sdarticle 1983

8/6/2019 sdarticle 1983

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Fibre Science and Technology 18 (1983) 265-286

F r i c t i o n a n d W e a r o f A d v a n c e d C o m p o s i t e M a t e r i a l s

T . T s u k i z o e an d N . O h m a e

Osaka Univers i ty , Department o f Prec i s ion Eng ineer ing ,

Facu l ty o f Eng ineer ing , Ya m ada-K am i , Su i ta , Osaka (Japan)

S U M M A R Y

Fric t ion an d wear pro pert ies between u nidirect ional ly oriented f ibre-

re inforced plast ics an d carbon stee l have been investigated. A wide varie ty

o f f b re - re i n f o rc e d p l a s ti c s we re p re p a re d f o r e x p e r im e n t s ; t h e f ib re -

re in forcement s used were h igh- tens i le - s trength carbon fb re , h igh-

mod ulus carbon f ibre , E-g lass f ibre , s ta in le ss s tee l f i bre and ara mid ibre

( Kev lar-49) , whi le epox y res in , po lyes t e r res in a nd P T F E were employed

as mat r i x mater ia l .

The law of mix tu res in the calculat ion o f the f r ic t io n coef ficient o f

com posi te materials i s deduced, and the val idity o f this law is discussed by

a compar i son o f computed values wi th exper imenta l da ta .

The wear per form ances o f seven d i ff e ren t k inds o f f i bre -re in forced

plas t ic s are summari sed . Sur faces o f compo s i t e mater ia l s a f t e r wear are

s tud ied us ing scanning e lec t ron microscopy , and a m ode l i s prop osed

s ta t ing tha t the wear o f compos i t e m ater ia l sproceeds by wear- th inn ing o f

the . fi bre-re in forcement s , subsequent breakdo wn o f the f ibres and by

p e e l i n g - o f f o f t h e f i b re s f ro m t h e m a t r i x . T h e e q ua ti on o f we a r o fcompos i t e m ater ia ls is a lso prop osed s ta t ing tha t the Young ' s modulus

and in te r laminar shear s trength o f fbre -re in forc ed p las t i c s are the

in[tuential fa ct or s on their specif ic wea r rates.

1 . I N T R O D U C T I O N

A d v a n c e d c o m p o s i t e m a t e r ia l s , su c h as f i b r e - r e i n f o r c e d p l a s t i c s ( F R P ) o r

f i b r e - r e in f o r c e d m e t a l s ( F R M ) , h a v e r e c e iv e d h i g h l y t e c h n o l o g i c a l a n d

265Fibre Science and Technology0015-0568/83/0018-0265/$03"00 © Applied Science Publishers

Ltd, England, 1983. Printed in Great Bri ta in

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266 T . T suk i zoe , N . Ohrnae

i n d u s t r i a l a t t e n t i o n in r e c e n t y ea r s . A m o n g t h e s e c o m p o s i t e m a t e r i a ls ,

F R P h a s b e e n p o t e n t ia l ly u s e f u l in m a n y f ie ld s o f i n d u s t r y b e c a u s e o f i ts

g o o d m e c h a n i c a l p r o p e r t i e s , e s p e c i a ll y i ts h ig h - s p ec i fi c s t r e n g th . F r i c t i o n

a n d w e a r p ro p e r t ie s o f F R P h a v e n o t b e e n fu l l y u n d e r s t o o d , a l th o u g hp i o n e e r in g r e s e a r c h b y L a n c a s t e r a n d G i l t r o w h a s s h o w n a n u m b e r o f

s i g n if i ca n t f a c t o r s a f f e ct in g t h e f r i c ti o n a n d w e a r o f F R P . 1 - 7 T h e p r e s e n t

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

F R P in c o n t a c t w i t h c a r b o n s te e l, a n d d i s c u s s e d t h e i n fl u e n ce s o f t h e

v o l u m e f r a c t i o n o f t h e f ib r e s , a n d t h e k i n d s o f fi b re , a s w e l l a s t r i b o l o g i c a l

a n i s o t r o p y w i t h r e s p e c t t o s l id i n g d i r e c t i o n . 8 - iv

T h i s a r t ic l e r ev i e w s o u r r e c e n t w o r k o n t h e t r i b o l o g y o f F R P ; th e l a w o f

m i x t u r e s i n t h e c a l c u l a t io n o f th e f r i ct io n c o e f fi c ie n t o f F R P , w e a r

p e r f o r m a n c e s o f F R P , t h e w e a r r a te e s t im a t i o n b y a w e a r e q u a t i o n f o rF R P a n d a sy s te m s a p p r o a c h t o t he w e a r o f F R P .

2. E X P E R I M E N T A L P R O C E D U R E S

T h e u n i d i r e c t i o n a l l y o r i e n t e d f i b r e - r e i n f o r c e d p l a s ti c s w e r e p r e p a r e d b y

t h e l e a k y - m o u l d m e t h o d 14 t o o b t a i n a w i d e v a r i e ty o f f ib r e v o l u m e

f r a c t i o n s a n d a u n i f o r m d i s p e r s i o n o f t h e fi b re s in th e m a t r i x .

T a b l e 1 s h o w s t h e e ig h t k i n d s o f F R P u s e d i n t h e e x p e ri m e n t s . T y p i c a l

T A B L E 1Constitution of Composites Tested

N o . S y m b o l o f F R P F i b r e - re i n fo r c e m e n t s R e s i n - m a t r ic e s

1 H S - C F R P H i g h - s t r e n g t harbon fibre Epoxy resin or polyesterresin

2 HM -CF RP Epoxy resin3 NT -CFR P Epoxy resin

4 G F R P

5 SFR P

6 A F R P

7 C FR T P PT FE8 Hybrid FR P Epoxy resin

High-modulus carbon fibreHigh-strength carbon fibre

(no surface treatment)E-glass fibre

Stainless steel fibre

Kevlar-49

(aramid fibre)High-strength carbon fibreHigh-strength carbon fibre

and E-glass fibre

Epoxy resin or polyesterresin

Epoxy resin or polyesterresin

Epoxy resin

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F r i c ti o n a n d w e a r o f a d v a n c e d c o m p o s i t e m a t e r i a l s 2 6 7

. o

"~

oo~oo111

r ~

0

0

o ~

0

N N

- 6

6

~.~ ~ .~

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2 6 8 T. Tsukizoe, N. Ohmae

.. o

e~

0

e~

p

e ~

%

-~ ~

r ~ ~

I

M

. . . . . . . . . 6 6 6 ~ o 6 ~

,- z

[-.,

8/6/2019 sdarticle 1983


Friction and wear of advanced composite materials 269

0

0

e~

p

. . . . 6 ~ 6 6 6 ~

e~

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@

T. Tsukizoe, N. Ohmae

T A B L E 6

Mechanical Properties of FRP (PTFE Composites)

V o l u m e Y o u n g ' s B e n d i n g M odulus o f

frac t ion m o d u l u s s trength r ig id i ty

(V f, %) (GPa) (GPa) (GPa)

Shore Interlaminar

hardness she ar strength

( m P a )

CF RT P 42 93 0.13 8-6 72

67a 109 0.14 9-0 65

AFRTP 42 32 0.12 14-0 68

67 42 0-12 18.6 64

SFRTP 42 47 70

67 54 68

a The specimen used in Figs 10, l l, 12 and 13.

m a t e r i a l p r o p e r t i e s o f th e f i b r e - r e i n f o r c e m e n t s a n d r e s in - m a t r i c e s a re

s h o w n i n T a b l e 2 , a n d t h e f a b ri c a t io n a l p a r a m e t e r s o f F R P a r e t a b u l a t e d

i n T a b l e 3 .

M e c h a n i c a l p r o p e r t i e s o f s e v e r a l k i n d s o f u n i d i r e c t i o n a l l y o r i e n t e d

F R P a r e l i st e d i n T a b l e s 4 , 5 , 6 a n d 7 .

T h e f r i c ti o n - t e st i n g a p p a r a t u s u s e d in t h e p r e s e n t s t u d y i s d i a g r a m -

m a t i c a l l y s h o w n i n F i g . 1, a n d t h e s h a p e o f t h e c a r b o n s te e l c o n e i n d e n t e r

270

Fig. I. Friction-testingapparatus. 1, Flexure pivot bearing. 2, Leaf spring. 3, Weight. 4,

Weight pan. 5, Cone indenter. 6, F RP specimen. 7, Traversing table. 8, Strain gauges. 9.

Bed. 10, Adjust screw. I1, Balance weight. 12, Vertical feed handle. 13, Reduct ion

gearbox. 14, Motor.

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F r i c ti o n a n d w e a r o f a d v a n c e d c o m p o s i t e m a t e r i a l s 271

t~, , d

0

0

r l .

e-

+

li

~a

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272

F i g . 2 .

T . T s u k i z o e , N . O h m a e

Shap e o f cone inden te r (0.2 % ca rb on s teel ).

L ~

Fig . 3 . W ear - te s t ing appa ra tu s . 1 , Sp ind le . 2 , Tran sm iss ion dev ice. 3 , Ho lde r o f C FR P

spec imen . 4 , F R P spec imen . 5 , C a rb on s tee l spec imen . 6 , Ho lde r o f ca r bon s teel spec imen .

7 , Lea f spr ing . 8 , Stra in gauge s . 9 , Bal l -bear ing . 10 , Balan ce weight . 11 , Lever . 12,

Suppor t ing po in t . 13 . Weigh t .

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F i g . 4.

4,30

!8 ~29 FR P

, I l l L , i J

¢48( a ) ( b ) - -

Shapes o f spec imens for wear tes ts , a , Carb on s tee l; b , FR P.

i n F i g . 2 . F r i c t i o n e x p e r i m e n t s w e r e c o n d u c t e d u n l u b r i c a t e d i n a i r

( t e m p e r a t u r e 2 5 + 1 ° C , r e l at i v e h u m i d i t y 5 5 - 6 0 % ).

F i g u r e 3 s h o w s t h e w e a r - t e s t i n g a p p a r a t u s , ~4 a n d F i g . 4 t h e s h a p e s o f

t h e s p e c im e n s . W e a r t e s ts w e r e p e r f o r m e d a t a t e m p e r a t u r e o f 2 0 - 2 5 ° C

a n d a r e la t iv e h u m i d i t y o f 5 5 - 6 0 % .

T h r e e d i f f e r e n t sl i d in g d i r e c t i o n s a r e t o b e i d e n t i fi e d in o r d e r t o c l a r i fyt h e t r ib o l o g i ca l a n i s o t r o p y o f u n i d i r e c t io n a l l y o r i e n t e d F R P w i t h r e s p e c t

t o s l i d i n g d i r e c t i o n s . F i g u r e 5 i l l u s t r a t e s a n F R P b l o c k i n d i c a t i n g t h r e e

s l id i n g d i r e c t i o n s , i .e . , p a r a l l e l, a n t i - p a r a ll e l a n d n o r m a l d i r e c t i o n s .

:fix

Fig. 5. FR P block indic at ing sl iding directions.

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2 7 4 T . T s u k i z o e , N . O h m a e

T h e w e a r v o l u m e o f F R P w a s c a lc u l a te d f r o m t he c h a n g e in s u rf a c e

p r o fi le s m e a s u r e d w i th a T a l y s u r f . T h e w e a r o f c a r b o n s te e l c o u l d b e

n e g le c te d , w h e n c o m p a r e d w i th t h a t o f F R P .

3 . R E S U L T S A N D D I S C U S S I O N S

3 . 1 . T h e l a w o f m i x t u r e s in th e c a l c u l a t i o n o f th e f r i ct io n c o e f f i c ie n t 1o,13

W h e n a c o u n t e r s u r f a c e s li de s a g a i n s t a n F R P s u r f a c e , b o t h n o r m a l l o a d

W a n d t a n g e n t i a l f o r c e F a r e s u p p o r t e d b y f i b re s a n d m a t r i x , s o t h a t t h e

f r i c t i o n c o e f f i c i e n t p c a n b e g i v e n b y

F F , - + F m

/[/ : -~ /V W f £ [ / V m (1 )

w h e r e s u ff ix e s f a n d m d e n o t e f i b r e a n d m a t r i x , r e s p e c t i v e l y . T h e n w e c a n

a s s u m e

A f = V f A 1

A m = V m A = ( 1 - Vf)A j (2 )

w h e r e A is t h e n o m i n a l a r e a o f c o n t a c t , a n d V f a n d Vm a r e t h e v o l u m e

f r a c t i o n s o f t h e f ib r e s a n d m a t r i x , r e s p e c t iv e l y . W h e n a p e e l i n g - o f f o f t h e

f ib r e s f r o m t h e m a t r i x , u n d e r t h e a c t i o n o f s h e a r d e f o r m a t i o n , d o e s n o t

o c c u r , w e c a n a s s u m e t h a t t h e s h e a r s t r a i n 7 A f is e q u a l t o ] :Am:

7Af = ?Am (3 )

I f G A f a n d GAIn , t h e m o d u l i o f ri g id i ty o f m a t e r i a l s u n d e r n e a t h t h e

c o n t a c t i n g s u r fa c e , a r e e q u a l , t h e n t h e s h e a r s t re s s r b e c o m e s c o n s t a n t ,

t h a t i s ,

F f F m ( 4 )7~f - - A f - - T m = A m

F r o m e q n s (2 ) a n d ( 4) , w e o b t a i n

F f = V f f ~

F m V m F J ( 5 )

B y t a k i n g i n t o a c c o u n t t h e r e l a t i o n o f W = W f + W m, w e h a v e

F Ff F m- + (6)

P Pr Pm

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Friction and wea r o f advanced composite materials 275

and finally

1 V f 1 1 ( 7 )~f + Vm #m

From this equation we are able to calculate the friction coefficient # of

FR P when the friction coefficients of the fibres,/~f, and of the matrix, Pm,

are given.

When the FRP is hybrid-reinforced with two fibres fl and f2, the law of

mixtures in the calculation of the friction coefficient is given by

1 1 1 1• ' + Vf2 '+ V m - - ( 8 )= V f, ~ ft ~2f2 ]~m

where

V : , + V : , + Vm = 1 (9)

3 , 2 . F r i c t i o n p r o p e r t ie s o f F R P

The measurement Of the fr iction coefficient was performed when the top

of the cone indenter became flattened (approximately 0.1 mm diameter)

and the fluctuation of friction force became small, typically after a sliding

distance of about 10 mm. 10The relationships between the friction coefficient and the volume

fraction of the fibres are shown in Figs 6, 7 and 8. Figure 9 shows typical

results of hybrid FRP. The thick solid, dotted and chain lines in these

figures show the calculated friction coefficient obtained from either

eqn (7) or eqn (8). As there is good agreement between the theoretical and

the experimental results, the assumption of eqn (3) might be reasonable

for the friction of FRP at low sliding speeds and light normal loads, in

which case fracture of FRP at the sliding surface does not take place.

From the results in Figs 6, 7 and 8, it is clear that carbon fibre is the bestreinforcement as far as the friction of FRP is concerned.

The friction anisotropy depending on the fibre orientation relative to

the sliding direction cannot be recognised in these figures. In Fig. 9 where

a medium hybrid FRP (V:~ = 35 %, V:2 = 35 %) is utilised instead of a

carbon fibre FRP (V:~ = 70 ~o, V:2 = 0 ~), there is only a slight increase in

the friction coefficient. Thus for a practical application of FRP where

friction becomes an important problem, the use of hybrid carbon FRP

can be recommended in regard to the performance/cos t ratio.

8/6/2019 sdarticle 1983


2 7 6 T, Tsukizoe, N. Ohmae

t

l I J I I ] I I I I I

[~; P a r a l l e l5 F R P ~ $ A r ~ t i p a r a l l e l v = l . $ m m / m i l l

0 . 5 [ ~ ) N o r m a l ' ,¢ = 1 . 5 2 N

CFRP Ant -par~lllel

0 . 4 Nor~

~ o.3

40 . 2 . . . .

0.1

0 1 [ I I I i I I I [0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

V O L U M E F R A C T I O N V f , 7.

F i g . 6 . I n f l u e n c e o f t h e v o l u m e f r a c t i o n

o f f i b re s o n t h e f r i c t i o n c o e f f i c ie n t o f e p o x y

c o m p o s i t e s ( N o . 1).

0 .5

0 .4

0 . 3

0 . 2

0 .1

0

I l l l l l l l l l l

G FR P I ~ P ~ r a l l e l v = l . 3 m m / m i n[ ~ A n t i - p a r a l ] e L

. . . . . . . . . . . . .4

I I I I I J I J I I J

1 0 2 0 3 0 1 , 0 5 0 6 0 7 0 8 0 9 0 1 0 0

V O L U M E F R A C T T O N V f , %


o f f i b re s o n t h e f r i c t i o n c o e f f i c ie n t o f e p o x y

c o m p o s i t e s ( N o . 2 ) .

0. 5

0. 4

0 , 3

0 .2

0.1

I I I I I ~ I [ [ I

{ ~ Par alle l v= [. 5ram/rain

A n t i - p a r a l l e l W = [ . 5 2 NI P a r a l l e l

A n t i - p a r a l l e l

N . . . |

{ ~ A n t i - p a r a l l e l S , , ~

[ ~ N . . . . 1 TT ~-" "

. _ . . . .

I I I l I I I

2 0 40 6 0 8 0 1o o

V O L U M E F R A C T I O N V f , 7o


o f ' f i b r e s o n t h e f r i c t io n c o e f f i c ie n t o f p o l y -

e s t e r c o m p o s i t e s .

i i . i i I ' I

0 . 4 H y b r i d F R P

P a r a l l e l d l ¢ l C t l o n

.~ ~ v = I 5 m m l m l n

0 . 3

0 . 2

~. o . i

1 I

o , ' o 2 ~ 3 0 4 ' o 5 ' o e ' o ¢ oV O L U M E F R A C T I O N O F C A R B O N F I B E R V f l , %

J i

7 0 ~ o 5 ' o 4 '0 3 ' o 2 'o , 'o oV O L U M E F R A C T I O N O F G L A S S F I B E R V f 2 , 7.

F i g . 9 . ] n f l u e n c e o f t h e v o l u m e f r a c t i o n

o f f ib r e s o n t h e f r i c t i on c o e f fi c i e nt o f h y b r i d

e p o x y c o m p o s i t e s .

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Friction and wear of adranced composite materials 277

3 . 3 . W ea r pro per t ie s o f F R P

T h e r e s u lt s o f o u r w e a r t e s ts 9 - 1 4 h a v e s h o w n t h a t w e a r v o l u m e i n c r e a se s

l in e a r ly w i t h s li d in g d i s ta n c e ; n o r u n n i n g - i n p e r i o d o f w e a r h a s b e e na p p a r e n t . T h u s i t is p o s s i b l e to c h a r a c t e r i s e t h e w e a r i n te r m s o f a s p e c if ic

w e a r r a t e w , w h i c h h a s a u n i t o f m m 3 / N m . F i g u r e s 10 , 11 a n d 12

s u m m a r i s e w e a r p e r f o r m a n c e s o f s e ve n k i n d s o f u n i d ir e c t io n a l l y o r i e n t e d

F R P , t h e v o l u m e f r a c t io n o f w h i c h i s a p p r o x i m a t e l y 7 0 % ( se e T a b le s 4

a n d 6 ) . T h e s e t h r e e f i g u r e s s h o w t h e r e l a t i o n s h i p s b e t w e e n t h e s p e c i f i c

w e a r r a t e a n d t h e f r ic t io n c o ef f ic i e n t, t h e Y o u n g ' s m o d u l u s a n d t h e

i n t e r l a m i n a r s h e a r s t r e n g t h , r e s p e c t iv e l y . A s f o r t h e t r i b o l o g i c a l a n i s o t-

r o p y , i t se e m s t h a t e v e r y F R P h a s g o o d w e a r - re s is ta n c e i n n o r m a l a n d

p a r a l l e l s l id i n g b u t p o o r w e a r r e s i s t a n c e i n a n t i - p a r a l l e l s l id i n g . I n n o r m a ls l id i n g , e v e ry F R P e x c e p t A F R P s u f f e r e d 's e i z u r e ' a f t e r s e v e ra l k i l o m e t r e s

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

F r o m t h e r e su l ts in F ig . 10, i t is e v i d e n t t h a t H S - C F R P a n d H M -

C F R P h a v e a s m a ll sp ec if ic w e a r r a t e o f t h e o r d e r o f 1 0 - 7 m m 3 / N m a n d a

l o w f r ic t i o n c o e ff ic i en t o f 0 .2 . I n c o n t r a s t , G F R P a n d S F R P s h o w a l a rg e

s pe cif ic w e a r r a te o f th e o r d e r o f 1 0 - 4 m m 3 / N m a n d a h ig h fr ic t io n

c o e f f ic i e n t o f 0 . 4. T h e l o w e s t f r i c t i o n c o e f f i c ie n t o f 0 .1 is o b t a i n e d f o r

C F R T P . T h e g o o d t r i b o lo g i c a l p r o p e r t i e s o f t h e c a r b o n - f ib r e - r ei n f o rc e d

p la st ic s g r o up ( C F R T P , N T - C F R P , H S - C F R P a n d H M - C F R P ) m a y b ec a u s e d b y t h e g o o d m e c h a n i c a l p r o p e r ti e s o f F R P , f o r in s ta n c e , h ig h

Y o u n g ' s m o d u l u s a n d h i g h i n t e r la m i n a r s h e a r s t r e n g th , a s w el l a s b y t h e

g o o d t r i b o l o g i c a l p r o p e r t i e s o f t h e f i b re s , e .g . , s e l f -l u b r i c a t i n g a b i l i ty a n d

h i g h s t r e n g t h .

F r o m t h e r e s u l t s i n F i g . 1 1 , i t i s n o t i c e d t h a t t h e F R P w i t h h i g h e r

Y o u n g ' s m o d u l u s a l w a y s sh o w s a b e t te r w e a r - r e s i st a n c e , a n d t h e

c o e f fi c ie n t o f c o r r e l a t i o n b e t w e e n t h e m is c a l c u l a t e d a s h i g h a s - 0 . 7 4 .

W h e n w e l o o k a t t h e r e s u lt s o f th e C F R P g r o u p i n F i g . 1 2, i t w i ll b e

n o t i c e d t h a t t h e i n t e r l a m i n a r s h e a r s t r e n g t h a l s o h a s a c l o s e r e l a t i o n w i t ht h e s p e c if ic w e a r r a t e ; t h e c o e f f i c ie n t o f c o r r e l a t i o n b e i n g e s t i m a t e d a t

- 0 . 8 8 .

3 . 4 . The w ea r equa t io n f o r F R P

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

a n d t h e sc a n n i n g e l e c t ro n m i c r o s c o p e o b s e r v a ti o n s o f w o r n F R P

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2 7 8 T . T s u k i z o e , N . O h m a e

I , , , ' , , , ' I , , , , , , , , I , , , , , ' ' ,

~ e

~ ~ ~ ° %

k ' ~ n ~ ~ '~ r '- -" l

i l l l l l i i I i l i i i i i l I i i i i i i i i

oo ~ _ =

o = .=

I , . , , , , , , I , , , , , , , , I ' " ' ' ' ' '

; ~ 1 1 ; , i i , I | l t , ii i i i I H I I l I I 1

t u N / t r a m ' a ~ ~ & V ~ ) / ~ 3 / ~, D I A I D Z d g

,o --

c ~

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F r i c t i o n a n d w e a r o f a d v a n ce d c o m p o s i t e m a t e r i a l s 279

s u rf a ce s ,S . 9A 1A,* t h e f o l l o w i n g m o d e l o f w e a r p r o c e s s e s c a n b e p r o p o s e d :

T h e w e a r o f F R P p r o c e e d s b y :

( a) w e a r - t h i n n i n g o f t h e f i b r e - r e i n f o r c e m e n t s ;( b) s u b s e q u e n t b r e a k d o w n o f t h e f ib r e s;

( c) p e e l i n g - o f f o f t h e f ib r e s f r o m t h e m a t r i x .

A s e q u e n t i a l o c c u r r e n c e o f t h e s e p r o c e s s e s g o v e r n s th e w e a r o f F R P . T h e

e s s e n t i a l f a c t o r s a f f e c t i n g t h e s e t h r e e p r o c e s s e s m a y b e a s f o l l o w s :

( a) i n t h e w e a r - t h i n n i n g o f t h e f i b r e s - - l o a d W a n d s l id i n g d i s t a n c e D ;

( b) in t h e b r e a k d o w n o f t h e f i b r e s - - s t r a i n lap/Eo f th e F R P c a u s e d b y

f r i c ti o n f o r c e , l o a d W a n d s l i d i n g d i s t a n c e D ;

(c ) in t h e p e e l i n g - o f f o f t h e f ib r es f r o m t h e m a t r i x - - i n t e r l a m i n a r s h e a rs t r e n g t h I s o f t h e F R P , s t r a i n lap/Eo f t h e F R P , l o a d W a n d s l i d in g

d i s t a n c e D . T h e r e f o r e , w e a r v o l u m e Q c a n b e g iv e n b y

1 D ) ( 1 0 )

A s f o r f i r s t - o rd e r a p p r o x i m a t i o n , w e c a n a s s u m e

# p lQ=k-~ ~ WD ( l l )

w h e r e k is a d i m e n s i o n l e s s c o n s t a n t . T h e n t h e s p e c if ic w e a r r a t e wr c a n b e

w r i t t e n a s

w~ = k / t p 1 ( 1 2 )E / s

o r

w r /s = k ( 13 )

Ew h e r e WrI a n d kpp/E a r e b o t h d i m e n s i o n l e s s q u a n t i ti e s . F i g u r e 13 s h o w s

t h e r e l a t i o n s h i p b e t w e e n wrIs a n d k#p/E u n d e r v a r i ed n o r m a l p r e ss u r e p

o f l , 1 .5 a n d 2 N / m m 2 f o r s e v e n k i n d s o f F R P . T h e s o l i d li n e i n t h i s f i g u r e

s h o w s t h e e x p e r i m e n t a l v a l u e s f o r p = 1 .5 N / m m 2, a n d t h e w e a r e q u a t i o n

a t a c o n s t a n t n o r m a l p r e s s u r e p i s g i v e n b y

wrIs = ~ (14 )

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280 T . T s u k i z o e , N . O h m a e

1 6 '

1 0 "

I 0 ~

1 0 °

F i g . 1 3 .

1 i I I I i i i i i i i i ]

/

o - GFR¢ /

/- S F R P

~ , - A F R P

0 - N T - C F R P

(1) - HS -C F RP d ] E ] E ]

(~ - I ' I4-*CFRP u , /

• - C F R T P

p o r a l l e l

, ~ "N l~ro l iel

A / "% N o? to ol

/ _~_ - a , - , 2 6 , , , , 2

/ 10NJ-n~ Nt'~'

+ 5 : /+ ' Y + I 'i i I I i 1 i 1 i i i |

10 + 10 "S

u .P / E

Relat i onship between wrl s and y p / E .

The values o f ~ and /~ ma y be calcul ated fr om the experimental line in

Fig. 13, and the experimental wear equation of FRP can be written as

wr = 1"40 x 10 t° -- (15)Ix

When the Young's mod ulus E (M Pa) and the interl aminar shear strength

I+ (MP a) of the F RP are given and the fric tion coefficient y between the

FRP and a carbon steel is known, we can estimate the specific wear ratewr (mm3/N mm) under the no rma l pressure p -- 1.5 N/m m2 f rom the wear

equation, eqn ( 1 5 ) .

4 . S Y S T E M S A P P R O A C H T O T H E W E A R O F F RP 16'1v

A method of systems analysis is introduced to the wear phenomenon of

unidirectionally oriented FR P. A compli cated system of the wear o f FR P

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is a f fe c t e d b y a n u m b e r o f v a r ia b l e s . T h u s i n o r d e r t o i d e n t i fy t h e

p r e d i c t o r v a r i a b l e s o f t h is s y s t e m , th e s t e p w i s e m e t h o d s ( b o t h f o r w a r d

a n d b a c k w a r d ) w e r e e m p l o y e d . T h e w e a r o f F R P w a s t r ea t e d a s a s t a t ic s

m o d e l w h e r e t h e b l a c k - b o x c u t t i n g w a s m a d e t o e s ta b l i sh a h i e r a rc h i c a ls y s t e m s m o d e l .

4 . 1 . S e l e c t i o n o f p r e d i c to r v a r i a b l es

A m u l t i p l e re g r e s s io n a n a l y s i s m o d e l is e x p r e s s e d b y

o r b y

I ! l ] ¸ [ i x x l• n X n l " " " X n p

I ! ° l + [ ! l n( 1 6 )

y = X f l + s ( 1 7 )

T h e n , a r e s id u a l s u m o f s q u a r e s i s w r i t t e n a s

S-~-gT.g

= [y - X /J] r . [y - X/~] (18)

T h e n o r m a l e q u a t i o n d e r iv e d f r o m e q n (1 8) le a d s to

fl = ( X T X ) - 1 X T y ( 19 )

U s i n g t h e l e a st s q u a r e s e s t i m a t e / ~ d e r i v e d f r o m e q n ( 19 ), w e o b t a i n

y = X/~ (20)

A n o r m a l i s a t i o n is m a d e o n e a c h v a r i a b le i n su c h a w a y t h a t t h e a v e r a g e

is z e r o a n d t h e v a r i a n c e i s u n i ty . T h e n o r m a l i s a t i o n e x c l u d e s th e p r o b l e m

o f u n i t s o f v a r ia b l e s . T h e s i g n i fi c a n c e o f m u l t i p l e r e g r e s s i o n i s t e s t e d b y

t h e v a r i a n c e a n a l y s i s .P r e d i c t o r v a r i a b le s a r e s e le c t e d b o t h b y s te p w i s e f o r w a r d a n d b a c k -

w a r d m e t h o d s . T h e f o r m e r i s b a s e d o n t h e c o r re l a t i o n , w h i le t h e la t te r o n

t h e m u l t ip l e c o r r e l a t i o n . I n a n a c t u a l o p e r a t i o n , a s e q u e n t ia l c a l c u l a t io n

o f th e s e a n a l y s e s i s m a d e b y a l a r g e - sc a l e c o m p u t e r ( F i g . 14).

F i v e m e c h a n i c a l p r o p e r t i e s w e r e t a k e n i n t h e s te p w i s e m e t h o d s ; t e n s i le

s t r e n g t h a B, Y o u n g ' s m o d u l u s E , b e n d i n g s t r e n g t h B , B a r c o l h a r d n e s s H

a n d i n t e r l a m i n a r s h e a r s t r e n g t h I~. I t w a s f o u n d t h a t t h e m o s t s i g n if ic a n t

p a r a m e t e r t o th e w e a r o f F R P is E a n d t h e s e c o n d m o s t s i gn i fi c a n t

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282 T. Tsukizoe, N. Ohmae

- ' 2 e

- ~ o

i - i'~' ~',~',

! ? ' ! ; o

_ _ ° ~

° i~ : : :

- - i

o

:A

©

c -

o

o

E

e..,

©

E

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F r i c t i o n a n d w e a r o f a d v a n c e d c o m p o s i t e m a t e r i a l s 283

para m ete rs a re aB an d I S. Th ere fo re , t he p resen t sy s t ems ana lys i s ag rees

w i t h e q n (1 2) c o n c e rn i n g t h e s i gn i f ic a n c e o f E a n d I So n t h e w e a r o f F R P .

4 . 2 . M o d e l b u i l d in g

Fi g u re 15 is a mo d e l o f t h e FR P w e a r s y s t e m. W e a r o f FR P p ro c e e d s fi rs t

b y w e a r - t h i n n i n g o f t h e f ib r es , t h e n b y b r e a k d o w n o f t h e fi br e s a n d f i n a ll y

by pee l ing -o f f o f t he f ib res , a s p ro po sed in Sec t ion 3.4 . F ro m a heu r i s t i c

o,o

SLI Di HGVELOCITY

TYPE OFFRP

SUB SYSTEIv

1

FRICTION

[ ]

SUB SYSTEM

2

RISE OF

TEMPERATURE

[]

SUB SYSTE]~

3

CHANCE IN

MECHANICAL

"-" PROPERTIES

[]

F i g . 15. Approach by systems methodology-hierarchical modelling.

c r i te r i o n th a t t h e w e a r o f F R P is c a u s e d b y a d e g r a d a t i o n o f m e c h a n i c a l

p ro p e r t i e s , t h e b l a c k -b o x c u t t i n g w a s d o n e ; s u b s y s t e m 1 i d en t if ie s t h e

f r ic t io n , s u b s y s t e m 2 , t h e s u r f ac e t e m p e ra t u r e , a n d s u b s y s t e m 3 , t h ed e g r a d a t i o n o f F R P d u e t o t e m p e r a t u r e r i s e .

A n i n p u t - o u t p u t r e l a ti o n o f e a c h s y s t e m is w r it te n a s

/a = f l ( W , v , M ) s u b s y s t e m 1 (2 1)

A T = fz ( / a , W , v , M ) s u b s y s t e m 2 (2 2)

A E = f 3 (A T , M ) }

A I S = f 4 ( A T , M ) subsys t em 3 (23 )

A a a = f s ( A T , M )

w h e re f is t h e c r i te r i o n fu n c t i o n , M is a p ro p e r t y o f ma t e r i a l, A T i s

t e mp e ra t u r e r i s e , a n d A E , A IS and A trB a r e t h e c h a n g e s i n Y o u n g ' s

m o d u l u s , i n t e r l a m i n a r s h e a r s t r e n g t h a n d t e n s i l e s t r e n g t h o f F R P ,

r e s p ec t iv e l y . A s s u m i n g a f u n c t i o n o f

AW r = f6 (A E , A Is , A a a . . . ) (2 4)

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where Aw, is the change in specific wear rate. The substitution of

eqns (21), (22) and (23) in eqn (24) leads to

w~=fv(W, v, M) (25)

Once the unknown parameters are identified for a certain FRP, the

present model can be tested for other FRP.

One of the results showing the prediction power of this model is

illustrated in Fig. 16. The present model predicts fairly well the values of

F i g . 1 6 .

10 -~

c~

1 0 6

10 7

PREDICTED EXPERIMENTAl,

C F R P o °

AFRP ~ •

GFRP o •

1 2 3 4 5 6 7 8 9 0

SAMPLE NUMBER

Comparison of predicted values of % with experimental data.

w . The results obtained for CFRP shows a higher wr than the measured

data. This may be attributed to the fact that the CFRP has a self-

lubricating ability to reduce wear.

Further, to estimate the dynamic tribological processes of FRP, an

autoregression (AR) model has been applied to the wear of FRP. The

model simulation is being carried out. An investigation on the develop-

ment of the system, when a foreign stimulus is introduced, is in progress.

The results of this prel iminary analysis recently appeared in Reference 18.

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Friction and wear of adt,anced composite materials 285

5. C O N C L U S I O N S

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

u n i d i r e c t i o n a l l y o r i e n t e d F R P a n d c a r b o n s te e l, th e f o l lo w i n g r es u lt s w e r eo b t a i n e d :

1. T h e l a w o f m i x t u r e s in t h e c a l c u l a t i o n o f t h e fr i c t io n c o e f f ic i e n t o f

F R P w a s d e d u c e d , a n d t h e v a li d i ty o f t h is la w w a s c o n f i r m e d b y

t h e e x p e r i m e n t a l r e s u l t s .

2 . C F R P g a v e a s m a l l s p ec i fi c w e a r r a t e a n d a lo w f r i c ti o n c o e f fi c ie n t .

I n c o n t r a s t , G F R P a n d S F R P p r o v i d e d l a r ge sp e ci fi c w e a r r a te s

a n d h i g h f r i c t i o n c o e f f i c i e n t s . T h e l o w e s t f r i c t i o n c o e f f i c ie n t o f 0 .1

w a s o b t a i n e d w i t h C F R T P .3. A m o d e l w a s p r o p o s e d s t a ti n g t h a t t h e w e a r o f F R P p r o c e e d s b y

t h e w e a r - t h i n n i n g o f t h e f ib re s w i t h s u b s e q u e n t b r e a k d o w n o f t h e

f ib r e s a n d b y p e e l i n g - o f f o f t h e f ib r e s f r o m t h e m a t r i x . U s i n g t h i s

m o d e l , t h e e x p e r im e n t a l e q u a t io n f o r th e w e a r o f F R P w a s

d e d u c e d . I t w a s f o u n d , b y c r i ti c is i ng th i s w e a r e q u a t i o n , t h a t t h e

m o s t s i g n if ic a n t p a r a m e t e r s i n t h e w e a r o f F R P a r e Y o u n g ' s

m o d u l u s a n d i n t e r la m i n a r s h e a r s tr e n g th .

4 . A m e t h o d o f s y s t em s a n a l y s is w a s a p p l i e d t o t h e w e a r o f F R P . T h e

s p ec if ic w e a r r a t e w a s f o u n d t o h a v e a c lo s e c o r r e l a t i o n w i t hY o u n g ' s m o d u l u s , t e n si le s t r e n g t h a n d i n t e r l a m i n a r s h e a r s tr e n g t h .

T h e t o t a l s y s t e m a t i c p r o g r a m m i n g s w e r e p e r f o r m e d ; t h e m o d e l

p r e d i c t e d t h e s p e ci fi c w e a r r a t e .

R E F E R E N C E S

1. J . K . Lanc as te r , Com pos i te se l f - lubr ica t ing bea r ing ma te r ia l s , Proc. Inst .

M ech . E n g r s , 182 (1, 2) (1967/68) p. 33.2 . J . P . G i l t row and J . K . Lan cas te r , Ca rbon - f ib re r e in forced po lym ers a s se lf -

lubr ica t ing ma te r ia ls , Proc . Ins t . Mech . Engrs , 182(3) (1967/68) p. 147.3 . J . K . Lanc as te r , The e f fect o f ca r bo n f ib re r e in force m ent on th e f r ic tion and

w e a r o f p o ly me r s , Bri t . J . Appl . Phys. , 2(1) (1968) p. 549.4 . J . P . G i i t row an d J . K . Lanc as te r , The ro le o f the counte r fa ce in the f r ic t ion

a n d w e a r o f c a r b o n f ib r e r e in f o r c e d t h e r mo s e t t i n g re s in s , W ea r , 16(5) (1970)p. 359.

5 . J . K . L a n c a s t e r , L u b r i c a t i o n o f c a r b o n f i b r e - re in f o rc e d p o ly me r s : P a r t I - -Wa te r a n d a q u e o u s s o lu t i o n , W ea r , 20(3 ) (1972) p. 315.

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6. J. K. Lancaster, Lubrication of carbon fibre-reinforced polymers: Part I I- -Organic fluids, Wear, 20(3) (1972) p. 335.

7. J. P. Giltrow, Friction and wear of self-lubricating composite materials,Composites, March (173) p. 55.

8. N. Ohmae, K. Kobayashi and T. Tsukizoe, Characteristics of fretting ofcarbon fibre reinforced plastics, Wear, 29(3) (1974) p. 345.

9. T. Tsukizoe and N. Ohmae, Wear performance of unidirectionally orientedcarbon-fibre-reinforced plastics, Tribology lnternl., 8(4) (1975) p. 171.

10. T. Tsukizoe and N. Ohmae, Friction properties of advanced compositematerials, Proc. JS ME-ASME Joint Western Conference on AppliedMechanics (Hawaii, March 1975), JSME paper No. D-2.

11. T. Tsukizoe and N. Ohmae, Tribo-mechanics of carbon-fibre-reinforcedplastics, Industrial Lubrication and Tribology, 28(1) (1976) p. 19.

12. T. Tsukizoe and N. Ohmae, Friction and wear of with parallely oriented

fibre reinforced plastics--tribological assessment for CFRP, GFRP andSFRP, J. Japan Society of Lubrication Engrs, 21(5) (1976) p. 330 (in

Japanese).13. T. Tsukizoe and N. Ohmae, Friction properties of composite materials,

Trans. Japan Society of Mech. Engrs, 43(367) (1977) p. 115 (in Japanese).14. T. Tsukizoe and N. Ohmae, Wear mechanism of unidirectionally oriented

fibre-reinforced plastics, Trans. ASME, 99(4) (1977) p. 401.15. T. Tsukizoe, Friction and wear of fibre reinforced plastics, J. Japan Society

of Lubrication Engrs, 23(1) (1978) p. 11 (in Japanese).16. M. Yukumoto, T. Tsukizoe and N. Ohmae, Systems approach to the wear of

fibre-reinforced plastics, J. Japan Society of Lubrication Engrs, 23(12)

(1978) p. 881 (in Japanese).17. N. Ohmae, M. Yukumoto and T. Tsukizoe, Analysis of System Structure in

the Wear of FRP, Proc. 2nd European Tribology Congress (Diisseldorf,October 1977), Band II/II1, 57/1.

18. N. Ohmae, An Introduction to Tribo-Engineering, Fundamentals o[Tribology (ed. Suh and Saka), MIT Press, 1980, p. 1183.

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