RELATIONSHIP BETWEEN INTERNAL FRICTION AND SHEAR MODULUS FOR Fe-0.2 Ti ALLOY WITH OIL LAYER

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RELATIONSHIP BETWEEN INTERNAL FRICTION AND SHEAR MODULUS FOR Fe-0.2 Ti ALLOY

WITH OIL LAYER

B. Augustyniak, Gilbert Fantozzi

To cite this version:

B. Augustyniak, Gilbert Fantozzi. RELATIONSHIP BETWEEN INTERNAL FRICTION AND

SHEAR MODULUS FOR Fe-0.2 Ti ALLOY WITH OIL LAYER. Journal de Physique Colloques,

1983, 44 (C9), pp.C9-493-C9-498. �10.1051/jphyscol:1983972�. �jpa-00223422�

JOURNAL DE PHYSIQUE

Colloque C9, suppliment au n012, Tome 44, dkembre 1983 page C9-493

R E L A T I O N S H I P BETWEEN I N T E R N A L F R I C T I O N AND SHEAR MODULUS FOR Fe-0.2 T i .ALLOY W I T H O I L LAYER

B. Augustyniak and G. Fantozzir

I n s t i t u t e o f Physics, Technical University of Gdafisk, 80-952 Gdafisk, Poland

*I.~v.s.A. de Lyon, Bdt. 502, Physique des Matgriaux, 69 6 2 1 V i Z,Z,eurbanne Cedex, France

Re'sum6. Le maximum du frottement inte'rieur d'un composite mQtal-huile et le ddfaut du module de cisaillement apparaissent 1 la tempkrature de solidification de l'huile. Nous avons tests trois modsles Dour analyser la relation entre le frottement intsrieur et le module de cisaillement. Nous avons e'galement obtenu la variation du temps de relaxation avec la tempgrature.

A b s t r a c t

-

I n t e r n a l f r i c t i o n maximum w h i c h appears a t t e m p e r a t u r e o f s o l i d i f i c a t i o n o f o i l i s f o l l o w e d by a shear modulus d e f e c t . The t h r e e models were a p p l i e d t o a n a l y s e

the r e l a t i o n s h i p between t h e o i l i n t e r n a l f r i c t i o n and t h e shear modulus s p e c t r a . The t e m p e r a t u r e dependence o f r e l a x a t i o n t i m e was obtained.

INTRODUCTION

Low t e m p a r a t u r e i n t e r n a l f r i c t i o n peaks and shear modulus d e f e c t s observed f o r o i l c o a t e d samples a r e connected w i t h t h e s o l i d i f i c a t i o n process o f o i l l a y e r [1,2,3J

.

There a r e some p r o - blems t o s o l v e . The F i r s t concerns t h e s t r u c t u r e o f damping spectrum. I n t e r n a l f r i c t i o n appears as s i n g l e peak o n l y when specimen i s annealed. I t i s e v i d e n t t h a t i n t e r n a l f r i c t i o n s h o u l d be a t t r i b u t e d t o t h e l a y e r p r o p e r t i e s and t o p r o p e r t i e s o f sample s u r f a c e . The second problem i s w i t h an a n a l y t i c a l d e s c r i p t i o n o f t h e measured damping. I n t e r n a l f r i c t i o n o f l u b r i c a t e d sample g i v e s us i n f o r m a t i o n about dynamic p r o p e r t i e s o f o i l a t 1 0 ~ 4 temperature.

S e v e r a l methods o f i n t e r n a l f r i c t i o n d i v i s i o n i n t o t h e b u l k and t h e s u r f a c e l a y e r damping a r e developed[4,5]. They assume t h a t d e f i n e d s u r f a c e l a y e r i s l i n k e d t o t h e sample.

T h i s paper r e p o r t s t h e r e s u l t o f analogous t r e a t m e n t f o r an o i l

-

l a y e r v.hich l e a d s t o t h e damping d i v i s i o n and t o t e m p e r a t u r e dependence o f r e l a x a t i o n time. Three t h e s i m p l e s t models a r e t e s t e d : a t f i r s t t h e Nowick and B e r r y model when c o m p o s i t e i s t r e a t e d as s t a n d a r d s o l i d w i t h any r e l a x a t i o n process, t h e n two models r i h i c h d e s c r i b e t h e v i s c o u s and v i s c o e l a s t i c p r o p e r t i e s o f o i l l a y e r deposed on an e l a s t i c base.

EXPERIMENTAL RESULTS

Measurements of i n t e r n a l f r i c t i o n were performed ~ i t h a t o r s i o n a l pendillum o s c i l a t i n g a t 1

Hz

C6J r q i t h c o n s t a n t v a l u e o f v i b r a t i o n a m p l i t u d e f = 2

.

The energy l o s s due t o damping Nas a u t o m a t i c a l l y recorded. Temperature was changed from 80 t o 300 K w i t h c o n s t a n t h e a t i n g r a t e 0.2 K/min.

Samples o f Fe-0.2Ti a l l o y were o f t e c h n i c a l p u r i t y and i n t h e form o f * i r e s 1 mm i n d i a m e t e r and 50 mm i n l e n g t h . I n t h e i n i t i a l s t a t e t h e a l l o y was c o l d worked d u r i n g p r o d u c t i n g . B e f o r e t h e measurements t h e samples were annealed a t t h e t e m p e r a t u r e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983972

JOURNAL

DE

PHYSIQUE

973 # f o r 4 hours.

T h i n m i n e r a l o i l l a y e r u a s p u t on t h e m e t a l s u r f a c e by greasing.

The t y p i c a l r e s u l t s o f i n t e r n a l f r i c t i o n and shear modulus measurements performed d u r i n g h e a t i n g a r e shown i n Fig. 1. I n t e r n a l f r i c t i o n o f uncoated sample i n c r e a s e s ~ e a k l y w i t h t e m p e r a t u r e and shear modulus decreases l i n e a r l y as can be seen f r o m c u r v e s l a and l b , r e s p e c t i v e l y . A f t e r c o a t i n g an asymmetric i n t e r n a l f r i c t i o n peak appears /Q" =2.6.10'~/ a t t h e t e m p e r a t u r e

T

= 205

t ?

I<

/ c u r v e Za, F i g . l/. The shear modulus d e f e c t i s c o r r e l a t e d w i t h t h e damping maximum / c u r v e 2b, Fig.

11.

A t h i g h t e m p e r a t u r e t h e shape o f t h e i n t e r n a l f r i c t i o n spectrum / c u r v e Za, F i g . l / seems t o be due t o t h e e x i s t e n c e o f a second damping maximum a t t e m p e r z t u r e near by 230 K. T h i s process l e a d s a l s o t o t h e s m a l l s t e p on t h e modulus d a t a / c u r v e 2b, F i g . l/.

L e t us a t f i r s t c a l c u l a t e t h e o i l l a y e r i n t e r n a l f r i c t i o n . Next, i n t e r n a l f r i c t i o n w i l l be a n a l y s e d i n terms o f t h e ad,opted models, The measured i n t e r n a l f r i c t i o n o f t h e composite,

Q' ,

^can

b? d i v i s e d i n t o two p a r t s : i n t e r n a l f r i c t i o n o f uncoated sample,

Q ' . ,

and an unknown i n t e r n a l f r i c t i o n o f o i l ,

: Q .

We use f o r t h i s t h e s t a n d a r d f o r m u l a

L4.51:

where : f, and f

-

t h e v i b r a t i o n f r e q u e n c i e s o f uncoated and c o a t e d sample, r e s p e c t i v e l y . U i v i s i o n was made t & i c e l y f o r two s e t s of i n i t i a l r e s u l t s , A t f i r s t , t h e c a l c u l a t i o n s were performed w i t h o u t t h e s u b s t r a c t i o n o f t h e second damping process. We assume t h a t t h i s process s h o u l d be due t o t h e i n t e r a c t i o n o f o i l w i t h deformed m e t a l s u r f a c e [ 7 1 . T h e L v a l u e s b e r e used as i l u s t r a t e d by c u r v e s 2a f o r U-' and l b f o r f, /Fig.l/. I n t h e n e x t step, t h e i n t e r n a l f r i c t i o n spectrum buss a r b i t r a r y s e p a r a t e d a t h i g h e r t e m p e r a t u r e , l e a d i n g t o t h e r e s u l t s w h i c h a r e s h o w by t h e c u r v e 3a /Fig. 1/, The d a t a f o r t h e f t f u n c t i o n o f t h e uncoated sample vvere as t h a t r e p r e s e n r e d by c u r v e 3b.which i s ~ a r a l l e l t o t h e p r e v i o u s c u r v e

l b ' / ~ i ~ . l / .

.

₁

Such two procedures g i v e t h e d i f f e r e n t

Q-'

T-' ) f u n c t i o n s w h i c h a r e p r e s e n t e d i n Fig. 2 b y c u r v e s 1 and 2, r e s p e c t i v e l y . The remarl<able d i v e r g e n c e appears a t h i g h e r t e m p e r a t u r e , above T,,

.

^{I n}

t h e f i r s t case i n t e r n a l f r i c t i o n decreases a t h i g h temperature.

The c o u r s e o f t h e c o r r e c t e d r e s u l t s / c u r v e 2, Fig. 2/ depends s t r o n g l y on an assumed t e m p e r a t u r e c h a r a c t e r o f shear modulus / c u r v e 3b, Fig. I/. The two c u r v e s 1 and 2 , p r e s e n t e d i n Fig, 2,

l i m i t t h e a r e a o f t h e e s t i m a t e d v a l u e s o f zhe o i l i n t e r n a l f r i c t i o n .

L e t us assume t h a t t h e o i l l a y e r has t h i c k n e s s h and i s deposed on t h e w i r e sample txith r a d i u s R, The r e a l and i m a g i n e r y p a r t s o f complex modulus o f such composite can be d e t e r m i n e d from t h e f o l l o w i n g f o r m u l a e

C71

:

o"= 'I-

-C)

G&JrntjO

Luhere: oL

= ( R / ( K

+ h ) 1 4 - g e o m e t r i c f a c t o r ;

G,

- s h e a r m o d u l u s o f r i g i d , u n c o a t e d s a m p l e ;

G,

- o i l s h e a r m o d u l u s , d e t e r m i n e d f o r v e r y h i g h f r e q u e n c y ;

Re (

x a n d

In { x )

- r e a l a n d i m a g i n a r y p a r t s of t h e o i l c o m p l e x s h e a r m o d u l u s ;

x

- a p a r a m e t r e q u a l t o

W . 2

p r o d u c t , w i t h

'i-

a s r e l a x a t i o n time. The c o m p o s i t e

i n t e r n a l f r i c t i o n

'Q'

a n d t h e l a y e r i n t e r n a l f r i c t i o n Q;' a r e e s t i m a t e d a s f o l l o w s :

W e n a n t t o c o m p a r e t h e e x p e r i m e n t a l v a l u e s O F

(2''

w i t h t h e v a l u e s o f t h e s h e a r m o d u l u s d e f e c t a n d i n t h i s

way

t o d e t e r m i n e w h e a t h e r t h e p h y s i c a l e f f e c t s c a n b e c a l s s i f i e d u n d e r t h e g e n e r a l h e a d i n g o f r e l a x a t i o n e f f e c t o r n o t .

We

i n t r o d u c e a t f i r s r t h e n o r m a l i z e d m o d u l u s d e f e c t f u n c t i o n

G/T/

and t h e n o r m a l i z e d i n t e r n a l f r i c t i o n f u n c t i o n

F/T/,

T h e y a r e c a l c u l a t e d f r o m e x p e r i m e n t a l r e s u l t s a n d o n t h e o t h e r hand t h e y c a n b e d e f j n e d by t h e f o r m u l a e

/2/

a n d

/3/.

T h i s f u n c t i o n s a r e d e s c r i b e d , a s f o l l o n s :

n h e r e :

S =

"-d 6

d-

G*

^/5a/

a n d

5.

= ( f 2 / f $ -

^1)-

t h e maximal v a l u e o f s h e a r m o d u l u s c a l c u l a t e d a t t e m p e r a t u r e T o , /

T, (

T,/;

I<

- ,is t h e e x p e r i m e n t a l p a r a m e t e r d e f i n e d by f o l l o w i n g r e l a t i o n :

From t h e f o r m u l a e / 4 a / a n d /4b/ o n e c a n d e t e r m i n e t h e x v a l u e s when t h e r h e o l o g i c a l f u n c t i o n

I /I:/

a n d

R e

/x/ a r e a s s u m e d . The

So

a n d k p a r a m e t e r s w e r e e s t i m a t e d f r o m t h e r e s u l t s shov#n i n Fig.1.

F o r t h e r e s u l t s ~ i t h o u t t h e c o r r e c t i o n o n t h e s e c o n d i n t e r n a l f r i c t i o n p r o c e s s , c a s e / a / ,

_{- -}

t h e s e t n o p a r a m e t e r s h a v e v a l u e s :

So 10 = 3 15

2

0'5, k 10' = 163 -

+

10.

F o r t h e c o r r e c t e d - r e s u l t s . c a s e

/b/,

i s f o u n d t h a t so

10" = 16.52 0.5

a n d

k

l o 5

= 140

2

20.

T h e lorn v a l u e o f k p a r a m e t r s u g g e s t s t h a t m e a s u r e d damping c a n by p h e n o m e n o l o g i c a L l y d e s c r i b e d a s t h e r e s u l t o f r e l a x a t i o n p r o c e s s a i t h b r o a d d i s t r i b u t i o n f u n c t i o n o f r e l a x a t i o n times.

A s s u m i n g t h a t

S

p a r a m e t e r ,

/5a/,

i s i n d e p e n d a n t o n t e m p e r a t u r e

C9-496 JOURNAL DE PHYSIQUE

we c a n e a s i l y u t i l i z e t h e Nowick and B e r r y model by i n t r o d u c i n g t h e f o l l o w i n g r e l a t i o n s :

where and

Fs

a r e t h e Noviick and B e r r y f u n c t i o n s (83 and

p

^is

t h e Gaussian d i s t r i b u t i o n parameter. The @ v a l u e was e s t i m a t e d b a s i n g on k parameter v a l u e on t h e r e l a t i o n s h i p k = f / (5

/

c a l c u l a t e d by Norrick and B e r r y C81 :

$

= 5

2

0.2 f o r I< = 0.15 + 0.01. I n o r d e r t o d e t e r m i n e t h e x v s t e m p e r a t u r e dependence t s e

i o l l o ~ v i n g e x p r e s s i o n s were accepted: G/T/ = F /x/, f tom /5a/, and F/T/ = S,

-

^F,, from /4b/, z i t h n e g l e c t i n g t h e G f u n c t i o n i n denominator /4b/. i t l e a d s t o independent e s t i m a t i o n o f t h e x parameter from F and G f u n c t i o n s , The r e s u l t s as o b t a i n e d ~ i t h b o t h /a/ and / b / c o n d i t i o n s a r e p l o t t e d i n F i g . 2. The t h r e e f u n c t i o n s o f l n ( x ) v s T dependence a r e r e p r e s e n t e d by c u r v e s 3 , 4 and 5, r e s p e c t i v e l y . There appears a discrepant.; between c u r v e s 3 and 4. I t i n d i c a t e s t h a t t h e N o ~ i c k and B e r r y model can n o t be adopted f o r u n c o r r e c t e d data. I n t h e second case /b/ b o t h G and F f u n c t i o n s g i v e t h e same v a l u e s o f x parameter as show by c u r v e 5 i n F i g . 2. From t h e mean s l o p e o f t h i s c u r v e one can deduce t h e

a c t i v a t i o n e n t h a l p y v a l u e : H = 2.4

+

^0.2 eV and t h e

Yo

p ~ .ameter v a l u e

:

L g TO = -5555. That l a s t v a l u e proves t h a t t e s t e d mooel d e s c r i b e s o u r r e s u l t s o n l y p h e n o m e n o l o g i c a l l y .

i n

t h e

n e x t s t e p o f t h e a p p r o x i m a t i o n p r o c e d u r e we assume t h a t t h e S parameter v a l u e depend on temperature. The t e m p e r a t u r e dependence o f G, i s unknown. T h i s parameter s h o u l d decrease c o n t i n u o u s l y from t h e i n i t i a l v a l u e G, /TO/ t o t h e v e r y s m a l l v a l u e a t h i g h e r t h e n T temperature.

Two r h e o l o g i c a l models o f l i q u i d were v e r i f i e d . A t f r i s t t h e s i m p l e s t f.,axwell model f o r o i l d y n a m i c a l p r o p e r t i e s &as assumed.

The f o l l o w i n g e x p r e s s i o n s a r e assumed:

where: x = w ;

T

= @ / G m ; 1

-

s t a t i c v i s c o s i t y o f o i l . The x parameter v a l u e and S/So r a t i o v a l u e was deduced f r o m F and G f u n c t i o n . The t e m p e r a t u r e dependence o f shear modulus G ( T

1,

r e l a t e d t o G m ( T O ) was e s t i m a t e d . These new v a l u e s o f x and S / S , parameters a r e p r e s e n t e d by c u r v e 2 i n F i g . 3 and c u r v e 2 i n Fig.4, r e s p e c t i v e l y . Now t h e I n

or

v s T-' dependence / c u r v e 2, Fig. 3/ i s more r e a l i s t i c / c u r v e 2,Fig. 3/ b u t Gs shear modulus decreases s t r o n g l y , as shown by c u r v e 2 i n Fig. 4.

The second r h e o l o g i c a l model was as proposed by Earlom

C 9 ] .

The v i s c o e l a s t i c p r o p e r t i e s o f l i q u i d a r e r e p r e s e n t e d by r e a l and i m a g i n e r y p a r t s o f l i q u i d shear modulus, as f o l l o w s :

w h e r e : z = -ex. 1 2

T h e c a l c u l a t i o n s , a s m e n t i o n e d a b o v e , g i v e ;: a n d S/S, v a l u e s w h i c h a r e p l o t t e d a s c u r v e 3 , i n F i g . 3 a n d c u r v e 3 i n F i g . 4 , r e s p e c t i v e l y . F o r t h i s m o d e l t h e S/S, r a t i o v a l u e / c u r v e 3 , Fzg. 4/ d o e s n o t c h a n g e a s much a s p r e v i o u s l y , / c u r v e 2, F i g . 4/. I t i n f l u e n c e s t h e

t e m p e r a t u r e d e p e n d e n c e o f x p a r a m e t e r a s shown by c u r v e 3 i n Fig.3.

I t m u s t b e u n d e r l i n e d t h a t t h e t h r e e p r e s e n t e d a b o v e m o d e l s g i v e t h e s a m e r e l a t i o n s h i p f o r U< /T/ f u n c t i o n .

Me

c a n n o t d i s t i n g u i s h b e t w e e n t n o l a s t m o d e l s w i t h o u t t h e s u p p l e m e n t a r y i n i o r m a t i o n o n t h e t e m p e r a t u r e d e p e n d e n c e o f G,and

o~ p a r a m t e r s . S u c h m e a s u r e m e n t s s h o u l d h e l p u s t o d e t e r m i n e t h e p h y s i c a l m o d e l o f i n t e r n a l f r i c t i o n phenomenon w h i c h

i s

o b s e r v e d f o r s u c h c o m p o s i t e

a s

m e t a l i x i t h o i l l a y e r .

CONCLUSIONS

1. T h e c o m p o s i t e i n t e r n a l f r i c ~ i o n maximum c a n be d e s c r i b e d p h e n o - m e n o l o g i c a l l y by t h r e e m o d e l s : Norticlc a n d B e r r y , P i a x w e l l a n d B a r l o w , r e s p e c t i v e l y .

2. T h e t e m p e r a t u r e d e p e n d e n c e o f r e l a x a t i o n

time i s

d e t e r m i n e d s a t i s f a c t o r y o n l y when v i s c o - o r v i s c o p l a s t i c b c h a v i o u r oi l i q u i d o i l

i s

aocurned.The t e m p e r a t u r e d e p e n d e n c e o f G, a n d

oc

p a r a m t e r m u s t b e t e s t e d t o o . RE FERCNCES

1 CHOt4KA

-

^60, K a t o v i i c e , 9 1 / 1 9 b 0 / W,

,

PSTROKO~~SKI M., OENGA E., F 1 r o c e e d i n g s o f RENIOPl

-

2 C W O M I ~ V i , , DENGA E .

,

^{I.:OSER P.}

,

P ~ Y S . s t a t . SOL. /a/

62,

K 5 3

/

1980/

3 CHOI.:lG i d , , DENGA E . , J. P h y s i q u e 42, C 5

-

1 1 6 5 /1981/

4 POS7NII<OVri,S., I n t e r n a l f r i c t i o n i n m e t a l s , M e t a l l u r g i a , I.ioskori, 1 9 6 9 , p. 1 2 8

5 LEFEVRE D., PEREZ J., DUPERRAY B., Mat. S c i . Eng.

9,

1 9 3 /1979/

6 FANTOZZI G., ~ h g s e D o c t . S c i . P h y s . , 1 9 7 1 , Lyon.

7 AUGUSTYNIAK

B.,

FANTOZZI G , , P r o c e e d i n g s o f RENIOM

-

^82,

K a t o v i i c e , i n p r e s s .

8 NOWICK A.S., BERRY B.S., A n e l a s t i c R e l a x a t i o n i n C r y s t a l l i n e S o l i d s , A c a d e m i c P r e s s , NCVU Y o r k , 1 9 7 2

9 BARLOli' A.J.

,

^EKGINSAV A . , LAI'1B J . , ProC. ROY. S 0 c .

298,

^{481 /A9071}

C9-498 JOURNAL DE PHYSIQUE

F i g . 1 . I n t e r n a l f r i c t i o n /a/ F i g .2. O i l damping and

o r

on and modulus /b/ s p e c t r a : temperature dependence:

1

-

^{uncoated, 2}

-

^coated, 1 , 3 , 4

-

uncorrected d a t a , 3

-

w i t h c o r r e c t i o n . 5

-

Nowick-Berry model.

F i g . 3 . A r r h e n i u s p l o t s from F i g . 4 . O i l shear modulus on t h e models o f

r

1

-

temperature dependence Nowick-Berry

,

Z - M a x w e l l , from t h e models of :

3

-

B a r l o w . 1

-

Nowick-Berry,

2

-

M a x w e l l , 3

-

^Barlow,

4

-

modulvs d e f e c t .