neutron differ action measurement of the rs in the cementite and ferrite phase of cold drawn steel...

8/6/2019 Neutron Differ Action Measurement of the RS in the Cementite and Ferrite Phase of Cold Drawn Steel Wires

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~ PergamonP l l S 1 3 5 9 - 6 4 5 4 ( 9 6 ) 0 0 0 5 1 - 1

Acta mater. Vot. 44, No. 10, pp. 4039~4049, 1996Copyright C 1996 Acta M etallurgica Inc.Published by Elsevier Science LtdPrinted in Great Britain. All rights reserved1359-6454796 S15.00 + 0.00

N E U T R O N D I F F R A C T I O N M E A S U R E M E N T O F T H ER E S I D U A L S T RE SS IN T H E C E M E N T I T E A N D F E R R I T EP H A S E S O F C O L D - D R A W N S T EE L W I R E S

K . V A N A C K E R I, J . R O O T 2, P . V A N H O U T T E 1 a n d E . A E R N O U D T I~ D e p a r t m e n t o f M e t a l l u r g y a n d M a t e r i a l s E n g i n e e r i n g , K a t h o l i e k e U n i v e r s i t e i t L e u v e n , B e l g i u m a n dZ N e u tr o n a n d C o n d e n s e d M a t t e r S c ie n ce B r a n c h , A E C L . C h a l k R i v er . O n t a r io , C a n a d a

(Receh,ed 25 October 1995; in ret'ised form 15 Janua O" 1996)A b s t r a c t - - T h e r e s i d u a l s tr e s s s ta t e i n b o t h t h e c e m e n t i t e a n d f e r r it e p h a s e s o f c o l d - d r a w n p e a r l it i c w ir e sh a s b e e n m e a s u r e d b y n e u t r o n d i f f r a c t i o n . T h e p h a s e m i c r o s t r e s s i n t h e a x i a l d i r e c t i o n i s o b t a i n e d . I t i sf o u n d t h a t t h e c e m e n t i t e la m e l l a e a r e s u b j e c t ed t o a h i g h t e n s il e s t re s s , u p t o 2 0 0 0 M P a , a f t e r c o l d d r a w i n g .M e a s u r e m e n t s o n e t c h e d w i r e s s h o w e d t h a t t h e p h a s e m i c r o s t r e s s i s n e a r l y c o n s t a n t w i t h t h e d i s t a n c e t ot h e w i r e a x i s . C o m b i n a t i o n o f t h e s e d a t a w i t h c o m p l e m e n t a r y X - r a y d i f f r a c t i o n m e a s u r e m e n t s o n t h ef e r r it e d e t e r m i n e s t h e r e s p o n s e o f e a c h p h a s e t o t h e m a c r o s t r e s s o r a n a p p l i e d s t r e s s. A d d i t i o n a l l y , t h ep e a k b r o a d e n i n g a n d t e x t u r e o f b o t h p h a s e s h a v e b e e n s t u d i e d u s i n g t h e n e u t r o n d i f f r a c t i o n t e c h n i q u e .T h e t e x t u r e i s l e s s s h a r p i n t h e c e m e n t i t e t h a n i n t h e f e r r i t e . I n t h e c o l d - d r a w n s a m p l e s t h e d i f f r a c t i o np e a k s a r e v e r y b r o a d , w h i c h s u g g e s t s p l a s t i c d e f o r m a t i o n o f t h e c e m e n t i t e l a m e l l a e . Copyright ~ 1996Acta Metallurgica hw.R6sum6--Les con t ra in tes r6s idue l les de la fe r r i t e e t de l a c6ment i te d 'un f i l t r~f i l~ f i f ro id on t 6 t6 mesur6ss 6 p a r 6 m e n t p a r d i f f r a c ti o n d e n e u t r o n s . L e s m i c r o c o n t r a i n t e s d e p h a s e s o n t o b t e n u e s d a n s l a d i re c t i o nax ia le . On a t rouve que les l amel les de c6ment i te son t soumises b . une con t ra in te de tens ion t r~s 61ev6e .jusq u ' / t 2000 M Pa apr~s t r6 f i lage fi f ro id . De s mesure s sur des i ll s a t t aq ues on t mo nt re q ue lesm i c r o c o n t r a i n t e s d e p h a s e r e s t e n t c o n s t a n t e s s u r t o u t e l a s e c t i o n t r a n s v e r s a l e . E n c o m b i n a n t c e s d o n n e e sd e s m e s u r e s d e d i f f r a c t i o n d e s r a y o n s X s u r l a f e r r i t e , o n d & e r m i n e l a r ~ p o n s e d e c h a q u e p h a s e f i l am a c r o c o n t r a i n t e o u f i u n e c o n t r a i n t e e x t 6 r i e u r e a p p li q u 6 e . D e p l u s , l '6 1 a r g is s e m e n t d e s p i c s e t d e l a t e x t u r ed e s d e u x p h a s e s o n t 6 t6 6 tu d i 6 s p a r l a t e c h n i q u e d e d i f f r a c t i o n d e s n e u t r o n s . L a t e x t u r e d e l a c e m e n t i t ees t moin s p rono ncee que ce lle de la fe r r i t e . D ans les 6chan t i l lons tr6 fi l6s f i f ro id , l e s p ics de d i f f rac t ionsont t res l a rges , ce qu i l a i s se sugg6rer qu ' i l y a d&ormat ion p las t ique dans les l amel les de cement i te .Zusammenfassung--Diei g e n s p a n n u n g e n s o w o h l d e r Z e m e n t i t - a l s a u c h d e r F e r r i t - P h a s e i nk a l t g e z o g e n e n p e r l i t i s c h e n D r / i h t e n i s t m i t N e u t r o n e n s t r e u u n g g e m e s s e n w o r d e n . D a b e i w u r d e d i eM i k r o e i g e n s p a n n u n g i n d e r a x i a le R i c h t u n g b e s t i m m t . M a n f i n d e t , d a b d i e Z e m e n t i t l a m e l l e n e in e r h o h e n ,b i s z u 2 0 0 0 M P a , Z u g s p a n n u n g n a c h d e m k a l t z i e h e n a u s g e se t z t si n d . M e s s u n g e n a n g e ~ it zt en D r / i h t e nz e ig t en , d a b d i e P h a s e n m i k r o s p a n n u n g s ic h k a u m m i t d e m A b s t a n d z u r D r a h t a c h s e ~ in de rt . A u s d e rK o m b i n a t i o n d i es e r D a t e n m i t z u s f it z l ic h e n R 6 n t g e n b e u g u n g s u n t e r s u c h u n g e n d e r F e r r i t - P h a s e e r h /i l t m a nd a s V e r h a l t e n j e d e r P h a s e a u f m a k r o s k o p i s c h e o d e r a n g e l e g t e S p a n n u n g e n . Z u s ~ it zl ic h w u r d e m i t H i l f ed e r N e u t r o n e n s t r e u u n g d i e R e f l e x v e r b r e i t e ru n g a n d d i e T e x t u r i n b e i d e n P h a s e n u n t e r s u c h t . D i e T e x t u ri s t w e n i g e r s c h a r f i m Z e m e n t i t v e r g l i c h e n z u m F e r r i t . D i e b e u g u n g s r e f l ex e d e r k a l t g e z o g e n e P r o b e n s i n ds e h r b r e i t , w a s a u f p l a s t i s c h e D e f o r m a t i o n e n d e r Z e m e n t i t l a m e l l e n h i n d e u t e t .

1 . I N T R O D U C T I O NT h e c e m e n t i t e l a m e l la e a r e s u b j e c t e d t o l a r g e s t re s s e sd u r i n g c o l d d r a w i n g o f f u ll p e a r l i t i c w i r e s . S o m ea u t h o r s a r e c o n v i n c e d t h a t t h e l a m e l l a e w i ll f r a g m e n t[ 1, 2 ] d u e t o t h e s e s t r es s e s . O t h e r s c l a i m t h a t t h ec e m e n t i t e w i ll d e f o r m p l a s t i c a l l y [ 3 - 5 ]. A c c o r d i n g t oL a n g f o r d [6] t h e e x p o n e n t i a l h a r d e n i n g o f d r a w np e a r l i t i c w i r e is o n l y p o s s i b l e w h e n f i n e c e m e n t i t el a m e l la e d o n o t f r a g m e n t a t a l l. I n v i e w o f t h isd i s c u s s i o n , t h e k n o w l e d g e o f t h e s tr e s s s t a t e i n t h ec e m e n t i t e a f t e r d r a w i n g t o l a r g e s t r a in s i s o f m a j o ri n t e r e s t .

I n t h i s a r t i c l e , t h e r e s i d u a l s t r e s s s t a t e i n t h ec e m e n t i t e a s w e l l a s i n t h e f e r r i t e i s s t u d i e d

e x p e r i m e n t a l l y . T h e m e a s u r e m e n t s a r e m a i n l y b a s e do n n e u t r o n d i f fr a c t io n . T h e e x a m i n e d w i r e s h a v e af i ne p e a r l i t i c s t r u c t u r e a n d a r e u s e d a s r e i n f o r c e m e n t si n a u t o m o b i l e t i re s . T h e y a r e d r a w n f r o m a d i a m e t e ro f 3 .2 5 m m t o d i a m e t e r s o f 1 .2 2 a n d 0 . 8 9 m m , w i t ht o t a l s t r a i n s 1 .9 6 a n d 2 . 5 9 , r e s p e c t i v e l y .

S o m e w o r k o n t h e X - r a y d i ff r a c t io n d e t e r m i n a t i o no f t h e r e s i d u a l s t r e s s e s i n t h e c e m e n t i t e h a s a l r e a d yb e e n r e p o r t e d [ 7 -1 1 ] . H i g h i n t e n s i t y X - r a y r a d i a t i o no r i g i n a t i n g f r o m a r o t a t i n g a n o d e o r a s y n c h r o t r o nw a s u s ed . H o w e v e r , t h e s e a u t h o r s m a d e m e a s u r e -m e n t s o n l y o n w i r e s w i t h c o a r s e p e a r l it i c m i c r o s t r u c -t u r es , w h i c h w e r e n o t i n t h e a s - d r a w n c o n d i t i o n . N od i s t i n c t io n w a s m a d e b e t w e e n m i c r o s t re s s e s w h i c ha r e i n d u c e d b y t h e p l a s ti c fl o w a n d m i c r o s t r e s s e s

4 0 3 9


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4040 VAN ACKER et a l .: NEUTRON DIFFRACTION MEASUREMENTcaused by the different elastic properties of the ferriteand cementite phases. Neutron diffraction determi-nation of the stress state in such thin wires has somelimitations, but also some important advantagescompared to the classical X-ray method. The lowattenua tion of ne utrons in steel makes it possible tomeasure the lattice strains of the cement ite within theferrite matrix, in the as-drawn state. Neutrondiffraction also provides information on the influenceof plastic deformation on the diffraction peak widthand the crystallographic texture. These stress andtexture results are complemented with X-ray diffrac-tion measurements on the ferrite.

2. METHODOLOGY2 . 1 . T h e o r e t i c a l in t r o d u c t i o n

In a two-phase mater ial the residual stress state candiffer from phase to phase. In a particular grain (orlamella) of phase ~, the phase stress a ~ ( g ) is acting(see Fig. 1 for a schematic representation of thestresses defined in this paragraph). The parameter gexpresses the ori entat ion of that grain with respect tothe sample [12]. The phase stress is the real stress ata microscopic scale. On a larger, macroscopic scale,the mean stress of all phases together is called themacros tress a M. On that scale, a vo lume V can bedefined which consists of many grains, but is muchsmaller than the entire body. The two phases ~ andfl are present in V with volume fract ion c" and d,respectively. The values o f c and c ~ are equal to themacroscopic volume fractions in a homogeneousmaterial. The total phase stress o" is the average ofthe phase stress o '(g ) in V , the sub-volume of phases i n V

in elastic properties between the two phases. If atensile macrostress exists (or an ex ternal macroscopicstress is exerted), the total stress in the stiffer phasewill be higher than the macrostress. I f the stress in thematerial is caused by purely elastic phenomena, themicrostress will be proportional to the macrostressaccording to linear elastic models. In that case,Aa'(g) will be called the elastic interaction stressAea~(g).

A microstress can also be caused by differences inplastic flow or thermal expansion (see e.g. Ref. [13]),In these cases the microstress is not necessarilyproportional to the macrostress. If the macrostress isthen relaxed a part of the microstress is still retained.This retained phase-interaction stress is called here,for simplicity, the "phase microstress N o ~ ( g ) " ', not tobe confused with the term "(total) microstress inphase ~" introduced above. In general, the mi-crostress A a ' ( g ) in phase ~ has two components, theelastic interaction term and the phase microstress

Aa'(g) = A'a'(g) + Na'(g). (4)When the phase stress a ' ( g ) and the macrostress a Mare known, an experiment could be set up to measurethe phase microstress A'a'(g). In such an experiment,a macros tress - a Mshould be imposed on the sample.Note that an elastic interaction term -A"a~(g) inphase ~ corresponds with the applied macrostress-a M. The phase stress [a'(g)]* measured in such anexperiment is exactly the phase mierostress Na'(g)

[a'(g) ]* = a=(g) -- a M-- Aca~(g)= Aa'(g) - Aa'(g) = Na' (g) . (5)

f a ~ ( g ) f l ( g ) d ga ~ - ( 1 )w f l ( g ) d g

In equation (1)fl(g) is the distribution function of thegrain orientations in phase a. The macrostressexpressed by the tensor a M is then

a M = c~a ~ + c~o ~ . (2)It is the macrostress that causes a deformation of thesample when it is macroscopical ly etched Based onthis phenomeno n, many mechanical methods exist todetermine the macrostress. However, neutron orX-ray me thods measure the total phase stress a ~. Themagnitude of the phase stress is important for crackinitiation and propagation , stress corrosion, etc.

On a microscopic scale, the phase stress a ' ( g )deviates from the macrostress a M. Tha t deviat ion iscalled here the microstress A a ~ ( g ) in phase ~ anddefined as

Aa'(g) = a ' ( g ) - - a M . (3)The mierostress Aa'(g) can originate from differences

o ~ a )

. . . . . . . . . . . . . . . . . . . & " ' &

p h a s e m ic r o ,s t re s s A r G O r , ( g ) ' , , A r O ' O .e la s ti c in te ra c t io n A e ( ~ g ) ~ :I . . . . i { A e O ( zm a c r o s t r e s s o M : ] : : : :

. . . . . . . . . . . . . . . . . . gr'ain-1] 2 "3 7 4:5 I) , ) , ) )

V o l u m e Vp h a s e s ( z a n d

Aro.~ ~ i w i t h a p p l i e d s t r e s s

p h a

Fig. 1. Schematic representation of different kinds of s t r e s s e sdefined in the tex t on the macroscopic level containingseveral phases and on the level of one phase, containingseveral grains.


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V A N A C K E R et a l .: N E U T R O N D I F F R A C T I O N M E A S U R E M E N T 4041~cted13

Fig. 2. Definition o f the stress components in a cylindricalcoo rdin ate system and definition of the angles ~0 and ~0 inthe neutron diffraction experiment.

T h e p h a s e m i c r o s t r e s s i s, i n o t h e r w o r d s , t h e c o n s t a n tt e r m o f t h e m i c r o s t r e s s in a p a r t i c u l a r p h a s e , w h i c hi s n o t d e p e n d e n t o n t h e m a c r o s t r e s s [ 1 4 ] . T h i sm i c r o s t r e s s h a s t o b e a c c o u n t e d f o r i f o n e w a n t s t op r e d i c t t h e t o t a l s t r e s s i n a p h a s e w h i l e i m p o s i n g ak n o w n e l a s ti c ( m a c r o ) s t r e s s o n t h e s a m p l e . I na n a l o g y t o t h e t o t a l p h a s e s t r e s s , a t o t a l p h a s em i c r o s t r e s s A ' a ~ c a n b e d e f i n e d f o r e a c h p h a s e . I t i so b v i o u s f r o m e q u a t i o n s ( 2 ) a n d ( 5 ) t h a t e q u i l i b r i u me x i s t s b e t w e e n t h e t o t a l p h a s e m i c r o s t r e s s e s o f a l lp h a s e s

c ' A ~ a ~ + c P A ~ a # = O . (6 )

2 . 2 . S t r e s s m e a s u r e m e n t sS t re s s d e t e r m i n a t i o n b y m e a n s o f n e u t r o n o r X - r a y

d i f f r a c ti o n i s e s s e n t ia l l y a m i c r o s c o p i c s t r a i n m e a s u r e -m e n t . T h e a m o u n t o f s t r a in i n a c e r ta i n d i r e c t i o n isd i r e c t l y r e l a t e d t o t h e d i f f e r e n c e b e t w e e n t h e l a t t i c ep l a n e s p a c i n g dh~ i n t h e e x a m i n e d s a m p l e a n d t h es p a c i n g d ~ i n a s t r a i n -f r e e re f e r en c e s a m p l e o f t h es a m e m a t e r i a l. I f t h e s p a c i n g b e t w e e n ( h k l ) p l a n e si n t h e d i r e c t io n o f t h e m e a s u r e m e n t i s l a r g e r t h a n i nt h e r e f e r e n c e s a m p l e , a t e n s i l e s t r a i n i s p r e s e n t . T h es t r a i n i n t h e d i r e c t i o n o f t h e d i f f r a c t i o n v e c t o r Q i st h e n

dh~.t -- d~ /e o - d O ( 7 )

A c o m p l e t e s t r a i n t e n s o r c a n b e d e r i v e d i f s t r a i nm e a s u r e m e n t s a r e m a d e i n s e v e r a l d i r e c t i o n s . T h ee x a c t l a t ti c e p l a n e d i s t a n c e d ~ i s d e t e r m i n e d b ya c c u r a t e m e a s u r e m e n t s o f 2 0 , t h e s c a t t e r in g a n g l e ina d i f f r a c t i o n e x p e r i m e n t , t h r o u g h B r a g g ' s L a w [ 15 ].C l a s s i c a l l y , o n e d i f f r a c t i o n p l a n e i s u s e d a n d t h es am ple i s t i l t ed by the a ng le s q~ an d ~k ( s ee F ig . 2 ) .T h i s m e t h o d i s c a l l e d t h e d -s in 2 ~, m e t h o d a n d i s u s e di n X - r a y d i f f r a c t i o n [ 1 6 ] a s w e l l a s i n n e u t r o nd i f f r a c t i o n m e a s u r e m e n t s [ 1 7 , 1 8 ]. A g e n e r a [ e q u a t i o n

f o r t h e c a l c u l a t i o n o f th e s t r e s s t e n s o r i s1c ~ = ~ s z ( 0 . ~ t cos:~o + 0.~: sin2~0 + 0.:2 si n: ~

1- 0.3Dsin-~ ~ $20.33 S l( al l 0"22 0"33)

1 s2(0 .~s c o s + 0. :t s in ~0)sin2ff, (8)in w hich s ~ and s2 a re d i f f r ac t io n e la s t i c con s tan t s .T h e y a r e d i f f e r e n t f r o m t h e m a c r o s c o p i c e l a s t i cc o n s t a n t s f o r b u l k m a t e r i a l a n d c a n b e c a l c u l a t e df r o m t h e s i n g l e - c r y s t a l e l a s t i c c o n s t a n t s u s i n g a l i n e a re l a s t i c m o d e l s u c h a s R e u s s , V o i g t o r K r 6 n e r [ 1 6 ] . I ft e x t u r e d a t a a r e a v a i l a b l e , t h e O D F ( O r i e n t a t i o nD i s t r i b u t i o n F u n c t i o n ) c a n b e i n c o r p o r a t e d i n t h ec a l c u l a t i o n [ 1 9 ] . W h e n n o s i n g le - c r y s ta l d a t a a r ea v a i l a b l e , t h e d i f f r a c t i o n e l a s t i c c o n s t a n t s c a n b em e a s u r e d b y i m p o s i n g d i f fe r e n t k n o w n s t re s se s o n t h es a m p l e u s i n g a t e n si l e d e v i c e d u r i n g a n e u t r o n o rX - r a y s t r e s s d e t e r m i n a t i o n e x p e r i m e n t [ 1 6 ] .

T h e s e g e n e r a l c o n s i d e r a t i o n s h a v e t o b e t r a n s l a t e di n t o o u r p a r t i c u l a r s i t u a t i o n . T h e i n v e s t i g a t e ds a m p l e s c o n s i s t e d o f a c u b i c a l a r r a y o f t h i n w i r e s , o fl e n g t h 1 0 r a m . I n t h e n e u t r o n d i f f r a c t i o n e x p e r i m e n t ,t h e e n t i r e s a m p l e v o l u m e w a s i l l u m i n a t e d . I t i so b v i o u s t h a t t h e l a r g e d i f f r a c t i o n v o l u m e w i l l h a v ei m p o r t a n t c o n s e q u e n c e s f o r t h e s t r e s s a n d t e x t u r em e a s u r e m e n t s .

I n a d i f f r a c t i o n e x p e r i m e n t , e a c h p h a s e , w i t h ad i s t i n c t i v e a r r a y o f B r a g g p e a k s , i s e x a m i n e ds e p a r a t e ly . T h e t o t a l p h a s e s t re s s o f t h a t p h a s e i so b t a i n e d . I n a d r a w n w i r e, al l c o m p o n e n t s o f t h e t o t a lp h a s e s t r e s s a s w e l l a s t h e m a c r o s t r e s s a r e a s s u m e d t ob e i n d e p e n d e n t o f t h e c y l i n d r ic a l c o o r d i n a t e s x a n dz b e c a u s e o f t h e a x ia l s y m m e t r y o f t h e d r a w i n gp r o c e s s . ( T h e d e f i n i t i o n s o f t h e c y l i n d r i c a l c o o r d i -n a t e s x , z a n d r a r e i n d i c a t e d i n F i g . 2 . ) I t i sc o n v e n i e n t t o r e - w r i t e e q u a t i o n ( 8 ) i n c y l i n d r i c a lc o o r d i n a t e s

1E~ = ~ s,.(0.~,, cos"~o + 0" ;, s in2 ~ + a ~ s in:~o1 ,- 0.~:)sin:O + -5s20.._ + sl(0.~,, + 0.~,. + 0..':)

1+ ~ s,_(0.~: co s ~o + 0.~: sin ~0)sin2~k. (9)T h o u g h t h e m a c r o s c o p i c s tr e s s c o m p o n e n t s , a ~ a n da ~ , d i s a p p e a r b e c a u s e o f t h e a x i a l s y m m e t r y [2 0] , i ti s p o s s i b l e t h a t t h e s e s h e a r c o m p o n e n t s s t i ll e x i s t o nt h e s c a l e o f t h e p h a s e s . B e c a u s e o f t h e c o m p l e t ep e n e t r a t i o n t h r o u g h t h e w i r e i n a n e u t r o n d i f f r a c ti o ne x p e r i m e n t , a l l s tr e s s c o m p o n e n t s a ] w i l l b e a v e r a g e do v e r t h e e n t i r e w i r e s e c t i o n

-

0 . : = R - q j o j o r 0 . ( r ) d r d . ( l O )I n t e g r a t i n g e q u a t i o n ( 9 ) a s in e q u a t i o n ( 1 0) a n d u s i n g


4/11

4042 VAN ACKER e t a l . : NEUTRON DIFFRACTION MEASUREMENTthe definition of the hydrostatic stress a H~, we obtainas a formula for the neutron measurements on thinwires

~ is the mean value of the deviatoric stress s~: overthe entire wire section. Calculations have shown thatthe coefficient of crH~ is very small and the hydrosta ticstress cannot be obtained with the desired accuracy.However, a relation between the axial and deviatoricstress exists. The stress equilibrium in each micro-scopic volume of the material yields the followingrelation between a~ and a~, [20]

~Cr~r a,~ + a~ (12)a~ = a,~ + r - ~ - or a~, (R) - 2

neutron diffraction. Figure 3 illustrates the definitionof the different kinds of residual stress. In a singleX-ray experiment it is not possible to distinguishbetween these stresses.2 . 3 . M e a s u r e m e n t o f g r a d i e n t s i n p h a s e m i c r o s t r e s s e s

In order to get an idea of the values of the phasemicrostresses as a function of the distance to the wireaxis, the wires were etched to different diameters. Byetching the wire, the macrostresses are relaxed. As thephase microstresses act on a microscopic scale,independent of the macrostress, they are not altered,except in a shallow near-sur face region. If the wire isetched from diameter R0 to R~, the following equationholdsAra:~:R0rtR~ ~ Ara~:R,~R~ + Ara~:(Ro)Tr(R~ - R~). (15)

The radial stress component a ~ , ( R ) at the surface ofthe wire (distance R from axis) is the stress on a freesurface, which is always zero. F rom equa tion (12) andthe definiti on of the hydrostatic stress, it follows thatin the case of axial symmetry the average of thehydrostatic stress over the entire wire section equalsone third of the average of the stress component inthe axial direction

- - o..~_crH~_ ~-. (13)

Knowing relation (13), formula (11) then reduces toa more convenient one

2 . 4. T e x t u r e m e a s u r e m e n t sThe crystallographic texture obtained from the

neutron diffraction measurements must be inter-preted carefully. Due to the total penetration ofneutrons through the wire volume, a cylindricallyaveraged texture is detected. Note that the wire mayfeature texture gradients from the centre to thesurface, and that the surface texture may even be a"cyclic texture" with only a monoclinic "samplesymmetry" [21]. X-ray measurements are required todetermine the spatial distribution of texture in thewire.

Equati on (14) indicates that the neu tron experimentsprovide only the measurements of the axial stresscomponent. (Note that the cementite lamellae arealigned in the axial direction. This means that theaxial component of the stress is one of the mostrelevant components.)

Neutron diffraction extracts information only onthe average phase microstress. Recall that theexamined material consists of two phases, cementiteand ferrite. The macrostr ess a ~ is acting over the twophases. The macrostress can vary with the depth inthe wire, but has to be in equi librium over thecomplete wire section. Since the measured stress willbe an exact average over the wire cross section, it willnot be possible to determine the radial distri bution ofmacrostress in the neutron experiment. The averageof the elastic interaction stresses A~a~, which areproportional to the macrostress, cannot be distin-guished in the neutron measurement. However, thephase microstresses Ara ~, which have orig inat ed fromthe differences in plastic flow or thermal expansionbetween the two phases, are independent of themacrostress. Measuring on one phase, the averageAra ~ over the wire will not necessari ly be zero. It isthis average phase microstress that is measured by

3 . E X P E R I M E N T A L SET-UPThe wires under investigation were made of full

pearlitic eutectoid steel with 0.82%C. The initialdiameter was 3.25mm. The various specimentreatments are listed in Table 1.

The neutron stress experiments were performed onthe C2 high resolution powder diffractometer atAECL, Chalk River, Canada. A diffraction patternfrom 41 to 121 2 0 was acquired with an 800-channelmultiwire position-sensitive detector. The ne utron

~ e o ~ o - -

Fig. 3. Possible (but arbitrarily chosen) residual stressdistribution in one phase of the wire. Distinction is madebetween the macrostress a M, the total elastic interactionstress Aa~, and the total phase microstress Ara .


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V A N A C K E R e t a l . : N E U T R O N D I F F R A C T I O N M E A S U R E M E N TTable 1. Treatments of the examined wires

4043

Diameter af ter Total s train Final di am ete r Re fer red o indrawing ( m m ) E Treatment ( m m ) the text as1.22 1.96 - - 1.22 Sam ple 1.11.22 1 . 9 6 Ch e mic a l lytched 1.10 Sam ple 1.21.22 1 . 9 6 Ch e mic a l lytched 0.85 Sam ple 1.31.22 1.96 Hea t treated at 45 0C , 10' 1.22 Sam ple 1.00.89 2.59 - - 0.89 Sam ple 2.1

w a v e l e n g t h w a s 2 . 3 6 5 4 ~ , a n d h i g h e r o r d e r c o n t a m i -n a t i o n w a s s u p p r e s s e d b y a p y r o l y t i c g r a p h i c f i lt e r.T h e w i r e ax e s w e r e i n th e s c a t t e r i n g p l a n e . T h e a n g l e so f t h e w i r e a x e s w i t h t h e i n c i d e n t b e a m w e r e v a r i e df r o m 0 ~ t o 1 80 i n s t e p s o f 2 0 , a n d a d i f f r a c t i o np a t t e r n w a s o b t a i n e d a t e a c h o r i e n t a t i o n . T o d e t e c tt h e w e a k c e m e n t i t e p e a k s, l o n g c o u n t i n g t i m e s w e r er e q u i r e d , u p t o 4 h p e r d i f f r a c t i o n p a t t e r n .

T e x t u r e m e a s u r e m e n t s w e r e m a d e o n s o m es p e c i m e n s w i t h a n E u l e r i a n c r a d l e a n d a s i n g l e - d e t e c -t o r d i f f r a c t o m e t e r . H e r e , t h e s a m p l e s w e r e t i l t e dp e r p e n d i c u l a r t o t h e p l a n e o f i n c i d e n t a n d d i f f ra c t e db e a m s u c h t h a t t h e a n g l e 7 . f r o m t h e w i r e a x i s t o t h ed i f f r a c t i o n v e c t o r w a s v a r i e d f r o m 0 t o 9 0 i n s t e p so f 2 . 5 : .

4 . R E S U L T S4 . I . P e a k s h a p e a n d w i d t h

M o s t a u t h o r s p r e fe r t o d e te r m i n e t h e p e a kp o s i t i o n , i n t e n s i t y a n d t h e f u ll w i d t h a t h a l fm a x i m u m ( F W H M ) b y fi tt in g t h e m e a s u r ed d a t aw i t h a G a u s s f u n c t i o n [ 1 7 , 2 2]. F r o m F i g . 4 it i s c l e a r

7 0 0 G a u s s f u n c t i o n - r ~ = - 0 . 9 9 1 66O O

A 5O O0. ~ , 4 o oc 3 0 00c 2 0 o

l O O

1 0 9

7 o 06 0 0

AM 5 0 0v. _ ~ 4 o 0.=300-~ 21111

l O 0

1 1 1 1 1 3 1 1 5 1 1 72 0 ( o )V o i q t f u n c t i o n - r ' ~ - - 0 .9 9 9 1

1 1 9

1 0 9 1 1 1 1 1 3 1 1 5 1 1 7 1 1 92 0 ( o )Fig . 4 . Me asured (200) ct Fe d if f rac t ion peak and f i t t ing bya Gauss func t ion and Voig t func t ion , r espec t ive ly . Thecor re la t ion coef fic ien ts be tween f i t ted and measured curvesare expressed by r 2.

t h a t a V o i g t f u n c t i o n [2 3] i s m o r e a p p r o p r i a t e i n o u rc a se . T h e f i t t e d p a r a m e t e r s o f t h e V o i g t f u n c t i o n a r eu s e d t o c a l c u l a t e t h e p e a k p o s i t i o n , t h e i n t e g r a t e di n t e n s it y a n d t h e f ul l w i d t h a t h a l f m a x i m u m( F W H M ) .

W h e n t h e d if f r a c t io n p a t t e r n o f t h e c o l d d e f o r m e ds a m p l e 1 .1 is c o m p a r e d w i t h t h e re f e r e n c e s a m p l e 1 .0 ,t h e h u g e p e a k w i d t h o f th e a s - d r a w n s a m p l e s i s r e a l lys t ri k i n g . T h e v a r i a t i o n o f w i d t h o f t h e (3 0 1 )d i f f r ac t i o n p l a n e o f t h e c e m e n t i t e i s p l o t t e d v s s in : ~i n F i g . 5 . H e r e , ~ , i s t h e a n g l e t h e d i f f r a c t i o n v e c t o rm a k e s w i t h t h e w i re a xi s a n d o n e e x p ec t s th e F W H Mt o b e c o n s t a n t w i t h a n g l e ~ . T h e a v e r a g e p e a k w i d t h sf o r t h e e x a m i n e d s a m p l e s a r e g i v e n i n T a b l e 2 .

O n e e x p l a n a t i o n o f p e a k b r o a d e n i n g c o u l d b e t h ep r e s e n c e o f a l a rg e s t re s s g r a d i e n t t h r o u g h t h es p e c i m e n . I f s u c h a g r a d i e n t e x i s ts , e a c h a n n u l u s i nt h e w i r e w o u l d d i f f r a c t a t a d i f f e r e n t 2 0 a n g l e , w h i c hw o u l d b r o a d e n t h e o v e r a l l d i f f ra c t i o n p e a k o f t h ee n t i r e s a m p l e . H o w e v e r , s t a r t in g f r o m t h e 0 . 7 9 5 F W H M o f s a m p l e 1 .0 , e v e n a n e n o r m o u s g r a d i e n t( e .g . f r o m - 1 0 00 t o 1 0 0 0 M P a ) w o u l d o n l y c a u s e am e a s u r e d p e a k w i d t h o f 0. 81 9 F W H M . S o , s tr es sg r a d i e n t s a r e d e f i n i t el y n o t t h e m a i n c a u s e o f t h eo b s e r v e d l a r g e p e a k b r o a d e n i n g .

A b e t t e r e x p l a n a t i o n c a n b e fo u n d i n th e c o h e r e n t l yd i f f r ac t i n g d o m a i n s iz e . T h e c e m e n t i t e l a m e l l a e c a nb e c o m e v e r y t h i n [ 6, 2 4] . I f t h e l a m e l l a r w i d t h i s o n l y1 2 0 ~ , t h e F W H M c a n r is e to 2 . 5 0 H o w e v e r ,L a n g f o r d [6 ] r e p o r t s a l a m e l l a r s p a c i n g o f 30 0 0 , ~ i na p e a r l i t i c w i r e d r a w n t o a t o t a l s t r a i n , ~ = 2 . 5. T h i sc o r r e s p o n d s t o a c e m e n t i t e l a m e l l a e t h i c k n e s s o fa b o u t 3 0 0 / ~ a n d a m a x i m a l p e a k w i d t h o f o n l y1 .4 75 M o r e o v e r , t h e p e a k w i d t h f o r p a r a l l e lc e m e n i t e l a m e l l a e s h o u l d t h e o r e t i c a l l y b e d e p e n d e n to n t h e o r i e n t a t i o n o f th e d i f f ra c t i o n v e c t o r w h i c h c a nb e e x p r e s s e d b y si n- '~ k. T h e c a l c u l a t e d F W H M i s

3 . 0 0 1 F W H M o f F e s C ( 3 0 1 )="~ " - ~ . , . , . - - - ~ i x , . , . = = 2 . a r A1.60 E ~ ] I (heat reated), , Ib ,

, , . . , ,0 .5 0 -~ t for 120 A thick iarnellae

I.0 0 i0.0 0 .5 1 .0s l r ~Fig . 5 . The fu l l wid th a t ha lf maximum of the (301)cementi te d if f rac t ion peak as func t io n of s in2~, me asured insample 1 .3, in the hea t t r ea ted sample 1 .0 and ca lcu la ted fora lamella r th ickness of 120 ,~ .


6/11

4044 V A N A C K E R et al.: N E U T R O N D I F F R A C T IO N M E A S U R E M E N TTable 2. Averaged FW HM ov er all tO angles measured on one sam ple

Diffraction Sam ple 1.0plane (reference) Sa m ple1.1 Sample1 .2 Sample1.3 Sa m ple .1Fe (110) 0.493 0.651 0.681 0.704 0.695Fe (200) 1.026 1.518 1.583 1.649 1.595Fe~C (301) 0.795 2.177 2.305 2.137 2.298

Fe~C (121) 0.825 2.493 2.460 2.450 2.382

d r a w n i n F i g . 5. A s i m p l e f o r m u l a f o r t h e p e a k w i d t hA 2 0 h a s b e e n u s e d

A 2 0 2 sin..____~ 1813 (1 6 )/C O S0 7~ 'w h e r e t i s t h e t h i c k n e s s o f t h e l a m e l l a a n d ~b t h e a n g l eo f t h e d i ff r a c t i o n v e c t o r w i t h t h e i n - p l a n e d i r e c t i o n o ft h e l a m e l l a , a s s u m e d t o b e n e a r l y p a r a l l e l t o t h e w i r ea x i s .

H o w e v e r , t h e m e a s u r e d p e a k w i d t h d o e s n o tc h a n g e s i g n i f i c a n t l y w i t h a n g l e q J a n d i s s t i ll b r o a d e rt h a n t h e c a l c u l a t e d o n e . T h e o n l y r e m a i n i n ge x p l a n a t i o n m a y b e t h e p re s e n c e o f d i s l o c a t i o n so r i g i n a t i n g f r o m p l a s t ic f l o w o f t h e c e m e n t i t el a m e l l a e . T h i s i s c o n s i s t e n t w i t h e v i d e n c e f o r p l a s t i cd e f o r m a t i o n i n c e m e n t i t e t h a t h a s b e e n f o u n db y G i l S e v i l l a n o [ 3, 5 ]. T h e d e f o r m a t i o n o f t h ew i r e is n o t o n l y a c c o m m o d a t e d b y e l a s ti c d e f o r -m a t i o n o r f r a g m e n t a t i o n o f th e c e m e n t i t e l am e l l a e,b u t a l s o p l a s t i c d e f o r m a t i o n t a k e s p l a c e i n t h el a m e l l a e .4.2. Texture

T h e r e s u l t s o f th e t e x t u r e m e a s u r e m e n t s a r e s h o w n

i n F i g . 6 . T h e i n t e n s i t i e s a r e c o r r e c t e d f o r t h eb a c k g r o u n d a n d n o r m a l i z e d . A l e ss s h a r p t e x t u r e iso b s e r v e d i n t h e c e m e n t i t e p h a s e t h a n i n t h e f e rr i te . I ts u g g e s ts t h a t t h e c r y s t a l l o g r a p h i c r e l a t i o n s h i p b e -t w e e n c e m e n t i t e l a m e l l a e a n d i r o n w i l l c h a n g e d u r i n gd e f o r m a t i o n .

F r o m t h e d i a g r a m s f o r t h e f e rr i te , p o l e fi g u re sw e r e m a d e a s s u m i n g p e r f e c t c i r c u l a r s y m m e t r y ,w h i c h h a s t o b e i m p o s e d d u e t o t h e g e o m e t r y o f t h ee x p e r i m e n t a l s e t - u p (s e e F i g . 7 ). F r o m t h e s e t w oc o m p l e t e p o l e f i g u r e s t h e O D F w a s c a l c u l a t e d , a n da p p l i e d i n t h e s u b s e q u e n t s t re s s d e t e r m i n a t i o n . T h er e c a l c u l a t e d p o l e fi g u re s o f t h e O D F a r e c o m p a r -a b l e w i t h t h e r e c a l c u l a t e d p o l e f i g u r e s w h i c h r e s u l tf r o m t h e X - r a y t e x t u r e d e t e r m i n a t i o n o n t h e w i r es u r f a c e ( s e e R e f s [ 2 5 , 2 6 ] ) . T h e X - r a y t e x t u r em e a s u r e m e n t i s a n a v e r a g e o v e r a s m a l l a r c o f th ew i r e s u r f a c e . I f t h e t e x t u r e d e v i a t e s f r o m a p u r ef i b r e t e x t u r e , i t w i l l b e m e a s u r e d b y t h e X - r a ym e t h o d . U n f o r t u n a t e l y , o n l y t h e f e r ri t e t e x t u r ec o u l d b e m e a s u r e d b y X - r a y s . T h e r e s u l ts f o r t h e( 1 1 0 ) p o l e f i g u r e s a r e s h o w n i n F i g . 7 . T h e X - r a ym e a s u r e m e n t s c o n f i r m t h a t a f ib e r t e x t u r e i s p r e s e n ti n t h e f e r r i t e , a n e a r l y p e r f e c t ( 1 1 0 ) f i b e r .

7 . 0 0 . 5.0| , o~ ~ 5 " 0 ii 4 . 0 1 . 53 .02 . 0 1 . 0z ~ 1 . 0

0 . 0 ' 0 . 0 . . . . . . . . .0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0Z (0) Z ()3 . 0 - r ~ 3 . 02 . s t

I 1 . 51 .00 .5O 0 4 O1 0 2 0 3 0 6 0 7 0 8 0 9 0

2 .5e-~ 2 . 0~ 1 . Si 1 .0Z 0 . 5

0 .0- ,2 , . ,o _ . . o ,o o ,o11

Fig . 6 . Neu tron d if f rac t ion in tens i ty ver sus X for the ind ica ted fe r r i te and cementi te d if f rac t ion peaks . Xis the angle f rom the wire axis to the d if f rac t ion vec tor . The tex ture measurem ents were done with neu trondiffraction, 2 = 2.37A, at 20 = 71.5 for ~ Fe (110) , 111.5 for ~ F e (200) , 96.5 for Fe~C (301) and 84.4 for Fe3C (122).


7/11

.8 1.0 1.3 1.6 2.08 1.0 1.3 1.6 2.02 .5 3 .2 4 .~ _ _ 5 .0 6 .4

6 " 4 " " ~ u U .8 3.8

2 .0

2.5 3 .2 4.1~,.~ 5.0 6 .4

. 81 .6

VAN ACKER et al.: NEUTRON DIFFRACTION MEASUREMENT 4045

Fig. 7. (110) pole figure recalculated from the ODF. (a) The cylindrically averaged texture of the entirewire section measured wi th neutron diffraction and (b) the surface texture measured with XRD.4 .3 . L a t t i c e p a r a m e t e r

The lattice parameters a, b and c of the cementitecould be determined with high accuracy from theneu tron diffraction measurements on the (stress-free)heat treated sample 1.0, and are presented in Table 3.The uncertainty of the exact 200 position of areference sample is the main cause of the error in thelattice parameter determination.

The determination of these "stress-free'" referencelattice parameters was based on the diffraction peakposition of 6 planes, (131), (221), (122), (212), (301),and (311), and at 20 different 0-angles. By averagingover many crystal and specimen directions, the latticeparameters are expected to represent values forcementite that are free of deviatoric stress.4 . 4 . P h a s e m i c r o s t r e s s

The stress determin ation was based on eq uation(14). The ~Ik~ was also determined as an unknownparameter in each stress determination, as an extracheck for the data found in the previous paragraph.Indeed, this can be done writing equation (14) as

For different 0-angles we get a set of equationswith two unknown s, ~ and Na~:, which can becalculated using a least squares fit. For the diffractionelastic constants s~ and s: of the cementite, literature

T a b l e 3 . L a t t i c e p a r a m e t e r s o f c e m e n t i t e m e a s u r e d w i t h n e u t r o nd i f f r a c t i o nL a t t i c e ( ~ i r a m e t e r U n c e r t a i n t y ( st . d e v . )(A)

a 5 . 0 8 |6 0 . 0 0 0 7b 6 .7446 0 .0016c 4 . 5 2 0 6 0 . 0 0 0 7

values are used. Hanabusa e t a l . [27] obta ined s~ =-2 .1 8x 10-6MPa -~ and sz= 6.g x 10-~MPafor the (121) diffraction plane. These values are closeto what was found by Winho hz and Cohen [8] for the(250) plane in the cementite of tempered martensite.They based their values on X-ray experiments with arotating anode on samples with a coarse microstruc-ture compared to the drawn wires. The diffractionelastic constants of the ferrite were calculated fromsingle crystal values, using a Reuss model in whichthe ODF was incorporated. The method is explainedin detail by Van Hout te [19]. However, .such acalculation only holds for one point in the wire andinteg ration over the complete cross section of the wirehas to be carried out.

Examples of the measurements are represented as~-sin-'0 curves in Fig. 8. The experimental data aremore accurate for the ferrite phase because thediffracted intensity for the ferrite peaks is muchhigher. In Fig. 8 the fitted data are calculatedaccording to equation (17). The stress is proport iona lto the slope of the curves. Differences in the slopes ofthe cementite phase may result from the simplifica-tion that the diffraction elastic constants (DEC) arethe same for two different diffraction planes, namelythose reported by Hanabusa e t a l . for the (121)reflection (see abovel. Normally, the DEC depend onthe diffraction plane used. On the ferrite (110) plane,the influence of the texture on the DEC causes a dropin the fitted curve in the high sin-'0 region. There isalso a remarkable deviation of the measured datafrom the linear fitted curve in the ferrite (200) graph.This deviation is probably caused by grain mi-crostresses, also called retained inte rgranul ar stresses[28], which are caused by differences in plastic flow ofthe ferrite in differently oriented grains. A similareffect is observed by Pintschovius in neutron stressmeasurements of the ferrite phase in rolled steel sheet[29]. The presence of grain microstresses is probably


8/11

4 04 6 V A N A C K E R e t a l . : N E U T R O N D I F F R A C T IO N M E A S U R E M E N TE0 . 0004

0 . 00020 . 0000

. 0 . 0002

. 0 . 0004- 0 . 0006- 0 . 0008

0 .0

0 . 0150

E0 . 0 0 0 8

0 . 01000 . 00500 . 0000

. 0 . 0050

. 0 . 0100

0.00060.00040.00020.0000

-0.0002. 0 . 0004. 0 . 0006. 0 . 0008. 0 . 0010

0.2 0.4 s in 20'6~1/ 0.8 1.0 0.0 0.2 0.4 sin 20 ,6

0 . 0 0 . 2 0 . 4 sin= 0.8 1.0

0.0120

0 . 8

0.01000.00800.00000 . 0 ~ 00 . 0 ~ 00.0000.0.0~0.0.0~0. 0 . 0 0 0 0

1.0

0 . 0 0 . 2 0 . 4 s j n a ~ 0.8 1.0Fig . 8 . c -s in:~ , curves for cementi te and fe r r i te d if f rac t ion p lanes as measured with the neu tron d if f rac t iontechnique . The e r ror bar s g ive the 95% conf idence l imit fo r the measured s t r a ins .

t h e c a u s e o f t h e d i f f e r e n c e i n s tr e s s v a l u e f o r t h e ( 1 1 0 )a n d ( 2 0 0 ) p l a n e o f t h e f e r r i t e p h a s e ( s e e T a b l e 4 ) .F i n a l l y , w h e n c o m p a r i n g t h e e - s i n 2 ~ b c u r v e s i n t h ef e r r i t e a n d c e m e n t i t e , a s t r a i n - f r e e d i r e c t i o n a t~ , = 5 7 i s o b s e r v e d . T h i s i s a s u p p l e m e n t a r y p r o o f o ft h e v a l i d i t y o f t h e m e a s u r e m e n t s .

T h e r e s u l t s f o r t h e a x i a l p h a s e m i c r o s t r e s s i n t h ec e m e n t i t e a n d t h e f e r r i t e p h a s e s a r e s u m m a r i z e d i nT a b l e 4 . T h e o b t a i n e d v a l u e s a r e c o n s i s t e n t w i t h t h es t r e s s e q u i l i b r i u m b e t w e e n t h e p h a s e s e x p r e s s e d b ye q u a t i o n ( 6 ). T h e v o l u m e f r a c t i o n o f t h e c e m e n t i t ep h a s e c . . . . ~,e i s a p p r o x i m a t e l y 1 1 % . I f o n e s t a r t sf r o m e q u a t i o n ( 6 ) a n d t h e t o t a l p h a s e m i c r o s t r e s s i nt h e f e r r i t e p h a s e i n o r d e r t o c a l c u l a t e A r a : :'~e"'~'* an df r o m t h i s s t re s s t h e d i f f r a c t i o n e l a s t i c c o n s t a n t s , i t i ss e e n t h a t t h e o b t a i n e d v a l u e o f ~s., i s h i g h e r t h a n t h eo n e r e p o rt e d b y H a n a b u s a e t a l . [ 2 7 ] , wh ic h wa s u s e dh e r e, a n d c e r t a i n l y h i g h e r t h a n t h e c o n s t a n t g i v e n b yo t h e r a u t h o r s [8 , 9 ].

T h e s t r e s s r e s u l t s i n T a b l e 4 c o u l d a l s o b ec a l c u l a t e d u s i n g t h e l a t t i c e p a r a m e t e r s f o u n d i nS e c t i o n 4 .3 . V a l u e s o b t a i n e d b y t h is m e t h o d d i dn o t d e v i a t e m o r e t h a n 5 % f r o m t h e g iv e n d a t a . O n e

c o u l d a l s o u s e e q u a t i o n ( 1 1 ) t o c a l c u l a t e t h ed e v i a t o r i c s t re s s . It t u r n e d o u t t h a t t h ed e v i a t o r i c s t r e s s v a l u e s w e r e t w o t h i r d s o ft h e v a l u e s g i v e n i n T a b l e 4 . T h i s p r o v e s t h e u s eo f e q u a t i o n ( 13 ).

I t c a n b e c o n c l u d e d t h a t t h e f e r ri t e is u n d e rc o m p r e s s i o n , w h i l e a t e n s i l e s t r es s i s p r e s e n t i n t h ec e m e n t i t e . T h e s t re s s es i n t h e c e m e n t i t e a r e e x t r e m e l yh i g h , a r o u n d 2 0 0 0 M P a . S u c h a s tr e ss p a r t i t i o n o v e rt h e p h a s e s i s c o n s i s t e n t w i t h t h e r e l a t i v e v o l u m ef r a c t io n s a n d p r o p e r t i e s o f e a c h p h as e . T h e c e m e n t i t ei s a m u c h h a r d e r p h a s e t h a n t h e f e rr i t e a n d t h e o n s e to f p l a s ti c f l o w is d e la y e d . T h e c o n s e q u e n c e i s t h a t t h ec e m e n t i t e p h a s e i s u n d e r t e n s i o n a f t e r d r a w i n g .R e m a r k a b l e i s t h e l o w e r p h a s e m i c r o s t r e ss i n t h e w i r ew h i c h i s d r a w n t o h i g h e r s t r ai n s . T h e p h a s em i c r o s t r e s s i n t h e c e m e n t i t e m a y b e r e l a x e ds o m e w h a t d u r i n g f u r t h e r d r a w i n g , b e c a u s e a t h i g hs t ra i n s , m o r e f r a g m e n t a t i o n o f t h e c e m e n t i t e l a m e l l a et a k e s p l a c e . C o m p a r i n g t h e v a l u e s i n t h e s a m p l e se t c h e d t o d i f f e r e n t d i a m e t e r s , i t c a n a l s o b e c o n c l u d e dt h a t t h e r e i s n o s i g n i fi c a n t v a r i a t i o n o f t h e p h a s em i c r o s t r e s s w i t h t h e d i s t a n c e t o t h e w i r e a x i s . T h e

Table 4. S umm ary of axial phase m icrostresses. All stress values are given in MP a. The error (for a 95% confidence im it) is given betweenbracketsDiffractionplane Sam ple 1.1 Sam ple 1.2 Sam ple 1.3 Sam ple 1.0 Sam ple 2.1

~t Fe (110 ) - 152 (30) - 194 (36) - 147 (38) 50 (9) - 122 (33):t Fe (200) - 127 (36) - 127 (38) - 133 (39) 9 (4) - 114 (32)Fe~C (301) 2270 (310) 1990 (180) 2550 (140) - 28 (14) 1730 (170)Fe~C (131) 2050 (ll 0) 2250 (120) 2390 (190) 0 08 ) 1770 (50)


9/11

V A N A C K E R e t a l . : N E U T R O N D I F F R A C T I O N M E A S U R E M E N T 4047S a m p l e 2 , 0 C r K ( x ( 2 1 1 )

2 . 8 6 7 0 ~ M e e s u m d ! I 4 , > 0( ~ I _ < 0 . . . .2 . 8 6 6 0 -

2 . 8 6 5 0 . .

2 . 8 6 4 0 ' I ~ i ' I

m 2 . 8 6 7 0 ~

| 2 . 8 6 8 o - - i i - ' i ; :a .

, i , [

o~ 2 .s6 50 T J 2 . 8 6 4 0 ,

2 . 8 6 7 0

2 . 8 6 6 0 ~ 1 1 + ,

2 . ~ 4 0 b , I ' I0.0 0.2 0.4 0.6 0.8 1.0

s l n ~ *Fig. 9. X-ray stress m easu rem ents on th e ~t Fe (211)diffraction peak, visualized by d-sin:~k* curves. Thesupersc r ip t * draws a t ten t ion to the d if fe ren t def in i tion of ~oand ~ , com pared to the neu tro n d if f rac t ion se t-up.

m i c r o s t r e s s e s a re n e a r l y c o n s t a n t t h r o u g h t h e w i r es e c t i o n .

5. C O M P A R I S O N W I T H X -R A Y D I F F R A C T I O NS t r es s m e a s u r e m e n t s b y X - r a y s c a n b e c a r r i e d o u t

n e a r t h e s u r f a c e o f a n a r r a y o f p a r a l l e l w ir e s. T h em e a s u r e m e n t s h a v e t o b e c o r r e c t e d f o r t h e w i r eg e o m e t r y . T h e e x p e r i m e n t a l s e t - u p a n d c o r r e c t i o n sa r e d i s c u s s e d i n d e t a i l b y V a n A c k e r e t a l . [25] andF r a n c o i s [ 30 ]. T h e s t r e s s i s d e t e r m i n e d l o c a l l y i n as h a l l o w l a y e r u n d e r n e a t h t h e w i r e s u r fa c e , w h i c h i st h e m o s t i m p o r t a n t d i f fe r e n c e w i t h t h e n e u t r o n s t re s sd e t e r m i n a t i o n , i n w h i c h t h e s t r e s s w a s a v e r a g e d o v e rt h e e n t i r e w i r e s e c t i o n . T h e X - r a y e x p e r i m e n t s r e s u l ti n t h e t o t a l p h a s e s t r e s s a ~ i n p h a s e ~t a t t h e s u r f a c eo f t h e w i r e . U n f o r t u n a t e l y , e x p e r i m e n t a l d a t a c o u l do n l y b e o b t a i n e d f o r t h e f e r r i t e p h a s e , s i n c e t h ed i f f r a c ti o n p e a k s o f t h e c e m e n t i t e a r e f a r t o o w e a k .

T h e s t r ai n m e a s u r e m e n t s w e r e p e r f o r m e d f o rd i f f e r e n t ~ 0" a n d i f * a n g l e s . T h e s u p e r s c r i p t *i n d i c a t e s t h a t w e w e r e w o r k i n g w i t h t h e X - r a y s e t - u pa s s h o w n i n t h e i n s e t o f F i g . 9 . I n t h e s a m e f i g u r e t h ed - s i n 2 ~ p c u r v e s f o r t h e s a m p l e 1 . 1 a r e s h o w n a s w e l la s t h e c a l c u l a t e d c u r v e . T h e t o t a l p h a s e s t r e ss i nf e r r i t e i s c o m p r e s s i v e i n t h e a x i a l a n d t a n g e n t i a ld i r e c t i o n s ( s e e T a b l e 5 ) , w h i c h i s a f a v o u r a b l es i t u a t i o n f o r p r e v e n t i n g c r a c k g r o w t h .

S t r a i g h t f o r w a r d c o m p a r i s o n w i t h th e n e u t ro n

d i f f r a c t i o n r e s u l t s i s n o t p o s s i b l e , b e c a u s e t h e X - r a yd a t a g i v e t h e t o t a l s t r e s s i n t h e f e r r it e p h a s e a t t h es u r fa c e , w h e r e a s t h e n e u t r o n d a t a g i v e t h e a v e r a g ep h a s e m i c r o s t r e s s o f th e e n t i r e s a m p l e . H o w e v e r , t h ec o m b i n a t i o n o f t he t w o m e t h o d s g i ve s u s in f o r m a t i o na b o u t t h e m a c r o s t r e s s . F i r s t , t h e e l a st i c in t e r a c t i o ns t r e s s i n e a c h p h a s e h a s t o b e k n o w n . I t c a n b ed e r i v e d f r o m a s et o f m e a s u r e m e n t s i n w h i c h d i f fe r e n ta p p l i e d l o a d s a r e i m p o s e d o n t h e w i r e . H e r e t h e w i r ew a s l o a d e d i n a t e n s i l e d e v i c e t o 4 0 0 M P a i n st e p s o f1 00 M P a . T h e t e n s il e m a c h i n e w a s i n s t al l e d i n a nX - r a y d i f f r a c t i o n g o n i o m e t e r . I n t h e a x i a l d i r e c t i o n ,t h e e l as t ic i n t e r a c t i o n t e r m w a s f o u n d t o b e- 5 . 6 % ( + 0 . 8 % ) o f t h e a p p l ie d o r m a c r o s t re s s f ort h e f e r r i t e p h a s e . T h i s v a l u e i s l o w e r t h a n c a n b ed e r i v e d f r o m t h e l o w - c y c l e f a t i g u e e x p e r i m e n t s o fW i n h o h z a n d C o h e n [8 ]. H o w e v e r , d if f e re n c e s i n t h er a d i a l o r t a n g e n t i a l d i r e c t i o n m a y b e l i n k e d t o t h em o r p h o l o g y o f th e p e a r l it e . R e g a r d i n g t h e s tr e sse q u i l i b r i u m b e t w e e n t h e p h a s e s , t h e e l a s ti c i n t e r-a c t i o n t e r m i n t h e c e m e n t i t e p h a s e s h o u l d b e+ 4 8 . 6 % . T h e m a c r o s t r e ss i s n o w c a l c u la t e d b ys u b t r a c t i n g t h e p h a s e m i c r o s t r e s s i n t h e f e r r i t e f o u n da f t e r an a l y s i s o f t h e n e u t r o n d i f f r a c ti o n d a t a f r o m t h et o t a l p h a s e s t r e s s a n d l o w e r i n g t h e r e s u l t w i t h 5 . 6 %f o r t h e e l a s t i c i n t e r a c t i o n . T h i s c a n b e d o n e f o r t h ee t c h e d w i r e s . H e r e , t h e m a c r o s t r e s s h a s t o b ec o r r e c t e d f o r t h e r e l a x a t io n d u r i n g e t c h i n g . F i n a l l y ,a s i ll u s t r a t e d b y F i g . 1 0, t h e r e s u l t s o f X - r a y a n dn e u t r o n d i f f r a c t i o n t o g e t h e r a l l o w f o r t h e e s t i m a t i o no f th e m a c r o s t r e s s f o r t h e w i r e w h i c h w a s d r a w n t oE = 1 .9 6 . T h e m a c r o s t r e s s i s a f u n c t i o n o f th e d i s t a n c et o t h e w i r e a x i s a n d r e a c h e s a m a x i m a l v a l u e o f1 50 M P a i n s am p l e 1 .2 . T a k i n g t h e m a c r o s t r e s s i n t oa c c o u n t a n d t o g e t h e r w i t h t h e i n t e r a c t i o n t e r m i nc e m e n t i t e , t h e t o t a l s t r e s s i n t h e c e m e n t i t e d o e s r i s et o 2 2 5 0 M P a ( + 2 5 0 M P a f or t h e 9 5 % c o n fi d en c el i m i t) . B y t h i s c a l c u l a t i o n , t h e m a x i m a l s t r e s s p r e s e n ti n t h e c e m e n t i t e l a m e l l a e i s f o u n d .

6 . C O N C L U S I O N SN e u t r o n d i f fr a c ti o n e x p e r i m e n t s m a k e t h e d e t er m i -

n a t i o n o f t h e a v e r a g e r e s i d ua l s t r e ss i n b o t h t h ec e m e n t i t e a n d f e r r i t e p h a s e p o s s i b l e . I n t h e c a s e o ft h i n w i r e s , t h e m e a s u r e d a v e r a g e r e s i d u a l s t r e s s i s t h ep h a s e m i c r o s t r e s s o f t h e e x a m i n e d p h a s e . T h e s t r e ssi n t h e c e m e n t i t e o f t h e e x a m i n e d w i r e d r a w n t oe = 1 .9 6 i s h i g h l y t e n s i l e , w i t h v a l u e s o f 2 0 0 0 M P a . I nt h e f e r r i t e t h e s t r e s s is c o m p r e s s i v e w i t h v a l u e sa r o u n d - 1 4 0 M P a . F r o m e tc h in g , i t c o u ld b ec o n c l u d e d t h a t t h e p h a s e m i c r o s t r e s s i s u n i f o r m

Table 5. Total phase stress in sam ples I. I and 2.1, measured by X -raydiffraction wi th CrK , on the (211) plane. The error (for a 95%confidence limit) is give n in bracketso_-= o-'~ o: ,(MPa) (MPa) (MPa)

Sam ple 1.1 - 114 (8) - 94 (16) - 56 (23)Sam ple 2.1 - 156 (16) - 38 (38.) - 48 (53)


10/11

4 04 8 V A N A C K E R et al.: N E U T R O N D I F FR A C T I O N M E A S U R E M E N TP e a r l i t ic W i r e , = 1 . 9 6

2600 -~ . , ~ ;[,2300 . . ~ " i

2 ~ i " ,i1700 I

= lOO

0 w ~o. , o ~ ' s o .s o o . , 5 0 .4 0- s o T , '. . . . .

- 2 0 0 - - d i s t a n c e t o w i r e a x is ( m m ) p h a s e m i c r o s t r e ss o f F e 3 C

( n e u t r o n d i f f r a c t i o n m e a s u r e m e n t )m a c r o s t r e s s ( c a l c u l a t e d w i t hc o r r e c t i o n f o r r e l a x a t i o n )

p h a s e s t r e s s o f x -F e( X - r a v d i f f ra c t io n m e a s u r e m e n t ~

p h a s e m i c ro s t r e s s o f ( ~ -F e( n e u t r o n d i f f r a c t i o n m e a s u r e m e n t )

Fig . 10 . S t ress resu l t s on samples 1 .1 -1 .3 ob ta ined byn e u t r o n a n d X - r a y d i f fr a c ti o n a n d c o m b i n a t i o n o f t h e t w ot e c h n i q u e s . T h e d i a m e t e r o f t h e w i r e i s 1 .22 r a m . T h e s u r f a c eo f t h e w i r e i s a t 0 .6 1 m m i n t h e o r d i n a t e .

t h r o u g h t h e w i r e c ro s s s e c t i o n . T h e r e s u l t s i n t h ef e r r i t e a r e i n s t r e s s e q u i l i b r i u m w i t h t h e c e m e n t i t e ,t h o u g h t h e d - si n 2 ~ , c u r v e s o f t h e f e r ri t e a r e d i s t o r t e db y m i c r o s t r e s s e s i n t h e d i f f e r e n t l y o r i e n t e d p e a r l i t i cg r a i ns . T h e p h a s e m i c r o s t r e s s i n th e c e m e n t i t e p h a s eo f a w i r e d r a w n t o a h i g h e r s t r a i n ( 2 . 5 6 ) is l o w e r ,a b o u t 1 7 50 M P a . A n i n t e r e s t in g r e s u lt i s t h a t t h ep h a s e m i c r o s t r e s s i n t h e w ir e w i t h t h e h i g h e s t d r a w i n gs t r a i n i s l o w e r t h a n i n t h e w i r e w i t h t h e l o w e s td r a w i n g s t r a i n .

A d d i t i o n a l i n f o r m a t i o n a b o u t t h e r e s id u a l st r e sss t at e b e c o m e s a v a i l a b le w h e n c o m b i n i n g t h e n e u t r o nd i f f r a c t i o n w i t h X - r a y d i f f r a c t i o n d a t a f o r t h e f e r r i t e .T h e t o t a l p h a s e s t r e s s a t t h e s u r f a c e c o u l d b em e a s u r e d w i t h t h e X - r a y d i f fr a c t i o n t e ch n i q u e . T h er e s p o n s e o f t h e f e r r i te t o a n a p p l i e d s t r e s s l e a d s t o a ni n t e r a c t i o n t e r m f o r t h e f e r ri t e o f - - 5 . 6 % o f th em a c r o - ( o r a p p l i e d ) s t re s s. A t e n s il e m a c r o s t r e s s i n t h ea x i a l d i r e c t i o n w a s f o u n d i n t h e s u r f a c e l a y e r , w h i c hd e p e n d s s t r o n g l y o n t h e d i s t a n c e t o t h e w i r e a x is . T h em a x i m u m v a l u e w a s 1 50 M P a i n t h e w ir e d r a w n t o

= 1 .9 6 . A s h o r t c a l c u l a t i o n s h o w s t h a t t h e t o t a ls t r e s s in t h e c e m e n t i t e w i l l r i se t o 2 2 5 0 M P a .

T e x t u r e m e a s u r e m e n t s w e r e d o n e o n t h e fe r r it e a n dc e m e n t i t e . T h e O D F o f t h e f e r ri t e c o n t r i b u t e d t o ab e t t e r c a l c u l a t i o n o f t h e d i f f r a c ti o n e l a s t ic c o n s t a n t s .

I n t h e c e m e n t i t e , t h e t e x t u r e i s le s s s h a r p t h a n i n t h ef e rr i te . F i n a l l y , a s t u d y o f t h e p e a k b r o a d e n i n gs u g g e s t s t h a t p l a s t i c f l o w o c c u r s i n t h e c e m e n t i t el a m e l l a e .

Acknowledgements--This w o r k h a s b e e n m a d e p o s s i b l et h r o u g h t h e f i n a n c ia l s u p p o r t t h r o u g h t h e B e l g i a np r o g r a m m e o n I n t e r u n i v e r s i t y P o le s o f A t t r a c t i o n i n i t i a te dby the Be lg ian S ta te , Pr ime Min is te r ' s Off ice , Sc ience Po l icyP r o g r a m m i n g ( C o n t r a c t I U A P - 4 ) . O n e o f th e a u t h o r s( K V A ) g r a t e f u l l y a c k n o w l e d g e s t h e f i n a n c i a l s u p p o r t o f t h eN . F . W . O . T h e a u t h o r s a l s o t h a n k t h e c o m p a n y N . V .B e k a e r t f o r p r o v i d i n g t e s t m a t e r i a l . T h e s p e c i m e n s w e r ea s s e m b l e d f o r n e u t r o n d i f f r a c t i o n i n m o u n t s m a d e b y L .M c E w a n a t A E C L . R . D o n a b e r g e r a n d D . T e n n a n t a s si s te dw i t h t h e n e u t r o n p o w d e r d i f f r a c t o m e t e r .

R E F E R E N C E S

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neutron differ action measurement of the rs in the cementite and ferrite phase of cold drawn steel...

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