Strain hardening Mechanisms for Polycrystalline Molybdenum Alloys.pdf

7/30/2019 Strain hardening Mechanisms for Polycrystalline Molybdenum Alloys.pdf

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S O M E S T R A i N - H A R D E N I N G M E C h a N I S M S F O R P O L Y C R Y S T A L L I N EM O L Y B D E N U M A L L O Y S

I o D . G o r n a y a , V . F. M o i s e e v ,E . P . P e c h k o v s k i i , a n d V . i . T r e f i l o v

U D C 6 6 9 . 0 1 : 6 2 0 . 1 7 8 : 6 6 9 . 0 1 8 . 4

I n t r o d u c t i o n . H a r d e n i n g o f m e t a l s a n d a l l o y s d u r i n g p l a s t i c d e f o r m a t i o n i s c a u s e d , asi s w e l l k n o w n [ i -3 ]: b y a m a r k e d i n c r e a s e i n d i s l o c a t i o n d e n s i t y a n d r e d i s t r i b u t i o n t h r o u g h -o u t t h e v o l u m e t o f o r m d i f f e r e n t d i s l o c a t i o n s t r u c t ur e s .

A l t h o u g h c u r r e n t l y t h e r e a r e r e l a t i v e l y g o o d s t u d i e s o f i n d i vi d u a l s t r a l n - h a r d e n i n gm e c h a n i s m s c o n n e c t e d w i t h s p e c i f i c d l s l o c at i o t~ s t r u c t u r e s [ i, 3, 4] , t h e r e a r e p r a c t i c a l l yn o c o m p a r a t i v e s t u d i e s o f t h e e f f i c i e n c y o f d i f f e r e n t s t r u c t u r a l s t a t e s ( f r o m a " f o r e s t " o fd i s l o c a t i o n s t o a d i s o r i e n t a t e d l a t t i c e s t r u c t u r e) f o r s t r a i n h a r d e n i n g o f a l lo y s i n r e l a t i o nt o c o m p o s i t i o n , o r i g i n a l s t r u c t u r e , p r i o r t r e a t m e n t , test c o n d i t i o n s , e t c. T h i s i s m a i n l yd u e t o r e s e a r c h d i f f i c u l t i e s , s i n c e t h e y a r e c o n n e c t ed w i t h t h e n e c e s s i t y f o r s t e pw i s e m o ni -c o r i n g o f d i s l o c a t i o n s t r u c t u r e b y m e a n s o f t r a n s m i s s i o n e l e c t r o n m i c r o s co p y .

S i n c e d i s l o c a t i o n s t r u c t u r e s d i f f e r a c c o r d i n g t o t h e e f f e c t o f s t r a i n h a r d e n i n g [ i, 4] ,i t m i g h t b e e x p e c t e d t h a t t h e i r s u c c e s s i v e f o r m a t i o n d u r i n g d e f o r m a t i o n s h o u l d l e a d t o ac h a n g e i n l o a d i n g c u r v e p a t h . T h e p r o b l e m i n v o l v e s f i n d i n g a m e t h o d f o r t r e a t i n g c u r v e sw h i c h w o u l d m a k e i t p o s s i b l e t o r e v e a l t he s e c h a ng e s . T h i s w o u l d g r e a t l y s i m p l i f y s e t t i n gu p r e s e a r c h i n t o s t r a i n ha r d e n i n g , s i n c e i t w o u l d b e c o m e p o s s i b l e t o d e t e r m i n e t h e b o u n d a r i e so f i n d i v i d u a l s t r u c t u r a l s t a t e s d i r e c t l y f r o m t h e l o a d i n g c ur v e .

L o a d i n g c u r v e s f o r p o l y c r y s t a l l l n e m a t e r l a l s o n tr u e s tr es s- -~ ru e s t r a i n c o o r d i n a t e s h a v et h e us u a l p a r a b o l i c f o r m a n d m a y b e r e p r e s e n t e d [ 5] b y t h e r e l a t i o n s h i p

~ = ~ o + K 'E % ( 1 )w h e r e e o i s t he y i e l d p o i n t ; K ' , s t r a i n - h a r d e n i n g c o e f f i c i e n t ; E , t r u e s t r a i n ; n , s t r a i nh a r d e n i n g i n d e x .

T h e r e a r e o t h e r v a r i a t i o n s f o r d e s c r i b i n g l o a d i n g c ur v e s . F o r e x a m p l e , H o l l o m a n [ 6 ]p r o p o s e d a n e x p r e s s i o n

~ -- K " E m , ( 2 )w h i c h i s i n g o o d a g r e e m e n t w i t h e x p e r i m e n t a l d a t a f o r t h e u n i f o r m s t r a i n s e c t i o n. I n E qo( 2) m i s t h e s t r a i n - h a r d e n i n g i n d e x ; K " i s a c e r t a i n c o n s t a n t .

I n o r d e r ~ o d e s c r i b e s t r a i n - h a r d e n i n g c u r v e s , a s y s t e m o f t w o e q u a t i o n s o f t h e a f o r e -m e n t i o n e d t y p e w a s u s e d i n [ 7 ], e a c h of w h i c h d e s c r i b e s a s p e c i f i c s t r a i n s e c t i o n ( th e s o -c a l l e d d o u b l e - n m e t h o d ) . J a o u l [ 8] u s e d a n e x p r e s s i o n f o r t r e a t i n g s t r a i n c u r v e s

I n d a / d E = In K ' n + ( n - - 1) In E , ( 3 )o b t a i n e d b y d i f f e r e n t i a t i n g E q. ( i ) . W i t h t h i s t r e a t m en t i t i s p o s s i b l e t o d e t e r m i n e a l l oft h e p a r a m e t e r s , i . e . , c o t K ' ~ a n d n .

H o l l c m a n a n d M a n n [ 9] a n e l y z e d s t r a i n h a r d e n i n g b y m e a n s o f t h e e q u a t i o n1 ( d ~ ) ( 4 )~ - - - - = % + - Z E -d g- '

o b t a i n e d f r o m ( i ) . I n e x p r e s s i o n ( 4) d e / d E i s t h e s t r a i n - h a r d e n i n g r a t e d e t e r m i n e d a t s e v e r a lp o i n t s o n t h e h a r d e n i n g c u r v e .

O f o t h e r l o a d i n g c u r v e t r e a t m e n t s i t i s p o s s i b l e t o m e n t i o n t h e R a m a n i a n d R o d r l q u e sm e t h o d [ i0 ] i n w h i c h t o f i n d a s t r a i n - h a r d e n l n g i n d e x u s e i s m a d e o f t h e v a l u e o f w o r k Ae x p e n d e d i n s p e c i m e n d e f o r m a t i o n i n a c e r t a i n s t r a i n i n t e r v a l d E = E a -- E l:

I n s t i t u t e o f P h y s i c a l M e t a l l u r g y , A c a d e m y of S c i e n c e s o f t h e U k r a i n i a n S S R , K i e v . T r a n s -l a t e d f r o m P r o b l e m y P r o c h n o s t l , N o . 5, p p. 7 7 - 8 2 , M a y , 1 9 8 1 . O r i g i n a ! a r t i c l e s u b m i t t e dF e b r u a r y 7 , 1 9 8 0 .

6 2 8 0 0 3 9 - 2 3 1 6 / 8 1 / 1 3 0 5 - 0 6 2 8 5 0 7 . 5 0 9 19 8 2 P l e n u m P u b l i s h i n g C o r p o r a t i o n


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A ~ 1 { a ~ E ~ - - a i E i ] ( 5 )H e r e ~ a n d ~a a re t r u e s t r e s s e s r e l a t i n g t o s e l e c t e d s t r a i n v a l u e s E ~ a n d E 2. W o r k A i sd e t e r m i n e d a s t h e a r e a u n d e r t h e c u r v e o f r e l a t i o n s h i p ~-- E. I n c a se s o f s e v e r a l h a r d e n i n gs t a g e s , t h e a n a l y s i s i s p e r f o r m e d f o r e a c h s t ag e .

T h e m e t h o d s g i v e n a b o v e f o r e v a l u a t i n g l o a d i n g c u r v e s m a k e i t p o s s i b l e t o d e s c r i b es t r a i n h a r d e n i n g b y m e a n s o f s o m e e m p i r i c a l p a r a m e t e r s , i n p a r t i c u l a r c o e f f i c i e n t K' a n ds z r a i n - h a r d a n i n g i n d e x n ( or m ) , b u t t h e y d o n o t s h o w t h e p h y s i c a l n a t u r e a n d s p e c i f i cm e c h a n i s m o f t h i s h a r d e n i n g .

I n s p i t e of d i f f e r e n c e s i n o r i g i n a l m o d e l s , p h y s i c a l s t r a i n - h a r d e n i n g t h e o r i e s [ i, 3,4, ii, 12, etc.] le ad to a rela tion ship in the f o r m

= ~o + =oGbV~, (6)w h e r e a o i s a c o n s t a n t d e p e n d i n g o n t h e s p e c i f i c m o d e l ; G , s h e a r m o d u l u s ; b , B u r g e r s v e c t o r ;p , o v e r a l l d i s l o c a t i o n d e n s i t y . T h e p h y s i c a l i d e a o f e x p r e s s i o n ( 6) p r o p o s e d b y B a i l e y a n dH i r s h [ !i ] i n v o l v e s t h e f a c t t h a t s t r a i n h a r d e n i n g i s a r e s u l t of a c c u m u l a t i o n i n a v o l u m eo f m a t e r i a l o f a c e r t a i n d i s l o c a t i o n d e n s i t y n e c e s s a r y t o p r o v i d e a g i v e n s t r a i n l e v e l .H a r d e n i n g c a u s e d b y i n t e r a c t i o n o f d i s l o c a t i o n s w i t h d i s t a n t s t r e s s f i e l d s ( i n c l u d i n g t h os ed u e t o g r o u p s o f d i s l o c a t i o n s ) , c r o s s o v e r o f f o r e s t d i s l o c a t i o n s , o r d i s l o c a t i o n j o g g i n g ,a n d a l s o a n u m b e r o f m e c h a n i s m s n o t o n l y r e p r e s e n t e d b y m e a n s o f t h e s a m e e x p r e s s i o n , b u th a r d l y d i f f e r i n g i n c o e f f i c i e n t a o [ 13 ], m a k e s i t d i f f i c u l t t o a n a l y z e s t r a i n - h a r d e n l n gc r i t i c a l l y i n e a c h e a s e a n d p l a c e s a l i m i t o n t h e p u r e l y f o r m a l d e s c r i p t i o n o f t h e p r o c e s s .E x p r e s s i o n ( 6) c a n n o t b e u s e d d i r e c t l y t o a n a l y z e s t r a i n - h a r d e n i n g c u r v e s s i n c e i t d oe sn o t c o n t a i n s t r a i n i n a p l a i n f o r m , b u t b y u s i n g i d e a s a b o u t t h e m e a n d i s t a n c e o f f r e e d i s -l o c a t i o n t r a v e l i t is p o s s i b l e t o e s t a b l i s h a f o r m a l l i n k b e t w e e n e x p r e s s i o n s ( I) a n d (6 ) b ym e a n s o f a w e l l - k n o w n r e l a t i o n s h i p b e t w e e n s t r a i n a n d d i s l o c a t i o n d e n s i t y :

E = = x b gL , ( 7 )w h e r e ~ i s a n o r i e n t a t i o n f a c t o r ( a c c o r d i n g t o C o n r a d [ 14 ] , i = 0. 5 ) ; ~ , m e a n d i s t a n c e o ff r e e d i s l o c a t i o n ~ r a v e l . S u b s t i t u t i n g p , f o u n d f r o m E q. ( 7) i n e x p r e s s i o n ( 6 ) , w e o b ta i n :

= + Vb l V , < 8 )w h e r e u = = ~ o / u l = 1 . 4 1 ~ o .

I f w e t a k e ~ = c o n s t , t h e n i n f a c t w e a r r i v e a t o n e o f t h e T a y l o r s t r a i n h a r d e n i n gm o d e l s [ 15 ] w h i c h g i v e s a p a r a b o l i c r e l a t i o n s h i p b e t w e e n s t r e s s a n d s t r a i n . I n t h i s w a y n =0 .5 , a n d s t r a i n h a r d e n i n g c o e f f i c i e n t K ' t a k e s o n a n e n t i r e l y s p e c i f i c p h y s i c a l s e n s e :

K" = < 9 )F o r a n a l y s i s o f h a r d e n i n g c u r v e s a t d i f f e r e n t t e m p e r a t u r e s , e x p r e s s i o n ( 8) i s w r i t t e n

c o n v e n i e n t l y i n t h e f o r mA ~ = K V L ( l O )0

w h e r eA ( ~ - - - - ~ - - ~ o ; K - ~ - K ' / G - - - - I . 4 1 ~ o l / b - ~ . ( l l )

T h e r e l a t i o n s h i p b e t w e e n s t r e s s a n d t h e l e v e l o f s t r a i n i n E q. ( I 0 ) g i v e s a f o r m a ld e s c r i p t i o n o f t he p r o c e s s a n d t h i s i s c o n n e c t e d w i t h t h e a s s u m p t i o n t h a t L = c on s t . T h ev a l i d i t y o f t h is c r l t e r l o n c a n n o t b e v e r i f i e d d i r e c t ly , b u t i n f a ct r e c o n s t r u c t i o n o f l o a di n gcurves on c oord inate s u--E /a may serve to veri fy it, as a result of which loading curves arec o n v e r t e d i n t o s t r a i g h t l i n e s o r b r o k e n l i n e s w i t h s t r a i g h t s e c t i o n s. T h i s v e r i f i c a t i o n h a sb e e n s u c c e s s f u l l y c a r r i e d o u t b y a n u m b e r o f w o r k e r s f o r s i n g l e c r y s t a l s [ 1 3 , 1 6] , p o l y c r y s t a ll i n e m e t a l s [ 1 6 , 1 7] , p o l y c r y s t a l l i n e u - t l t a n i u m [ 18 ], a nd o t h e r a l l o y s . T h e r e s u lt s d o n o ti n f a c t c o n f o r m w i t h t h e i d e a o f t h e e x i s t e n c e o f a m e a n d i s l o c a t i o n t r a v e l p a t h ; i t i s m o s tl i k e l y t h a t f u l f i l l m e n t o f c o n d i t i o n ~ = c o n s t i s e x p l a i n e d b y n o n s t e a d y m e c h a n i s m s c o n t r o l -l i n g t h e o v e r a l l n u m b e r o f d i s l o c a t i o n s a n d t h e i r m o b i l i t y i n r e l a t i o n t o m a t e r i a l s t r u c t u r ea n d t e s t c o n d i t i o n s .

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~, ~gfl m 2- / / y

Fig. 1 Fig. 2Fig. I. Three stages of strain hardening in true stress--true straincurves replotted on coordinates o--E /~ for two-phase molybdenum alloyMTA (i) and single-phase alloy (4) at 400~ (In order to study dis-location structure in the first and second hardening sections, twosingle-phase alloy specimens were additionally extended to give strainlevels (2, 3).)Fig. 2. Dislocation on structure of molybdenum alloys in differenthardening sections: I, II) slngle-phase alloy (a~ b); II) two-phasealloy (c); III) slngle-phase alloy (d).

The aim of the present work is to find a relationship between structural changes occur-ring in molybdenu m alloys during deformation at different temperatures and the path of Thehardening curve replotted on coordinates u--E*/~.

Material and Procedure. Strain-hardening mechanisms were studied for vacuum-arc meltedpure molybdenum containing 0.003 wt.% (throughout the volume) of carbon, and approximatelythe same of nitrogen and oxygen, and also two-phase molybdenum alloy MTA [19] with 3.5 vol.%of titanium nitride in the form of 0.1-0.5 ~m spherical particles. Before testing all speci-mens were given a recrystall izatlon anneal at 1500~ and the mean grain size was 100 and 15~m in one and two-phase material, respectively. Changes in alloy dislocation structures weremonitored by means of transmission electron microscopy, and foils for this purpose were pre-pared directly from the gauge length of specimens extended by different amounts of strain ata rate of ~ = ~u sac .

Results an dDi scu ss ion . Replotting loading curves for single-phase molybdenum and MTAalloy on coordinates o--E /a made it possible to reveal (Fig. i) in the uniform strain regionthree rectilinear sections at whose boundaries a change in strain hardening coefficient oc-curred. It may be assumed that these sections correspond to different strain hardeningmechanisms.

Electron-microscope studies of dislocation structure for molybdenum and alloy MTA ineach of the strain-hardening sections showed that in the first of these there is relativelyunifo rm distrib ution of dislocations (Fig. 2a), but in the second section dislocation inter-lacing and bundles start to form, and there are still whol e areas of unclosed cell boundaries(Fig. 2b). In dispersion-harde ned alloy MTA particles of a second phase located within thebody of a grain (Fig. 2c) serve as interlacing centers in the second section. Finallyj inthe third section with the same law valu e of strain-hardening coefficient, formation of adeformed cellular structure (Fig. 2d) is observed.

Since the dislocation structures observed are connected with specific strain-hardeningmechanisms [I, 4, 12], treatment of loading curves on coordinates o--E:/z or Ao/G--E /2 pro-vides a structural basis which differs in principle from treatment by Eqs. (I) , (2), etc.

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Analysis of repl otted l oading curves for MTA alloy (Fig. 3) makes it possible toestablish some addition al straln-h ardenin g mechanisms. In particular, increas ing test tem-peratures in the range 200-1520~ leads to a reduction in strain-hardenlng coefficient K: bya factor of more than three, In this case critical strain E~ decreases, during which thereis a change in strain-h ardenlng coefficient caused by a change from a relativ ely unifo rmdislocation density to pile-ups, i.e., a change from hardeni ng by a forest of dislocationsto hardenin g resulting from reaction of mobile dislocations wit h groups of dislocations,The ratio K ~ / E ~ in this range at all temperatures turns out to be a constant value:

KJV = o.o72. (12)B y p l a c i n g e x p r e s s i o n s ( l l ) a n d (7 ) in ( 1 2 ) , w e o b t a i n :

o r2 a o p F J /2 Z F 1= O.0 7 2 ( 1 3 )

Ll " - '2 8 a o p u 2 , ( i 4 )wher e p: is overall dislo cation density tow ard the end of the first stage; L~ is distance offree dislocati on travel at this stage. Expressio n (14) reiterates the well-kn own theoreticalrelations hip of Holt [20] who showed that a unifo rm dislocation di stribut ion is unstab le andit strives to rebuild itself by formln~ interlacing or a cellular str ucture with an averagedcell size (or distan ce between interlacings) proportio nal to p-~/2.

As follows from (14), a reduction in dislocation density with increasing grain size[14], or test temperature [21] leads tO an increase in cell structure dimensions, which isin good agreement with known data for the dependence of cell size on pressing temperature andoriginal grain size [3]. A reducti on in dislocatio n density indicates that the contributionof each individual dislocat ion to the overall strain level increases. At elevated temperaturethis reduction may be explained by a reduction in the efficiency of barriers with a capacityto halt disloc ations, or what amounts to the same, an increase in the capacity of the latterto overcome these barriers due to activati on of transverse slip or unrestrained movement.

The reduction in strain-hardenlng coefficient at 20 to 90~ (Fig. 3) is of a differentnature and is connected with the differen ce in mobil ity of screw or edge dislocations in bccmetals at temperatures below (0.1-0.15)T [22 ]. This differenc e leads to a predomi nance inthe structure of screw dislocations in deformed metals which can comparati vely easil y departfrom barriers by transverse slip.

The density of dislocations pa rticipa ting in deforma tion in the first stage (up to E~)governs strain hardenin g not only at this stage, but in subsequent stages when interla cingand cellular structure disloc ation boundaries arise. This follows from the fact that theratios of strain hardening coefficients in the second and third stages, Ks and Ks, to coef-ficient K~ turn out to be constants of K~/K: = 0.43 and Ks/K, = 0.2 over the whole test tem-peratu re range (Fig . 4). The critical strain ratio Ea/E~ = 2.7 is also constant.

As comparison of the straln-hardening coefficient with the yield point for alloy MTAhas shown, the ratio K,/oo.s remains constant in the temperature range 200-800~ (Fig. 4)and it only diverges due to inclusion at high temperat ure of a dislocati on creep mecha nism[23], or as was pointed out above, due to the partlcul ar ro le of screw dislocations in low-temperature deformation,

Thus, by means of the ratios obtained betwe en strain hardening coefficient and criticalstrain EL and Ea, it is possible to plot for any temp erature a whole loading curve for aspecimen of alloy MTA in the unifor m strain region (up to the moment of specimen necking) ifcoefficient K~ is known or the rule for dislocati on densit y changes due to deformat ion at agiven temperature is known.

Keductio n in the straln-h ardenln g c oefficient in the second and third stages is explainedby partial adjustments of the elastic stress field for individual dislocations with formationof interlacing or low-angle boundaries , whic h in fact occurs when the distance between dis ~locations is several interatomi c distances [2 4]. Takeuchi [25] showed that a reduction instraln-ha rdenlng coefficient is caused above all by nonun iform distrib ution of dislocati onsin a structure. The Takeuchl coefficient q, equal to the ratio of mater ial flow stress withnonu nifor m and unifor m dislocation distrib ution always appears to be less than unity. In

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2oL ~ '~'~ / ~

90 s I I

l ~ l l~ r : I - . ~ : , l ~ z 1 0 . ~~ I ~ ~ m r n Z / k g f

n l J 'Z O O ~ 0 ~ 8 0 8 0 0 1 0 0 8 I ~ 0 T .

Fig. 3 Fig. 4Fig. 3. Effect of test temperature for alloy MTA on strain hard-ening curves on coor dina tes &~/G--EX/a: I) t = 20~ 2) 90~ 3)200~ 4) 400~ 5) 600~ 6) 8100C; 7) 1000~ 8) 13000C; 9)1520~Fig. 4. Temper ature de penden ce of the ratios K=/K: (I) , K3/K~(2), E~/E: (3) and K,/~ o.= (4) for alloy MTA.

fact, coefficie nt n calculated for alloy MTA varies from 1 at E~ to 0~775 at Ea, and withfurther defor mation it decreases acc ording to the expressi on

= 0.2 + 1.19 (15 )Thus, treatment of loading curves on coordinate 5~/G--E /= makes it possible, as was

shown in this study, to reveal the boundar ies of different structur al states and correspond-ingly stages in strain hardening directly from the load--strain diagram, and this markedlysimplifies the study of strain hardening in relation to such factors as temperature, grainsize, stra in rate, dispersed parti cle content, etc. It was shown that the factors listedaffect the efficienc y of strain hardening primaril y i n the first stage.

T h e w h o l e s t r a l n - h a r d e n l n g p r o c e s s i s d e s c r i b e d b y o n e e q u a t i o n o f t y p e ( 1 0 ) , a l t h o u g heach stage has its strain- hardeni ng coefficient, and at all temperatures a bove 0.15T theratio betw een strain -harden lng co efficient s in individual stages remains constant. Ther a t i o b e t w e e n c r i t i c a l s t r a i n s a t w h i c h t h e r e i s a c h a n ge i n s t r a i n - h a r d e n i n g m e c h a n i s m i salso constant in this temp erature range.

L I T E R A T U R E C I T E DI. A. N. Orlov, "S train- hardeni ng mechani sms for bcc metals ," in: Physics of Strain Harden-

ing for Single Crystals [in Russian], Naukova Dumka, Kiev (1972), pp. 22-39.2. V. I. Trefilov, "Effect of cellular structure on the behavio r of metals under load,"

in: Physics of Strain Hardening for Single- Crystals [in Russian], Na ukova Dumka, Kiev(1972), pp. 191-201.

3. V. I. Trefilov, Yu. V. Mil' man and S. A. Firstov. Physical Bases for the Strength ofRefrac tory Metals [in Kusslan], Naukova Dumka, Kiev (1975).

4. F. F. Lavrent'ev, "Effect of different disloca tion reactions on deforma tion stress inm e t a l q r y s t a l s , " i n: E l e m e n t a r y P r o c e s s e s o f P l a s t i c D e f o r m a t i o n i n C r y s t a l s [ i n R u s -sian], Nau kov a Dumka, Ki ev (1978), pp. 64-74.

5. P. Ludwik, Elements der Techn ologi schen Mechanlk, Spr lnger-Verlag, Berlin (1909).6. J. Ho Holloman, " Tensile deformat ion," Trans. AIME, 162, 268-290 (1945).7. Y. Bergst r~m and B. Aronsson, "The application of a disloc ation mod el to the strain and

temperat ure d ependen ce of the strain- hardeni ng exponent in the Ludwik--Holloman re lationbetween stress and strain in mild steels," Met. Trans., ~, No. 7, 1951-1957 (1972 ); J.Iron Steel Inst., 204, 230-234 (1966).

8. B. Jaoul, "Etude de la forme des courbes de deform ation plastiqu e," J. Mech. Phys.Solidi, ~, 95-114 (1957).

9. M. Hollzm ann and J. Mann, "Determ ination of friction stress in bcc polycry stals," J.Iron Steel Inst., 204, 230-234 (1966).I0. S. V. Ramani and P. Rodriques, "The work- harde nlng parameters of polycr ystalli nemateri als," Sci . Met., ~, No. !0, 755-760 (1970).

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i i . P . V ~ H i r s h a n d G . E . B a i l e y , " T h e d i s l o c a t i o n d e n s i t y f l o w s t r e s s a n d s t o r e d e n e r g yi n c o l d - w o r k e d p o l y c r y s t a l l i n e s i l v e r , " P h i l . M e g . t ~ , N o . 5 3, 4 8 5 - 4 9 7 ( 1 96 0 ).

1 2 . A . L . R o l t b u r d , " P h y s i c a l m o d e l s f o r s t r a i n h a r d e n i n g o f c r y s t a l s , " i n : P h y s i c s o fS t r a i n H a r d e n i n g f o r S i n g l e C r y s t a l s [ i n R u s s i a n ] , N a u k o v a D u m k a , K i e v ( 1 9 7 2 ) , pp . 5 -2 2 .

1 3 . V . S. I v a n o v a a n d V . A . E r m i s h k i n , S t r e n g t h a n d D u c t i l i t y o f R e f r a c t o r y M e t a l s a n d S i n g l eC r y s t a l s [ i n R u s s i a n ] , M e t a l l u r g l y a , M o s c o w ( 1 97 6 ).

1 4. H . C o n r ad , " S t r a i n - h a r d e n i n g m o d e l f o r e x p l a i n i n g t h e e f f e c t o f g r a i n s i z e o n f l o w s t re s si n m e t a l s , " i n : T h e S u p e r f i n e G r a i n i n M e t a l s [ i n R u s s i a n ] , M e t a l l u r g l y a , M o s c o w ( 1 9 7 3) ,p p . 2 0 6 - 2 1 9 .

1 5 . G . J . T e y l o r , " T h e m e c h a n i s m o f p l a s t i c d e f o r m a t i o n o f c r y s t a l s . P a r t I . T h e o r e t l c a l ~ "P r o c . R . S o c . , 1 4 5 , S e t . A , 3 6 2 - 3 8 7 ( 1 9 3 4 ) .1 6 . F . R . N . N a b a r r o , Z . S . B a z i n s k i i , a n d D ~ B. H o l t , D u c t i l i t y o f P u r e S i n g l e C r y s t a l s[ i n R u s s i a n ] , M e t a l l u r g i y a , M o s c o w ( 1 96 7 ).

1 7 . S . N . P o l y a k o v , A . S . K i d l a ~ , L . M . N a u g o l ' n l k o v a , a n d I . G . N e c h e p o r e n k o , " P r o c e d u r ef o r p l o t t i n g a n d a n a l y s i s o f t r u e t e n s i l e d i a g r a m s , " Z a v o d . L a b . , N o. 6 , 7 4 1 - 7 4 4 ( 1 96 6 ).

1 8 . R . O r o v a , G . S t o ne , a n d H. C o n r a d , " T h e e f f e c t s o f l o w t e m p e r a t u r e a n d s t r a i n r a t e o nt h e y i e l d a n d f l o w s t r e s s e s o f ~ - t l t a n i u m , " T r a n s . A S M , , 5 9 , 1 7 1 - 1 8 4 ( 1 96 6 ).

1 9 . V . I. T r e f i l o v , O . M . B a r a b a s h , V ~ F . M o l s s e v , e t e l . , E - f f e c t o f n i t r o g e n a n d t i t a n i u mo n t h e s t r u c t u r e a n d p r o p e r t i e s o f c a s t m o l y b d e n u m a l l o y s , " F i z . K h lm . M e k h . M a t e r . , N o .4 , 1 0 9 - 1 1 1 ( 1 9 7 6) .

2 0 . D . L . H o l t , " D i s l o c a t i o n c e l l f o r m a t i o n i n m e t a l s , " J . A p p l . P h y s . , 4 1 , N o . 8 , 3 1 9 7 -3 2 0 2 ( 1 9 7 0 ) .

2 1. A . L a w l e y a n d H . G a i g h e r , " D e f o r m a t i o n s t r u c t u r e s i n z o n e m e l t e d m o l y b d e n u m , " P h i l . M e g . ,1 0 , N o . 1 0 3 , 1 5 - 3 3 ( 1 9 6 4) .

2 2 . J . D . G i l m a n , " M i c r o d y n a m i c p l a s t i c i t y t h e o r y , " in : M i c r o p l a s t i c i t y [ i n R u s s i a n ] , M e t a l -l u r g i y a , M o s c o w ( 1 9 7 2) , p p . 1 8 - 3 7 .

2 3. M . F . A s h b y , " A f i r s t r e p o r t o n d e f o r m a t i o n - m e c h a n i s m m a p s , " A c t a M e t . , 20 , No . 7 , 8 8 7 -897 (1972).

2 4 . M . V . G r a b s k i i , S t r u c t u r e o f G r a i n B o u n d a r i e s i n M e t a l s [ i n R u s s i a n ] , M e t a l l u r g l y a ~M o s c o w ( 1 9 7 2 ) .

2 5. T . T a k e u c h i , " T h e o r y of h i g h - t e m p e r a t u r e t y p e w o r k - h a r d e n l n g o f b c c m e t a l s , " J . P h y s ,S o c . J p n . , 2 8 , N o . 4 , 9 5 5 - 9 6 4 ( 1 9 70 ) .

I N F L U E N C E O F T H E C R I TI C A L S T A G E O F P O L Y G O N I Z A T I O N O N T H EC H A R A C T E R I S T I C S O F D U C T I L I T Y O F T U N G S T E N I N H I G H - T E M P E R A T U R EM E C H A N I C A L T E S T S

V . S . K r a v c h e n k o a n d V . K. K h a r c h e n k o U D C 5 4 8 . 5 3 : 5 3 9 . 2 1 9

I n a n u m b e r o f c a s e s , h l g h - t e m p e r a t u r e d e f o r m a t i o n o f b c c m e ta l s a n d a l lo y s i s a c c o m -p a n i e d b o t h b y a r e d u c t i o n i n d u c t i l i t y i n s h o r t - a n d l o n g - t e r m t e s t s a n d b y s e p a r a t i o n a tt e m p e r a t u r e s e x c e e d i n g 0 . b T m e l t [ i, 2 ] . I n p a r t i c u l a r , s u c h a b e h a v i o r o f c h r o m i u m a n dm o l y b d e n u m b a s e a l l o ys w i t h a c e l l u l a r s t r u c t u r e f o r m e d i n t h e m w a s n o t ed i n [ i ] . D e s p i t em a n y i n v e s t i g a t i o n s ( s ee t h e r e v i e w i n [i , 2 ] ), t h e r e a s o n s f o r t h e r e d u c t i o n o f d u c t i l i t yi n m a t e r i a l s i n h l g h - t e m p e r a t u r e d e f o r m a t i o n h a v e n o t b e e n c l a r i f i e d i n a n u m b e r o f c a se s .

T h e p u r p o s e o f t h i s w o r k i s a s t u d y o f th e e m b r i t t l e m e n t m e c h a n i s m o f V - - P M t u n g s t e n i nt h e ar e a o f h i g h t e m p e r a t u r e s i n s h o r t - t e r m s t a t i c l o a d i n g .

T h e c h a r a c t e r i s t i c s o f s t r e n g t h a n d d u c t i l i t y w e r e d e t e r m i n e d o n a V T U - 2 V h i g h - t e m p e r a -t u r e u n i t [ 3] i n v a c u u m o n s t a n d a r d s a m p l e s w i t h a g a u g e l e n g t h d i a m e t e r o f 6. 0 m m a n d ag a u g e l e n g t h o f 3 0 m m . T h e d e f o r m a t i o n r a t e i n t e n s i o n o f s a m p l e s i n t h e 5 0 0 t o 2 5 0 0 ~ t e m -

--3 --Ip e r a t u r e r a n g e w a s a b o u t 1 . 1 0 s e c . S h o r t - t e r m c r e e p t e s t s w e r e m a d e a t 1 5 0 0 , 1 7 5 0 , a n d2 0 0 0 ~ w i t h a c o n s t a n t l o a d . T h e l e v e l s o f a p p l i e d s t r e s s e s w e r e a b o u t 5 0 - 8 0 % o f t h e c o t -

I n s t i t u t e o f S t r e n g t h P r o b l e m s , A c a d e m y o f S c i e n c e s o f t h e U k r a i n i a n S S R , K i e v . i n s t i -t u t e o f M e t a l P h y s i c s , A c a d e m y o f S c i e n c e s o f t h e U k r a i n i a n S S R , K i e v . T r a n s l a t e d f r o mP r o b l e m y P r o c h n o s t l , N o . 5 , p p . 8 2 - 8 8 , M a y , 1 98 1 . O r i g i n a l a r t i c l e s u b m i t t e d A u g u s t 8 , 1 9 8 0 .

0039-2316/81/1305-0633507.50 9 1 9 8 2 P l e n u m P u b l i s h i n g C o r p o r a t i o n 6 3 3

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