Planes Train Compression Copper

7/27/2019 Planes Train Compression Copper

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Plane St ra in Co m press ion o f Co pp er , Cu 6W t Pct A I ,and A g 4W t Pct Sn C rysta lsB . C . W O N S I E W I C Z A N D G . Y . C H I NC r y s t a l s o f v a r i o u s o r i e n t a t i o n s w e r e f o r c e d to u n de r g o p l a n e - s t r a i n c o m p r e s s i o n t o s im u -l a t e t h e d e f o r m a t i o n o f a g r a i n i n a p o l y c r y s t a l l i n e a g g r e g a t e . C o p p e r , C u - 6 w t p c t A 1, a n dA g - 4 w t p c t S n w e r e s t u d i e d t o e v a l u a t e t h e i n f lu e n c e o f s t a c k in g f a u l t e n e r g y o n th e m o d e lo f G . I . T a y l o r w h i c h a s s u m e s e q u a l h a r d e n i n g on a ll s l i p s y s t e m s . T h e c o m p r e s s i o n s t r e s ss t r a i n ( e - c) c u r v e s w e r e c o n v e r t e d t o r e s o l v e d s h e a r - s t r e s s : s h e a r - s t r a i n ( v- ), ) u s i n g t h ea p p r o p r i a t e T a y l o r f a c t o r . A q u a n ti t a t iv e a n a l y s i s o f l a t t i c e r o t a t io n d u r i n g d e f o r m a t i o n w a sm a d e a n d f o un d to be i n a g r e e m e n t w i t h t h e o r i e n t a t i o n c h a n g e d e t e r m i n e d w i t h t h e a i d o fX - r a y p o l e f i g u r e s . T h e c h a n g e i n T a y l o r f a c t o r a s s o c i a t e d w i th t h e r e o r i e n t a t i o n w a s c o m -p u t e d a n d u s e d i n c o n s t r u c t i n g t h e r - y c u r v e s . A d d i t i o n a l i n f o r m a t i o n o n t h e a c ti v e s l i p a n dt w i n s y s t e m s w a s p r o v i d e d b y o p t i c a l m e t a l l o g r a p h y . T h e r -~ , c u r v e s g e n e r a l l y f e l l i n to an a r r o w b a n d fo r a l l t h e s e m a t e r i a l s , i n d i c a t i n g t h a t th e a s s u m p t i o n o f e q u a l h a r d e n i n g w a sr e a s o n a b l y v a l i d f o r l o w s t a c k i n g f a u l t e n e r g y a l l o y s u n d e r c o n d i t i o n s o f m u l t i p l e s l i p i m -p o s e d i n t h e p r e s e n t e x p e r i m e n t . D e v i a t i o n s o c c u r r e d m a i n l y in t h e a l l o y c r y s t a l s w h i c he x h i b i t e d m e c h a n i c a l t w i n n in g . N e v e r t h e l e s s , t h e a c t i v e tw i n s y s t e m s i n t h e s e c r y s t a l s w e r es a t i s f a c t o r i l y p r e d i c t e d b y an e x te n d e d T a y l o r a n a l y s i s .

s t r e n g t h o f a c r y s t a l u n d e r g o i n g d e f o r m a t i o n d e -p e n d s o n th e c r y s t a l o r i e n t a t i o n a n d t h e i m p o s e d s h a p ec h a n g e. T h e d e t a i l s o f ho w s t r e n g t h d e p e n d s o n o r i e n -t a t io n ( p l a s t i c a n i s o t r o p y ) a r e i n t e r e s t i n g f o r tw o r e a -s o n s . F i r s t , i n c r e a s e s i n s t r e n g t h g a i n e d b y o r i e n t a -t i o n , " t e x t u r e h a r d e n i n g , ' '~ a r e a d v a n t a g e o u s i n t h ed e s i g n o f s t r u c t u r e s . T h e a p p l i c a t i o n of t e x t u r e d c o p -p e r a l l o y s f o r s p r i n g r e l a y s 2 a n d t i t a n i u m f o r s p a c ev e h i c l e s 3 a r e t w o e x a m p l e s . V a r i a t i o n s i n s t r e n g t hc a n a l s o b e e x p l o i t e d in c o n t r o l l i n g d e f o r m a t i o n p r o c -e s s i n g o p e r a t i o n s . T h e i m p r o v e d d e e p d r a w i n g s t e e l sa r e a n e x a m p l e . 4 S e c o n d l y , a b y - p r o d u c t o f a f u l l u n -d e r s t a n d i n g o f c r y s t a l p l a s t i c i t y w o u l d b e i n f o r m a t i o no n l a t t i c e r o t a t i o n d u r i n g d e f o r m a t i o n . H o p e f u ll y th i sw o u l d l e a d t o an u n d e r s t a n d i n g o f h o w p r e f e r r e d c r y s -t a l l o g r a p h i c o r i e n t a t i o n ( o r t e x t u r e ) a r i s e s d u r i n g th ed e f o r m a t i o n o f a p o l y c r y s t a l l i n e a g g r e g a t e . S i nc em a n y p h y s i c a l p r o p e r t i e s a r e s e n s i t i v e t o o r i e n t a t i o n( m a g n e t i c a n i s o t r o p y a n d e l a s t i c c o n s t a n t s a r e i m p o r -t a n t e x a m p l e s ) , a k n ow l e d g e of te x t u r e f o r m a t i o n i s o fp r a c t i c a l i n t e r e s t .

T h e m o s t c o m p r e h e n s i v e m o d e l o f th e d e f o rm a t i o no f c r y s t a l s w a s o r i g i n a t e d b y G . I . T a y l o r . 5 T h e b a s i cp r o b l e m i s to s e l e c t a c o m b i n a t i o n o f s l i p s y s t e m sw h i c h w i l l a c c o m p l i s h t h e i m p o s e d s h a p e c h a n g e w i tht h e l e a s t p o s s i b l e i n t e r n a l w o r k . F o r e x a m p l e , i n f c cm e t a l s , s l i p c a n o c c u r o n t w e l v e { 11 1} ( 1 10 ) s l i p s y s -t e m s . T h e i n c r e m e n t a l a m o u n t o f w o r k clW d o n e b y as h e a r s t r a i n d ), u n d e r a c r i t i c a l r e s o l v e d s h e a r s t r e s s( C RS S ) r o n t h e e a c h o f t h e t w e l v e s y s t e m s i s :

d W = ~ ~ ' i d ~ 'i [ 1 ]t= l

G e n e r a l l y no m o r e t h a n fi v e s y s t e m s a r e n e e d e d b e -c a u s e a n a r b i t r a r y s h a p e c h a n g e i s c o m p l e t e l y d ef i n e db y f i ve i n d e p e n d e n t s t r a i n c o m p o n e n t s ( a s s u m i n g c o n -s t a n t v o l u m e ) . T a y l o r s i m p l i f i e d t h e t a s k o f f i n di n g th e

B . C . W O N S I E W I C Z a n d G . Y . C H I N a r e M e m b e r s o f t h e T e c h n i c a lS t a f f , B e l l T e l e p h o n e L a b o r a t o r i e s , M u r r a y H i l l , N . J .

M a n u s c r i p t s u b m i t t e d F e b r u a r y 9 , 1 9 7 0 .

m i n u m u m w o r k b y a s s u m i n g t h e C R S S t o b e t h e s a m ef o r a l l s l i p s y s t e m s . T h i s a s s u m p t i o n i m p l i e s t h a t a l ls y s t e m s h a r d e n e q u a l l y w h e t h e r th e y h a v e o p e r a t e do r n o t . I n t h a t c a s e E q . [ 1 ] b e c o m e s

12d W = " r I d Y l l = r d y [ 2 ]

i= 1

w h e r e r s t a n d s f o r t h e s i n g l e C R S S f o r a l l s y s t e m s ,a n d d~ i s u n d e r s t o o d t o b e th e s u m o f t h e s h e a r s o na l l t w e l v e s y s t e m s . T h u s , t h e c o m b i n a t i o n o f s l i p s y s -t e m s w h i c h m i n i m i z e s t h e t o t al s h e a r d ~, w i l l a l s om i n i m i z e t h e w o r k . T h e l a b o r i o u s c a l c u l a t i o n s o f s e -l e c t i n g t h e m i n i m u m h a v e b e e n e l i m i n a t e d b y C h i n a ndM a m m e l 6 u s i ng a l i n e a r p r o g r a m m i n g t e ch n i qu e .

B i s h o p a n d H i l l 7 r e f o r m u l a t e d t h e m o d e l i n d i f f e r e n tt e r m s u s i n g a m a x i m u m e x t e r n a l w o r k p r in c i p l e ,w h i c h h a s r e c e n t l y b e e n s h ow n s t o be e n t i r e l y e q u i v a -l e n t t o th a t o f T a y l o r .O n e of t h e m a t e r i a l p a r a m e t e r s t h a t c o u l d c h a l l e n g et h e v a l i d i ty o f t h e T a y l o r a s s u m p t i o n o f e q u a l h a r d e n -i n g is t h e s t a c k i n g f a u l t e n e r g y ( S F E ). B o t h c r o s s - s l i pa nd i n t e rs e c t i n g s l i p p r o c e s s e s a r e m a d e m o r e d i ff i -c u l t b y th e e x t e n d e d d i s l o c a t i o n s a s t h e S F E i s l o w -e r e d . 9 I n i t ia l s t u d i e s t e s t i n g t h e T a y l o r t h e o r y w e r ec o n d u c t e d b y H o s f o r d o n a l u m i n u m 1 ~ a n d b y C h i n,N e s b i t t , a n d W i l l i a m s o n p e r m a U o y , 12 b o t h h i g hs t a c k i n g f a u l t e n e r g y m a t e r i a l s . S a t i s f a c t o r y a g r e e -m e n t w i t h t h e o r y w a s o b t a i n ed . M o r e r e c e n t l y ,M a y e r a n d B a c k o f e n i s e x t e n d e d t h e s t u d y t o l o w e r S F Em a t e r i a l s c o p p e r a n d C u - 7 w t p c t A1 a s w e l l a s i r o n , ah i gh S F E m e t a l . C r y s t a l r o d s w e r e d r a w n t h r o u g hc o n i c a l d i e s t o s i m u l a t e a x i s y m m e t r i c e x t e n s i o n . T h em e a s u r e d o r i e n t a t i o n d e p e n d e n c e of t h e d r a w i n g s t r e s sw a s i n k e e p i n g w i t h th e T a y l o r t h e o r y i n t h e c a s e o fi r o n , b u t c o n s i d e r a b l y l e s s s o in c o p p e r a n d C u - 7 p c tA 1. T h e a u t h o r s s u g g e s t e d t h a t d i s l o c a t i o n b a r r i e r ss u c h a s L o m e r - C o t t r e l l l o c k s a n d s e s s i l e j o g s , a s w e l la s m e c h a n i c a l t w i n n i n g , c o u l d c o n t r i b u t e t o a d e c r e a s ei n t h e o b s e r v e d s t r e n g t h a n i s o t r o p y . C h i n , M a m m e l ,a n d D o l a n ~4 r e e x a m i n e d t h e a x i s y m m e t r i c f l ow p r o b -l e m b y t a k i n g i n to a c c o u n t t h e e f f e c t o f m e c h a n i c a l

M E T A L L U R G I C A L T R A N S A C T I O N S V O L U M E 1 , O C T O B E R 1 9 7 0 - 2 7 1 5


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twinning. I t was concluded that the lat ter would indeeddecrease the s t reng th an i so t ropy in ax i symmet r ic ex-tensio n, al though i t would i n c r e a s e the anisotropy inc o m p r e s s i o n . Plane s t ra in compress ion t es t s con-ducted by Chin, Hosford, and Mendor f *s on cry st al s ofCo-8wt pct Fe, a very low SFE al loy, confirmed thattwinning was ch ief ly resp ons ib l e fo r s t reng th dev ia t ionsf rom the bas ic Taylor analys i s . The observed ac t ivesl ip and twin system s were cons is te nt with an extendedTaylo r a nalys is which included twinning.

In the present work, further s tudies have been madeon the low SFE mat er ial s c opper, Cu-6wt pct A1, and Ag-4wt pct Sn. The cryst als we re deforme d in plane s t r aincompress ion , which has cer ta in advantages over wi redrawing as an imposed deformat ion . Fi rs t , the com-p l et e s t r e s s - s t r a i n cu rve can be m eas u red w h ereasin wire drawing only the drawing st ress for a specifics t ra in i s avai l ab le . Secondly , the cons t ra in t s are bet -ter estab l ishe d and the shape change is more easi lymea sure d than in wi re d rawing , where the crys ta lfrequ ent ly cocks before ent eri ng the die. Special ef-forts have also been made to take into account the ef-fects of lat t ice rotat ion and deformation banding onthe s t re ss - s t ra in curve . Recognized though no t t akeninto account in the ear l ie r wo rks ci ted, such effectscont r ibu te sca t t er to da ta , par t i cu lar ly a t h igh s t ra ins .

E X P E R I M E N T A L P R O C E D U R ECrystals of copper, Cu + 6wt pct A1, and Ag-4wt pct

Sn were grown from the mel t in sol id graphi te c ruc i-b les sea led in evacuated quar tz ampules . Samples werespark machined to rec tangular p r i sms of approximate ly3 by 6.5 by 8 mm. After a brief chemical pol ish, thecopper and Cu-A1 samp les wer e an nealed at 900~ for12 hr under vacuum. The Ag-Sn al loys were s implyelect ropol i shed in a KCN solut ion. The composi t ion ofeach sample was determine d by X-ray f luorescenc eand found to be within 10 pet of the nomi nal compo si-t ion. The final orientat io n was checked by Laue backrefle ct ion and found to be within 1 deg of the n omin alor ien ta t ion .

Compression test ing was conducted in a Teflon lu-br ica t ed channel whose wal l s res t r i c ted l a tera l f low. 2 '1sDeformat ion was in ter rup ted for renewal o f lubr ican t ,meta l lographic and X-ray po le f igure observat ions ,and observ at ion on the shape change. As wil l be notedla ter , specimen prof i l e d id no t always remai n rec tang-u lar bu t o f t en sheared in to a para l l e logram. The ref l ec-t ion po le f igures were ob ta ined us ing Ni - f i l t e red C u K ~rad ia t ion on a Siemens goniometer .

RESULTSCopper Crys ta l s

Large d i f ferences in s t reng th were observed in crys -ta l s iden t i ca l in every res pect bu t o r i en ta t ion . Thet ru e co m p res s i o n s t r e s s - s t r a i n cu rv es for th e cop p e rcrys ta l s ar e p resen ted in Fig . 1. The f low s t re ss a t ast r ain of about 0.10 for cr yst al 1 was appr oximat ely4 t imes that for crystals 4, 5 , or 6. To determine i fthe lar ge diff erence was due solely to the differentamounts o f shear requ i red (as assumed) i t was neces -sary to conver t the curves to a she ar- s t r ess : shear -strain (T-Z) plot.

The r- 7 and a-E plots can be rela ted by equat ingthe in te rna l work due to slip, Eq. [1], to work done bythe ex ternal s t ress es . Taking x , y , z as the compres -s ion ax is , channel wal l normal , and channel ax i s , r e-spect ively, we have

d W = " rd T = ( Y x x d E x x + C r y y d E y y + ~ z z d s + ( r y z d s z+ a z x d s + ( Y x yd E x y [3]

This equat ion can be s implified i f we assume that thewal l s o f the channel p revent l a te ra l spread ing d e y y = 0and main ta in a rec tang ular cross sec t ion on the z face ,d e x y = O . Fur the r , the Tef lon lubr ica t ion reduces thef r i c t ional s t re sse s p rac t i ca l ly to zero . a z z = e y z = C z x= 0. With the above simp lifi cat ion

r d: y = % x d E x x [4]Defining the Taylo r factor M as the rat io of cry stal lo-graphic shear to the compress ion s t ra in M - d ~ / d c x x ,the compress ion s t re ss - s t ra in curve can be reso lvedi nt o a s h ea r - s t r e s s : s h ea r - s t r a i n cu rv e t h ro u gh t here la t ions

~- = ~ x x [ S a ]Md T = M d e x x [Sb]

If we s imply assume no lat t ice rotat ion so that Mdoes not va ry d uri ng the test, then V = ME. Tabl e Il i s t s the o r ien ta t ion of each crys ta l , the Taylorfac tor , and ac t ive sys tems for re laxed deformat iontypical of the channel test ( r = E x y = 0) and for theful ly constrained case (Eyy = E y z = E z x = E x y = 0 ) . Th ela t t er p rov ides condi t ions fo r an upper-bou nd so lu t ionand i s approached in channel deformat ion o r ro l l ingof po lycrys ta l l ine mater ia l where neighbor ing crys ta l sprovide the two addi t ional shear cons trai nts . The s l ipsys tem notati on is that of Ref. 15 and is i nclude d inTable II.F i g. 2 r ep re s en t s t he s h ea r - s t r e s s : s h ea r - s t r a i nplot for the copper cry sta ls based on a constant ini t ial

IOOr 1| NO. ORIENTATIONl - - ~ // 2 ( H I ) [ 1 12 ] /- - 6 0 0I 3 (~,, ~ T,o] - I/ 4 ( . o ) [ h 2 ] // s (u O ) [O O I ] /| 6 (001) I/T o] COPPER |/ , y . . . . . . . . . . . . . . . . - ' l

/ 2 400s o l . . . . . 3 ~ . / z

I i z , . . , S ' / ~ qI

"5

.25 .50 .75sFig. 1 --Tru e-stre ss : true-stra in curves for plane straincompression of copper crystals.2716-VOLUME 1, OCTOBER 1970 METALLURGICAL TRANSACTIONS


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T a b l e INo. O rien t a t i on MS l ip S l ip S ys t ems Rota t i on Tw inning Tendency

(110) [110] 2X/6( 1 1 1 ) [ i i2 ] 1.5(111) [i10] 1.5 V~*(uo ) [ i]21 ~g t(llO ) [001] V~"(0o~) [ i io ] ~/~

I 2 2[ 5 7 g 10 ~ M4 , Fig. 3(c) yesSt 5 9 1-2 M ,1, F ig . 3 (a ) ye s (a f t e r ro t a t i on)7r 5 7 8 10 i 2" M, ~ F ig . 3 (d) no2 4"t" M con stant no1 2 4 5 M c o n s t a n t n o1 2" 4 5 M 1,1" Fig. 3(b ) ye s

*M = (5/ 3) X/6"sl ip on I 2 ff 5 7 g 10 1-i i f ful ly constrained.i ' M=( 3 /2)~ / ' 6 - s l i p on T 2 4 5 7 ~" 10 H i f fu l l y const rained .

30

20

NO . O RIENT AT IO Nr ( I I 0 ) [ J o ]2 (Hi ) [Ti2]3 ( J J l ) [ i l o ]4 (flO) [ h z ] COPPER5 ( H o ) [ o o f l6 (001) [T[O]

. . . . . . . . . 2;,....#.~ ~ 2 :"''~r'---'--".... 3

/I I

20 0

~EzIOO

I 2F i g . 2 - - S h e a r - s t r e s s : s h e a r - s t r a i n c u r v e s f o r c o p p e r c r y s -t a l s n e g l e c t i n g r o t a t i o n d u r i n g d e f o r m a t i o n a n d a s s u m i n gc o n s t a n t M , T a b l e I .

M v a l u e . T h e i n i t i a l p o r t i o n o f t h e c u r v e s f a l l in t o an a r r o w b a n d , b u t a t i n c r e a s i n g s t r a i n s , t h e c u r v e sb e g i n t o d i v e r g e d u e t o c h a n g i n g v a l u e s o f M w i t h l a t -t i c e r o t a t i o n . C r y s t a l s 4 a n d 5 , ( 1 10 ) [ 1 1 2] a n d ( 11 0)[ 00 1 ], m a y b e t a k e n a s r e f e r e n c e c r y s t a l s s i n c e th e yd i d n o t r o t a t e f r o m t h e i r o r i g i n a l o r i e n t a t i o n s . T h u st h e i n i t i a l M = f f f , s e e T a b l e I , s h o u l d b e a p p l i c a b l et h r o u g h o u t t h e t e s t f o r t h e s e t w o s a m p l e s . U s i n g t hes t r e s s - s t r a i n c u r v e s o f c r y s t a l s 4 a n d 5 a s a r e f e r e n c e ,t h e n c r y s t a l s 1 , 2 , a n d 3 a p p e a r t o h a r d e n l e s s r a p i d l ya n d c r y s t a l 6 in th e l a t t e r s t a g e s o f t h e t e s t i s h a r d -e n i n g m o r e r a p i d l y . A s w i l l b e d e v e l o p e d l a t e r , m o s to f t h e d i v e r g e n c e i n F i g . 2 c a n b e r e l a t e d t o th e l a t t i c er o t a t i o n o f t h e c r y s t a l d u r i n g d e f o r m a t i o n . C r y s t a l s 1 ,2 , a n d 3 r o t a t e t o o r i e n t a t i o n s m o r e f a v o r a b l e f o r s l i p ;t h a t i s , t o l o w e r M , w h i l e c r y s t a l 6 e v e n t u a l l y r o t a t e st o a l e s s f a v o r a b l e o r i e n t a t i o n ; t h a t i s , h i g h e r M .S i n c e th e a m o u n t o f s li p on e a c h s y s t e m i s o n e o ft h e p r e d i c t i o n s o f t h e T a y l o r a n a l y s i s , t h e r o t a t i o n sc a n b e o b t a i n e d d i r e c t l y b y s t a n d a r d a n a l y s i s , z~ T h ee f f e c t o f r o t a t i o n o n M , h e n c e o n t h e T -~ , c u r v e , w a sc a l c u l a t e d a s f o l lo w s : T h e d e f o r m a t i o n i s a p p r o x i -m a t e d a s a s e r i e s o f i n c r e m e n t a l s t r a i n s a~xx ( s a y0 .0 1 ) d u r i n g w h i c h M r e m a i n s c o n s t a n t ( o r a l t e r n a -t i v e l y t h e o r i e n t a t i o n d o e s n o t c h a n g e ) . B e g i n n i n g w i tht h e i n i t i a l o r i e n t a t i o n , t h e a m o u n t o f s h e a r zx),~ n e c e s -s a r y f o r t h e f i r s t i n c r e m e n t AExx i s c a l c u l a t e d a l o n gw i t h th e r o t a t i o n o f t h e c r y s t a l a x e s c a u s e d b y t h i ss t r a i n . A n ew v a l u e o f M a l o n g w i t h t h e n e x t i n c r e -m e n t o f s h e a r A 72 i s t he n c a l c u l a t e d b a s e d o n th e r o -M E T A L L U R G I C A L T R A N S A C T I O N S

T a b l e I I . T h e T w e l v e { 1 1 1 } ( 1 1 0 ) S l i p S y s t e m sp la n e 1 11 1 i l i l l l i ldirection 011 101 1i0 6i1 101 ]1~ 61T 101 110 6i ] i01 110sys tem 1 2 3 4 5 6 7 8 9 10 11 12

t a t e d c o o r d i n a t e s . A f t e r n s t e p s( I XXT -Mnn [ 6 ]

w h e r e M i = ATi/ AEx x i s t h e T a y l o r f a c t o r a p p r o p r i a t ef o r t h e i t h s t e p .T h e m o d e l is a d a p t a b l e to p r o g r a m m i n g t e c h n i q u e s ,

a n d a p r o g r a m h a s b e e n w r i t t e n w h i c h p r o v i d e s Mi, 7,t h e M i l l e r i n d i c e s o f t h e r e o r i e n t e d s p e c i m e n a x e s( x, y , z ) , a n d t h e c o m p l e t e s t r a i n t e n s o r a s s o c i a t e dw i t h th e d e f o r m a t i o n .

L a t t i c e R o t a t io n a n d C o r r e c t e d T - 7 C u r v e sI) S T A B L E O R I E N T A T I O N S

C r y s t a l 4 , ( 11 0 ) [ 1 12 ] , c a n d e f o r m b y s l i p o n a s i n g l ep a i r o f s y s t e m s , n a m e l y , 2 a n d i , T a b l e I . T h i s c a s eh a s b e e n a n a l y z e d b y C h i n , N e s b i t t , a n d T h u r s t o n . z8T h e c r y s t a l d e f o r m s w i th c o n s i d e r a b l e Cyz s h e a r b u tn o c h a n g e i n o r i e n t a t i o n . E v e n i f t h e ey z s h e a r w e r es u p p r e s s e d ( w h ic h i t w a s n o t) b y th e o p e r a t i o n o f a d -d i t i o n a l s y s t e m s , a n a l y s i s s h o w s t h at th e o r i e n t a t i o ni s s t i l l s t a b l e . N o r o t a t i o n w a s o b s e r v e d i n an y o f t h en o . 4 c r y s t a l s .

C r y s t a l 5 - - (1 1 0 )_ [0 0 1 ]. F l o w o c c u r s b y s l i p o n t w op a i r s o f s y s t e m s 1 , 5 a n d 2 , 7t w i t h no r o t a t i o n . A n a l y -s i s s h o w s t h a t m i s o r i e n t a t i o n b y r o t a t i o n a b o u t t h e xa x i s w i l l r e s u l t i n a s h e a r Cy z i f t h e p r e v i o u s t w op a i r s o p e r a t e , b u t no r o t a t i o n w i ll o c c u r . H o w e v e r , i feyz is s u p p r e s s e d b y t h e a d d i t io n a l o p e r a t i o n o f 10a n d 1 1 , a r o t a t i o n t o w a r d a f i n a l ( 11 0 ) [ 1 1 2 ] o r i e n t a -t io n w i l l o c c u r . N o r o t a t io n w a s o b s e r v e d i n o u r c r y s -t a l s w h i c h w e r e f r e e t o u n d e r g o Ey z s h e a r . R o t a t i o n st o w a r d ( 1 10 ) [1 1 2 ] h a v e b e e n r e p o r t e d i n h e a v i l y c o l d -r o l l e d c r y s t a l s , p r e s u m a b l e d u e t o a Ey z c o n s t r a i n t , z72) U N S T A B L E O R I E N T A T I O N S

C r y s t a l 2 - - ( l l l ) [ i i 2 ] . T h e d e f o r m a t i o n o f t h i s i n -t e r e s t i n g o r i e n t a t i o n h a s b e e n r e p o r t e d i n d e t a i l in a

V O L U M E 1 , O C T O B E R 1 9 7 0 - 2 7 1 7


4/8

2 1 , ; , 1. I .2 .3 .4 .5

21 ~ ~ ~ , I ~ ~ ~ ~ I I. 5 1 . 0

5 .............................................................................. J 2V"~"c ) ( i , o ~ [ho]

.5 1 .0

. I .2 .3 ,4 .5S T R A I N , - E xx

Fig. 3 --Summar y of theo reti cal cal culati on of M as a functionof strain for plane strain compress ion of various orientations.(a) If fully constrained, M follows dotted line. If Q x is unre-strained, rotation is to either (110) [001] (lower full line) or(112) [111] (upper full line). The average M for the last tworotations is shown as the broken line. (b) Fully constrained-dotted line. Fre e Qx--full line. (c) Fully_cons trained-dott edline. Free ~y z --full line. (d) Slip on 10, 12 with large e x y - -line 1. Slip on 5, 10 with smaller E x y - - l i n e 2. Slip on 5, 10,with Exy = 0--1ine 3. Lines 1 and 2 correspond to rotations 1and 2, respectively, in Fig. 6.

sepa rate paper .ZSIn sum mar y, if Ez~ she a r i s pe r mi t t e d ,the cry st al can rotate e ith er t oward (112) [111] or to-ward (110) [001] . The sens e of rotation is det ermi nedby the loca l s t re sses and the c rys ta l i s obse rved todiv ide in to four sy mmetr ica l pa r ts , two of each of thef inal or ientation s. The rate and sense of rotation ar ein good ag reement wi th theore t ica l predic t ions . 2E

During deformation, M decreases from 1.5~6-to ~6-for the portion of the cry st al which rot ates to (110)[001] , Fig. 3(a) , while remaining relatively constantat 1.5~6" for the portion ro tati ng to (11 2)[ ii l ] . Theassumption that M = 1.5,/-6- throughout the test clearlyis an overes t imate and th is expla ins the downwarddrop of crys tal 2 in Fig. 2. A bett er esti mate is to takethe avera ge of the instant aneous values of M for thetwo or ienta t ions . This procedur e would be cor rec t i fthe stra in E x x was the same in both or ientations andif both or ienta tions were about half of the volume ofthe sample . With th is procedu re , the shear - s t res s :shear - s t r a in curve in F ig . 4 fa l l s nea r those of thereference crystals (4 and 5) .

Cry sta l 6--(001)[110] . As pointed out previo usly, zath is or ienta t ion i s uns table wi th respec t to ro ta t ionsabout y axis, leading to eit her (11 2)[ li l] or (112)[111]if EzxiS unre str aine d. I f Ez~ = 0, a si mil ar rotation is ex -pected but the stable or i entati on is a t 8 deg 14 mm fr om{112}. z9 Both theoret ical and obs erve d ro tation s are pre -sented in Fig. 5. The observ ed rotation is somewhats lower than predic tedby the re laxed shear curve . This

L3 0 | N O, ORIENTATION 200/ i ( H o ) D ~ o ]2 (HI) [TT2]3 (~H) h o ]4 ( H O ) [ T i 2 ]5 ( i J o ) [ o o l ]6 (001) [ ]TO] COPPERI ~ ; . ~ . ~ - - . . ~ ob l ~ - , / . s I _ / / ~ _ ~ ' -#s J,o / y / / "

i ii 2

z d ) , iFig. 4--She ar-stress : shear-strain curves for copper crys-tals, adjusted for rotation during deformation.

NEz

I 0 0 " j

4 0- ( H Z ) [ H T ]o 0 ~ a ~ j a a:". o 5 0 E z x #

~E oa . . . .m 20

b A / a C u10 / o / o Cu+ 6WI OAI

O ~ - 0 . 2 - 0 . 4 - 0 . 6 - 0 . 8 - I . 0 - (0 0 11 r ll O ]E xx

Fig. 5--Rotation about the [110] axis of the compressionplane normal x as a function of compres sive strain ex x forcrystals initially oriented for (001) [110] deformation. Solidlines indicate the calculated rotations for relaxed'Ezx andfor no shear strai ns. Stable orientat ion for no shear (dashedline) is 8 deg 14 min short of that for ~ree e z x , (112) [111].Symbols indicate the obs erved orientations as determinedfrom the intensity maximum of pole figures taken after de-formation to the strain Exx .could be due to the operation of the sy st ems which act tosup pres s ez~ she ar . The or ienta tion rea che d af ter E = 1.0is near (112) as predicted by relaxed E z x . Fig. 3(b)shows the effec t of rotat ion (due to str ain) on M forth is or ienta t ion . Af te r a smal l dec l ine , M inc reasestoward 1.5 x/B-as the s table or ient ation is approached.The upward divergence of crystal 6 a t ) / ~ 1.3 in Fig.2 ref lects the increasing M. When the M based on theobserved ro ta t ion i s used , F ig . 4 , the d ive rgence i sprac t ica l ly e l imina ted .

Crys ta l 1- (110) [110] . The e ight s l ip sys tems, f a -vored at the init ia l or ientation, Table I , can lead to anins tabi l i ty wi th ro ta t ion about the compress ion (x)axis . I f the ro ta t ion i s toward [ i l l ] , ca lcula t ions showtha t the e ight ac t ive s [ s tems a re reduced to four ;namely, 2, 4, 10, and 11. Rotation in the oppositesense towa rd [111] occur s by operatio n of remai nin gfour syste ms. In eith er case, M dec rea ses from 2V~-to 1.Sv~- with rotation, Fig. 3(c) , thus explaini ng thedrop in the unco r rec t ed T-y curve of th is c rys ta l vsthe re fe rence curves in F ig . 2 . The obse rved ro ta t ionwas complex, but rotations about the x axis were ap r om ine n t f ea tu r e . The m ic r os t r uc t u r e wa s c ha r a c t e r -

2718-VOLUME 1, OCTOBER 1970 METALLURGICAL TRANSACTtONS


5/8

ized by many deformation bands with large local rota-t ion of s l ip l ines consis tent with the rotat ion about thex d i rec t ion . Simi lar banding observat ion s have beenmade on a permal loy crys ta l wi th cons i s ten t sof ten ingin the 7- 7 curve. ~2 An alum inum cry stal s tudied byIfosford, n however, did not rotate nor form bands;the 7-7 curve Iikewise did not deviate from the averagecurve. Since our crysta2 did harden less rapidly thanthe other cr ysta ls , we have cor rec ted the T-7 plot usingthe theoret ical variat ion of M as shown in Fig. 3(c).Although i t is an oversim plifi cat i on (other rota t ionsevide nt in the pole figure also tend to lower M), theadopted procedure should rep res en t the major correc t ion .

Cry sta l 3--(111) [110]. If the cr yst al is free to shear,i .e , i f c. . = 0 is the only cons tra int , s ix s l ip syst ems9 Y-Y s -are fav ore d at (111) [110] and M = 1.5 f6, Table I. flow -

ever , i f the shear s t ra ins are res t r a ined , then e ightsys tem s operate and M is in cre ase d to (5/3) 4~-. Ine i ther case , the o r ien ta tion i s uns tab le and ro ta tes toorie ntat ions of lower M. The decl in e in M is evidentin uncorrec ted T-7 plot of Fig. 2 where the curve forcry sta l 3 fal ls below that for cry sta ls 4 and 5 whichdo not rotate. A pole f igure, Fig. 6, indicates the ro-tat ion after a s t rain of 0.59~ The rotat ion is morecomplex than in p rev ious cr ys ta l s which were s implerota t ions about the x or y axis . The pole f igure can beapproximated by two {110} (112) components with con-side rable spre ad toward ~ (358) [523]. The micr ost ru c-tu re was character i zed by many complex deformat ionbands. Pr omin ent t races cons i s ten t with s lip e i theron (111) or on (l i l ) were observed. The argumentsfor one of these components apply to the other and wewi l l d i scuss on ly pr im ary s l ip on ( l i l ) .

Fig. 6---~111) pole figure of copper crys tal deformed in planestrain compression, ex x = --0.59. Tr iang les indicate the ori-ginal (111) [110] orientation. Solid arrows, 1, repre sent rota -tion calculated for slip on 10, 12 with consider able ~xy shear.Broken arrows marked 2 indicate rotation calculated for slipon 10, 5 or 10, 5, 2 with less ~xy shear and no exy shear, re-spectively. Unmarked arrow s are the analogous rotation s _from the sym metrica l counterparts, i .e., 8. 7; 8, 4; and 8, 4,1, respectively.

Slip on 10, 12, with no widening s = 0, will rotatethe crystal to (101) as shown by path (1) in the polefigure, Fig. 6. During rotat ion, M dec rea ses as shownby curve 1 in Fig. 3(d). [The comp leme ntar y case for( i l l ) is s lip on 7, w leadi ng to (011)]. A ra th er lar geCxy would occur and th is shea r should be res t ra i nedby the square cross section imposed by the channelwails and the platens. A combinat ion of sys te ms whichproduc es les s ~xy shear is 10, 5 which rota tes thecrystal to approximately (358) as indicated by thebroken l ine--path (2)--in the pole f igure, Fig. 6. Mdecl ines during this rotat ion but not as much as i f exywere unc onstr aine d, curve 2, Fig. 3(d). If exy is com-pletely suppre ssed, s l ip occu rs on 10, 5, and2 with ahighe r in itia l M, (5/3) 4~, curv e 3, Fig. 3(d), but a ro-tat ion s imilar to 10, 5. Rotat ion s tops after about 20deg at ~(358) when slip on 10, 3 or 10, 3, 2 becomesfavored 9

The T-7 curve fal ls nearest to crystals 4 and 5 i fthe M correct ion, Fig. 3(d), curve 2, based on l imitedexy shea r, that is, 5, 10, is used , Fig. 4. The othertwo mechanisms, slip on 10, 12 or 10, 5, 2, yieldedcurves too high and too low, respect ively. The actualdeformation may be more complex than these threesimple choices. One possibi l i ty is that s l ip begins on10, 12 with the exy shear no t complete ly suppressedby the channel . After some deformation, the Crxy ex-erted by the channel reach es a sufficient ly high levelto cons t ra in fu r ther exy and slip then occurs by 5, 10or 5, 10, 2. Such a pro ce ss would yield an M vscurve between curves (1) and (2) and the 7-7 plot wouldbe shifted upward toward the center of the envelope ofthe other curves.

An inte rest ing outcome is an explanat ion of the s ta-bility of the (358) orientation due to competing slip on10, 5 and 10, 3 at this orientat ion. Severa l worke rshave roi led copper s ingle cry sta ls and found this to bea s table orientat ion.2~

When correc t ions are thus made for o r ien ta t ionchange during the test , the r-7 curve s for the s ix ori -en ta t ions tes ted f~t l l in to a reasona bly narr ow bandeven to ~ ~ 2, as shown in Fig. 4. In Fig. 7 the enve-lopes of the band are plotted together with the T-Vcurve s obtained by Saimoto 2a using ten si le tests . Forthe two single crystals, the M values are 1.5~/B-and

20 IOPPER~ foe a

2

fflg,o E,oo]5

I I i f i0,2 0.4 0.6 0.8 1.0 1.2SHEAR STRAIN

Fig. 7--Comparison of plane strai n compression re sults(shaded band) with tensile results for a polycrystal and twosingle cryst als of multiple slip orientations.METALLURGICAL TRANSACTIONS VOLUME 1. OCTOBER 1970-2719


6/8

2O

5 . ~ , , , ' ~30 NO. ORIENTATION 2: J4 ~" -, ( , ,o ) [ ,To] . . ;~ / / -2 ( I l l ) [ i [2] ]~ I" / , .-3 ( il l) [TIo] /.4" / . - ' _ . . ' "4 (ItO) it2] _// / ." ./s (,,o} oo,] /~" /./.."-6 (oo,) [no] ///./~'//I / / . . ' ; / " ~ + ~ . , o A~

o " t 9

I II 2z d 7 i

Fig. 8--Shear-stress : shear -stra in curves adjusted for ro-tation dur ing deformation. Cu-6wt pet A1.

%IOO

x/B- fo r [111] and [100] , respect ive ly . For the po lycr ys -tal l ine material , Saimoto used an M = 2.66 rather than3 .06 appropr ia te fo r randomly or ien ted mater ia lsince the sample was believed to exhibit a weak texture. If M = 3.06 is used, the cu rve fa l ls just belowthe band. The c urve s d ete rmi ned by other work ers 24-26fal l with the band if M = 3.06 is used . There fore, wecan conclude that the Taylor theory gives reasonablecorre la t ion between po lycrys ta l and s ing le crys ta lt ens ion t es t s and p lane s t ra in compres s ion for copper .Cu-A1 AND Ag-Sn RESULTS

The shear -s t r ess : she ar- s t r a in curves for the twolow s tack ing fau l t energy a l loys a re p resen ted in Figs .8 and 9. Correct ions for rotat ion were made usingFig. 3(a) to (d) with the exception of crystal 6 for Ag-4pct Sn as noted below. Complicat ions arose from me-chanic al twinning not exhibi ted in the copper cry stal s .

Po le f igure and meta l lographic observat ion ind ica tedmec hani cal twinning in crys tal s 1, 2, and 6 of the lowstacking faul t energy al loys in agreement with an ex-tended Taylor anal ys i s J 5 Twinning was mos t p ro-nounced in Ag-Sn, but was evident in the later s tagesof deformation of the Cu-A1 alloy.Orien tat ion 2 shows twinning in the sect ion of thecrys t a l which ro ta ted toward (112)[1 i l ] . The behaviorof th i s cr ys ta l has been analyzed in deta i l p rev ious ly , la

Twinning was pronou nced in the (001) [ l i 0] (no. 6)Ag-Sn crystal. A {111} pole figure taken after Exx= -0 .2 7 is i l lus trat ed in Fig. 10. The orientat ion isco nsi ste nt with a 13 deg rota tio n about the y axis dueto sl ip, followe d by twinn ing on (111) [112] and (111)[112]. The o rienta t ion of the twinned mate ria l wouldbe very close to {110} (001> (7 deg away) and wouldhave an M factor for slip within the twin of about0.95~E. Since M thus re mai ns near ly x/E with this as-sumption of ini t ial s l ip fol lowed by twinning, we haveused a con stant M = ~/E in const ruct ing curve 6 forFig. 9. This proce dure r esu l te d in a negat ive devia -t ion (softening) from the average, especial ly in theini t ial s tages of deforma tion. The softening may havecome f rom ear ly twinn ing, since for the (001) [110]2 7 2 0 - V O L U M E 1 , O C T O B E R 1 9 7 0

200NO. ORIENTATION

t (t~O) DTO]2 ( i l l ) [H213 (ill) CTio]4 ( l lo) [T iz ]20 5 (ll Ol [001] SILVER-TIN6 (oot) [T[o]

2 _ . . . / L ~

10 A, . , 9 / S"/

I II 2Xd),

Fig. 9--Shear- stress : shear-st rain curves adjusted for rota-tion during deformation. Ag-4wt pct Sn.

%I0 0

z h,,~

Fig. 10-~111} pole figure of Ag-4wt pct Sn crystal no. 6 de-formed in plane strain compression. ~xx = -0.27. Originalorienta tion (001) [110]. Open symbols in dicate orient ationafter a 9 13 deg rotation about the y axis due to slip. Thesolid symbols indicate the corresponding twin orientations.o r ien ta t ion the twin sys tems ar e mo re favorab ly or i -ented than the s l ip sy stem s, i .e . , they sus tain a higherresol ved shea r s t r es s (see Fig. 4 of Ref. 15).

The rot ation of the Cu-A1 (001) [110] is e sse nti all ythat due to slip, so M was adjusted according to theobserve d rotat ion, Fig. 5, as in the case of the coppercrystals . Weak intensi ty in the twin orientat ion couldbe detected in the lat ter s tages of deformation.

The rem ain ing cr ysta l which had twinned was (110)[i l0 ], no. 1. The conv ersio n from the a-e curve to theT-~, curve was made in the same way as for copper,s ince a quant i tat ive analysis of separat ing the individ-ual effects of s l ip and twinning could not be provided.As may be seen in Figs. 8 and 9, the T-7 curves ofthis orie ntat ion (no. 1) show extra hard enin g in theini t ial port ion, m ore so with Ag-Sn. Chin et al. 15 ha d

M E T A L L U R G I C A L T R A N S A C T I O N S


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prev ious ly observed a very seve re harden ing for th i sorientat ion in Co-8 pct Fe, which exhibi ted even morepronoun ced twinning than Ag-Sn. The ex tra harden ingundoubtedly comes from the complex twin and s l ip in-t ersec t ions imposed on th i s o r i en ta t ion .

With the except ion of comp licat ions from twinning,the sca t te r of the ~'-y data is about the same as thatfor copper . Hence, the basic val idi ty of the Taylo rapproach i s reasonably c onf i rmed in the low s tack ingfau l t energy mater ia l s a l so .

DISCUSSIONIn the pres ent work, we have gone considera bly be-

yond prev ious s tud ies in analyzing the s t res s -s t ra i nbehavior o f Crys ta l s sub jec ted to cons t ra in ed defor-mat ion . In par t i cu lar , account was t aken of the ef fec t sof constraint relaxat ion and of lat t ice rotat ion on theTaylor factor , and hence the conve rsion from the a-~curve to the r -y curve . Wi th such appropr ia te correc-t ions, the scat ter in the data is s ignifica nt ly reducedespecia l ly a t l a rge s t ra ins .

The sugges t ion f rom examining the r -y curves o fFigs. 4, 8, and 9 is that except f or twinn ing, the basicTaylor assumpt ion of equal harden ing remains essen-t ial ly val id to low stacking faul t energy materials .T h i s m e a n s t h a t a n y u n e q u a l h a r d e n i n g b r o u g h t a b o u tb y e x t e n d e d d i s l o c a t i o n s , i f i n d e e d o c c u r r i n g , i so b s c u r e d b y t h e b a n d o f s c a t t e r i n t h e d a t a ( ~ : L I 0 p c t ) .I n r e c e n t y e a r s , a n u m b e r o f l a t e n t h a r d e n i n g e x p e r i -m e n t s h a v e b e e n c o n d u c t e d t o g a i n i n s i g h t a b o u t s l i ps y s t e m i n t e r a c t i o n s . M o s t o f t h e s e e x p e r i m e n t s i n v o l v et h e t e c h n i q u e o f f i r s t c a u s i n g s l i p i n o n e s y s t e m a n dt h e n m e a s u r i n g t h e f l o w s t r e s s o n a p r e v i o u s l y i n a c t i v e( l a t e n t ) s y s t e m . T h e g e n e r a l c o n c l u s i o n i s t h a t p r i o rs l i p o n o n e s y s t e m h a r d e n s a l l o t h e r s y s t e m s m o r et h a n i t s e l f . A n e x c e p t i o n i s t h e c o p l a n a r s y s t e m ,w h e r e t h e h a r d e n i n g i s a b o u t e q u a l . F o r a l u m i n u m i nstage III, the ex tra har den ing is about 20 pct; 27 forcopper in stage H, about 40 pct; 2a and for sil ver instage III, about 40 pct. 2s The re is thus a sugg estio nthat noncoplanar harden ing inc rea ses with low SFE.However , s ince these exper iments were performe dby fi r s t act ivat ing one system and then the other, theyare les s app l icable to the mult iple s l ip s i tuat ion wheresevera l s l ip sys tems become act ive s imul taneous ly .The greater number o f s l ip in terac t ions in the l a t t eris expected to provide a more uniform dislocat iondi s t r ibu t ion and hence the d i s loca t ions of each sys tem,act ive or no t , would face s i mi la r hurd les in the i rmovements . Thi s idea i s suppor ted by Nakada 's ob-servat i ons of l a ten t harden ing in the t ens i l e d eforma-t ion of aluminu m cryst als orie nted for mult iple s l ip. 3~He observed that crystals pul led along [111] cont inuedto deform at the same reso lved shear s t ress whensubsequ ent ly pul led along [100]. Six s l ip sy stem s wer eact ive in the [111] deformation, and eight systems,with only two previously act ive and two in the reversesense, beca me act ive during the subseq uent [100] de-format ion . Simi lar ly , there was no change of s t res swhen the crystal was fi rs t deformed along [100] andthen in the [111] orientation.

It should be pointed out, however, that although thereduce d lat ent harden ing may not show up beyond nor -mal sca t t e r o f the s t r ess -s t r a in data, i t is expectedto influence the developm ent of deformation t exture s , al

The lat ter depends se nsi t iv ely on which of sev er alnear ly equ ivalen t combinat ions of s l ip sy s tems areact ive dur ing deformat ion .As for mec hanical twinn ing, the obse rved in i t i a lact ivat ion of the appropr iate twin sys tem s is in agree -ment with an extended Taylo r analy sis . 15 However, anyincor porat ion of such twinning into ana lys is of the lat ers tages o f the s t r ess - s t ra in curve i s at bes t qual i t a t iveat prese nt . In addi t ion to changing twinned volume dur-ing the test , l i t t le is known about the mechanism oftwinning, and even less so about s l ip-tw in and twin-twin interact ions. I t is hoped that these issues wil l beclar i f i ed in fu ture s tud ies .

SUMMARYThe Taylor theory of cons t ra ined deformat ion was

examined by p lane s t ra in compress ion of s ing le crys -tals of copper, Cu-6 pct Al, and Ag-4 pct Sn. The re-su l t s and conclus ions are summa rized as fo l lows:

l ) Meta l lographic observat ions of ac t ive s l ip sys -tems and X-ray pole f igure s tudies of lat t ice rotat ion,are cons i s ten t wi th p red ic t ions o f the bas ic Taylortheory.

2) The shea r-s t re ss : shea r-s t ra in d iagr ams ob ta inedfrom p lane s t ra in compress ion are in good agreementwi th s ing le crys t a l and po lycrys ta l l ine t ens i l e da ta fo rcopper avai l ab le in the l i t e ra tur e .

3) Twinning occ urr ed m ost e asi ly in Ag-4 pct Sn,less so in Cu-6 pct A1, and was not detected in copper.The ac t ive twin sys tems and the i r o r i en ta t ion depen-dence agree wi th an ex tended Taylor analys i s .

4) Twinning in low stacking faul t energ y ma te ria lscont r ibu tes exp la inab le sca t t er to the s t r ess s t ra incurves. However, quant i tat ive incorporat ion of twin-ning to the detai ls of the s t r es s s t ra in c urve s couldnot be made a t p rese n t .

5) The basic Taylor assumption of equal hardeningamong a ll s l ip sys te ms rem ains bas ica l ly val id to thelow stacking faul t energy al loy crystals .

ACKNOWLEDGMENTSThe authors wish to thank Mes srs . D. Dorsi and

R. R. Har t fo r the i r a ss i s t an ce in the exper iments .Mes srs . T. D. Schlabach and J . H. Wernick kindly re -v iewed the manu scr ip t .

R E F E R E N C E S1. W. A. Backofen,W. P. Hosford, and J. J. Burke:ASM Trans. Quart. , 1962,vol. 55, pp. 264-67;W. F. Hosford and W. A. Backofen:Fundamentals oJ"Deformation Processing, W. A. Backofen t al., eds., pp. 259-98, SyracuseUniversityPress, N.Y., 1964.2. G. Y. Chin,R. R. Hart, and B. C. Wonsiewiez: rans. TMS-AIME, 1969,vol.245, pp. 1669-71.3. H. W. Babeland D. L. Corn:Metals Eng. Quart. , 1967,vol. 7, pp. 45-52.4. R. L. White|y:Trans. ASM , 1960,vol.52, p. 154.5. G. I. Taylor:J. Inst. Metals, 1938,vol.62, pp. 307.24;S teph en T imoshenko ,69th Anniversary Volume, pp. 218-24, The MacmillanCo., New York, 1938.6. G. Y. Chinand W. L. Mammel:Trans. TMS-AIME, 1967,vol. 239, pp. 1400-05.7. J. F. W. Bishop and R. Hill:Phil. Mag., 195 I, vol.42, pp. 414-27, 1298-1307.8. G. Y. Chinand W. L. Mammel:Trans. TMS-AIME, 1969,vol. 245, pp. 1211-14.9. F. R. N. Nabarro, Z. S. Basinski,and D. B. Holt:Advan. Phys. , 1964,vol. 13,p. 193.10. W. F. Hosford:Trans. TMS-AIME, 1965,vol. 233, p. 329.

METALLURG|CALTRANSACTIONS VOLUME l, OCTOBER 1970-2721


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1 1 . W. F . H o sfo rd : Acta Met., 1 9 6 6 , v o l . 1 4 , p p . 1 0 8 5 -9 4 .1 2 . G . Y . C h i n , E . A . Nesb i t t , an d A . J . W i l l iams : ActaMet., I 9 6 6 , v o l . 1 4 , p p .

4 6 7 - 7 6 .1 3 . G . May er an d W. A . B ack o fen : Trans. TMS-AIME, 1 9 6 8 , r e1 . 2 4 2 , p p . 1 5 8 7 -9 4 .1 4 . G . Y . C h i n , W. L . Mamm el , an d M. T . Do l an : Trans. TMS-AIME, 1 9 6 9 , v o l .2 4 5 , p p . 3 8 3 -8 8 .

1 5 . G . Y . C h i n , W. F . Ho sfo rd , an d D . R . M en d o r f : Prec. Roy. Soc., 1 9 6 9 , v o l .A 3 0 9 , p p . 4 3 3 - 5 6 .1 6 . G . Y . C h i n , R . N . Th u r s t o n , an d E . A . Nesb i t t : Trans. TMS-AIME, 1 9 6 6 , v o l .2 3 6 , p p . 6 9 -7 5 .1 7 . C . S . B ar r e t t an d W. F . S t ead m an : Trans. TMS-AIME, 1 9 4 2 , v o l . 1 4 7 , p . 5 7 .

1 8 . B . C . Wo n s i ewi cz an d G . Y . C h i n : Met. Trans., 1 9 7 0 , v o l . 1 , p p . 5 7 -6 1 .1 9 . I . L . D i Uamo re , E . B u t l e r , an d D . Gree n : MetalSci. J., 1 9 6 8 , v o L 2 , p p . 1 6 1 -

6 7.2 0 . Y . C . L i u : Trans. TMS-AIME, 1 9 5 7 , v o l . 2 0 9 , p p . 8 3 6 -4 2 .

2 1 . C . A . Verb raak : ActaMet., 1 9 5 8 , v o l . 6 , p p . 5 8 0 -9 7 .2 2 . W . R . H i b b a r d , J r . a n d W . R . T u l l y : Trans. TMS-AIME, 1 9 6 1 , v o L 2 2 1 , p p .3 3 6 -4 3 .

2 3 . S . Sa i mo t o , Ph .D . Th es i s , 1 9 6 4 , p . 1 7 .2 4 . R . P . C ar r ek er , J r . an d W . R . H i b b ard , J r . : ActaMet., 1 9 5 3 , v o l . 1 , p . 6 5 4 .2 5 . G . May er : Ph D . Th es i s , 1 9 6 7 , p . 5 2 .2 6 . A . Ko ch en d Sr f er an d M. Swan so n : Arch. Eisenhuettenw., 1 9 6 0 , v o l . 3 1 , p p .

5 4 9 -5 3 .2 7 . U . F . Ko ck s an d T . J . B ro wn : ActaMet., 1 9 6 6 , v o l . 1 4 , p . 8 7 .2 8 . P . J . J ack s o n an d Z . S . B as i n sk i : Can. J. Phys., 1 9 6 7 , v o l . 4 5 , p . 7 0 7 .2 9 . B . R amasw ami , U . F . Ko o k s , an d B . C h al mer s : Trans. TMS-AIME, 1 9 6 5 , v o l .

2 3 3 , p . 9 2 7 .3 0 . Y . Nak ad a: B el l Te l e p h o n e L ab o ra t o r i es , A l l en t o wn , Pa . , 1 9 7 0 , u n p u b l i sh edresear ch .3 1 . G . Y . C h i n : Textures in Research and Practice, J . G r e w a n a n d G . W a s s e r m a n n ,ed s . , p p . 5 1 -7 9 , Sp r i n g er -Ver l ag C o . , B er l i n , 1 9 6 9 .

2 7 2 2 - V O L U M E 1 , O C T O B E R 1 9 7 0 M E T A L L U R G I C A L T R A N S A C T I O N S

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