n i n g i n the same m a t e r i a l .  sub-  The b a r r i e r s r e p r e s e n t e d  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 s i m u l t a n e o u s l y , by d i s l o c a t i o n s moving i n the s l i p p l a n e ; thus the s t r o n g e r b a r r i e r s s h o u l d determine C a l c u l a t e d v a l u e s of O Q ^ f  r  o  the f l o w s t r e s s . Orowan and H a l l - P e t c h e q u a t i o n s  m  are p l o t t e d a g a i n s t p a r t i c l e s p a c i n g and domain (or s u b g r a i n ) 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 e q u a t i o n (2) has  been used; i . e .  , a  0.2  =  a  s  2 x c o n s t . x Gb  D  +  ( 3 2 )  When the e x p e r i m e n t a l d a t a f o r t h e s i m p l e aged a l l o y ( S e c t i o n 5.1.2.1) are p l o t t e d a c c o r d i n g to t h i s e q u a t i o n (see F i g . 60 i n A p p e n d i x ) , i t i s found t h a t  a  „ 0.2 A  =  5300  +  8900 D  1  s  (33)  O  Orowan E q u a t i o n ,  a  „ = 5300 + 8900 D 0.2 s  -1  n  60  Hall-Petch Equation,  a  2  =  1800 + 1 1 5 0 0  I  -1/2  50  40  3  ON  30 Experimental Range o f D  20  10 E x p e r i m e n t a l Range o f D or I  I  I 0.8  F i g u r e 55.  I  L 1.6  1  2.0 I or D , microns s C o m p a r i s o n o f 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  J  L  2.8 f o r various values  3.6 o f I or D  - 127 -  The H a l l - P e t c h p l o t o f F i g . 55 was based on t h e v a l u e o f k determined from e q u a t i o n  o  The The  Q  2  (31); i . e .  =  1800  +  11.5 x 1 0  3  jf  e n t i r e e x p e r i m e n t a l range o f D  corresponding  g  1  /  (34)  2  v a l u e s was 1.3 t o 2.2 y.  range o f b o t h measured s u b g r a i n s i z e s and X-ray domain  s i z e s f o r t h e cold-worked-and-annealed a l l o y was 0.09 t o 2 y.  Obser-  v a t i o n o f F i g . 55 r e v e a l s t h a t w i t h i n these r a n g e s , c a l c u l a t e d subboundary s t r e n g t h e n i n g i s a t l e a s t as g r e a t as d i s p e r s i o n s t r e n g t h e n i n g . I n f a c t , f o r most o f t h e deformed-annealed m a t e r i a l s , t h e domain s i z e (or measured a v a l u e ) was much l e s s than t h e i n t e r p a r t i c l e s p a c i n g , and sub-boundary s t r e n g t h e n i n g can c l e a r l y be expected a f t e r t h e h e a v i e s t a n n e a l i n g treatment both D  s  and I  t o dominate.  Even  o f 15 hours a t 300°C, where  (measured) were about 2 m i c r o n s ,  c a l c u l a t e d hardening  from  the H a l l - P e t c h e f f e c t i s as g r e a t as t h a t from t h e Orowan e f f e c t . I t i s concluded  t h a t i n a l l the over-aged Al-4Cu m a t e r i a l s which  were s u b j e c t e d t o thermo-mechanical t r e a t m e n t , t h e  observed  strength  i s due almost e n t i r e l y t o 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 , as i n t h e case o f pure aluminum.  T h i s i s i n marked c o n t r a s t t o t h e c o n c l u s i o n f o r t h e  s i m p l e over-aged a l l o y , where t h e i n t e r p a r t i c l e s p a c i n g was i n a l l cases much l e s s than t h e g r a i n s i z e , and where no f i n e s u b s t r u c t u r e was p r e s e n t . I n a l l cases o f 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 s p a c i n g s , Clegg sub-boundary strengthening predominated.  a l s o concluded  The s t r e n g t h e n i n g e f f e c t o f  that  - 128  -  the d i s p e r s e d 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 o f the e f f e c t of the p a r t i c l e s on the o p e r a t i o n 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 p r o v i d e t o dynamic  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 r e c o v e r y and  recovery,  recrystallization.  I t s h o u l d be n o t e d t h a t s u b s t r u c t u r e s can be d e s c r i b e d  alternatively  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).  I n 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 t o the " m a t r i x y i e l d s t r e s s " i n the Orowan e q u a t i o n , ( 2 ) , and  thus i t i s perhaps r e a s o n a b l e  t h a t of the p a r t i c l e s .  t o add t h e i r c o n t r i b u t i o n to  T h i s i s i n c o n t r a s t to the p r e v i o u s  approach,  where d i s l o c a t i o n s were c o n s i d e r e d o n l y i n r e l a t i o n t o the c e l l s s u b g r a i n s w h i c h they bound, and where Orowan s t r e n g t h e n i n g was considered  to be a d d i t i v e t o s u b g r a i n s t r e n g t h e n i n g .  or  not  The method of  adding these s t r e n g t h e n i n g 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 c o n t a i n i n g G.P.  i n c l u d i n g Dew-Hughes and Robertson"*" w i t h A l - C u a l l o y s 7  5 32 81 zones, Hansen ' w i t h A l - A ^ O ^ p r o d u c t s , and Webster  w i t h d i s p e r s i o n hardened nichrome (TDNiC). A l - 4 C u ('B' 0.2  S e r i e s ) 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  pet y i e l d s t r e n g t h of 41,100 p s i .  y i e l d s t r e n g t h of t h i s a l l o y was  I n the over-aged c o n d i t i o n the  o n l y 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 s o c i a t e d w i t h d i s l o c a t i o n d e n s i t y i s 27,800 p s i . 10 d i s l o c a t i o n d e n s i t y o f t h i s a l l o y i s at l e a s t 4 x 10 p o s s i b l y h i g h e r by a f a c t o r of two obtained range 0.4  from e q u a t i o n t o 0.6,  pure aluminum.  a  (see T a b l e X I ) .  The  -3 cm.cm  and  The v a l u e of y  (30) u s i n g these d a t a i s found t o be i n the  w h i c h may  be compared w i t h the v a l u e of 0.45  for  - 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 a n a l y s e the performance of A l - 4 C u .  of the 'C'  Series  These m a t e r i a l s were c o l d r o l l e d 70% i m m e d i a t e l y a f t e r  s o l u t i o n t r e a t m e n t , and were then aged a t 300°C f o r v a r i o u s amounts of time.  The second phase was  thus i n t r o d u c e d o n l y a f t e r d e f o r m a t i o n .  By  c o n t r a s t , a l l o y s of the A or B S e r i e s were c o l d worked e n t i r e l y i n the presence of the second phase. the ' C  1  Compared to a l l o y s of the A o r B S e r i e s ,  S e r i e s a l l o y s e x h i b i t e d h i g h e r s t r e n g t h s b o t h a t R.T.  300°C f o r any p r i o r thermo-mechanical  and a t  treatment.  I n the cold-worked s t a t e the 'C' S e r i e s had an u n u s u a l l y h i g h y i e l d s t r e s s ; about 49,000 p s i , compared to a v a l u e of 41,000 p s i f o r S e r i e s 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 t o  contain fine substructure c e l l s .  However, a f t e r a s h o r t time a t room  t e m p e r a t u r e , t h e r e i s a marked i n c r e a s e 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 . and Nicholson''" have mentioned  the r e s u l t s of G r a f , who  Kelly  showed t h a t  p l a s t i c d e f o r m a t i o n 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 A l - C u l e a d s t o the f o r m a t i o n of G.P.  zones a t room temperature much more  r a p i d l y than would o c c u r i n the absence of p r i o r d e f o r m a t i o n . the 8000 p s i increment i n y i e l d s t r e n g t h of the 'C  1  Thus  Series alloy i s  p r o b a b l y due to the u n a v o i d a b l e p r e c i p i t a t i o n of some G.P. room temperature a f t e r c o l d r o l l i n g and p r i o r t o t e n s i l e  zones a t testing.  P r e c i p i t a t i o n phenomena a r e i n f a c t commonly a f f e c t e d by c o l d work p r i o r to a g e i n g .  The n a t u r e o f the p r e c i p i t a t e s formed and the r a t e o f  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 t h e amount of p r i o r c o l d work, the a g e i n g temperature,and t u r n , determine the r a t e of h a r d e n i n g .  the time of a g e i n g .  These, i n  - 130 -  Generally p r i o r 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  prior  to ageing increases the rate of nucleation of an intermediate p r e c i p i t a t e . I t 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 h e a v i l y d i s t o r t e d l a t t i c e the nucleation of the noncoherent e q u i l i brium 9 phase i s favoured.  A f t e r 70% r o l l i n g deformation  the a l l o y  contains regions of high d i s l o c a t i o n density ( c e l l w a l l s ) and of lower d i s l o c t i o n density.  regions  Thus p r e c i p i t a t i o n of both 0 and 0 '  may  s t a r t simultaneously during subsequent ageing at 300°C, 0 nucleating at the regions of high d i s l o c a t i o n density and  0  1  at regions nearly  free of d i s l o c a t i o n s . The 0 ' and 9 phases can be d i s t i n g u i s h e d by e l e c t r o n d i f f r a c t i o n , but more e a s i l y by t h e i r t y p i c a l and d i f f e r e n t 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 t h e i r mechanism of formation; i n 83 deformed a l l o y s they are found to be almost spheres.  This i s shown  i n F i g . 56a which i s a transmission e l e c t r o n micrograph of Al-4Cu, 'C' S e r i e s , reduced 70% by cold r o l l i n g and then aged at 300°C for one A f t e r the p r e c i p i t a t i o n of 9 ' phase, the d i s l o c a t i o n s rearrange  hour.  to form sub-boundaries ( F i g . 56b).  Large  0 ' p a r t i c l e s grow and 84  f i n a l l y transform i n t o 9 phase, while small ones d i s s o l v e .  At longer  ageing times the subgrain s i z e increases, and the m i s o r i e n t a t i o n between subgrains increases. coarsening of the  These two phenomena are governed by the  9 phase.  No X-ray d i f f r a c t i o n studies were c a r r i e d out on the C Series alloys.  Thus, only measured subgrain s i z e s are a v a i l a b l e f o r the  i n t e r p r e t a t i o n of y i e l d strength i n terms of a Hall-Petch r e l a t i o n s h i p .  - 131 -  F i g u r e 56.  T r a n 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 of A l - 4 C u (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 h r . (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  -  I n view of the emphasis p l a c e d 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 A l - C u 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 t h a t the domain s i z e of ^ 1000  A r e v e a l e d by X-ray  s t 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 t r u e s i z e , the s u b g r a i n s t r e n g t h e n i n g c o u l d be a p p r e c i a b l e . equation  subgrain  According  to  ( 3 4 ) , based on A l - C u d a t a , the y i e l d s t r e n g t h s h o u l d be about o  38,000 p s i f o r I = 1000 observed s t r e n g t h .  A.  T h i s i s o n l y s l i g h t l y h i g h e r than the  I t i s s i g n i f i c a n t to n o t e from T a b l e XI t h a t c o l d  r o l l e d A l - C u 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 s t r e n g t h s . Several workers^'  8  ^  have c l a i m e d  s t r e n g t h e n i n g i n S.A.P.-type a l l o y s .  to show e v i d e n c e f o r Orowan 9 32  Hansen '  c o n t a i n i n g a wide range of o x i d e c o n t e n t s . Al^O^  worked w i t h  alloys  He found t h a t h i s  lower  m a t e r i a l s c o u l d be f u l l y r e c r y s t a l l i z e d by h e a t t r e a t m e n t ,  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 s u b s t r u c t u r e . Hansen proposed t h a t s t r e n g t h was  due m a i n l y  thus  For such m a t e r i a l s 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 b o u n d a r i e s .  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 t h a t the 5 hardening  substructure  32 '  c o u l d be added d i r e c t l y t o Orowan h a r d e n i n g .  To  account  f o r the s u b s t r u c t u r e 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 s h i p i n c o n j u n c t i o n w i t h measured s u b g r a i n 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  recrystallized  - 133 -  a l l o y s , was so l a r g e t h a t t h e s l o p e o f Hansen's H a l l - P e t c h p l o t s was low; i . e . t h e s u b s t r u c t u r e c o n t r i b u t i o n t o s t r e n g t h was s m a l l 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 h i g h  o x i d e c o n t e n t S.A.P. a l l o y s , he found t h a t they c o u l d n o t be r e c r y s t a l l i z e d ; thus he was not a b l e t o 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 t o t h e s t r e n 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 o f h i s s t r e n g t h  data w i t h measured c e l l o r s u b g r a i n s i z e s , and took t h e i n t e r c e p t s a t £ =  oo to be the Orowan c o n t r i b u t i o n . F o r an a l l o y  essentially  i d e n t i c a l t o the S.A.P. used i n t h e p r e s e n t work, he c l a i m e d an i n t e r c e p t o f 26,000 p s i , w h i c h he argued was a r e a s o n a b l e v a l u e f o r Orowan s t r e n g t h e n i n g when h i s r e s u l t s w i t h lower o x i d e c o n t e n t s  (recrystal-  l i z e d ) were e x t r a p o l a t e d . o  The measured mean p l a n a r i n t e r p a r t i c l e s p a c i n g , D , was. about 800 A g  for  S.A.P. m a t e r i a l s i n t h e p r e s e n t work.  Applying equation  (2) w i t h  a p p r o p r i a t e c o n s t a n t s 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 o f ^ 100,00 p s i i s o b t a i n e d ; i . e . s e v e r a l times h i g h e r than the observed value.  S i n c e t h e c o n s t a n t s i n the Orowan e q u a t i o n f o r aluminum a r e  w e l l t e s t e d by t h e work of o t h e r 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 t h a t the m e t a l l o g r a p h i c t e c h n i q u e s used t o determine D c o n s i d e r a b l y underestimated  the s p a c i n g .  g  i n S.A.P. have  P a r t of the d i f f i c u l t y a r i s e s  from t h e f a c t t h a t the o x i d e p a r t i c l e s a r e 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 a r e i d e n t i f i e d as " p a r t i c l e s " , t h a t i s , i f t h e  s p a c i n g o f 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 n e g l e c t e d , the mean p l a n a r s p a c i n g i s much h i g h e r . Assuming t h a t o n l y Orowan-type s t r e n g t h e n i n g i s s i g n i f i c a n t i n t h e S.A.P. of the p r e s e n t work, e q u a t i o n  (2) r e v e a l s t h a t the o x i d e  particle  - 134 s p a c i n g s h o u l d be about 0.3  -  ]i to account f o r the observed f l o w s t r e s s .  I n a l l c o n d i t i o n s i n w h i c h i t was  examined, the S.A.P. of  p r e s e n t work c o n t a i n e d a f i n e s u b s t r u c t u r e . accepted,  I f Hansen's a n a l y s i s were  26,000 p s i would be a t t r i b u t a b l e t o d i r e c t p a r t i c l e  s t r e n g t h e n i n g , and 6000-8000 p s i would be due are s e v e r a l reasons why  the  (Orowan)  to s u b s t r u c t u r e .  There  t h i s i n t e r p r e t a t i o n o f the r e s u l t s must be  rej ected: (a)  I n the presence of b o t h s u b g r a i n or c e l l b o u n d a r i e s  and  p a r t i c l e s , t h e r e i s no r e a s o n to expect the e f f e c t s of each b a r r i e r to be s i m p l y a d d i t i v e . (b)  I f sub-boundary s t r e n g t h e n i n g i s t o be i n c l u d e d , i t s c o n t r i -  b u t i o n s h o u l d be c o n s i s t e n t w i t h t h a t observed i n pure aluminum and A l - 4 C u i n the p r e s e n t work.  The v e r y f i n e s u b s t r u c t u r e s i n S.A.P.  s h o u l d be c a p a b l e 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 n o t e d 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 n a t u r e 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 t o 51) makes i t d i f f i c u l t t o have any metallographic  confidence  i n v a l u e s of D  g  or H determined by  techniques.  Thus a l l the observed s t r e n g t h of S.A.P. a l l o y s can be e x p l a i n e d i n terms of 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 .  adequately  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 s t r e n g t h e n i n g i n t h i s alloy. I t i s p o s s i b l e to use the a f o r e m e n t i o n e d a l t e r n a t i v e view of subs t r u c t u r e as an a r r a y of d i s l o c a t i o n s g i v i n g a s t r e n g t h e n i n g c o n t r i b u t i o n  - 135 -  a = 2.24 Y P G b  •  The X-ray d a t a o f T a b l e X I show t h a t t h e s t r e n g t h  of S.A.P. can be e x p l a i n e d  on t h i s b a s i s when a comparison i s made  w i t h cold-worked A l - 4 C u (see S e c t i o n 5.1.2.2). 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 s f o r S.A.P. (see F i g s . 49 and 51) show the presence o f c l u s t e r s o f o x i d e p a r t i c l e s b o t h i n c e l l and  along c e l l w a l l s .  interiors  A f t e r 50% c o l d work (see F i g s . 50a t o 50c) most  of t h e c e l l i n t e r i o r s were f r e e o f d i s l o c a t i o n s .  T h i s would p r o b a b l y  i n d i c a t e t h a t a s i g n i f i c a n t f r a c t i o n o f t h e 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 h e l d up between the o x i d e p a r t i c l e s i n t h e clusters.  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 a r e u n a b l e t o break away  upon h e a t i n g .  This i s probably the reason f o r the high d i s l o c a t i o n  d e n s i t y and f o r t h e i n s i g n i f i c a n t d e c r e a s e i n s t r e n g t h o f cold-worked S.A.P. even a f t e r a n n e a l i n g  5.2  f o r 24 hours a t 540°C; see T a b l e X I .  S t r e s s - S t r a i n Curves and D u c t i l i t y a t 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 a r e 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 r e v e a l e d .  I t i s n o t p o s s i b l e from the c u r v e s o f F i g . 57 t o compare  i n i t i a l w o r k - h a r d e n i n g r a t e s , because o f t h e c o a r s e s c a l e o f the s t r a i n a x i s i n the p l o t .  Thus, f o r example, t h e low s l o p e o f t h e c u r v e f o r  annealed 'B' S e r i e s A l - 4 C u a l l o y a t > 1% s t r a i n i s i n d i c a t i v e o n l y o f a low n e t r a t e o f h a r d e n i n g a f t e r v e r y l a r g e s c a l e d i s l o c a t i o n m o t i o n has  occurred..-  The n e t r a t e o f work h a r d e n i n g i n t h i s m a t e r i a l was i n  f a c t h i g h a t .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.  the c u r v e s r e v e a l t h e e f f e c t s o f combined h a r d e n i n g and dynamic  Thus, recovery  - 136 -  54  1.  M l , 70% C.W.  2.  M l , 70% C.W. + annealing at 300°C f o r 6 hrs  3.  Al-4Cu, over-aged  4.  Al-4Cu, h o t - r o l l e d  5.  Al-4Cu, B, C.W. 70%  6.  Al-4Cu, B, C.W. 70% + annealed at 300°C f o r 1 hr.  7.  Al-4Cu, B, C.W. 70% + annealed at 300°C f o r 4 hrs. S.A.P., C.W. 50%  8. 9.  0.02 Figure 57.  0.04  S.A.P., C.W. 50% + annealed at 540°C f o r 24 hrs.  0.06 0.08 True S t r a i n  0.1  0.12  0.14  20°C True s t r e s s - t r u e s t r a i n curves f o r 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  F i g u r e 58.  0.02 0.03 True S t r a i n 20°C True s t r e s s - t r u e s t r a i n c u r v e s f o r Al-4Cu (B S e r i e s ) r o l l e d 70% and annealed at d i f f e r e n t t e m p e r a t u r e s .  cold-  - 138 -  p r o c e s s e s , t h e l a t t e r o f w h i c h become more i m p o r t a n t w i t h  increasing  strain. 86 As v i s u a l i z e d by A l d e n ,  dynamic r e c o v e r y i s a s s o c i a t e d w i t h two  e f f e c t s ; (a) t h e a n n i h i l a t i o n o f i n t e r a c t i n g d i s l o c a t i o n s w h i c h a c t s to lower the average f l o w 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 . s u b g r a i n f o r m a t i o n w h i c h l e a d s t o t h e f o r m a t i o n o f " s o f t s p o t s " w h i c h can y i e l d a t s t r e s s e s average f l o w s t r e s s .  lower than t h e  The shapes o f t h e c u r v e s o f F i g s . 57 and 58 can  be e x p l a i n e d i n t h e s e terms. H e a v i l y c o l d worked m e t a l s o r a l l o y s , o r any m a t e r i a l s ( e . g . S.A.P.) c o n t a i n i n g  a dense, f i n e d i s l o c a t i o n s u b s t r u c t u r e a t t h e s t a r t  of t h e t e n s i o n t e s t a r e u n l i k e l y t o undergo much dynamic r e c o v e r y d u r i n g t h e t e s t as a r e s u l t o f a change i n d i s l o c a t i o n i . e . e f f e c t (b) above. and  "dispersion",  Any c e l l s p r e s e n t a r e a l r e a d y e x t r e m e l y f i n e ,  " 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, t h e 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 h i g h t h a t  small  a d d i t i o n a l s t r a i n i n t e n s i o n causes a " s a t u r a t i o n  l e v e l " of density to  be a c h i e v e d i n w h i c h d i s l o c a t i o n s a r e a n n i h i l a t e d  as f a s t as o t h e r s  are g e n e r a t e d .  Thus t h e maximum s t r e s s on such m a t e r i a l s  i s attained  a f t e r r e l a t i v e l y s m a l l u n i f o r m s t r a i n (low u n i f o r m e l o n g a t i o n This i s true for h e a v i l y and  values).  cold-worked pure aluminum, over-aged A l - 4 C u ,  S.A.P., as w e l l as f o r "annealed S.A.P." w h i c h s t i l l has a dense  substructure a f t e r annealing. A l t h o u g h a l l t h e above m a t e r i a l s  e x h i b i t low e l o n g a t i o n v a l u e s  f o r t h e broad reasons n o t e d , i t i s s i g n i f i c a n t t h a t 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 A l - 4 C u o r 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 ,  slip  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 i n t h e l a t t i c e than i n the case o f a pure m e t a l .  can be  "stored"  Thus 70% c o l d work  on pure aluminum has produced p o l y g o n i z e d s t r u c t u r e ,  and f r e s h  produced by t e n s i l e s t r a i n a r e r e a d i l y a n n i h i l a t e d w i t h i n e x i s t i n g polygonized sub-boundaries.  occurs  dislocations  the pre-  Recovery thus accompanies s t r a i n  h a r d e n i n g almost from t h e o u t s e t o f t h e t e n s i o n t e s t .  By  contrast,  the 70% c o l d worked d i s p e r s i o n - h a r d e n e d a l l o y s can a s s i m i l a t e more dislocations  d u r i n g t e n s i l e s t r a i n i n g b e f o r e r e c o v e r y b e g i n s t o keep  pace w i t h s t r a i n h a r d e n i n g . The  as-aged A l - C u a l l o y ( v i r t u a l l y no s u b s t r u c t u r e i n i t i a l l y ) and  the h o t r o l l e d A l - C u 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 but  contain a dispersion  contribute  The second phase p a r t i c l e s  t o v e r y r a p i d d i s l o c a t i o n g e n e r a t i o n when t h e s e  are f i r s t s t r a i n e d locations  of a second phase.  i n tension.  densities  materials  I n the e a r l y stages of f l o w , the d i s -  a r e homogeneously d i s t r i b u t e d .  With i n c r e a s i n g  strain,  however, c e l l s d e v e l o p ; i . e . " s o f t " and " h a r d " s p o t s a r e 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 a r e 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 t h e r e c o v e r y c o n t r i b u t i o n  o f e f f e c t (b)  i n t h e A l d e n t h e o r y may be i m p o r t a n t w h i l e w e l l - d e f i n e d  c e l l s o r sub-  grains are s t i l l forming.  A p p r e c i a b l e s t r a i n can be accommodated ( i . e .  r e l a t i v e l y h i g h e l o n g a t i o n ) d u r i n g t h e f o r m a t i o n of a f i n e s u b s t r u c t u r e . At l a r g e s t r a i n s t h e h i g h d i s l o c a t i o n d e n s i t y  l e a d s t o the s a t u r a t i o n  e f f e c t d e s c r i b e d 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 t h e a t t a i n m e n t o f the maximum s t r e s s .  The e f f e c t o f 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 p m a l l e r as t h e c e l l s i z e has decreased w i t h increasing  strain.  - 140 F i n a l l y , t h e b e h a v i o u r o f m a t e r i a l s such as annealed pure aluminum and c o l d worked-and-annealed A l - 4 C u i n F i g . 57 can be c o n s i d e r e d .  In  annealed pure aluminum, t h e r e a r e no second phase p a r t i c l e s t o 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 g e n e r a t i o n o r s m a l l c e l l f o r m a t i o n beyond t h e very e a r l i e s t s t r a i n region.  The f o r m a t i o n o f c o a r s e p o l y g o n i z e d  cell  w a l l s l e a d s t o an i m p o r t a n t r e c o v e r y e f f e c t due t o (b) above, b u t l a r g e s t r a i n s can be accommodated i n the p r o c e s s ; i . e . t h e m a t e r i a l e x h i b i t s a high uniform elongation.  A l s o , d i s l o c a t i o n s which s l i p  the sharp s u b g r a i n w a l l s (see F i g s . 29 and 30) a r e p r o b a b l y w i t h r e l a t i v e ease.  into  annihilated  Thus, t h e s l o p e o f t h e 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. Al-4Cu i s more d i f f i c u l t  The b e h a v i o u r o f c o l d worked-and-annealed to i n t e r p r e t .  The s t a t i c a n n e a l a t 300°C a f t e r  heavy c o l d work has produced a p o l y g o n i z e d s u b s t r u c t u r e i n w h i c h the sub-grain boundaries F i g s . 43 through 45).  a r e e x t r e m e l y w e l l - d e f i n e d y e t c l o s e l y spaced (see D u r i n g 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 o f t h e f r e s h l y - p r o d u c e d d i s l o c a t i o n s , such t h a t d i s l o c a t i o n s a r e r e a d i l y a n n i h i l a t e d , and s o f t s p o t s a r e c o n s t a n t l y regenerated.  T h i s keeps the n e t r a t e o f work h a r d e n i n g  low. However,  the g e n e r a t i o n o f d i s l o c a t i o n s a t p a r t i c l e s permits a h i g h s t r a i n t o be accommodated b e f o r e the r e c o v e r y 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 t h a t t h e r e i s a g r a d u a l  decrease  i n t h e u n i f o r m e l o n g a t i o n o f A l - 4 C u , S e r i e s B, w i t h i n c r e a s i n g a n n e a l i n g temperature  up t o about 200°C, above w h i c h u n i f o r m e l o n g a t i o n i n c r e a s e s  very r a p i d l y . at  The r a t e o f work h a r d e n i n g o f these a l l o y s , p a r t i c u l a r l y  low p l a s t i c s t r a i n s , i s seen i n F i g . 58 t o i n c r e a s e w i t h p r i o r  a n n e a l i n g temperature  up t o 200°C,beyond w h i c h i t decreases  considerably.  - 141 -  When t h e work h a r d e n i n g r a t e i s h i g h , t h e u l t i m a t e s t r e n g t h i s reached a f t e r v e r y s m a l l p l a s t i c s t r a i n s , thereby p r o d u c i n g uniform  a decrease i n  elongation.  I n summary, t h e 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 c u r v e s and elongation values are associated 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 r e s p e c t t o t h e d e n s i t y and d i s t r i b u t i o n o f dislocations i n the i n i t i a l substructure.  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 , well-polygonized  substructure i n a dispersion-  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 t o a marked r e d u c t i o n i n t h e r a t e o f w o r k - h a r d e n i n g a t s t r a i n s >0.2  5.3  percent.  T e n s i l e P r o p e r t i e s a t 300°C According  t o Guyot and R u e d l , _3  350°C), f o r a s t r a i n f o 2 x 10  87 88 ' above room temperature (up t o  t h e movement o f d i s l o c a t i o n s i n t h e  r e c r y s t a l l i z e d m a t r i x o f A l - 4 C u and l o w - o x i d e 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 c l i m b , as i n pure aluminum. a c t i v a t i o n energies  f o r deformation  The h i g h observed  o f S.A.P. ( r e a c h i n g 10 o r more  times t h e s e l f - d i f f u s i o n energy) measured above 350°C suggests t h a t t h e h i g h temperature d e f o r m a t i o n from those i n pure aluminum.  mechanisms i n S.A.P. a r e r a d i c a l l y d i f f e r e n t I n t h e pure m e t a l , t h e c l i m b o f d i s l o c a -  t i o n s i s t h e c o n t r o l l i n g p r o c e s s up t o t h e m e l t i 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 t o t h a t o f s e l f - d i f f u s i o n .  models such as (a) g r a i n boundary s l i d i n g ,  Different  (b) d i s l o c a t i o n g e n e r a t i o n  from g r a i n b o u n d a r i e s , (c) p a r t i c l e b y - p a s s i n g  by g l i d e , and (d) t h e r m a l  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 w o r k e r s , have been 88 d i s c u s s e d by Guyot and R u e d l . These v a r i o u s models a r e 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 d o u b t f u l t h a t a s i n g l e mechanism c a n , a t h i g h 87  temperatures, suggested  u n i q u e l y d e s c r i b e t h e f l o w mechanism.  However, Guyot  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 p l a n e 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 t o c o n t r o l , perhaps i n p a r a l l e l w i t h c l i m b , t h e p l a s t i c d e f o r m a t i o n o f S.A.P. 86  I n terms o f Alden's  theory,  t h e rearrangement and a n n i h i l a t i o n  p r o c e s s e s o f r e c o v e r y can proceed more r e a d i l y a t 300°C than a t 20°C because o f t h e r m a l a s s i s t a n c e , and s t r e s s i s no l o n g e r n e c e s s a r y i n c o n j u n c t i o n w i t h temperature  t o cause these r e c o v e r y p r o c e s s e s t o  occur. Dynamic r e c o v e r y mechanisms f o r h o t w o r k i n g  c o n d i t i o n s have been  89  d i s c u s s e d by Jonas e t a l .  Dynamic r e c o v e r y i n a h i g h  temperature  t e n s i l e t e s t i s n o t e q u i v a l e n t t o t h a t w h i c h would o c c u r i n a s t a t i c a n n e a l a t t h e same temperature stress.  without the a p p l i c a t i o n of the a p p l i e d  Jonas e t a l . conclude t h a t under dynamic c o n d i t i o n s o f  d e f o r m a t i o n and heat treatment  ( c h a r a c t e r i s t i c o f h i g h temperature  tensile  t e s t s ) , the f o r m a t i o n o f a p o l y g o n i z e d d i s l o c a t i o n s u b s t r u c t u r e i s a p p a r e n t l y d i s c o u r a g e d by t h e m o b i l i t y of t h e sub-boundaries the a c t i o n o f 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  under anneal  f o l l o w i n g p r i o r c o l d work, r e c o v e r y p r o c e s s e s can l e a d t o the development o f a p o l y g o n i z e d s u b s t r u c t u r e i n w h i c h t h e d i s l o c a t i o n s have c l i m b e d i n t o b o u n d a r i e s  t o p r o v i d e a s t a b l e c o n f i g u r a t i o n o f lower  energy. Another f a c t o r t o c o n s i d e r i s t h e d i r e c t e f f e c t o f t h e d i s p e r s e d second phase on t h e h i g h temperature  y i e l d strength.  Because o f t h e  - 143  -  ease of c r o s s - s l i p and c l i m b , 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 v e r y 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 s u b s t r u c t u r e ) was p l o t t e d a g a i n s t the parameter D - 2r s s log.._(— )/(P - 2r ) i n F i g . 53. From the s t r a i g h t l i n e and 10 2b s s intercept  (a ) g  o b t a i n e d i n t h i s p l o t , one  the  can say t h a t the Orowan  t h e o r y i s a p p a r e n t l y 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 s t r a i n s ) even a t t h i s h i g h temperature. y i e l d s t r e n g t h of A l - A ^ O ^ p r o d u c t s was  9 10 Hansen, ' found t h a t the i n agreement w i t h the Orowan t h e o r y  41 at 400°C.  On the other, hand Clegg  argued t h a t the bowing out  of  d i s l o c a t i o n s between d i s p e r s e d p a r t i c l e s s h o u l d not be c o n s i d e r e d high temperatures. and/or continuous  at  Rather he argued t h a t the b a r r i e r s must be s t a b l e t o 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 o n l y 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 s u b s t r u c t u r e d i s l o c a t i o n w a l l or a g r a i n boundary.  According  g r a i n boundaries,  t o C l e g g , the second phase s t a b i l i z e s the  sub-  thereby m a i n t a i n i n g t h e i r c o n t r i b u t i o n t o h i g h s t r e n g t h .  From these apparent d i f f e r e n c e s i n o p i n i o n 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 s h o u l d be e x p l a i n e d on the b a s i s o f the s t r e s s necessary  t o 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 p r e s e n c e of a  d i s l o c a t i o n s u b s t r u c t u r e the sub-boundaries s h o u l d be c o n s i d e r e d as  the  p r i n c i p a l b a r r i e r s to f l o w . S o l i d s o l u t i o n hardening temperatures.  becomes l e s s e f f e c t i v e at e l e v a t e d  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 s h o r t  - 144 -  range i n n a t u r e , and t h e r m a l 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 t o escape from a s o l u t e atom o r atmosphere.  Thus most o f the s o l i d  s o l u t i o n increment due t o 0.16% a t % Cu i n t h e A l - 4 C u a l l o y a t 20°C may n o t be e f f e c t i v e a t 300°C.  T h i s i s s u p p o r t e d by t h e r e s u l t s o f  12 Starr et a l .  who o b t a i n e d a 0.5 p e t f l o w s t r e s s o f 1500 p s i a t  300°C and a t a s t r a i n r a t e o f 0.118 min ^ f o r a s o l i d s o l u t i o n o f aluminum c o n t a i n i n g 0.194 a t % Cu.  From t h i s we can r e a s o n a b l y assume  the 300°C 0.2 p e t f l o w s t r e s s o f aluminum c o n t a i n i n g 0.16 a t % Cu t o -3 -1 be l e s s than 1000 p s i a t a s t r a i n r a t e o f 6.25 x 10 min . T h i s i s w i t h i n 200 p s i o f t h e y i e l d s t r e n g t h r e p o r t e d f o r r e c r y s t a l l i z e d 67 pure aluminum a t 300°C.  5.3.1  Pure Aluminum The g e n e r a l l y low s t r e n g t h o f pure aluminum a t 300°C ( F i g s . 12  and 13) i n d i c a t e s t h a t t h e sub-boundaries produced by a n n e a l i n g t h e cold-worked m e t a l a r e n o t s t a b l e b a r r i e r s t o d i s l o c a t i o n movement under the c o n d i t i o n s o f a h i g h temperature t e s t .  T h i s i s presumably  due t o the r e l a t i v e l y h i g h m o b i l i t y o f t h e sub-boundaries i n t h e pure m e t a l under a p p l i e d s t r e s s and temperature. I t was shown i n S e c t i o n 5.1.1 t h a t t h e room temperature y i e l d s t r e n g t h of aluminum c o n t a i n i n g s u b g r a i n s c o u l d be r e l a t e d t o t h e s u b g r a i n diameter by t h e H a l l - P e t c h r e l a t i o n [ e q u a t i o n (28)J.  At high  t e m p e r a t u r e s , dynamic growth o f s u b g r a i n s d u r i n g t h e t e s t , p r e v e n t s 89 I n f a c t , Jonas e t a l . have  t h i s r e l a t i o n s h i p from b e i n g v a l i d .  suggested t h a t a more g e n e r a l r e l a t i o n s h i p s h o u l d be a p p l i e d a t -M elevated temperatures; i . e . r j 2 a  =  °0  +  ' ^ w  e r e  ^  a n <  ^ ^'  a  r  e  c o n s t a n t s . From t h e i r r e v i e w o f t h e r e s u l t s o f v a r i o u s w o r k e r s , M was  - 145 -  o  t>  i  CN  d D t>0  o  I, F i g u r e 59.  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 t o v a r y between 1 and 2. The above e q u a t i o n was i n v e s t i g a t e d i n t h e p r e s e n t work by p l o t t i n g log(aQ 2 ~ g ) v s . l o g I i n F i g . 59. a  A s t r a i g h t l i n e was f i t t e d by the 67  method o f l e a s t s q u a r e s . I n o r d e r t o draw t h i s l o g p l o t , a r e p o r t e d v a l u e o f O Q = 800 p s i was used.  From F i g . 59, v a l u e s o f M = 0.75 and  K'~= 1.56 x 1 0 p s i ( m i c r o n ) ^ ' ^ ^ 3  a  r  e  obtained.  Thus, t h e 300°C y i e l d  s t r e n g t h o f pure aluminum can be e x p r e s s e d i n t h e f o l l o w i n g  o = 800 + 1.56 x 10 a)"°' 3  75  Q2  form:  (35)  U n i f o r m e l o n g a t i o n v a l u e s f o r aluminum a t 300°C were found t o be l e s s than those a t room temperature f o r any a n n e a l i n g treatment.  The  aforementioned dynamic growth o f s u b g r a i n s i s a form o f r e c o v e r y .  At  s m a l l s t r a i n s , t h e r a t e o f s o f t e n i n g due t o s u b g r a i n 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 o f h a r d e n i n g due t o 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 . t h e maximum ( u l t i m a t e ) u n i f o r m 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 u n i f o r m s t r a i n .  5.3.2  Alumirium-4 Copper From Table V I I i t can be seen t h a t t h e 300°C y i e l d s t r e n g t h o f 12  over-aged Al-4Cu (no s u b s t r u c t u r e ) i s 5,900 p s i .  Starr et a l .  determined t h e f l o w s t r e s s o f Al-4Cu a t such h i g h t e m p e r a t u r e s .  also For a  v o l u m e t r i c mean f r e e p a t h o f 7.8 u between t h e C u A ^ p a r t i c l e s t h e y i e l d s t r e n g t h was found t o be about 3,500 p s i . The i n t e r p a r t i c l e s p a c i n g i n the p r e s e n t work was much f i n e r , and a y i e l d s t r e s s o f 5,900 p s i i s thus r e a s o n a b l e .  I n v i e w o f t h e low y i e l d s t r e n g t h o f  aluminum a t 300°C, and t h e i n s i g n i f i c a n t s t r e n g t h increment due t o 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 A l - 4 C u  a p p a r e n t l y i n d i c a t e s t h a t there i s a l a r g e component  of strengthening  due d i r e c t l y t o t h e presence of t h e C u A ^ p a r t i c l e s .  I t was shown i n  S e c t i o n 5.3 t h a t the 300°C y i e l d s t r e n g t h o f over-aged A l - 4 C u c o u l d be e x p l a i n e d on t h e b a s i s o f the Orowan model.  From t h e Orowan p l o t i n F i g .  53, a , w h i c h c o r r e s p o n d s t o t h e y i e l d s t r e n g t h o f t h e base m e t a l , was found t o be 800 p s i . 53 i s 1.24 x 10  3  The s l o p e o f t h e Orowan p l o t a t 300°C i n F i g .  p s i . u compared t o t h e v a l u e o f 2.5 x 10  3  p s i . u at  room temperature. T h i s low s l o p e may i n d i c a t e t h a t t h e Orowan model does n o t a p p l y at h i g h temperatures and t h a t p a r t i c l e s a r e i n s t e a d by-passed by o t h e r mechanisms such as c r o s s - s l i p and c l i m b . Hot  r o l l i n g f o l l o w e d by c o l d r o l l i n g d r a s t i c a l l y reduced b o t h  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 o f over-aged A l - 4 C u , the former b e i n g a f f e c t e d more than t h e l a t t e r .  S t a t i c annealing  after  c o l d r o l l i n g i n c r e a s e d t h e 300°C y i e l d s t r e n g t h b u t d e c r e a s e d t h e 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 t o t h e c o l d r o l l e d c o n d i t i o n . The  i n c r e a s e i n 300°C y i e l d s t r e n g t h due t o s t a t i c a n n e a l i n g was  found t o r e l a t e g e n e r a l l y t o an i n c r e a s i n g amount o f cold-work VI).  (Table  A n o t h e r i n t e r e s t i n g o b s e r v a t i o n was t h a t i n t h e c o l d worked c o n d i -  t i o n s t h e 300°C y i e l d s t r e n g t h o f pure aluminum was h i g h e r than t h a t of A l - 4 C u (Table v ) .  A l s o , t h e 300°C y i e l d s t r e n g t h o f t h e pure m e t a l  was i n c r e a s e d by i n c r e a s i n g amounts o f 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 e x p l a i n e d by a u n i f i e d argument. I t had been shown p r e v i o u s l y by Clegg  41  and by Towner  42  that t h e i r  - 148  -  cold-worked a l l o y s had h i g h temperature s t r 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 o r e x t r u d e d a n n e a l i n g o f the c o l d worked p r o d u c t s  that s t a t i c  r e s t o r e d , at l e a s t  the s t r e n g t h at e l e v a t e d t e m p e r a t u r e s . cold-worked A.P.M. p r o d u c t s  a l l o y s and  The  partially  low s t r e n g t h of h e a v i l y  at e l e v a t e d temperatures had been q u a l i t a t i v e l y  42 e x p l a i n e d by Towner  as b e i n g due  f a c i l i t a t i n g d i s l o c a t i o n climb.  to a h i g h c o n c e n t r a t i o n of  vacancies  H e a t i n g the c o l d worked m a t e r i a l a t  e l e v a t e d temperatures t o produce r e c o v e r y b e f o r e t e n s i l e  testing  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 t o c l i m b . t h a t most of the d e f o r m a t i o n - i n d u c e d  vacancies  However, i t i s known  i n pure aluminum  i n a few minutes a t room temperature and t h a t complete 90 can occur at about 200°C.  disappear  annealing-out  Thus, Towner's e x p l a n a t i o n f o r the  i n c r e a s e i n h i g h 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 o t h e r hand, e x p l a i n e d 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 p o l y g o n i z e d s t a t i c annealing.  substructure  I n the case of d i s p e r s i o n s t r e n g t h e n e d  during  materials,  the d i s p e r s o i d p a r t i c l e s a r e thought t o e x e r t a p i n n i n g e f f e c t on b o u n d a r i e s due t o 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 e n e r g i e s .  The  resulting  s t a b i l i z a t i o n of the s u b s t r u c t u r e has a l s o been observed i n the study.  the  present  Sub-boundaries a r e 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 t o i n t e r p r e t the remarkable h i 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  transmission  e l e c t r o n m i c r o s c o p e o b s e r v a t i o n s , annealed aluminum and A l - 4 C u a l l o y s are known t o c o n t a i n a p o l y g o n i z e d sub-boundaries.  substructure with w e l l delineated  The Al-4Cu a l l o y has a l s o been shown t o 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 t h e 70% c o l d - r o l l e d c o n d i t i o n , b u t t h e c e l l w a l l s a r e not s h a r p l y d e f i n e d i n comparison w i t h c o l d - r o l l e d aluminum. then,suggest t h a t t h e development o f a p o l y g o n i z e d  We c a n ,  substructure with  w e l l d e f i n e d sub-boundaries i s r e s p o n s i b l e f o r the i n c r e a s e i n h i g h 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 a n n e a l i n g . numerous t a n g l e d d i s l o c a t i o n s p r e s e n t worked A l - 4 C u can p r o b a b l y processes  I n c o n t r a s t , the  i n the c e l l i n t e r i o r s of c o l d -  a c c e l e r a t e d i s l o c a t i o n c l i m b and c r o s s - s l i p  t o produce y i e l d i n g a t lower s t r e s s l e v e l s .  Since c o l d -  worked, aluminum c o n t a i n s v e r y 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 h i g h e r than t h a t o f A l - 4 C u . A f t e r about one hour o f a n n e a l i n g a t 300°C, t h e s u b g r a i n s  i n aluminum  become v e r y l a r g e , and a r e n o t as e f f e c t i v e as b a r r i e r s t o d i s l o c a t i o n m o t i o n , thereby g i v i n g a y i e l d s t r e n g t h lower than t h a t o f A l - 4 C u CFig. 1 2 ) . S i n c e sub-boundaries are formed by t h e rearrangement o f 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 a n n e a l i n g w i l l p r o b a b l y be h i g h e r f o r a m a t e r i a l w h i c h has had more p r i o r c o l d work.  Such sub-  b o u n d a r i e s can be expected t o be s t r o n g e r 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 t o s t a t i c a n n e a l i n g i n c r e a s e d w i t h i n c r e a s i n g amounts o f 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 T a b l e V f o r A l - 4 C u t h a t t h e h i g h e r was the amount o f p r i o r c o l d work, t h e lower was t h e 300°C y i e l d s t r e n g t h , the o p p o s i t e b e i n g t r u e f o r pure aluminum.  I n pure aluminum, s i n c e t h e  sharpness o f c e l l w a l l s i s known t o i n c r e a s e w i t h i n c r e a s i n g amounts of c o l d work., ^  t h e 300°C y i e l d s t r e n g t h i s expected t o i n c r e a s e i n  the same o r d e r .  However, i n A l - 4 C u , reduced 70% by c o l d r o l l i n g , sharp  - 150 -  c e l l w a l l s were n o t observed (see F i g s . 38a t o 38c).  The apparent  d e c r e a s e 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 o f c o l d work can then be a t t r i b u t e d t o t h e d e n s i t y o f t a n g l e d o r 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 density apparently  amounts o f p r i o r d e f o r m a t i o n and  increases with increasing  and enhances p r o b a b l e d i s l o c a t i o n c l i m b  c r o s s - s l i p p r o c e s s e s t o g i v e r i s e t o a v e r y low y i e l d  strength  a t 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 t h e 300°C y i e l d s t r e n g t h o f over-aged A l - 4 C u (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 t o Orowan S i n c e t h e 0-phase d i s p e r s i o n i s s t i l l p r e s e n t  strengthening.  i n t h e c o l d worked-and-  annealed a l l o y s , i t i s e s s e n t i a l t o 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 possible explanations  can be  considered: Ca) Orowan s t r e n g t h e n i n g  i s n o t r e s p o n s i b l e f o r t h e h i g h 300°C  s t r e n g t h o f as-aged A l - 4 C u , 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 o f 8 p a r t i c l e s as b a r r i e r s t o d e f o r m a t i o n at 300°C i s g r e a t l y reduced by the presence o f a d i s l o c a t i o n substructure. 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 c o l d worked-and-annealed A l - 4 C u CB S e r i e s ) i s much d i f f e r e n t than i n t h e s i m p l e aged a l l o y f o r the same a g e i n g t r e a t m e n t o f 15 hours a t 300°C; i . e . a n n e a l i n g t h e a l l o y c o n t a i n i n g a dense s u b s t r u c t u r e has caused major changes i n t h e 0 phase. Explanation be i n v o k e d alloy.  Ca) r e q u i r e s t h a t some o t h e r source o f s t r e n g t h e n i n g  t o account f o r t h e h i g h 300°C s t r e n g t h o f t h e as-aged  The o n l y p o s s i b l e mechanism n o t a l r e a d y d i s c u s s e d would appear  - 151 -  to be g r a i n boundary s t r e n g t h e n i n g . alloys  However, t h e g r a i n s i z e i n aged  was l a r g e , and was no s m a l l e r than i n pure annealed aluminum.  Thus e x p l a n a t i o n (a) must be r e j e c t e d , and Orowan s t r e n g t h e n i n g a t 300°C i n t h e aged a l l o y must be . Explanation  accepted.  (b) seems r e a s o n a b l e  l o s s o f Orowan s t r e n g t h e n i n g  t o account f o r a t l e a s t some  i n the presence of a s u b s t r u c t u r e .  It  i s a l s o c o n s i s t e n t w i t h t h e e a r l i e r argument used t o e x p l a i n why s t a t i c a n n e a l i n g improved t h e 300°C y i e l d s t r e n g t h o f c o l d r o l l e d A l - 4 C u . Considerable  support  f o r e x p l a n a t i o n ( c ) i s p r o v i d e d by comparing  F i g s . 42 t o 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 ) . elongated,  The p r e c i p i t a t e p a r t i c l e s i n t h e as-aged a l l o y a r e  a f a c t which c o n t r i b u t e s to a s m a l l e r planar  interparticle  s p a c i n g than would be t h e case f o r s p h e r i c a l p a r t i c l e s o f t h e same volume.  I n marked c o n t r a s t , t h e p a r t i c l e s o f 0 i n t h e deformed-and-  annealed a l l o y a r e much more s p h e r i c a l i n shape.  There i s a l s o some  e v i d e n c e t h a t t h e average p a r t i c l e s i z e has been i n c r e a s e d by t h e thermomechanical treatment,  growth o f p a r t i c l e s p o s s i b l y h a v i n g been  f a c i l i t a t e d by d i f f u s i o n a l o n g s u b g r a i n b o u n d a r i e s (see F i g . 4 2 b ) . The  300°C u n i f o r m e l o n g a t i o n o f cold-worked A l - 4 C u was much  h i g h e r than b o t h i t s 20°C u n i f o r m e l o n g a t i o n (compare F i g s . 6 and 14) and  t h e 300°C u n i f o r m e l o n g a t i o n o f pure aluminum.  I t was mentioned  e a r l i e r t h a t t h e rearrangement and a n n i h i l a t i o n p r o c e s s e s  of recovery  can proceed a t a f a s t e r r a t e a t 300°C because o f t h e r m a l a s s i s t a n c e . However, t h e second phase p a r t i c l e s c o n t r i b u t e t o a h i g h r a t e o f dislocation multiplication.  Thus, t h e r e i s perhaps a b a l a n c e  between  the r a t e o f s o f t e n i n g due t o 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 o f  - 152 hardening Al-4Cu  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  i s l i k e l y to undergo h i g h e r u n i f o r m e l o n g a t i o n b e f o r e  the maximum s t r e s s . i n c r e a s e s and  opposing  attaining  Upon s t a t i c a n n e a l i n g , the 300°C y i e l d s t r e n g t h  the 300°C u l t i m a t e s t r e n g t h d e c r e a s e s .  e l o n g a t i o n i s expected two  -  Thus, the u n i f o r m  to decrease i n s p i t e of the f a c t  p r o c e s s e s occur  t h a t the p r e v i o u s  simultaneously.  By c o n t r a s t , the d i s l o c a t i o n d e n s i t y of the as-aged Al^-4Cu s u b s t r u c t u r e ) i s i n i t i a l l y v e r y low.  The  d i s l o c a t i o n s generated  t e s t i n g at 300°C are r e a d i l y a n n i h i l a t e d due This behaviour 5.3.1).  (no  to thermal  during  activation.  i s s i m i l a r to t h a t of pure aluminum at 300°C ( S e c t i o n  As expected,  over-aged  Al-4Cu  shows a v e r y low u n i f o r m  elonga-  tion.  5.3.3  S.A.P. In the case of as-aged Al-4Cu,  to Orowan s t r e n g t h e n i n g .  300°C y i e l d s t r e n g t h was  A f t e r c o l d working,  a n n e a l i n g the a l l o y , Orowan s t r e n g t h e n i n g was because the d i s p e r s i o n had tions f a c i l i t a t e d  coarsened,  attributed  or c o l d working  not r e a l i z e d a t 300°C  and because s u b s t r u c t u r e d i s l o c a -  the b y - p a s s i n g of the p a r t i c l e s at the h i g h  In c o n t r a s t to over-aged  Al-4Cu,  and  temperature.  the d i s p e r s i o n 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 o r m e c h a n i c a l  Moreover, t h e r e was  always a f i n e s u b s t r u c t u r e p r e s e n t i n the S.A.P.  m a t e r i a l s , whereas Al-4Cu  treatments.  i n the as-aged c o n d i t i o n c o n t a i n e d no  s i g n i f i c a n t s u b s t r u c t u r e , and o n l y i n the c o l d worked c o n d i t i o n was the s u b s t r u c t u r e as f i n e as i n S.A.P. I t now  becomes important  to decide whether the h i g h  observed  300°C s t r e n g t h of S.A.P. i n the p r e s e n t work (9,000-13,000 p s i ) i s  - 153 a t t r i b u t a b l e t o Orowan s t r e n g t h e n i n g , 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 , o r some compromise mechanism. From a p l o t o f measured 300°C y i e l d s t r e n g t h v s . 60 i n A p p e n d i x ) , hardening  t h e s i m p l i f i e d Orowan e q u a t i o n  ^— s  (see F i g .  (32) f o r d i s p e r s i o n  o f A l - 4 C u i s found t o be o f t h e form  a  = 1900  +  3.9 x 10 D 3  _  (36)  1  s o  U s i n g t h e measured D  g  v a l u e o f 800 A f o r S.A.P. i n e q u a t i o n  a c a l c u l a t e d y i e l d s t r e s s o f 50,000 p s i .  (36) g i v e s  T h i s i s s e v e r a l times  higher  than t h e observed v a l u e . F o l l o w i n g our p r e v i o u s arguments f o r S.A.P. i n S e c t i o n 5.1.3, the o x i d e p a r t i c l e s p a c i n g s h o u l d be about 0.35 y t o 0.5 y t o account f o r t h e observed f l o w s t r e s s i n terms o f Orowan-type s t r e n g t h e n i n g . o  S i n c e t h e domain s i z e o f about 1000 A o b t a i n e d from X-ray a n a l y s i s (Table X I ) f o r S.A.P. i s i d e n t i f i e d w i t h t h e s u b g r a i n s i z e , boundary s t r e n g t h e n i n g can be s i g n i f i c a n t a t 300°C.  subgrain  Based on pure  aluminum d a t a , t h e 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 e q u a t i o n (35) o  f o r % = 1000 A i s about 10,000 p s i .  T h i s compares w e l l w i t h t h e  observed 300°C s t r e n g t h o f S.A.P. (9,000-13,000 p s i ) . S e v e r a l reasons can be suggested f o r a t t r i b u t i n g t h e 300°C s t r e n g t h o f S.A.P. t o s u b s t r u c t u r e . (a)  I n t h e presence o f b o t h a f i n e s u b s t r u c t u r e and d i s p e r s o i d  p a r t i c l e s , t h e r e i s a g a i n no r e a s o n t o b e l i e v e t h a t t h e two types of b a r r i e r g i v e a d d i t i v e s t r e n g t h e n i n g .  From t h e X-ray s t u d i e s  (Table  X I ) , t h e s u b s t r u c t u r e o f S.A.P. i s known t o be v e r y s t a b l e even a f t e r  - 154 -  s t a t i c a n n e a l i n g a t 540°C f o r 24 h o u r s .  Thus, t h e h i g h s t a b i l i t y o f  the f i n e s u b s t r u c t u r e o f S.A.P. can p r o b a b l y be m a i n t a i n e d c o n d i t i o n s o f t h e h i g h temperature t e n s i l e t e s t . o x i d e p a r t i c l e s can be c o n s i d e r e d  under t h e  I n t h i s case t h e  t o 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 substructure. (b)  The c o n t r i b u t i o n from s u b g r a i n boundary s t r e n g t h e n i n g i s  found t o be c o n s i s t e n t w i t h t h e o b s e r v a t i o n s made i n pure aluminum and A l - 4 C u i n t h e p r e s e n t work.  I t was shown i n t h i s s e c t i o n t h a t t h e  300°C y i e l d s t r e n g t h o f S.A.P. can be t e n t a t i v e l y e x p l a i n e d i n terms of e q u a t i o n  ( 3 5 ) , based on d a t a f o r pure aluminum.  I t i s a l s o found t h a t t h e e f f e c t s o f p r i o r c o l d w o r k i n g and c o l d w o r k i n g and a n n e a l i n g on t h e 300°C y i e l d s t r e n g t h o f S.A.P. can be e x p l a i n e d i n terms o f t h e arguments suggested f o r two-phase A l - 4 C u a l l o y s ; i . e . t h e development o f a f i n e p o l y g o n i z e d  substructure with  sharp sub-boundaries due t o s t a t i c a n n e a l i n g o f the cold-worked m a t e r i a l improves t h e h i g h temperature s t r e n g t h o f d i s p e r s i o n materials.  I n support  strengthened  o f t h i s argument, T a b l e I X shows t h a t the h i g h e s t  temperature of h e a t i n g , w h i c h 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 t h e 300°C y i e l d  strength  of cold-worked S.A.P. I n c o n c l u s i o n t h e remarkably h i g h s t r e n g t h o f S.A.P. a t e l e v a t e d temperatures can be a t t r i b u t e d t o t h e p r e s e n c e o f a f i n e s u b s t r u c t u r e , s t a b i l i z e d by o x i d e p a r t i c l e s . r e l a t i v e l y coarse p o l y g o n i z e d  polygonized  By c o n t r a s t , t h e  s u b s t r u c t u r e produced as a r e s u l t o f  c o a r s e n i n g o f t h e C u A ^ p a r t i c l e s can be t h e cause f o r t h e lower of A l - 4 C u a t h i g h t e m p e r a t u r e s .  strength  6.  1.  SUMMARY AND CONCLUSIONS  Substructure  i n pure aluminum, over-aged A l - 4 C u and S.A.P.,  produced by s u i t a b l e m e c h a n i c a l and t h e r m a l  treatments,  was s t u d i e d  by 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 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 t h e s t r u c t u r e and the t e n s i l e s t r e n g t h a t two t e s t t e m p e r a t u r e s , R.T. (0.32 Tm) and 300°C (0.62 Tm). 2.  The 0.2 p e t y i e l d s t r e n g t h s o f s i m p l e aged A l - 4 C u a l l o y s (no  s u b s t r u c t u r e ) were found t o be c o n s i s t e n t w i t h t h e Orowan model o f d i s p e r s i o n - s t r e n g t h e n i n g b o t h a t R.T. and a t 300°C. 3.  A f t e r c o l d w o r k i n g and a n n e a l i n g  t o produce a s u b s t r u c t u r e ,  the y i e l d s t r e n g t h s o f aluminum and over-aged A l - 4 C u obeyed t h e relationship  0.2  CT  =  °0  +  k  1  where I i s i d e n t i f i e d as t h e measured c e l l s i z e ( o r X-ray domain s i z e ) of t h e s u b s t r u c t u r e . 4.  I n t h e case o f A l - 4 C u w i t h a c e l l o r s u b g r a i n s i z e s m a l l e r  than t h e 0 phase i n t e r p a r t i c l e s p a c i n g , t h e 20°C y i e l d s t r e n g t h  could  not be i d e n t i f i e d w i t h t h e Orowan type mechanism; r a t h e r , t h e subb o u n d a r i e s were found t o be  strength-determining.  - 156 5.  S i m i l a r l y , t h e observed 20°C y i e l d s t r e n g t h o f S.A.P. a l l o y s  c o u l d be e x p l a i n e d o n l y i n terms o f s u b s t r u c t u r e  strengthening.  Orowan s t r e n g t h e n i n g was a g a i n found t o 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 t h e presence o f 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 t h e c o n c l u s i o n s r e c e n t l y p u b l i s h e d by Hansen. ' 6.  As an a l t e r n a t i v e v i e w , t h e 20°C y i e l d s t r e n g t h o f pure  aluminum, A l - 4 C u and S.A.P. i n t h e presence o f a d i s l o c a t i o n  substructure  c o u l d be a s s o c i a t e d p a r t i a l l y w i t h t h e t o t a l d e n s i t y o f d i s l o c a t i o n s and n o t w i t h the s u b g r a i n s i z e .  Under such c o n d i t i o n s , t h e y i e l d  s t r e n g t h o f A l - 4 C u and S.A.P. was c o n s i d e r e d  as a s u p e r p o s i t i o n o f  d i s 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 s u b s t r u c t u r e 7.  strengthening.  The 20°C s t r e s s - s t r a i n curves f o r pure aluminum, A l - 4 C u 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 e x p l a i n e d i n terms o f the b a l a n c e between w o r k - h a r d e n i n g and dynamic r e c o v e r y p r o c e s s e s  i n these  materials. 8.. The 300°C y i e l d s t r e n g t h o f 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 o f t h e form  0.2  CT  "  a  0  +  K  4  where <JQ and K.' a r e c o n s t a n t s and i i s t h e measured s u b g r a i n 9.  The 300°C y i e l d b e h a v i o u r  diameter.  o f 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 s u b s t r u c t u r e was comparable t o t h a t o f o x i d e 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 a n n e a l i n g a t 300 C b e f o r e t e s t i n g removed t h e  d e t r i m e n t a l e f f e c t s o f p r i o r c o l d work on t h e 300°C s t r e n g t h o f A l - 4 C u and S.A.P. by p r o d u c i n g a more s t a b l e , p o l y g o n i z e d s u b s t r u c t u r e . 11.  The h i g h e r 300°C s t r e n g t h o f S.A.P. compared t o Al-4Cu has  been i n t e r p r e t e d i n terms o f t h e f i n e r and more s t a b l e s u b s t r u c t u r e 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 s p a c i n g o f t h e o x i d e  p a r t i c l e s i n S.A.P. i s conducive domain o r s u b g r a i n s i z e .  to the formation of a very  fine  By c o n t r a s t , t h e 9-phase p a r t i c l e s i n A l - C u  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 o f w o r k - a n n e a l t r e a t m e n t s , and t h e s u b s t r u c t u r e i s c o a r s e r and l e s s s t a b l e .  - 158 -  APPENDIX  T a b l e XIV: Room Temperature and 300°C Y i e l d S t r e n g t h s and t h e C o r r e s ponding S u b g r a i n Diameters f o r Pure Aluminum A f t e r  Various  Thermo-mechanical Treatments.  Material Condition  -1/2 Subgrain Diameter i n microns  I  0.2 p e t y i e l d If2  (micron)  s  t  r  e  n  S  t  n  ^ Ksi n  R.T.  300°C  Cold r o l l e d 60%  0.82  1.10  12.9  2.51  Cold r o l l e d 70%  0.76  1.15  14.6  2.63  Cold r o l l e d 80%  0.70  1.20  15.6  2.83  Cold r o l l e d 80% and annealed a t 300°C f o r 1 hr.  1.90  0.720  Cold r o l l e d 70% and annealed a t 300°C f o r 30 min.  1.33  0.87  C o l d r o l l e d 70% and annealed a t 300°C f o r 1 hr.  1.58  0.80  7.5  2.00  Cold r o l l e d 70% and annealed a t 300°C f o r 2 hrs.  2.28  0.66  5.7  1.65  Cold r o l l e d 70% and annealed a t 300°C f o r 6 hrs.  3.15  0.56  2.4  0.76  C o l d r o l l e d 70% and annealed a t 100°C f o r 1 hr.  0.85  1.09  14.00  Cold r o l l e d 70% and annealed a t 250°C f o r 1 hr.  1.00  1.00  12.60  1.57  10.7  2.40  - 159 -  T a b l e XV:  Room Temperature Y i e l d S t r e n g t h s and t h e C o r r e s p o n d i n g S u b g r a i n Diameters f o r A l - 4 C u , B S e r i e s , Annealed  after  70% C o l d Work.  Annealing  Treatment  1 h r . a t 200°C  ,"1/2  Subgrain Diameter, SL, i n microns  i n (micron)  0.30  1.82  _ < 1  2  0.2 p e t y i e l d s t r e n g t h a t R.T. . in Ksi 32.50 31.20  15 min. a t 300°C  0.55  1.35  23.10  30 min. a t 300°C  0.65  1.24  20.9  1 h r . a t 300°C  0.90  1.05  18.6  2 h r s . a t 300°C  1.08  0.96  17.4  4 h r s . a t 300°C  1.41  0.84  15.1  8 h r s . a t 300°C  1.98  0.71  13.4  - 160 -  Table XVI:  C a l c u l a t e d V a l u e s o f 20°C a  from Orowan and H a l l - P e t c h  Equations f o r Al-4Cu. I or D  OQ 2 C a l c u l a t e d  from  H a l l - P e t c h e q u a t i o n (34) i n microns  in Ksi  a  n  „ Calculated  from Orowan e q u a t i o n (33) in Ksi  0.1  38.2  94.30  0.2  27.6  49.80  0.3  22.8  35.00  0.4  20.0  27.50  0.5  18.0  23.10  0.6  16.7  20.10  0.8  14.7  16.40  1.0  13.3  14.20  1.6  10.9  10.20  2.0  9.9  9.75  2.6  8.9  8.30  3.0  8.4  7.90  3.4  8.0  7.60  - 161 -  ol  0  I  I  0.2  0.4  I  I  0.6 0.8 1 . ,-1 — — , (micron) s  I  1.0  1  1.2  J  1.4  t  ure 60.  S i m p l i f i e d Orowan p l o t f o r the 20°C and 300°C y i e l d s t r e n g t h o f over-aged  Al-4Cu.  _ |  1.6  - 162 -  BIBLIOGRAPHY 1.  K e l l y A. and N i c h o l s o n R.B. , P r o g r e s s i n M a t e r i a l s S c i e n c e , IC), 151391 (1963).  2.  Orowan E., Symposium on I n t e r n a l S t r e s s e s , 451-453, I n s t , o f M e t a l s , London (1948).  3.  G e r a l d V. and Mayer G. , Z. M e t a l l i c . , 58. 698-702 (1967).  4.  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