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Slip continuity across grain boundaries in aluminum 1959

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SLIP CONTINUITY ACROSS GRAIN BOUNDARIES IN ALUMINUM by KEITH GORDON DAVIS A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of MINING AND METALLURGY We accept this thesis as Conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE. Members of the Department of Mining and Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA May, 1959 .ABSTRACT A study of s l i p continuity across grain boundaries i n high- purity aluminum has been carried out, both on bicrystals and on polycrystal s t r i p . Metaliographic methods have been used to show that s l i p continuity is not confined to the surface, but i s a true continuity present within the metal. Orientations favouring continuity have been determined, which indicate that screw dislocations can pass through grain boundaries more easily than edge or mixed dislocations. In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the 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, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree th a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permission. Department The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date i ^ r f a y iqg-q ACKNOWLEDGEMENTS The author i s grateful for the advice and encouragement given by his research director, Dr. E. Teghtsodnian, and for technical assistance given by Mr. R.G. Butters and Mr. R, Richter. The work was carried out with the help of the Defence Research Board Grant Number 7510-29. Financial assistance was also received from the National Research Council and in the form of an Inco Fellowship. TABLE OF CONTENTS Page INTRODUCTION . 1 The Deformation of Polycrystals „ . . 1 Previous Work on P l a s t i c i t y i n Bi c r y s t a l s . . . . . . . . . . . 3 The Problem . • 5 EXPERIMENTAL PROCEDURE . . 7 B i c r y s t a l Work . . . . . . . . . . . 7 Preparation . , . . . « ' 7 Orientation determination • . . . . . . . . . 7 Electropolishing . . . . . . . . . . . . . . . . . . . . . 9 Testing . . . . . . . . « . © « • . * • • . 10 Work on Thin Polycrystal S t r i p 10 Methods Used to Try to see S l i p Bands i n the I n t e r i o r as Revealed by Further Polishing After Testing . . . . . . . . 12 i (a) X-ray microscopy 12 (b) Etching . . . . . o . . . . . . . . . . . . . . . . o 12 (c) P r e c i p i t a t i o n of a second phase 12 BICRYSTAL ORIENTATIONS . . . . . . . . 15 RESULTS • • o o a o o » 6 o e o a o » o * * o * * » » o « o o o a o 17 Observations on Continuity . . . . . . . . . . . . . . . . . . 17 S l i p at the Boundaries 19 (1) Where s l i p i s continuous 19 (2) Where there i s no continuity 19 Stress-St r a i n Curves • O » » o o * » o o o * o o o o 9 o » o 20 Observations on Thin Polycrystal S t r i p e * • o » 20 si' TABLE OF CONTENTS (continued) Page Slip Below the Surface 20 (1) X-ray microscopy 20 (2) Etching 22 (3) A l - k% Ag alloy strip 22 Slip Continuity in Annealed Bicrystals . . . . . . 23 Slip Continuity Observed on Anodised Surfaces 23 DISCUSSION 24 1. The Slip Systems Active in Symmetric T i l t Bicrystals . . . 2k 2. Slip in the Interior 2k 3. Slip Band Continuity . . 25 4. Possible Mechanisms for Slip Band Continuity 25 (a) A theoretical treatment of dislocation source activation across a boundary 27 (b) An examination of the possible movement of dislocations through a boundary ,. 30 5. Theoretical Considerations on the Effect on Continuity of the Angle of Dislocation Twist (0) at the Boundary . . 32 6. Theoretical Estimation of the Frequency of Continuous Slip Across Boundaries in a Polycrystal . . . . . . . 34 7. Further Evidence for the Transparency of Crystal Boundaries to Screw Dislocations . . . . . . . . . . 34 8. Reasons Why Screw Dislocations Should Pass More Easily Through Grain Boundaries than do Edge or Mixed Dislocations 37 9. Conclusions ' 38 TABLE OF CONTENTS (continued) Page APPENDIX I 40 Electropolishing Large Areas of Aluminum 40 Introduction » 40 Experimental details 40 Results . . . . . . 41 Perchloric acid-ethyl alcohol solution 41 An electropolish for rapid removal of metal 42 Summary 42 APPENDIX II 43 The Shear Stresses Acting on Slip Planes Ahead of a Pile-up of Dislocations , 43 APPENDIX III . 45 An Analysis of the Energy Considerations in the Formation of a Stepped Dislocation at a Twist Boundary 45 BIBLIOGRAPHY 50 MICROGRAPHS r • • • 5 2 LIST OF FIGURES Page 1. Experiment of Bainbridge et a l on a zinc b i c r y s t a l 2 2. Orientations of the: aluminium b i c r y s t a l s used by Fleischer and Chalmers 3 3. The cryst a l growing furnace -. . . 8 4. The t e n s i l e t e s t i n g apparatus 11 5. Schematic diagram for Berg-Barret X-ray microscopy . . . 13 6. Orientation of the symmetric b i c r y s t a l s 13 7. Orientation of the twist boundary b i c r y s t a l 16 8. Orientation of the b i c r y s t a l s Q l, Q2 16 9. S l i p traces on the symmetric t i l t b i c r y s t a l s 18 10. Standard cubic stereographic plot showing the stress axis f o r the symmetric t i l t b i c r y s t a l s 18 11. Work hardening slopes i n the symmetric b i c r y s t a l s 21 12. The formation of a stepped di s l o c a t i o n i n c r y s t a l 2 when a dislocation crosses from c r y s t a l 1 26 13. Values of N for bent continuity : . . . 28 14. Values of N for straight continuity . 29 15. As i n Fi g . 12, when steps i n the di s l o c a t i o n i n cr y s t a l 2 j o i n neighbouring s l i p planes 26 16. Area of the boundary plane favourable to s l i p band continuity i f 0 max * 15° 35 17. Dislocation structure f o r a low angle t i l t boundary - 35 18. The passage of a disloc a t i o n through a boundary . v . 47 LIST OF TABLES Page 1, Test for accuracy of orientation determination 9 2, Orientation of the symmetric bicrystals 15 3, Observations on bent continuity . . . . . . 17 k» The angle between s l i p direction and the boundary plane for the symmetric t i l t boundary 31 5. Angle of dislocation twist 0 . . 31 SLIP CONTINUITY ACROSS GRAIN BOUNDARIES IN ALUMINUM INTRODUCTION The Deformation of Polycrystals. Single crystals are weaker than polycrystals. One of the basic problems i n physical metallurgy i s to fi n d out precisely why t h i s i s so. I t i s hoped that such knowledge w i l l help i n the development of poly c r y s t a l material with greater strength. Two mechanisms strengthen polycrystals r e l a t i v e to single c r y s t a l s . The f i r s t , and i n many cases probably the most important mechanism, arises'from the need for several s l i p systems to act i n each grain i n order to keep neighbouring grains i n contact. Von Mises"'" has shown that unless at least f i v e s l i p systems per grain are active, gaps w i l l appear at the boundaries, a result that has never been challenged. Interaction between these s l i p systems w i l l cause hardening. The question of which extra s l i p systems w i l l be activated and how much s l i p each w i l l give has been the subject of extensive research based on comparison between s t r e s s - s t r a i n curves for single crystals and for p o l y c r y s t a l specimens (see Refs. 2, 3, U, 5). In l a t e r remarks the term •complexity hardening' w i l l be used to describe t h i s type of mechanism. The second mode of strengthening i n polycrystals i s the holding up of moving dislocations at grain boundaries. McLean^ c a l l s t h i s 'barrier hardening', and his terminology w i l l be followed. Where two s l i p systems of neighbouring crystals nearly coincide, lower b a r r i e r hardening might be expected. For F.C.C. and B.C.C. metals with many s l i p systems per grain, . - 2 - barrier hardening w i l l be less important than i n C.P.H. metals,(poly- c r y s t a l l i n e G.P.H. metals tend to have very rapid rates of work hardening compared with t h e i r single c r y s t a l s ) . Alloys with a hard phase may be considered an extreme case of barrier hardening where the b a r r i e r v i r t u a l l y never breaks down. The strength of a boundary as a dislo c a t i o n b a r r i e r appears to be greatly enhanced by the presence of a solute with small atomic diameter which gives C o t t r e l l locking. Sharp y i e l d of the type observed i n mild s t e e l i s now generally held to be caused, i n the cases investigated, by the presence of such solutes: the y i e l d i s thought of as a catastrophic break through of dislocations across boundaries. That even a low angle boundary can act as a dislocation trap has 7 been demonstrated c l e a r l y by Bainbridge et a l . A low angle boundary zinc b i c r y s t a l was stressed as shown In F i g . 1. As the stress was increased, dislocations t r a v e l l i n g along the basal planes were trapped i n the boundary and the boundary angle increased. There must therefore be some degree of ba r r i e r hardening even from such low angle boundaries. To c l a r i f y the r e l a t i v e importance of complexity hardening and barr i e r hardening, studies have been carried out on the deformation ch a r a c t e r i s t i c s of b i c r y s t a l s . ,low angle boundary s l i p (basal) planes load F i g . 1. Experiment of Bainbridge et a l on a zinc b i c r y s t a l . - 3 - F i g . 2. Orientations of A l Bi-x's used by Fleischer and Chalmers. In A, s l i p directions are p a r a l l e l to the boundary. In B, one c r y s t a l has i t s s l i p d i r e c t i o n p a r a l l e l and the other nearly normal to the boundary. Previous Work on P l a s t i c i t y i n B i c r y s t a l s . B i c r y s t a l s of Zn, Sn and Alhave been tested. In a l l the cases to be described the boundary was kept p a r a l l e l to the stress a x i s . Zn (a) Kawada^ grew symmetric b i c r y s t a l s with basal planes i n c l i n e d at equal angles to the boundary. They showed the same strength as single c r y s t a l s . A r e l a t i v e rotation about the stress axis gave some strengthening. , (b) Gilman^ confirmed Kawada's results that i n symmetric b i c r y s t a l s the boundary gives no hardening. He also found a high degree of strengthening i n b i c r y s t a l s with a r e l a t i v e r o t a t i o n about an axis normal to the boundary. Sn Chalmers grew symmetric b i c r y s t a l s , varying the angle between the s l i p directions. The stress needed to produce a standard small extension was measured. He found that - (1) the stress increased l i n e a r l y with orientation difference between the two crystals from 0 -90° . (2) varying the orientation of the boundary so that i t was Inclined to the stress axis gave no difference i n strength f o r the same r e l a t i v e orientation between the two c r y s t a l s . High-purity Al (a) Clark and Chalmers 1 1 carried out experiments on two crystals with a common {111} s l i p plane at U5° to the stress axis, rotations being made in these {111} planes to vary the angle 0 between favoured s l i p directions. They found that - (1) the yield stress increases with 0 up to 0 = 30°, and then remains steady. ...... (2) the i n i t i a l work hardening rate increases linearly with 0 up to 0 = 60°. 12 (b) Aust and Chen grew symmetric bicrystals based on a seed crystal with a<110> stress axis and a {"100} plane facing upwards. Rotations were made about the ̂110> axis. Yield stress and i n i t i a l work hardening rate both increased with misorientation angle0 from 9 = 5° to 0 = 85°, but the effect was less than that with Clark and Chalmers• bicrystals. (c) Fleischer and Chalmers grew two series of bicrystals. In one (A) the preferred s l i p direction was parallel to the boundary i n both crystals. In the other (B) the preferred s l i p direction i n one crystal was parallel to the boundary and in the other crystal nearly normal to the boundary (see Fig. 2). Series A bicrystals showed l i t t l e strengthening due to the boundary. Series B showed a large boundary effect. Double s l i p near the boundary was observed only in series B bicrystals. No clear conclusions about the relative importance of barrier- hardening and complexity hardening can be drawn from these data. The important factors that do emerge are - (1) the strengthening effect of a boundary depends on the relative orientation of the component crystals i n a f a i r l y systematic manner. (2) aluminum is strengthened only when double s l i p occurs near the boundary. - 5 - The Problem. When metals are polished and deformed, surface s l i p bands i n general fade out near to the grain boundaries. In some cases, however, the s l i p bands pass right through a boundary. Ogilvie"1"^' has studied this i n polycrystalline aluminum and 3-brass. He found that continuity of s l i p occurred only - (1) across straight boundaries. (2) where the line of intersection with the boundary of the two active s l i p planes i n neighbouring crystals had <110> , <112> and <123> directions (within 2 ° ) . The directions were not necessarily the same i n both grains. Other observations of s l i p across grain boundaries have been published. Lacombe and Beaujard^ observed s l i p across low angle boundaries in high-purity aluminum. Observations of s l i p continuous across twin boundaries 16 have been made in several metals, and Gilman has recently noted that s l i p i s always continuous i n symmetric zinc bicrystals. It was thought that a further investigation of s l i p across boundaries may be useful. Information was sought on the following questions: (a) Is s l i p band continuity as observed on polished surfaces a true continuity or purely a surface effect? (b) What is the orientation dependence? (c) What i s the actual mechanism for s l i p through grain boundaries? Do dislocations pass through the boundary, or do pile-ups in one crystal activate dislocation sources in a neighbour? (d) Is there a connection between barrier hardening and s l i p band continuity? - 6 - Answers to the f i r s t two questions should shed light on the third, which i s of course the crux of the problem. Of interest is the investigation 17 by Urie and Wain ' on the deformation of polycrystalline aluminum. They deposited photographically a fine grid on the surface before deformation, and found that in general deformation was less at grain boundaries than near grain centres. However, where s l i p passed through, the grain boundary had no effect 18 on deformation. Other interesting work was carried out by Kawada on coarse polycrystal aluminum. Sensitive measurements of extension under load showed that, i n the early stages of deformation, commercial aluminum between 100°C and 350°C showed sudden elongation »jumps* of the order of a few microns. There were no jumps when s l i p was continuous across the boundary, and such jumps were never seen in high-purity aluminum. EXPERIMENTAL PROCEDURE B i c r y s t a l Work. Preparation Bi c r y s t a l s of 99.99% pure aluminum with approximate dimensions 4 1/2" -x 3/4" x 3/S" were prepared by a modified Bridgman technique. Seed crystals were l a i d i n a graphite boat i n contact with a machined slug of aluminum which was covered by a l i d . The boat was placed i n a Vycor tube, through which helium was slowly passed. A resistor-type furnace was drawn along over the tube by a small e l e c t r i c motor (see F i g . 3). I t was found necessary to j o i n the seeds to the melt by mechanical a g i t a t i o n . The s o l i d - l i q u i d interface was approximately 3" within the furnace. Some trouble was encountered with shrinkage on s o l i d i f i c a t i o n . Shrinkage was reduced by providing a small reservoir of aluminum joined to the melt by a narrow hole. After s o l i d i f i c a t i o n the aluminum remaining i n the reservoir could be e a s i l y cut o f f . Growth rate was controlled by the speed of furnace t r a v e l . This was kept at four cms. per hour, higher growth rates giving pronounced lineage structures. Stray crystals or changes i n orientation were rare. About 20% of the crystals showed a few coarse lineage t i l t boundaries with orientation differences of around 1 1/2*. There r a r e l y occurred more than two such boundaries per c r y s t a l , and i n a l l cases they could be etched up e a s i l y . Orientation determination. Crystals were taken from the boat, etched i n 'Tucker's etch' and oriented by the X-ray Laue back-reflection method. The accuracy of the method was tested by repeatedly mounting a c r y s t a l on the X-ray set, taking a picture, demounting the c r y s t a l , and repeating the procedure. A t y p i c a l example of the Fig. 3» The crystal growing furnace. - 9 - values obtained i s given i n Table 1. In t h i s case the orientation desired had a {100} plane facing the f i l m holder and a <110>axis v e r t i c a l . The values 9 , 0 represent rotations about the v e r t i c a l and horizontal axes i n the f i l m needed to give a perfect (100) <110> orientation, and a represents the rotation needed about an axis perpendicular to the f i l m . 0 , 0 and a are a l l three needed to define the misorientation completely. The method appears accurate to within -1°. Traverses across a specimen surface were sometimes taken to test for low angle lineage boundaries. Except for the e a s i l y etched boundaries of some 1/2 to 1 1/2°, the structures were perfect within the l i m i t s of the method. TABLE 1 Test f o r accuracy of orientation determination. Test Number 0° 0° a° 1 1 1/2 2 0 2 1 1/2 2 1/4 3 1 2 1 4 1 1/2 1 1/2 0 5 1 2 1/2 1/2 6 0 3 0 Electropolishing (for d e t a i l s see Appendix l ) Several electropolishes were t r i e d , the f i n a l choice being 15$. perchloric acid i n acetic acid. With a current of some 3/4 amp at 25-35 V, a good polish was obtained i n about 1 1/2 hours. Cooling was effected by a jacket of cold running water. The best results were obtained when s t i r r i n g was kept very slow, just s u f f i c i e n t to prevent the specimen from overheating A region about 1 " long i n the middle of the specimen was polished, the rest being masked off by e l e c t r i c a l tape. Preliminary treatment was r e s t r i c t e d to grinding with a coarse-grade emery paper. I t i s believed that the worked - 10 - layer was t o t a l l y removed. X-ray pictures of the polished surface showed no asterism, and annealing caused no r e c r y s t a l l i s a t i o n . Testing. Electropolished crystals were mounted i n a Hounsfield tensometer (see F i g . 4). Simple V-block f r i c t i o n grips were machined from aluminum a l l o y , and the gripping surface covered with coarse emery paper. I t . was thought that the more usual serrated gripping surfaces would give unnecessary deformation at the ends of the specimens. Thin rubber was at f i r s t t r i e d , but proved i n s u f f i c i e n t l y strong. Even the l i g h t aluminum grips gave appreciable bending stresses from t h e i r own weight. The tensometer was therefore mounted i n the v e r t i c a l position from a w a l l bracket. To look f o r s l i p continuity, widely spaced s l i p bands were preferable. To observe the formation of s l i p bands a t r a v e l l i n g microscope with magnification around lOOx was placed i n front of the specimen. The load was removed when s l i p bands were f i r s t seen to form, at 70 - 100 lb s . S tress-strain curves were recorded while t e s t i n g . The gripping system was not r i g i d , and some bending i n e v i t a b l y accompanied the t e n s i l e t e s t s . For two b i c r y s t a l s , SR 4 e l e c t r i c a l resistance strain-gauges were cemented on to opposite faces. Both showed extension up to approximately 0.5$ on one face, with either a s l i g h t compression or a small extension on the other. This was reflected i n the frequent d i s p a r i t y between the density of s l i p bands on opposite faces. Work on Thin Polycrystal S t r i p . Thin polycrystal s t r i p , a few hundredths of a mm.-thick'was prepared to see i f any correlation between s l i p bands on the two opposite surfaces could be found. I d e n t i f i c a t i o n of the same boundary on both sides i s much easier i f the grains are large. The s t r i p was therefore r o l l e d , annealed at  - 12 - 640°C, given a further small reduction and re-annealed at 640°C for several days. Grains passing right through the str i p with diameters of the order of a centimeter resulted. This strip was polished and tested i n the same manner as the bicrystal. Methods Used to Try to See Slip Lines i n the Interior as Revealed by Further Electropolishing after Testing. (a) X-ray microscopy. In this technique, devised by Berg1*? and applied 20 to metals by Barrett, a large area of the specimen surface i s bathed in a diverging beam of characteristic X-rays. The photographic plate must be placed within a few mms. of the specimen surface (see Fig. 5). Each point on the plate represents a point on the surface, the plate being viewed, after development, on a metallograph. In this way, inhomogeneities i n the structure such as deformation bands, low angle boundaries and scratches can be shown up, (b) Etching. Two etches were tried. The f i r s t , due to Lacombe and Beaujard,1-^ gives a very large number of small pits, which are believed to be nucleated at least in part by dislocations. The etch contains U6% HNO-j, 50% HC1, 3% HF. It must be kept around 0°C by surrounding the dish with melting ice. The second etch, due to Barrett and Levenson,21 has nine parts HC'l, three parts HNO3, two parts HF., five parts H2O. This develops much larger pits. For both etches the specimen i s immersed in the solution for a few seconds, (c) Precipitation of a second phase. Failure of the f i r s t two methods led to the adoption of a precipitation technique. Age-hardening A l - k% kg alloys were prepared in the form of coarse-grained polycrystal st r i p . The strip was homogenised at 600°C, quenched, deformed, and aged at 200°C for 24 hours. Silver quenched in solution precipitated out preferentially in s l i p bands. The surface had to be anodised before s l i p bands could be detected. specimen Fig. 5 Schematic diagram for Berg-Barret X-ray microscopy. Fig. 6 . .Orientation of the symmetric bicrystals. - 14 - Several attempts to etch up the precipitate in the electropolished surface, removing the necessity for anodising, proved abortive. Perchloric acid-acetic acid electrolytes used in electropolishing pure aluminum were unsuitable for the aluminum-silver alloy, and a 20% perchloric acid in ethanol electrolyte at 40 V was used. This gave a high current, around SA, accompanied by rapid heating.. After 20-30 seconds the current was switched off and the solution allowed to cool. It was found that i f in the f i n a l polish the voltage was slightly reduced for a few seconds before the current was switched off a good anodised surface was given. - 15 - BICRYSTAL ORIENTATIONS A series of symmetric b i c r y s t a l s was grown based on a seed c r y s t a l with a {100} face upward and a <110> axis along i t s length. .Seeds for the b i c r y s t a l s were prepared by t i l t i n g t h i s seed about i t s length axis by an angle 9 (Fig. 6). The two values of 9 f o r a b i c r y s t a l varied by up to 3 ° . At least three crystals were tested f o r each orientation. One twist boundary was prepared, with 9 = 9 ° (see F i g . 7). Single crystals oriented f o r single TABLE 2. Orientation of the symmetric t i l t b i c r y s t a l s . Orientation Difference (2 9°) Code 1 2 3 4 A 5 6 8 B 21 24 25 C 26 1/2 D ' 39 40 40 E 75 70 74 73 F 92 93 93 G 113 115 114 1L2 H 150 151 150 s l i p were prepared, and two series of b i c r y s t a l s grown from them. In the f i r s t , b i c r y s t a l Q 1, the preferred s l i p directions were p a r a l l e l to the boundary surface. In the second, Q 2, the directions of easy s l i p l a y i n a plane nearly p a r a l l e l to the top surface of the b i c r y s t a l s (see F i g . 8). - 1€ - Fig. 8. Orientation of the bicrystals Q 1, Q 2. directions are shown. The s l i p - 17 - RESULTS Observations on Continuity. There i s no clear cut d e f i n i t i o n between no continuity and continuity. I t has been found convenient to use the following terms of description - •excellent*, *good*, ' f a i r ' , 'traces'. I t i s hoped that with the accompanying micrographs a f a i r description of what was observed w i l l be accomplished. I t should be emphasized that some of the specimens varied over t h e i r length, giving continuity at some places and not at others. The picture, therefore, cannot be wholly representative. Symmetric b i c r y s t a l s have two possible sets of s l i p continuity, straight or bent (Figs. 9-and-10). Straight continuity was seen only once, and then f a i n t l y , i n the symmetric b i c r y s t a l s ( i n H 1, 2, 3). For b i c r y s t a l A, i t was not possible to d i f f e r e n t i a t e between the two cases. Observations on bent s l i p are summarised i n Table 3 and micrographs 1 to 7. The series of pictures does not give a very true representation. Continuity i n E was abundantly clearer than i n the other b i c r y s t a l s , and the straight continuity i n H (Micros 11, 12) was clearer than could be shown. The twist boundary b i c r y s t a l s and b i c r y s t a l s Q 1, Q 2 showed no continuity. Both t r i c r y s t a l s showed good continuity. TABLE 3 Observations on bent continuity Code Orientation difference (20°) 1 2 3 A 6 Good Good Good ...B...... 23 Good F a i r Traces C 26 1/2 F a i r - -D 40 Good Good Good E 73 Excellent Excellent Excellent F 93 Good Good -G 114 F a i r Traces F a i r H 150 Traces Traces Traces Fig. 1 0 . Standard cubic stereographic plot showing the stress axis for the symmetric t i l t bicrystals. - 19 - S l i p at the Boundaries ( l ) Where s l i p i s continuous. When s l i p continuity was examined i n d e t a i l , the following interesting facets were revealed. (a) In several cases examined there was a displacement of the boundary where crossed (Micro 13). This displacement was of the same order of magnitude as the step height of a s l i p band. (b) Inbent continuity, the s l i p , band sometimes crossed the boundary straight f o r a short way before j o i n i n g a s l i p band i n the second c r y s t a l (Micros 14, 15) • Across the boundary s l i p bands sometimes became wavy f o r a short distance (Micro 16). (c) Ogilvie had stated that s l i p bands were continuous only over straight boundaries. This i s not so (Micros 17, 18, 19). Further, the orientation conditions he stipulated were not followed here. (d) S l i p bands can turn through quite sharp angles, up to nearly 70° (see, for example, Micro 20). "(2) Where there i s no continuity. (a) The s l i p bands often faded out near to the boundary, giving way to wavy s l i p or a generally 'rumpled' surface (see Micros 21, 22, 23). (b) The s l i p bands tended to run along p a r a l l e l to the boundary when held up there (Micros 23, 24, 25), occasionally crossing before so doing (Micro 25). (c) ' In b i c r y s t a l s G (~110°) the s l i p d i r e c t i o n was very nearly p a r a l l e l to the polished surface, making the observation of s l i p bands d i f f i c u l t . A wide region of very wavy s l i p occurred along the boundary (Micro 26). - 20 - Stress-Strain Curves The Hounsfield tensometer gave a direct load-extension curve. The early parts of the curve, up to around 30 lbs load, were found to be highly- variable. E l e c t r i c a l strain-gauge measurements showed that up to t h i s load there was no appreciable extension of the specimen, and i t was assumed that any extension shown was caused by taking up slack at the grips. With few exceptions the load-extension curves were l i n e a r above 30 l b s . load; i t was believed that the slope i n t h i s region indicated a true work-hardening of the b i c r y s t a l s o Values were found from t h i s slope for extensions at 125 l b s , load over a 3 cm. length, t h i s being a measure of the inverse slope of the curve,, Results were not of great precision, due to ( l ) bending stresses introduced, (2) inaccuracies i n the load measuring device, and (3) rather crude estimates of cross-sectional area and distance between the grips. I t i s however f e l t that the values, obtained were consistent enough to be s i g n i f i c a n t . A plot i s made i n F i g . 11. The b i c r y s t a l s E, which showed the -best continuity, appear to be more e a s i l y deformed than the b i c r y s t a l s D and 12 F. Aust and Chen gave values of the work hardening slope steadily increas- ing from 0 - 9 0 ° misorientation. Observations on Thin Polycrystal S t r i p No correlation could be found between the s l i p band spacing on opposite faces of the s t r i p . I t was noted, however, that where continuity was present oh a boundary, s l i p was also continuous over the same boundary i n the other face when not obscured by secondary s l i p (Micros 27, 28). S l i p Below the Surface. (1) X-ray Microscopy 0 The method proved i n s u f f i c i e n t l y sensitive to reveal c l e a r l y the s l i p band continuity, although s l i p bands could be detected. Extension at 125 lbs. load over a 3 cm. gauge length (units of 0.01 m.m.) 30 25 20 15 10 i i \ M \ L \" o o o o »'o~> less reliable values / — I 1 -I 1 -J -4 1 1 -l 1 1 _ l l i i | i | 10 20 30 40 50 60 70- 80 - 90 100 -110- 120 130 140 150 160 170 180 ' "J:. .Orientation.difference (2.©)...for the bicrystals. ^ Fig. 11 Work hardening slopes in the symmetric bicrystals. _ 22 - More suited to this technique would be the examination of sub-boundaries or deformation bands. (2) Etching. In no case were s l i p lines revealed. Wyon and Marchin, in an extensive research into the etching of dislocations i n high purity aluminum, noted that »»it was never found possible to reveal s l i p markings by this method.* * Their findings can only be echoed. The etch-pit patterns are of interest i n their own right. Micros 29.. and 30 show the effect of the Lacombe and Beaujard etch on a bicrystal with a -(111} plane very nearly par a l l e l to the surface, annealed, after growth, at 600°C for several days. Micro 29 shows the surface after severe attack and Micro 30 reveals the dark patches to be overlapping etch pit s . Two s i g n i f i - cant conclusions may be drawn. F i r s t , the boundary suffers very l i t t l e preferential attack, and second, there is no sign of polygonisation or c e l l - structure. The electropolish has apparently removed completely any surface deformation. Micros 31, 32, and 33 were taken from etched surfaces of crystals electropolished (Subsequent to deformation. In none do the etch pits align along s l i p bands. Micro 31 illustrates the difference i n size between etch pits given by the two etches. The large triangular pits were given by Barrett and Levenson's etch and the small ones by Lacombe and Beaujard Ts, Micro 32 i l l u s t r a t e s the very perfect equilateral triangle pits given by Lacombe and Beaujard»s etch on a { i l l } surface, and Micro 33 shows the square pits given by this etch on a crystal near to the cube orientation. {111} surfaces were etched within a few seconds whereas {100} surfaces needed the order of a minute, (3) Aj ~ Id Ag Alloy -Stpjp. Pictures of the anodised surfaces taken under polarised light are shown in Micros 34, 35, 36 and 37. They show clearly - 23 - that s l i p band continuity can be present i n the i n t e r i o r as w e l l as on the surface. There i s of course no guarantee that the Same follows f o r high-purity aluminum with no s i l v e r addition, but there i s no reason for there to be any difference i n deformation mechanisms. The surface appearance of specimens of the A l - U% Ag a l l o y electropolished and p u l l e d i s i d e n t i c a l with that of the pure aluminum. The frequency of continuity i n the i n t e r i o r of a polycrystal i s not markedly different from that on the surface. S l i p Continuity i n Annealed B i c r y s t a l s . Two b i c r y s t a l s , B3 and E4, were annealed at 600°C for several days before t e s t i n g . No very s i g n i f i c a n t difference i n s l i p behaviour was noted, although b i c r y s t a l B3 did show poorer continuity than B l or B2. S l i p Continuity Observed on Anodised Surfaces. A few b i c r y s t a l s and polycrystals were anodised before deformation. No difference i n s l i p continuity c h a r a c t e r i s t i c s could be detected. - 24 - DISCUSSION 1. The Slip Systems Active in the Symmetric T i l t Bicrystals. At room temperature aluminum slips in <110> directions on £lll} planes. There are four s l i p planes, (111), (111), (111) and ( i l l ) , each with three possible s l i p directions, making twelve s l i p systems per crystal. The choice of crystals with a <110> stress axis greatly simplifies the picture. A cubic stereogram i s given i n Fig. 11. Slip planes ( T i l ) , (111) are parallel to the applied stress, and having no shear stress component across them w i l l not give s l i p . Slip direction [llti] (or \j-10~] ) is perpendicular to the applied stress and therefore inoperative. The s l i p systems reduce to: (111) LlOl] , Loll] "; (111) [ O i l ] , [lOl] For symmetric bicrystals obtained by a rotation of the standard seed about i t s IJLlQj axis, superscripts1 and 2 w i l l be used to represent s l i p elements in crystals 1, 2. It i s easily seen that (111)1 and ( i l l ) 2 , (or (111)2 and (Hl)^) w i l l intersect the top surface i n parallel lines, whereas (111)1 and (111)2, or (ill)" 1 - and ( i l l ) 2 , w i l l intersect in lines at an angle, giving a herring-bone structure (see Fig. 9). The twist boundary w i l l of course give s l i p bands normal to the length axis, and the bicrystal Q oriented for single s l i p w i l l give bands parallel i n the two crystals but inclined to the length axis. 2. Slip i n the Interior. The Al - 4$ Ag alloys show conclusively that s l i p band continuity i s not just a surface effect, but that s l i p bands join at the boundary throughout the metal. Further, were i t simply a surface effect, a specimen with an anodised surface might possibly behave differently from an electro- - 25 - polished one, but no such difference was observed. This conclusion poses something of a problem. Unless the active s l i p planes i n neighbouring crystals intersect i n a l i n e i n the boundary, dislocations cannot pass d i r e c t l y from one c r y s t a l to the other. Consider the s i t u a t i o n depicted i n F i g . 12. The disloc a t i o n must take on a stepped form i n order to l i e completely on s l i p planes i n c r y s t a l 2 and keep i t s continuity with the s l i p plane i n c r y s t a l 1. On moving out into c r y s t a l 2 the steps are presumably removed by g l i d i n g out of the di s l o c a t i o n . Were t h i s not so s l i p would, to an observer, be taking place on a non-octahedral plane. No record of such an observation i s known. 3. S l i p Band Continuity and Work Hardening. The t e n s i l e tests indicate (Fig. 10) that the b i c r y s t a l s E, where s l i p band continuity was very marked, showed rather less work hardening than expected. I t appears, therefore, that s l i p band continuity i s a true stress-relaxation, but too much credence should not be placed on t h i s . The scatter i n results shows that more r e l i a b l e data, taking a greater number of tests per example and using a more sensitive machine, should be obtained before a detailed t h e o r e t i c a l 12 explanation i s j u s t i f i e d . I t should be noted that Chen and Aust tested no b i c r y s t a l s with misorientation between 55° and 85°, and would therefore have missed a minimum i n work hardening slope at around 70°.• The observations of Urie and Wain-'-''' t i e i n with the data presented here. 4. Possible Mechanisms f o r S l i p Band Continuity. There are two basic mechanisms that could account f o r the observed continuity. Either the dislocations p i l e up against the boundary and t h e i r stress f i e l d s activate dislocation sources i n the next c r y s t a l , or the d i s l o c a - tions i n some way pass right through the boundary. The source activation theory w i l l be treated f i r s t . - 26 - ^/dislocation coming from crystal 1 Fig. 12. Formation of a stepped dislocation in crystal 2 when a dislocation crosses from crystal 1. The plane of the diagram i s the boundary plane. The dotted line represents the dislocation in crystal 2. / / Fig. 15. As Fig..12, where steps in the dislocation in crystal 2 join neighbouring s l i p planes. - 27 - (a) A t h e o r e t i c a l treatment of disloc a t i o n source activation across a boundary. When M dislocations with Burgers vector b p i l e up against a boundary under an applied shear stress, they possess a stress f i e l d ahead of the pile-up with a value equivalent to that of a single d i s l o c a t i o n of Burgers • 23 vector M b at the centre of gravity of the pile-up. There i s therefore a stress concentration at the head of a s l i p band. This stress w i l l be pure shear i n the s l i p plane of c r y s t a l 1. I f the c r y s t a l l a t t i c e i s assumed e l a s t i c a l l y i s o t r o p i c , and i n aluminum t h i s should lead to no serious inaccura- c i e s , the stress i n c r y s t a l 2 ahead of the s l i p plane i n c r y s t a l 1 w i l l also be pure shear. For a given shear stress T acting ahead of a s l i p system of c r y s t a l 1 i n c r y s t a l 2, shear stresses NT acting on each of the four s l i p systems of c r y s t a l 2 can be found, where N i s a geometrical factor. The shear stress from the applied t e n s i l e load w i l l be the same on a l l eight s l i p systems ! (four per c r y s t a l ) . A method to calculate N i s given i n Appendix 2. I f continuous s l i p i s caused by dis l o c a t i o n source a c t i v a t i o n , high values of N between any two s l i p systems i n the two crystals should lead to observed s l i p 1 2 continuity. N-value s between s l i p systems i n ( i l l ) and ( i l l ) and between systems ( i l l ) and ( i l l ) have been calculated for symmetric crystals with misorientations from 0 - 180°j high values f o r the f i r s t should lead to bent continuity and high values f o r the second to straight continuity. Plots are given i n Figs. 13 and 14. A l l s l i p systems being equally favoured, i t i s assumed that each i s capable of giving r i s e to pile-ups at the boundary. It i s seen that the best bent continuity would be expected at around 40° misorientation, and good straight continuity around 130°. Comparison of Figs. 13 and 14 with Table 3 shows there to be l i t t l e c o rrelation between these predictions and the observed continuity. For example, b i c r y s t a l B with misorientation 23° should give better N Orientation difference (26) Fig. 13. Values of N for bent continuity. 0 10 20 30 40 50 oO 70 80 90 100 110 120 130 140 150 Io~6 170 .180 Orientation difference (20) 1 Fig. 14. Values of N for straight continuity. w o 1 - 30 - continuity than b i c r y s t a l E with 73° ; the opposite i s observed. The disloc a t i o n source activation idea appears i n v a l i d . , • ( b ) An examination of the possible movement of dislocations through the boundary. I f dislocations are to pass through the boundary, three c r i t e r i a would appear to be cont r o l l i n g ; 1) the edge or screw character of the dislocations„ 2) the nature of the boundary. 3) the angle 0 through which the di s l o c a t i o n must turn at the boundary (see F i g . 12), which i s the angle between the l i n e s of intersection of the active s l i p planes i n the two crystals with the boundary plane. 0 w i l l i n future be referred to as "the angle of disloc a t i o n twist" at the boundary. Consider f i r s t the symmetric t i l t b i c r y s t a l s . They showed ( l ) best bent continuity at a misorientation angle around 70° , and (2) straight continuity only i n b i c r y s t a l s H with misorientation 150°, and then not very c l e a r l y . For bent continuity, the angle of dis l o c a t i o n twist i s zero. I t i s instructive to investigate the nature of the dislocations approaching the boundary. Table 4 gives the angle a between the s l i p d i r e c t i o n and the boundary plane. Small values f o r a mean that the s l i p d irection i s nearly p a r a l l e l to the boundary plane, i . e . the dislocations coming up to the boundary are screw dislocations. Comparison of Tables 3 and 4 indicate that, except f o r the low angle boundary b i c r y s t a l A, good s l i p band continuity corresponds to low values f o r Screw dislocations appear able to traverse the boundary better than edges. - 31 - Table 4. The angle a between s l i p direction and the boundary plane for the symmetric t i l t boundary. Misorientations a° 0 30 30 10 26 34 20 22 38 23 (Bicrystal B) 20 40 30 17 42 50 8 49 70 0 55 90 8 59 110 17 63 114 19 130 26 58 150 34 54 For criterion 3)> values of the angle of dislocation twist at the boundary 0 have been read from a stereographic plot. The results are given in Table 5. Table 5 Angle of dislocation twist 0 (for straight continuity only i n the symmetric t i l t bicrystals). Symmetric t i l t bicrystals orientation difference 0° 0 70 24 68 40 66 60 62 80 54 100 48 120 38 140 28 150 20 18° twist boundary bicrystal 18 bicrystal Ql 78 »» Q2 38 t r i c r y s t a l 1 (13°) 1 t t 2 (39°) 3 The symmetric bicrystals H (misorientation 150°) showed some slight i - 32 - straight continuity, whereas the twist boundary b i c r y s t a l showed none. A • c r i t i c a l 0-value for continuous s l i p between 15° and 20° would appear l i k e l y The remarkably small 0-values i n the t r i c r y s t a l s should be noted. T r i c r y s t a l 2, where the outside c r y s t a l s , t i l t e d 39° , have s l i p nearly p a r a l l e l to the boundary, showed exceptionally good continuity, rather better than t r i c r y s t a l 1. I t compared w e l l with b i c r y s t a l E, where the seeds had nearly the same orientations as the outside crystals of t r i c r y s t a l 2„ The excellent continuity i n b i c r y s t a l E i s not, therefore, actuated by any p e c u l i a r i t y i n i t s boundary misorientation of 74° , but simply by the screw character of the dislocations coming up against the boundary. Bicrystal. Ql also has s l i p d i r e c t i o n p a r a l l e l to the boundary, but continuity of the s l i p bands i s prevented by a high angle of d i s l o c a t i o n t w i s t . 5. Theoretical Considerations on the Effect on Continuity of the Angle of Dislocation Twist (0) at the Boundary. I t has been shown that to pass, through a boundary with a twist element a;dislocation must take on a stepped form (Fig. 12). What w i l l happen to such a dislocation when i t expands into the s l i p planes of c r y s t a l 2? The long segments w i l l probably bow out under the applied shear stress, and the short segments w i l l act as drags on the movement. It i s of interest to consider how strong t h i s drag w i l l be. The s i t u a t i o n i s analogous to that f o r the movement of a jogged d i s l o c a t i o n . Annealed aluminum w i l l have the order of 10 - 10 dislocations per square centimeter. When one centimeter length of a d i s l o c a t i o n moves one centimeter forward, i t must pick up 10^ - 10^ jogs, i . e . one jog per 2 1/2 - 25 a where a i s the l a t t i c e parameter. I f 0 i s as before the angle of • .. dislocation twist at the boundary, and the step3 produced j o i n neighbouring - 33 - s l i p planes, then the distance d between these steps w i l l be given approximate- l y by d = a (see F i g . 15 and Appendix 3 ) o 2 s i n 0 When 0 = 5 ° d = 8 a 0 » 1.0° d = 4 a 0 - 2 0 ° d = 2 a It can readily be seen that the number of jogs produced i n a di s l o c a t i o n when passing through a low angle boundary w i l l not be much greater than the number i t would pick up i n a normal s l i p process i n annealed metal. In general, jogs are thought not to produce a large dragging force on dislocations i n aluminum^ (see for example A. Seeger, " G l i d e and Work Hardening i n M e t a l s " , Lake P l a c i d Conference, 1956, p„243)o In many cases they can glide along e a s i l y with the rest of the d i s l o c a t i o n , or can mutually annihilate. It i s possible that s l i p continuity can be prevented by the extra energy needed to give a stepped d i s l o c a t i o n rather than by d i f f i c u l t y i n moving such a di s l o c a t i o n once formed. An analysis of energy changes when a dislocation becomes stepped has been carried out i n Appendix 3o Insufficient information about the location of the s l i p sources make i t impossible to calculate a maximum 0-value above which s l i p continuity would become impossible 0 I t i s , however, quite c l e ^ r that applied forces can supply s u f f i c i e n t energy to give steps i n the d i s l o c a t i o n . Step formation can be eliminated as a mechanism for preventing s l i p continuity unless the s l i p sources are very near (less than 0,1 inches) from the boundary. E l a s t i c interactions between the s t r a i n f i e l d s of the moving s l i p dislocations and the dislocations i n the boundary are l i k e l y to give stronger 2L blocking. Dehlinger has shown that such interactions can assume large valueso The problem cannot be solved u n t i l exact models of boundary structure - 34 - have been developed. Theoretical Estimation of the Frequency of Continuous S l i p Across Boundaries i n a P o l y c r y s t a l . Observations on po l y c r y s t a l aluminum show that s l i p bands are continuous across a few percent of the grain boundaries. What proportion would be crossed i f the maximum angle of dislocation twist 0 i s taken, as 15°? Suppose that there i s only one s l i p plane active i n each c r y s t a l near the boundary. Then the problem i s a very simple one. Take the intersection of the s l i p plane i n c r y s t a l 1 with the bojjndary as a fi x e d a r b i t r a r y l i n e . In a random aggregate, the s l i p plane from c r y s t a l 2 i s equally l i k e l y , to cut the boundary i n any l i n e . The pr o b a b i l i t y f o r a favourable r e l a t i v e orienta- t i o n of the two grains i s (see F i g . 16) -29. = 1. With more than one s l i p 180 o plane active the proportion w i l l r i s e . I t has, therefore, been demonstrated that i t i s not unreasonable to suppose that t h i s condition must be s a t i s f i e d before continuity can occur. 7.. Further Evidence f o r the Transparency of Crystal Boundaries to Screw Dislocations. Screw dislocations can e a s i l y change t h e i r plane of . s l i p . Consequently, straight s l i p bands give way to wavy bands when s l i p i s carried out by the movement of dislocations with nearly pure screw character. Examine Micro 16. It w i l l be observed that the prominent s l i p band i n the lower c r y s t a l i s straight as far as the boundary. Once across the boundary i t peters out into a wavy s l i p trace before joining a s l i p band i n the second c r y s t a l . The s l i p across the boundary i s not always wavy, as can be seen from Micros 15, 17j but t h i s need cause no discrepancy i n the argument that only screws ^ penetrate. A screw di s l o c a t i o n w i l l change i t s s l i p plane only i f some b a r r i e r  - 36 - to motion i n the s l i p plane i s encountered, such as a second active s l i p system near the boundary,, Micros 21, 22, 23, and 24 i l l u s t r a t e the prevalence of wavy s l i p i n the boundary region, even when there i s no continuity. In a l l these pictures the dislocations approaching the boundary w i l l be of nearly pure screw orientation, but s i m i l a r observations have been made on other b i c r y s t a l s . Micro 23 makes i t quite clear that the dislocations do not reach the boundary before being held up and so caused to cross s l i p . As soon as the s l i p bands reach the region of double s l i p near the boundary, short wavy lines s t a r t to branch out. At the boundary there i s a very large obstacle to s l i p , and screw dislocations escape from the s l i p plane i n large numbers giving r i s e to the short region of s l i p along the boundary seen i n Micros 23, 24, and 25. In Micro 25 one of these s l i p bands p a r a l l e l to the axis of stress occurs across the boundary from i t s generating s l i p band. Micro 26 shows the effect of the boundary,in the case where the s l i p d i r e c t i o n i s nearly p a r a l l e l to the polished surface. Wavy s l i p i s observed over quite a wide region around the boundary. The s l i p bands.seen on a single c r y s t a l of such a specimen would be caused by dislocations of nearly screw orientation. S l i p f a r from the boundary takes the normal form of closely-spaced bands, and i t can be assumed that, to get wavy s l i p , d i s - locations of pure screw orientation are needed. In b i c r y s t a l s of type Q2 there i s a very large size effect and a large amount of double s l i p w i l l be present at the boundary. This accounts f o r the wide regions over which screw dislocations are released by c r o s s - s l i p . Perhaps the best evidence f o r the generation of screw dislocations at boundaries comes from Micro 20, where the s l i p bands bend round to j o i n s l i p bands i n the neighbouring c r y s t a l a f t e r passing through the boundary. The dislocations causing these bent s l i p bands cannot l i e on one s l i p plane, and must therefore be screw dislocations. To sum up, the properties of dislocations show that the movement of screw dislocations w i l l lead to wavy s l i p . This i s supported by the available evidence and there i s no reason to doubt i t s v a l i d i t y . Observations of wavy and bent s l i p at the boundary support the view that those dislocations penetrating the boundary are pure screws. 8. Reasons Why Screw Dislocations should Pass More E a s i l y Through Grain Boundaries than do Edges or Mixed Dislocations. For a low angle t i l t boundary the pos i t i o n i s f a i r l y clear (see F i g . 17). An edge or mixed dislo c a t i o n coming down i t s s l i p plane towards the boundary w i l l enter the s t r a i n f i e l d of the boundary dis l o c a t i o n s . I t w i l l pass through the boundary under a minimum applied stress when i t s s l i p plane bisects the space d between neighbouring boundary dislocations. The distance between such dislocations i s given by: s i n 0 = a J2 . 2d where a = l a t t i c e parameter 2 6 = boundary misorientation The number of s l i p planes cutting the boundary i n distance d, n = d distance between the s l i p planes = J J d = 1/4 JT a I s i n 6 5° 10° 15° 20° 14 7.2 4.7 3.6 For misorientation 2 9 = n = - 38 - For low angle boundaries, 5° or below, most dislocations w i l l penetrate the boundary,, Consider now the s i t u a t i o n f o r a screw di s l o c a t i o n . This can ea s i l y change i t s s l i p plane. The easiest path through the boundary w i l l be i n effect a v a l l e y i n the energy f i e l d set up by reactions between the stress f i e l d s of the moving screw and the boundary dislocations; the dis l o c a t i o n w i l l follow t h i s v a l l e y . A screw di s l o c a t i o n w i l l therefore always be i n a favourable s l i p plane to penetrate the boundary. For boundaries with misorientation above 20° the disloc a t i o n model i s no longer satisfactory. A model f o r grain boundary structure used frequently 25 i s Mott's suggested 'islands' of good f i t i n a 'sea' of bad f i t . To t h i s model s i m i l a r arguments to those just put forward can be applied. The islands of perfect l a t t i c e w i l l be easy to penetrate, and the screw dislocations w i l l seek them out. The island must be large enough to allow a stable loop of dislocation to b e l l y out through i t . Having no way for estimating the diameter of the islands with a s u f f i c i e n t degree of accuracy t h i s condition cannot be tested. The mechanism envisaged i s that a screw d i s l o c a t i o n moves up to the boundary and positions i t s e l f to be across the diameter of several of the islands of perfect f i t . At such points i t w i l l pass into the next c r y s t a l and spread out on the s l i p plane, giving a segmented s l i p band. This i s perhaps connected with the observation that where continuity i s good the s l i p bands near the boundary tend to be wide* 9. Conclusions (a) S l i p band continuity i s a true bulk effect and i s not confined 1 to the surface. (b) Work hardening appears to be lowered by good s l i p band continuity. - 39 - (c) Dislocation source activation theory i s incompatible with the results obtained here. (d) Factors favouring continuity are: 1) a low angle boundary 2) a small angle of di s l o c a t i o n twist at the boundary, a l i m i t i n g value of 0 max = 15 - 20° being indicated. 3) s l i p d irection nearly p a r a l l e l to the boundary, i . e . screw dislocations pushed at the boundary. (e) Detailed metallographic study of deformation markings at the boundary support the idea that screw dislocations are released by cross- s l i p near the boundary and that screw dislocations pass through the boundary. - 40 - APPENDIX I Electropolishing Large Areas of Aluminum* Introduction There are many descriptions in the literature* of electropolishes for aluminum. Most of these refer to procedures for the preparation of specimens with small surface area for micrographic examination. Electro- polishing large areas presents much greater problems in heat dissipation and electrolyte-flow. Experimental details. The following polishing solutions were tried: Alcoa bright dip (chemical polish) Perchloric acid-ethyl alcohol mixtures, A phosphoric acid electrolyte 1 part n i t r i c acid to four parts methyl alcohol, 15$ perchloric acid in acetic acid. Most electropolishes are effective only in a restricted temperature range, usually below 20°C. Efficient cooling i s therefore essential. For these aluminum polishes, surrounding the bath with ice was generally ineffective (5 amps at 50 volts puts in enough energy to melt 12 grams of ice per second). In practice,the most successful arrangement ut i l i s e d a stainless steel beaker as cathode, surrounded by cold running water, the liquid i n the beaker being stirred. A glass beaker and aluminum cathode were sometimes used where cooling was less c r i t i c a l . - 41 - Results.' E l e c t r o l y t e Current Density Temperature Quality of F i n i s h Alcoa bright dip 90-110°C Good general surfaces with p i t t e d areas, s t r i a t i o n s v e r t i c a l i n bath. Rather incon- s i s t e n t . 70$ orthophos- phoric27, 28 2.5$ water 26.51% " c a r b i t o l " 1% HF 6.3-0.5 amps/cm^ not c r i t i c a l 20-70°C Some p i t t i n g . Tendency to get white deposit on the surface. 20$ perchloric acid i n ethyl alcohol 0.5-1.0 amps/cm 10-18°C Quite good i n some cases. Greater C.D., better polish. See next section for d e t a i l s . 1 part HNC|9 4 parts CH30H 0.5-0.7 amps/cm 10-20°C Good at low magnification Some roughness shown up at x600 magnification and above. 15$ perchloric i n acetic acid '2 0.1-0.3 amps/cm. 14-20°C. Good. Slower acting than the previous electrolytes Perchloric acid-ethyl alcohol solutions. These are the most widely used electropolishes on aluminum. For ' large surfaces, however, they have certain disadvantages. The best polish i s obtained at high current densities, but t h i s i s accompanied by rapid heating of the solution. With the present arrangement, runs are l i m i t e d to 30-45 seconds.(this applies also to the HN03-CH50H e l e c t r o l y t e ) . A further drawback i s a black deposit that frequently forms over part of th*e surface, under which there i s no pol i s h . This happens most frequently i n solutions with 20$ strength (S.G. 1.25) perchloric acid. A solution with concentrated (60$) perchloric never gave the deposit, but areas of severe p i t t i n g developed. In both solutions the trouble was minimised by obtaining a smooth flow of - 42 - elect r o l y t e past the surface, but results were far from consistent. The 30 following explanation has been put forward. Turbulence at the surface leads to l o c a l overheating, and the following reactions: C10^~ > CI" + 0 C 2H 50H+ 0 —* 2 C+ 3 H20 With the strongest a c i d , the carbon deposit i s further oxidised to CO, COj leaving a pitted area. This suggestion i s backed by the following observations: (1) A l or A l oxide can act as a strong catalyst f o r such reactions. (2) The HNO^ CĤ OH electrolyte can give a si m i l a r deposit df allowed to overheat. (3) At the same CD., the specimen cheats up very much fa s t e r i n the e l e c t r o l y t e with the 60$ perchloric than i n that with the 20$ perchloric. This i s attributed to heat evolved at the specimen surface while the carbon i s oxidised o f f . An electropolish f o r rapid removal of metal When i t i s desired to remove layers of aluminum several microns thi c k , e.g. to remove surface working, a 15$ perchloric acid i n ethyl alcohol solution i s recommended. Temperature must be kept below 20°C for a pol i s h . There must be no s t i r r i n g . Summary^ For electropolishing large areas of aluminum, the most consistent of the solutions t r i e d i s 15$ perchloric acid i n acetic acid. The polishing action i s slow, needing 1-1 1/2 hours for a good f i n i s h . Grain boundaries are delineated by t h i n l i n e s . - 43 - APPENDIX I I The Shear Stresses Acting on S l i p Planes Ahead of a Pile-up of Dislocations. The mathematics of the procedure to be described were developed by o, 32 A.E. Love-3-1, i t has been applied to s l i p i n metals i n a paper by Davis et a l . The basic equation iss P i = PN = P[(ei.ei x l i . l i ) (e, . l i x e i . l j ) ] , where P i i s the shear stress on s l i p systems i , caused by an applied shear stress P on s l i p systems.1. The vectors are unit vectors, such that t h e i r dot products are cosines. e i , e i are normal to the s l i p planes _ i , l i , l i are s l i p directions. Values of N are derived, with N =[cos(angle between s l i p plane normals) x cos(angle between s l i p directions}) + (cos(angle between normal to s l i p p l a n e l and s l i p d irection i ) x . cos(angle between normal to plane i and s l i p d i r e c t i o n ! )J. For each b i c r y s t a l , a stereogram i s plotted giving the s l i p planes ;and directions for both cr y s t a l s . Angles between a l l active s l i p directions and s l i p plane normals are read off from the stereogram. For each s l i p system i n c r y s t a l 1, N-values are found for a l l the s l i p systems 'in c r y s t a l 2. I f s l i p band continuity i s caused by s l i p source activation across the boundary, high N-values should lead to good continuity. Figs. 13 and 14 show N-values for symmetric b i c r y s t a l s with misorientation from 0° to 180°. Each c r y s t a l has 12 s l i p systems. In the general case 144 N-values would have to be calculated. The b i c r y s t a l s grown for t h i s investigation, however, had crystals with t h e i r <110> axes p a r a l l e l to the stress axis, and the applied stress w i l l give appreciable shear stresses only on two s l i p - 44 - planes per c r y s t a l , each plane having two possible s l i p d i rections. There are therefore only four s l i p systems per c r y s t a l that need be considered, greatly reducing the labour involved. - 45 - APPENDIX I I I An Analysis of the Energy Considerations i n the Formation of a Stepped Dislocation at a Twist Boundary, Data for aluminum: shear modulus = 2.7 x 10 gms/cm. c r i t i c a l shear stress £ 0 = 5 x 103 gms/cm.2 energy f o r a jog i n an edge di s l o c a t i o n — 0.4 e.v. energy for a jog i n a screw d i s l o c a t i o n = 2/3 x .4 e.v. l a t t i c e parameter a, = 2.5 A A low angle twist boundary can be represented by dislocations with screw components. When a s l i p d islocation moves through such a boundary i t w i l l receive jogs where i t cuts the boundary dislocations; the screw component of these dislocations w i l l lead to those parts of the jogs that l i e i n the boundary plane. For s i m p l i c i t y , assume that the jogs are equally spaced along the s l i p d i s l o c a t i o n and perpendicular t o i t s l i n e . Jogs w i l l form that have a minimum energy, and those that j o i n the s l i p planes i n the shortest l i n e s w i l l be favoured. There are four s l i p planes i n aluminum, and there w i l l , except i n special cases, be three possible jog directions. An angle f a i r l y near to 90° between jog l i n e s and the dislo c a t i o n l i n e i s therefore l i k e l y . (The boundary grown had a {l00} boundary plane; the dislocation l i n e and the jogs w i l l therefore be exactly perpendicular). On t h i s model (see F i g , 15), a = d s i n 0 d = a {2 s i n 0 46 •- f o r 0 = 5° d = 8 a 0 =10° d = 4 a 0 =15° d = 2.7 a 0 = 20° d = 2 a 0 = 25° d = 1.7a 0 = 30° d = 1.4 a Variations from 90° i n the angle between s l i p d i r e c t i o n and jog w i l l have l i t t l e effect on d u n t i l d becomes greater than 2 a (e.g. i f t h i s angle i s 70°, at 0=20 d = 1.98 a). I t i s desirable to calculate the shear stresses needed to give the: jog densities indicated. To do t h i s the microscopic d e t a i l s of the process- must be considered. The mechanism envisaged i s i l l u s t r a t e d i n F i g . 18.. Increase i n energy i n the formation of each step i n a dislocation with Burger's vector b i s given .bys. A E = the energy f o r a jog - /Ah* d(l< - cos 0.) for 0 = 20°,/*b 2 d ( l - cos 0) =/ib2d 0.06 = 0.06 e.v. This i s negligible compared to the energy f o r a jog (•—0.4 e;.v.,) i n the- accuracy of these calculations. . For a l l 0-values considered,. A'E='0.4. e.v. Work done by the d i s l o c a t i o n i n forming each jog. = force x distance = 1/2 force ; x d s i n 0 = 1/2-6b d- dr sin.0 where £~ = shear stress at the dislocation = N 60 - kl - s l i p dislocation boundary (a) Formation of one step. (b) Dislocation with the f u l l number of jogs. Fig. 18. The passage of a dislocation through a boundary. - 48 - with N= number of dislocations i n a pile-up tending to push the dislocation through the boundary. Now equating energy needed to cause the stepped dislocation with the work done "n i t s formation, A.E -_1 60 N a d 2 s i n 0 2 vT .4 x 1.6 x 10* 1 2= N x 50 x 10 6 x 2.5 3 x 10~ 2 4x K 2 s i n 0 ergs 2/T where d»Ka now N = 2.3 x 10 3 K 2 s i n 0 f o r 0 = 25 , K = 1.7 N 0 = 20 , K = 2 N 0 = 10 , K = 4 N = 1.9 x 10 3 1.7 x 10 3 = 0.85 x 10 3 These values are probably r e l i a b l e to ±50$. The number of dislocations expected i n a pile-up under shear 23 stress 6 3 i s given by N a TT L 60 where L = the length of the pile-up. Thus N = 3.2 x 10%, for . L = 1 cm. N = 3.2 x 10 4 L = 1_ cm. N = 3.2 x 10 3 10 Again, accuracy i s probably about ±50$. When a stress s u f f i c i e n t to give s l i p l i n e s i s applied, pile-ups - 49 - of these orders w i l l form at the boundary. Comparison with the N-values needed to give steps i n a di s l o c a t i o n line,, show that a l l s l i p sources distant 1/10 cm. or more from the boundary w i l l be able to give these steps. . A factor not yet mentioned i s the p o s s i b i l i t y of thermal fluctua- tions activating the formation of the steps. The a c t i v a t i o n would presumably have to push enough of the di s l o c a t i o n through the boundary to enable i t to expand out into the second c r y s t a l . The c r i t i c a l radius f o r a dislo c a t i o n i n aluminum i s of the order 10~3 - 10"^ cms.; a large number of steps would therefore have to be activated simultaneously. I t i s u n l i k e l y that thermal activation i s a s i g n i f i c a n t factor at room temperature. - 50 - BIBLIOGRAPHY 1. R. Von Mises, Z. Agnew.U, Mech., 8, 161, 1928. 2. G. Taylor, "Strains i n a Cr y s t a l l i n e Aggregate", from "Deformation and Flow of Solids"? International Union of Theoretical and Applied Mechanics! Colloquium, Madrid, 1955. 3. J . Bishop and R. H i l l , P h i l . Mag. '£2, 414, 1298, 1951. 4. B. Jaoul, J . Mech. Phys. Solids, j>, 2, 1957. 5. A. Kochendorfer, "Plastische Eigenschaften Von K r i s t a l ] e n " , Springer 1941. 6. D. McLean, "Grain Boundaries i n Metals", Oxford 1957. 7. D.W. Bainbridge, C.H. L i and E.H. Edwards, Acta Met. 2, 322, 1954. 8. T. Kawada, J . Phys. Soc. of Japan, 6, 363, 485, 1951. 9. J . J , GiLman, Acta Met. 1, 426, 1953. 10. B. Chalmers, Proc. Roy. Soc. A "162. 120, 1937. 11. R. Clark and B. Chalmers, Acta Met. 2, 80, 1954. 12. K.T. Aust and N.K. Chen, Acta Met, 2, 632, 1954. 13. R.L, Fleischer and B. Chalmers, Acta Met,, 6,- 265, 1958 14. G.J. Ogilvie, J . Inst. Metals 81, 491, 1952-53. 15. P. Lacombe and L. Beaujard, J . Inst. Metals 74., 1, 1948. 16. J.J. Gilman, Trans. A.I.M.E., 212, 783, 1958. . 17. V.M, Urie and H.L. Wain, J . Inst. Metals, 81, 153, 1952. 18. T. Kawada, J . Phys. Soc. of Japan 7, 240, 1952. 19. W. Berg, Z. K r i s t . 8£, 286, 1934. Naturwissenschaften 19., 391, 1931. 20. C.S. Barrett, Trans. A.I.M.E. l 6 l , 15, 1945. 21. C.S. Barrett and L.H. Levenson, Trans. A.I.M.E., 13J7, 76, 1940. 22. G. Wyon and J.W, Marchin, P h i l . Mag, 46, 1120, 1955. 23. A.H, C o t t r e l l , "Dislocations and P l a s t i c Flow i n Crystals", Oxford 1952, pp. 106, 107 24. U, Dehlinger, Solvay Conference, 415, 1951. 25. N.F. Mott, Proc. Phys. Soc. 60, 391, 1948, - 51 - BIBLIOGRAPHY (continued) 26o P.A, Jaquet, Me t a l l u r g i c a l Reviews, 1, 157, 1956. 27. E.C. Pearson, G. Marchand, and R.H. Hay, Canadian Mining and Metallurgical B u l l e t i n , 45_, 598, 1952. 28. A. Hone and E.C. Pearson, Metal Progress, j>3_, 363, 1948. 29. G„E. P e l l i s s i e r , H. Markus and R.F. Mehl, Metal Progress 3.8, 554, 1940. 30. D.R. Wiles, Private communication. 31. A.E. Love, "A Treatise on the Mathematical Theory of E l a s t i c i t y " , Cambridge University Press, 1927. 32. R.S. Davis, R.L. Fleischer, J.D. Livingstone and B. Chalmers, Journal of Metals, 7, 136, 1957. 33. A. Seeger, "Report of a Conference on Defects i n C r y s t a l l i n e Solids", Physical Society of London, p. 391, 1955. MICROGRAPHS (The background pattern seen i n some of these pictures was caused 1/ interference effects within the metallo- graph, l a t e r corrected). Bent Continuity i n Symmetric T i l t B i c r y s t a l s . Mag: xlOO. I A Micro 1. B i c r y s t a l A. 29 = 6° Micro 2. B i c r y s t a l B 29 23° / B i Crystal C 26 r Micro 6. B i c r y s t a l F 29 = 93°   - 57 - Non-Continuity Across an 18° Twist Boundary- Micro 9. Mag: xlOO Micro 10. Mag: xlOO - 59 - Straight Continuity i n B i c r y s t a l H Micro.12. Mag: x200  Micro 15. Same as Micro 14 Mag: x200 - 62 - S l i p Band Becoming Wavy After Crossing the Boundary Micro 16„ B i c r y s t a l E2 Mag: x200 - 63 - S l i p Bands Continuous Through Bent Boundaries Micro 17. Polycrystal s t r i p Mags xlOO Micro 18. Polycrystal s t r i p . MagsxlOO - 64 - S l i p Bands Bent at the Boundary Micro 20. Polycrystal s t r i p Mag; x200 - 66 - Wavy S l i p Near the Boundary Micro 22. B i c r y s t a l Ql Mags xlOO - 67 - S l i p Band Segments P a r a l l e l to the Boundary Kicro 23. 3 i c r y s t a l Ql -lagtxlOO Micro 2U. B i c r y s t a l E2 Mag: xlOO Micro 25. B i c r y s t a l E2 Mag; xlOO Micro 26. Mags x30 - 70 - The Same Boundary Viewed from Opposite Faces of Thin S t r i p Micro 28. Mag: xlOO Micro 30. As Micro 29 Mag: x2,000 Micro 31. Etched consecutively i n Lacombe and Beaujard's, and i n Barrett and Levenson's reagents. Mag; xlOO. Micro 32. Etched in Barrett and Levenson's reagent. Surface near £lll} orientation. Mag; xlOO. - 7 3 - Micro 33. As Micro 32, but surface near $100}orientation. Mags xlOO. S l i p Band Continuity i n the In t e r i o r at A l - k% Ag Alloys as Revealed by Electropolishing. Viewed on an anodised surface under polarised l i g h t , Mag; xlOO. Micro 34. grain boundary Micro 35. Micro 36. grain Micro 37.

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