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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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2 6 8 T. Tsukizoe, N. Ohmae
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Friction and wear of advanced composite materials 269
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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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Friction and wear of advanced composite materials 273
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.
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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 , %
F i g . 7 . 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 . 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
F i g . 8 . 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 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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Friction and wear of advanced composite materials 281
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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284 T. Tsukizoe, N. Ohmae
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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286 T. Tsukizoe, N. Ohmae
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.