1 Contact Deformation and Static Friction of Polymers Influences of Viscoelasticity and Adhesion Horst Czichos
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Bundesanstalt für Materialprüfung, Federal Institute for Materials Research and Testing, Berlin-Dahlem, Federal Republic of Germany
In using a newly developed tribometer which allows the microscopic "in-situ" investigation of i n t e r f a c i a l t r i b o l o g i c a l processes through an optically transparent counterbody, contact deformation and static f r i c t i o n of thermoplastic polymers were studied. Examination of the contact deformation of polymers under load revealed that the contact deformation displacement is mainly influenced by the viscoelastic properties of the polymers. By measuring relaxed moduli and relaxation times the Hertzian theory of contacting bodies could be extended leading to a contact deformation formula which includes viscoelastic effects. For the onset of motion of polymer/polymer sliding pairs the static f r i c t i o n appears to be connected with i n t e r f a c i a l adhesion. When data of the surface energy of the examined polymers were used, the experimentally determined f r i c t i o n values could be related to the adhesion energies of the different p o l ymer/polymer sliding pairs.
A l l t r i b o l o g i c a l p r o c e s s e s , i . e . f r i c t i o n a n d wear p r o c e s s e s o f i n t e r a c t i n g m a t e r i a l s s t a r t w i t h two e l e m e n t a ry steps: (i)
The f o r m a t i o n o f t h e c o n t a c t a r e a u n d e r a g i v e n load.
(ii)
The i n i t i a t i o n o f r e l a t i v e m o t i o n between t h e c o n t a c t i n g b o d i e s by o v e r c o m i n g s t a t i c f r i c tion. 0097-6156/ 85/ 0287-O003S07.00/ 0 © 1985 American Chemical Society
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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The b a s i s f o r t h e c h a r a c t e r i z a t i o n o f t h e c o n t a c t b e h a v i o u r o f c u r v e d b o d i e s i s g i v e n by t h e w e l l known c l a s s i c a l Hertzian theory (1). Because t h i s t h e o r y b a s i c a l l y applies only to p e r f e c t l y e l a s t i c materials with i d e a l smooth s u r f a c e s , some a d d i t i o n a l f a c t o r s must be c o n s i d ered i n d i s c u s s i n g the contact behaviour of m a t e r i a l s l i k e polymers. J o h n s o n , K e n d a l l and R o b e r t s (2) e x t e n d e d t h e H e r t z i a n theory t a k i n g i n t o account the molecular a t t r a c t i o n o f i n t e r f a c i a l a d h e s i o n between c o n t a c t i n g b o d i e s . T h e i r a n a l y s i s w h i c h has b e e n e x p e r i m e n t a l l y confirmed f o r e l a s t o m e r - g l a s s c o n t a c t s (2, 3, 4 ) , shows t h a t due to the e x i s t e n c e of molecular a t t r a c t i o n f o r c e s contact a r e a and e l a s t i c d i s p l a c e m e n t a r e l a r g e r t h a n v a l u e s d e duced from the H e r t z i a n t h e o r y . In a d d i t i o n , the i n f l u e n c e o f v i s c o e l a s t i c i t y on c o n t a c t d e f o r m a t i o n has b e e n s t u d i e d , see e . g . (5 t o 1 2 ) . These t h e o r e t i c a l a n a l y s e s m a i n l y c o n c e r n i n g the c o n t a c t between a r i g i d i n d e n t e r and a v i s c o e l a s t i c h a l f - s p a c e i n d i c a t e a l s o t h a t c o n t a c t a r e a and c o n t a c t d i s p l a c e m e n t s a r e l a r g e r f o r v i s c o e l a s t i c m a t e r i a l s t h a n f o r p u r e e l a s t i c mate r i a l s and t h a t a d i f f e r e n c e b e t w e e n l o a d i n g and u n l o a d i n g i s t o be e x p e c t e d w i t h v i s c o e l a s t i c m a t e r i a l s (13) . I n t h i s p a p e r ( i ) c o n t a c t d e f o r m a t i o n and ( i i ) i n i t i a l f r i c t i o n a r e s t u d i e d e x p e r i m e n t a l l y and a t t e m p t s a r e made t o c o r r e l a t e t h e e x p e r i m e n t a l r e s u l t s w i t h b u l k and s u r f a c e p r o p e r t i e s o f t h e p o l y m e r s i n v e s t i g a t e d . EXPERIMENTAL I n t h e e x p e r i m e n t a l i n v e s t i g a t i o n s a b a l l - o n - d i s c and a p i n - o n - d i s c c o n f i g u r a t i o n were u s e d c o n s i s t i n g o f an op t i c a l l y transparent d i s c (glass or o p t i c a l l y transparent p o l y m e r ) and a p o l y m e r s p e c i m e n . For the contact d e f o r m a t i o n i n v e s t i g a t i o n s , c o m p l i a n c e and c o n t a c t s i z e were m e a s u r e d by means o f an i n d u c t i v e d i s p l a c e m e n t transdu c e r and an o p t i c a l m i c r o s c o p e c o n n e c t e d w i t h a TV s e t respectively. The a c c u r a c y o f t h e s e measurements was b e t t e r t h a n + 0.1 μπι f o r t h e d i s p l a c e m e n t measurements and b e t t e r t h a n ± 1 % f o r t h e d e t e r m i n a t i o n o f t h e c o n t a c t diameter. In F i g u r e 1 the arrangement o f the main p a r t s o f t h e t e s t e q u i p m e n t i s shown s c h e m a t i c a l l y . F i g u r e 2 shows a p h o t o g r a p h o f t h e e x p e r i m e n t a l a p p a r a tus. The t e s t s y s t e m o p e r a t e d u n d e r c o n t r o l l e d c o n d i t i o n s o f a m b i e n t t e m p e r a t u r e (T = 23 °C) and e n v i r o n mental atmospheric humidity (50% r e l . h u m i d i t y ) . For the f r i c t i o n experiments with the help of a d r i v i n g u n i t s u p p o r t e d by an a i r b e a r i n g and a l o a d i n g d e v i c e , s l i d i n g m o t i o n and l o a d c o u l d be a p p l i e d . The n o r m a l f o r c e and t h e f r i c t i o n a l f o r c e a c t i n g on t h e
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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1. C Z I C H O S
Contact Deformation and Static Friction of Polymers
F i g u r e 1. S c h e m a t i c a r r a n g e m e n t configuration.
Figure
2.
o f experimental
Photograph o f t h e t r i b o m e t e r .
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
5
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P O L Y M E R W E A R A N D ITS
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p o l y m e r s p e c i m e n were d e t e c t e d by a two-component f o r c e t r a n s d u c e r (14) and t h e s i g n a l s o f t h i s f o r c e t r a n s d u c e r were f e d t o an e l e c t r o n i c d i v i d e r w h i c h c a l c u l a t e d d i r e c t l y the f r i c t i o n c o e f f i c i e n t . Normal l o a d , t a n g e n t i a l f r i c t i o n a l f o r c e , and f r i c t i o n c o e f f i c i e n t were r e c o r d e d on a t h r e e - c h a n n e l r e c o r d e r . A block diagram of t h i s t r i b o m e t e r i s g i v e n i n F i g u r e 3. D e t a i l s of the e x p e r i mental equipment, the m a t e r i a l s s t u d i e d , the p r e p a r a t i o n o f t h e s p e c i m e n s and t h e p e r f o r m a n c e o f t h e t e s t s a r e g i v e n elsewhere (15).
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CONTACT DEFORMATION The e x p e r i m e n t s were p e r f o r m e d w i t h mers: - Polyoxymethylene - P o l y a m i d e 66
(PA
- Polypropylene
the
following poly
(POM) 66)
(PP)
- Polytetrafluoroethylene
(PTFE)
A l l m a t e r i a l s belong to the c l a s s of s e m i - c r y s t a l l i n e thermoplastic polymers. C h a r a c t e r i s t i c appearances of s p h e r u l i t i c m i c r o s t r u c t u r e s o f t h e p o l y m e r s a r e shown i n F i g u r e s 4 and 5 f o r t h e e x a m p l e s o f POM and PA66. The c o n t a c t d e f o r m a t i o n o f t h e s e thermoplastic poly mers was s t u d i e d e x p e r i m e n t a l l y by p r e s s i n g p o l y m e r i c b a l l s (of 4 mm d i a m e t e r ) w i t h c o n t i n u o u s l y i n c r e a s i n g l o a d (0.6 N/s) a g a i n s t an o p t i c a l l y smooth g l a s s s u r f a c e and m e a s u r i n g b o t h c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t and c o n t a c t s i z e u n d e r l o a d as d e s c r i b e d above (see F i g u r e 1). The p o l y m e r b a l l s had a mean p e a k - t o - v a l l e y r o u g h n e s s o f R 0.6 - 1.0 μπι and a c . l . a . r o u g h n e s s o f R « 0.2-0.3 ζ a μιη. 0
T y p i c a l p l o t s of the v a r i a t i o n of contact diameter and d i s p l a c e m e n t i n c o m p r e s s i o n f o r i n c r e a s i n g and de c r e a s i n g l o a d s f o r one o f t h e p o l y m e r s i n v e s t i g a t e d a r e shown i n F i g u r e 6 t o g e t h e r w i t h t h e o r e t i c a l c u r v e s c a l c u l a t e d w i t h t h e w e l l known H e r t z i a n f o r m u l a s : ι
a
3
=
R
1
1 /3
/3
73 F
4 Ε
1
16
Ε
12
R
N
2
1
where Ε V
1
R:
0
f
:
Poisson s
Ball
1
1
V
" 2
1
ratio;
E.
0
: Elastic
modulus;
radius
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1. C Z I C H O S
1
Contact Deformation and Static Friction of Polymers
Tn bo me ter Test system
Driving device
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Force transducer] Loading device J
Divider
>
3 Channel Recorder
iDiscriminatorl Signât
Figure
Figure
3.
4.
Block
feedback
diagram
Microstructure
of the
tribometer.
of polyoxymethylene.
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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P O L Y M E R W E A R A N D ITS C O N T R O L
Figure
5.
M i c r o s t r u c t u r e of polyamide
F i g u r e 6. Contact diameter displacement curves.
and
contact
66.
deformation
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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1. C Z I C H O S
Contact Deformation and Static Friction of Polymers
9
In a d d i t i o n t o t h e continuous l o a d i n g and u n l o a d i n g p r o c e d u r e , a s t e p w i s e mode o f l o a d i n g was a l s o a p p l i e d . I n F i g u r e 7, c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t s f o r b o t h c o n t i n u o u s a n d s t e p w i s e l o a d i n g a r e drawn f o r one o f t h e polymers i n v e s t i g a t e d . The p l o t s o f F i g u r e 6 a n d t h e c o r r e s p o n d i n g graphs f o r t h e o t h e r polymers s t u d i e d i n d i c a t e a r e s i d u a l d e f o r m a t i o n b e h a v i o u r w h i c h may be d i s cussed i n connection with t h ee l a s t o p l a s t i c hardness o f the m a t e r i a l s . I n a d d i t i o n i t i s obvious t h a t large d i f f e r e n c e s between e x p e r i m e n t a l c o n t a c t d e f o r m a t i o n d a t a and t h e o r e t i c a l v a l u e s c a l c u l a t e d o n t h e b a s i s o f t h e c l a s s i c a l H e r t z i a n t h e o r y e x i s t so t h a t b e s i d e s t h e p r o p e r t i e s and o p e r a t i n g v a r i a b l e s o f t h e H e r t z i a n t h e o r y some o t h e r i n f l u e n c i n g f a c t o r s must be c o n s i d e r e d . G e n e r a l l y s p e a k i n g , t h e f o l l o w i n g m a i n phenomena may i n f l u e n c e t h e c o n t a c t d e f o r m a t i o n b e h a v i o u r o f p o l y mers : 1.
Elastic
deformation
processes
2.
Viscoelastic
deformation
processes
3.
Viscoplastic
deformation
processes
4.
Strain hardening/softening effects
5.
Interfacial
adhesion
F i r s t , thep o s s i b l e influence o f i n t e r f a c i a l adhesion was s t u d i e d b y p e r f o r m i n g l o a d i n g - u n l o a d i n g t e s t s w i t h u n l u b r i c a t e d and l u b r i c a t e d specimens. I f i n t e r f a c i a l adh e s i o n e x e r t s a dominant i n f l u e n c e on c o n t a c t deformat i o n b e h a v i o u r , t h i s i n f l u e n c e s h o u l d be s i g n i f i c a n t l y reduced by a l u b r i c a n t . ( F o r example, J o h n s o n , K e n d a l l and R o b e r t s (2) f o u n d t h a t i f t h e c o n t a c t o f r u b b e r s p h e r e s was immersed i n a s o l u t i o n o f s o d i u m d o d e c y l s u l f a t e , t h e i n f l u e n c e o f i n t e r f a c i a l adhesion vanishes and t h e r e s u l t s o f c o n t a c t r a d i u s measurements a g r e e d e x a c t l y with the Hertz t h e o r y ) . From t h e r e s u l t s shown i n F i g u r e 8 i t c a n be s e e n t h a t t h e c o n t a c t d e f o r m a t i o n b e h a v i o u r i s n o t s i g n i f i c a n t l y changed through a l u b r i c a n t f o r the experimental c o n d i t i o n s o f t h i s i n v e s t i g a t i o n . A l t h o u g h no c o m p a r a t i v e c o n t a c t d i a m e t e r measurements were performed, (because t h e l u b r i c a n t p e r m i t t e d a c l e a r m i c r o s c o p i c d i s t i n c t i o n o f t h e c o n t a c t boundary) from t h e r e s u l t s o f F i g u r e 8, i t i s o b v i o u s t h a t i n t e r f a c i a l a d h e s i o n a p p e a r s n o t t o be a d o m i n a n t i n f l u e n c i n g f a c t o r f o r t h e c o n t a c t deformation displacement o f t h e polymers studied. 1
A Model f o r t h e c o n t a c t Deformation
o f polymers
In o r d e r t o e x p l a i n t h e e x p e r i m e n t a l l y observed c o n t a c t d e f o r m a t i o n b e h a v i o u r a s shown i n F i g u r e 6, a s i m p l e r h e o l o g i c a l model w h i c h c o m b i n e s e l a s t i c , v i s c o e l a s t i c
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS
CONTROL
Polypropylene stepwise loading Omin duration at every load step)
140pm 120-
100-
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80-60 QJ Ε eu
continuous loading (0.6 N/s)
-1.40 Hertzian theory
0
2
4
6
)
10 Load F
12
14
16
18 Ν 20
N
F i g u r e 7. D i s p l a c e m e n t stepwise loading.
curves
f o r c o n t i n u o u s and
lubricated minerol oil. SAE10.q= 52 mPos (23*0 PTFE
Load F M
F i g u r e 8. D i s p l a c e m e n t c u r v e s f o r u n l u b r i c a t e d a n d l u b r i c a t e d polymer-glass contacts.
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1. C Z I C H O S
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Contact Deformation and Static Friction of Polymers
and v i s c o p l a s t i c i n f l u e n c e s i s c o n s i d e r e d , s e e e . g . (16, 1 7 ) , F i g u r e 9. A s i l l u s t r a t e d i n t h e u p p e r p a r t o f F i g u r e 9, w i t h t h e h e l p o f a f o u r - p a r a m e t e r o r B u r g e r model t h e d e f o r m a t i o n b e h a v i o u r o f p o l y m e r s may be a p p r o x i m a t e d t h r o u g h a c o m b i n a t i o n o f s p r i n g s a n d dampers. The s p r i n g E c h a r a c t e r i z e s t h e pure e l a s t i c s t a t e o f t h e polymer. I n a d d i t i o n , a t i m e - d e p e n d e n t v i s c o e l a s t i c component d e s c r i b e d by t h e s o - c a l l e d V o i g t - K e l v i n c o n f i g u r a t i o n , i . e . t h e c o m b i n a t i o n o f s p r i n g Ε a n d damper Yf comes into action. F u r t h e r , a v i s c o p l l s t i c f l o w component may e x i s t , m o d e l l e d b y t h e damper o f v i s c o s i t y ^ · Q
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0
C o n s i d e r now a p o l y m e r u n d e r t h e i n s t a n t a n e o u s a c t i o n o f a c o n s t a n t u n i a x i a l s t r e s s 6* . A s s u m i n g t h a t t h e d e f o r m a t i o n b e h a v i o u r may be d e s c r i b e d b y t h e m o d e l shown i n F i g u r e 9, we may h y p o t h e s i z e t h a t t h e r e s u l t i n g deformation £ , . i s t h e sum o f total Ί
(i)
elastic
deformation Ε
Ί
el (ii)
viscoplastic
(iii) v i s c o e l a s t i c
(Ε : e l a s t i c ο
modulus)
deformation
(y :
deformation £
( E : r e l a x e d modulus)
Q
"viscosity")
r
T h e s e d e f o r m a t i o n components a n d t h e i r sum a r e p l o t t e d s c h e m a t i c a l l y i n F i g u r e 9. I f t h e a s y m p t o t e f o r t h e r e sulting £ . . - c u r v e i s c o n s t r u c t e d , t h e r e l a x e d modulus E may be d e t e r m i n e d f r o m t h e i n t e r s e c t i o n o f t h i s asymp tote with the £ -axis. I n a d d i t i o n , t h e r e l a x a t i o n time T * c a n be e s t i m a t e d a s i l l u s t r a t e d i n F i g u r e 9 Although t h e d e f o r m a t i o n m o d e l shown i n F i g u r e 9 i s e x t r e m e l y s i m p l i f i e d a n d n e g l e c t s some i m p o r t a n t f a c t o r s ( e . g . t h e f a c t , t h a t i n s t e a d o f a s i n g l e r e l a x a t i o n time a compli c a t e d r e l a x a t i o n s p e c t r u m may be v a l i d ) , t h e m o d e l may serve as a b a s i s f o r t h e d i s c u s s i o n o f t h e contact de formation behaviour o f polymers. r
Discussion o f theExperimentally observed Deformation Behaviour
Contact
In o r d e r t o study t h e i n f l u e n c e o f v i s c o e l a s t i c i t y on t h e experimentally observed contact deformation behaviour, i n a n a l o g y t o t h e model i l l u s t r a t e d i n F i g u r e 9 t h e d i s p l a c e ments u n d e r g i v e n l o a d a s f u n c t i o n o f t i m e were d e t e r mined. A t y p i c a l r e s u l t f o r one o f t h e p o l y m e r s i n v e s t i g a t e d i s shown i n F i g u r e 10. T h e s e d i a g r a m s were d e t e r mined f o r a l l f o u r polymers and t h e r e l a x e d m o d u l i Ε o f t h e p o l y m e r s a n d t h e i r n o m i n a l r e l a x a t i o n t i m e s T were e s t i m a t e d i n a s i m i l a r manner a s i l l u s t r a t e d i n F i g u r e 9. The r e s u l t s c o m p i l e d i n T a b l e I i n d i c a t e t h a t b o t h r e l a x e d moduli and r e l a x a t i o n times v a r y c o n s i d e r a b l y w i t h i n the range o f t h e a p p l i e d e x p e r i m e n t a l c o n d i t i o n s . -
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS C O N T R O L
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''total = (Έ '-ο
Ίο
• t (1 - e - τ ) ) σ f
0
L
f
t - τ - β - ' -0.368
F i g u r e 9. F o u r - p a r a m e t e r o r B u r g e r model f o r t h e deformation behaviour o f polymers.
Polypropylene
°0
1
2
3 4 time t
F i g u r e 10. V a r i a t i o n o f c o n t a c t ment a s f u n c t i o n o f t i m e .
5 •
6
7 3 8 1Q
S
deformation displace
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1. C Z I C H O S
Contact Deformation and Static Friction of Polymers
13
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In a d d i t i o n t o t h e s t u d y o f v i s c o e l a s t i c i t y a n d t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f r e l a x e d moduli and r e l a x a t i o n time, p o s s i b l e i r r e v e r s i b l e v i s c o p l a s t i c contact d e f o r m a t i o n e f f e c t s were a l s o s t u d i e d . A f t e r a c e r t a i n l o a d i n g t i m e , t h e l o a d was t o t a l l y r e l e a s e d a n d t h e r e c o v e r y o f t h e p o l y m e r s was m e a s u r e d . The r e s u l t s o f F i g u r e 11 show no v i s c o p l a s t i c e f f e c t s f o r b o t h PA66 a n d POM, a m i n o r i n f l u e n c e f o r PP b u t a c l e a r e f f e c t o f v i s c o p l a s t i c i t y f o r P T F E . (Note t h a t t h e r e c o v e r y c u r v e s o f F i g u r e 11 a r e g o v e r n e d b y much h i g h e r r e l a x a t i o n t i m e s than t h o s e determined under an a p p l i e d l o a d and l i s t e d i n T a b l e I . T h i s a g a i n i n d i c a t e s t h e dependence o f r e l a x a t i o n times o r r e l a x a t i o n s p e c t r a on o p e r a t i n g c o n d i tions) . The r e s u l t s o f F i g u r e 11 i n d i c a t e t h a t t h e p o l y m e r s s t u d i e d were s u b j e c t t o d i f f e r e n t m i c r o s t r u c t u r a l d e f o r m a t i o n mechanisms. I n t h i s c o n n e c t i o n i t must be b o r n e i n m i n d t h a t t h e maximum n o m i n a l d e f o r m a t i o n o f POM a n d PA66 was o n l y 1% w h e r e a s PP a n d PTFE were d e f o r m e d up t o 1.8% a n d 3.3% r e s p e c t i v e l y . T h e r e f o r e i t may be assumed t h a t f o r POM a n d PA66 o n l y a n i n s t a n t a n e o u s l y r e v e r s i b l e d e f o r m a t i o n o f t h e amorphous m a t r i x o f t h e s p h e r u l i t i c m i c r o s t r u c t u r e o c c u r r e d (18) w h e r e a s f o r PP a n d PTFE some i r r e v e r s i b l e effects, l i k e interlamellar shearing or r e o r i e n t a t i o n o f t h e l a m e l l a e may have t a k e n p l a c e . With the determination o f v i s c o p l a s t i c displacements f r o m F i g u r e 11 a n d t h e d a t a o f v i s c o e l a s t i c i t y c o m p i l e d i n T a b l e I we a r e now i n a p o s i t i o n t o d e r i v e o n t h e b a s i s o f t h e m o d e l i l l u s t r a t e d i n F i g u r e 9, a s i m p l e c o n t a c t d e f o r m a t i o n f o r m u l a i f we assume t h a t i n t e r f a c i a l a d h e s i o n ( s e e F i g u r e 8) i s n e g l i g i b l e . As c o m p i l e d i n F i g u r e 12, i t i s assumed t h a t t h e t o t a l c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t i s t h e sum o f a n e l a s t i c , a v i s c o e l a s t i c and a v i s c o p l a s t i c d e f o r m a t i o n component. Forthe f i r s t component t h e H e r t z i a n t h e o r y i s assumed t o be v a l i d a n d f o r t h e s e c o n d component i n a n a l o g y t o t h e model d e s c r i b e d i n F i g u r e 9, t h e e l a s t i c modulus Ε i s r e p l a c e d b y a t e r m w h i c h i n c l u d e s t h e r e l a x e d modulus Ε a n d t h e r e l a x a t i o n timeT". I f t h e v i s c o p l a s t i c component c a n be n e g l e c t e d , t h e c o n t a c t d e f o r m a t i o n f o r m u l a , g i v e n i n F i g u r e 12, r e sults. I t must be p o i n t e d o u t t h a t t h e f o r m u l a g i v e n i n F i g u r e 12 i s e x t r e m e l y s i m p l i f i e d b e c a u s e i t h a s b e e n d e r i v e d i n a n a l o g y t o t h e model i l l u s t r a t e d i n F i g u r e 9 u n d e r t h e a s s u m p t i o n s o f a l i n e a r s u p e r p o s i t i o n o f d e f o r m a t i o n com ponents and t h e a c t i o n o f an i n s t a n t a n e o u s c o n s t a n t l o a d . B e c a u s e o f d i f f e r e n c e s between t h e s e i d e a l i z e d assumptions and t h e a c t u a l e x p e r i m e n t a l c o n d i t i o n s ( e . g . c o n t i n u o u s loading instead o f instantaneous loading) t h e formula s h o u l d be c o n s i d e r e d o n l y a s a f i r s t r o u g h a p p r o x i m a t i o n .
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS C O N T R O L
Table
I.
Polymer
M a t e r i a l parameters o f polymers
Elastic modulus E [N/mm ] 2
Q
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POM
3200
PA 66
3000
PP
1600
PTFE
600
Relaxed modulus E Elastic modulus E_
Load F [N] N
r
Relaxation time r[s]
0
2 8 20
0.56 0.58 0.61
25-9
2 8 20
0.54 0.60 0.65
18^6
2 8 20
0.13 0.22 0.49
27
2 8 20
0.21 0.41 0.57
52tl5
ts
Load : F= 20 Ν Loading time: 1 min N
PTFE
0
3
6
9 12 15 18 Time after deloading t
F i g u r e 11. R e c o v e r y c u r v e s a f t e r of polymers.
21
24
27 min 30
contact deformation
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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1. C Z I C H O S
Contact Deformation and Static Friction of Polymers
15
The s i m p l i f i e d f o r m u l a g i v e n i n F i g u r e 12 i s valid o n l y f o r t h e l o a d i n g mode o f c o n t a c t d e f o r m a t i o n . F o r t h e u n l o a d i n g mode ( i . e . F d e c r e a s i n g ) f u r t h e r a s p e c t s must be c o n s i d e r e d . I f a f t e r a c e r t a i n l o a d i n g time t * the load i s l o w e r e d , t h e e l a s t i c component 6 , i n s t a n t a n e o u s l y drops t o t h e displacement c o n n e c t l a w i t h the lower l o a d o r s t r e s s l e v e l . F o rthe v i s c o e l a s t i c component, however, t h e w h o l e l o a d i n g - u n l o a d i n g h i s t o r y must be t a k e n i n t o c o n s i d e r a t i o n : On t h e one h a n d , t h e v i s c o e l a s t i c component S reduces t o the corresponding l o w e r l o a d o r s t r e s s l e v e ï i n a d e l a y e d manner d e p e n d i n g on t h e r e l a x a t i o n t i m e . On t h e o t h e r h a n d , a t t h e l o w e r l o a d o r s t r e s s l e v e l t h e v i s c o e l a s t i c component i n c r e a s e s a g a i n because o f i t s dependence on t i m e . In addition, a p o s s i b l y r e m a i n i n g i r r e v e r s i b l e v i s c o p l a s t i c component must a l s o be p a i d r e g a r d . Summing up a l l t h e s e components, a contact deformation formula f o r t h e unloading mode r e s u l t s w h i c h i s a l s o g i v e n i n F i g u r e 12. ( I t s h o u l d be m e n t i o n e d t h a t f o r t h e sake o f s i m p l i c i t y t h e same r e l a x a t i o n t i m e T * i s assumed t o be v a l i d f o r b o t h t h e l o a d i n g a n d u n l o a d i n g mode. T h e o r e t i c a l l y , i t s h o u l d be d i s t i n g u i s h e d between a " r e t a r d a t i o n t i m e " f o r t h e l o a d i n g mode a n d a " r e l a x a t i o n t i m e " f o r t h e u n l o a d i n g mode.) I n F i g u r e s 13 t o 16 t h e e x p e r i m e n t a l l y d e t e r m i n e d contact deformation displacement values together with curves c a l c u l a t e d with t h e deformation formulas o f F i g u r e 12 a n d t h e H e r t z i a n f o r m u l a a r e p l o t t e d . In the d i s p l a c e m e n t - l o a d g r a p h s f o r POM a n d PA66 o n l y e l a s t i c a n d v i s c o e l a s t i c components were t a k e n i n t o c o n s i d e r a t i o n w h e r e a s f o r PP a n d PTFE a l s o v i s c o p l a s t i c components ( s e e F i g u r e 11) were i n c l u d e d . I t c a n be s e e n t h a t a r e a s o n a b l y good c o r r e l a t i o n b e t w e e n e x p e r i m e n t a l d a t a a n d t h e o r e t i c a l l y d e t e r m i n e d c u r v e s r e s u l t s , so t h a t t h e f o r m u l a s c o m p i l e d i n F i g u r e 12 may be u s e d f o r t h e a p p r o x i m a t i v e estimation o f t h econtact deformation behaviour o f curved thermoplastic polymeric materials. STATIC
FRICTION
In a d d i t i o n t o t h e i n v e s t i g a t i o n s on c o n t a c t d e f o r m a t i o n , the i n i t i a l stage o f f r i c t i o n has been s t u d i e d (19). Whereas i n r e c e n t y e a r s s e v e r a l i n v e s t i g a t i o n s have b e e n p e r f o r m e d o n p o l y m e r / m e t a l s l i d i n g p a i r s (a c o m p r e h e n s i v e r e v i e w was p u b l i s h e d r e c e n t l y b y B r i s c o e (20) r e l a t i v e l y l i t t l e work h a s b e e n done t o s t u d y t h e t r i b o l o g i c a l b e h a v i o u r o f polymers s l i d i n g a g a i n s t polymers. In the f r i c t i o n investigations a pin-on-disc configuration with t h e f o l l o w i n g p o l y m e r s was u s e d ; t h e p o l y m e r p i n s were c u t w i t h a m i c r o t o m e i n o r d e r t o o b t a i n a f l a t smooth polymer s u r f a c e a t t h e b e g i n n i n g o f t h e t e s t s :
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS C O N T R O L
Contact deformation = f (elasticity, viscoelasticity, viscoplasticity) s
total
=
— g - ^
(1
δ
Γ
ο
)
r
where E : Relaxed modulus
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r
τ
: Relaxation time
If & = 0 , for a ballon-plate contact it follows 9 n r9d-e«/r)=l u
5
t
o
t
a
l
Γ
"
M
[l6 E i ' Rj
F
N
+
L l 6 E
;
r
R j
FN ''' 2
Unloading mode (t > t* ; t*: Loading time) : total N Nmax'
ft
(F
t#)=6
(F
)
(F
Nmax, *
t)+5 (F V
+
t
-(t-t»)
)
f r ^Nmax/**
"*r
( Ρ
Ν/*> - * v
^Nmax^J
e
T
F i g u r e 12. S i m p l i f i e d f o r m u l a s f o r t h e c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t s o f polymer b a l l s .
Experimental data:
*« : load increasing ο : load decreasing
Load F
N
F i g u r e 13. E x p e r i m e n t a l l y d e t e r m i n e d c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t a n d c a l c u l a t e d c u r v e s f o r POM.
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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CZICHOS
Contact Deformation and Static Friction of Polymers
Load F
•
N
F i g u r e 14. E x p e r i m e n t a l l y d e t e r m i n e d c o n t a c t d é f o r m a t i o n d i s p l a c e m e n t a n d c a l c u l a t e d c u r v e s f o r PA66.
0
2
4
6
8 10 Load F N
12
14
16
18 Ν 20
· -
F i g u r e 15. E x p e r i m e n t a l l y d e t e r m i n e d c o n t a c t d é f o r m a t i o n d i s p l a c e m e n t a n d c a l c u l a t e d c u r v e s f o r PP.
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS
18 Pin
Polyoxymethylene
materials:
(POM)
P o l y a m i d e 66
(PA66)
Polypropylene
(PP)
Polytetrafluoroethylene Disc
Acrylonitrile-styrene
materials:
Polystyrene
(PTFE) (ANS)
(PS)
Polymethyl methacrylate
(PMMA)
The s u r f a c e r o u g h n e s s d a t a o f t h e p o l y m e r p i n s were R c= 0.3 ο ο
^
0.2 0,1 50
100
150 200 250 Sliding distance s
300 •
350
400 pm 450
F i g u r e 17. F r i c t i o n o f p o l y m e r / p o l y m e r p a i r s POM, PA66, PP a g a i n s t A N S ) .
(PTFE,
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
P O L Y M E R W E A R A N D ITS C O N T R O L p-0108-η F=10N;V = 2.410"Vs;S = 4 5 0 p m T = 2 3 ° C ^ = 5 0 % r e l . h u m i d i t y N
0.7-
x
;
a
Φ2
Disc: PS
Pin :PTFE POM PA66 PP
0.6-
1 0.5-
1 0.40.3-
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S
a ο "o
Κ
£0,20.10
50
100
150 200 Sliding distance s
250
^
300
350
F i g u r e 18. F r i c t i o n o f p o l y m e r / p o l y m e r POM, PA66, PP a g a i n s t P S ) .
400
pairs
p
m
450
(PTFE,
ρ—ΦΊΡ8—-j
F=10N;V = 2.41u^Ws;S = 450pm î 23°C ip=507oreLhumidity
J^P 0.7-
N
x
:
aS
:
Φ2
Disc: PMMA
Pin:PÏFE POM PA66 PP
0.6-
|o.5^0,4ο
10.3"ο
0.1i
0
V 50
100
150 200 250 Sliding distance s
300 ^
F i g u r e 19. F r i c t i o n o f p o l y m e r / p o l y m e r POM, PA66, PP a g a i n s t PMMA).
350
400
pairs
p
m
450
(PTFE,
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1. C Z I C H O S
Contact Deformation and Static Friction of Polymers
21
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adhesion computed b y E r h a r d (21) a n d t h e e x p e r i m e n t a l l y d e t e r m i n e d f r i c t i o n a l work, Ε . The f r i c t i o n a l work, Ε , was d e t e r m i n e d b y i n t e g r a t i n g t h e m e a s u r e d f r i c t i o n a l f o r c e s p l o t t e d i n F i g u r e s 17 t o 19 o v e r t h e s l i d i n g d i s t a n c e . The r e s u l t s a r e t h a t t h e d a t a f o r PTFE s l i d i n g a g a i n s t t h e t h r e e d i s c m a t e r i a l s a r e l o w e s t and t h e d a t a f o r t h e PA66 p i n s , s l i d i n g a g a i n s t t h e t h r e e disc materials aregenerally highest. I n F i g u r e 20 t h e e x p e r i m e n t a l l y d e t e r m i n e d f r i c t i o n a l work i s p l o t t e d a s a f u n c t i o n o f t h e c a l c u l a t e d work o f a d h e s i o n . On a l o g a r i t h m i c s c a l e t h e f r i c t i o n a l work i n c r e a s e s w i t h t h e work o f a d h e s i o n a n d t h e e x p e r i m e n t a l d a t a seem t o be i n a r e a s o n a b l y good c o r r e l a t i o n w i t h t h e t h e o r e t i c a l l y calculated values. (An e x c e p t i o n p e r h a p s may be t h e c o m b i n a t i o n o f PP s l i d i n g a g a i n s t P S ) . I t a p p e a r s that f o r t h e f l a t - t o - f l a t conformai contact o f the p o l ymer c o m b i n a t i o n s s t u d i e d , t h e a d h e s i o n component a t t h e i n t e r f a c e may be t h e d o m i n a n t f a c t o r g o v e r n i n g t h e i n i t i a l f r i c t i o n a l behaviour o f polymer-polymer s l i d i n g p a i r s . In c o n t r a s t , i n t h e c a s e o f t h e c o n t a c t d e f o r m a t i o n d i s placement o f b a l l - t o - f l a t c o u n t e r f o r m a l c o n t a c t s d i s c u s s e d above no e f f e c t o f a d h e s i o n was f o u n d a s compared w i t h t h e i n f l u e n c e o f t h e (bulk) v i s c o e l a s t i c p r o p e r t i e s o f t h e materials. ( T h i s may be due t o e l a s t i c r e l i e f f o r c e s w h i c h may b u r s t a d h e s i v e j u n c t i o n s d u r i n g t h e l o a d i n g unloading contact deformation cycles.) CONCLUSIONS From t h e i n v e s t i g a t i o n s o f ( i ) c o n t a c t d e f o r m a t i o n a n d ( i i ) i n i t i a l s t a t i c f r i c t i o n o f t h e r m o p l a s t i c polymers t h e f o l l o w i n g c o n c l u s i o n s may be drawn: a)
The c o n t a c t d e f o r m a t i o n b e h a v i o u r o f c o u n t e r f o r m a l polymer/glass contacts i s considerably influenced by t h e ( b u l k ) v i s c o e l a s t i c p r o p e r t i e s o f t h e p o l y m e r s .
b)
The c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t f o r t h e u n l o a d i n g mode i s c o n s i d e r a b l y h i g h e r t h a n f o r t h e l o a d i n g mode.
c) The c o n t a c t d e f o r m a t i o n d i s p l a c e m e n t i n l o a d i n g / u n l o a d i n g c y c l e s c a n be e s t i m a t e d w i t h a s i m p l i f i e d extended H e r t z i a n formula i n c l u d i n g r e l a x a t i o n c h a r a c t e r i s t i c s o f t h e polymers. d)
The s t a t i c f r i c t i o n a t t h e o n s e t o f m o t i o n o f c o n formal polymer/polymer s l i d i n g p a i r s i s i n f l u e n c e d mainly by i n t e r f a c i a l adhesion.
e) A c o r r e l a t i o n between e x p e r i m e n t a l l y m e a s u r e d f r i c t i o n a l work a n d t h e o r e t i c a l l y e s t i m a t e d work o f a d h e s i o n was f o u n d .
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
22
P O L Y M E R W E A R A N D ITS C O N T R O L
Table I I . Pin
Work o f f r i c t i o n Disc
Frictional work E I Ν mm] F
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PTFE
PP
POM
PA 66
and adhesion o f polymers Work of adhesion Δ γ =7
1
+7
2
-7
ANS
0.328
54.7
PS
0.343
55.4
PMMA
0.324
53.6
ANS
0.795
73.0
PS
1.215
75.3
PMMA
0.730
73.0
ANS
0.619
84.5
PS
0.760
81.0
PMMA
0.850
87.3
ANS
0.987
88.0
PS
0.864
83.1
PMMA
1.128
92.1
1
2
10 1
6
Nmm/mm ] 2
Nmml
F i g u r e 20. C o r r e l a t i o n work o f a d h e s i o n .
between f r i c t i o n a l
work a n d
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1.
CZICHOS
Contact Deformation and Static Friction of Polymers
23
Acknowledgments I t h a n k e n g i n e e r s Mr. N. K e l l i n g a n d Mr. J . S c h w e n z i e n o f B A M - L a b o r a t o r y "Wear P r o t e c t i o n , T r i b o m e t r y a n d T r i b o p h y s i c s " f o r having s k i l l f u l l y performed the ex p e r i m e n t s , a s w e l l a s D r . P. F e i n l e f o r h e l p f u l d i s c u s s i o n s a n d D i p l . - P h y s . H. T i s c h e r o f t h e BAM-Document a t i o n S e r v i c e on T r i b o l o g y f o r p r o v i d i n g background literature material. F i n a n c i a l s u p p o r t from t h e Deut s c h e F o r s c h u n g s g e m e i n s c h a f t (DFG) i s g r e a t f u l l y a c k n o w l edged.
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Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. J. 9. 10. 11. 12.
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Gladwell, G. M. L . "Contact Problems in the C l a s s i cal Theory of E l a s t i c i t y " , Sijthoff and Noordhoff, Alphen aan den Rijn, 1980. Johnson, K. L.; Kendall, K . ; Roberts, A. D. "Surface Energy and the Contact of Elastic Solids", Proc. R. Soc. London, Ser. A 324 (1971) 301. Barquins, M . ; Courtel, R. "Rubber F r i c t i o n and the Rheology of Viscoelastic Contact", Wear 32 (1975) 133. Barquins, M. "Adhesive Contact and Kinetics of Adherence between a Rigid Sphere and an Elastomeric Solid", Int. J. Adhesion and Adhesives 3 (1983) 71. Lee, Ε. H . ; Radok, J. R. M. "The Contact Problem for Viscoelastic Bodies", Trans. ASME (J. Appl. Mech.) 27 (1960) 438. Ting, T. C. T. "The Contact Stresses between a Rigid Indenter and a Viscoelastic Half-Space", Trans. ASME (J. Appl. Mech.) 33 (1966) 845. Comninou, M. "Contact between Viscoelastic Bodies", Trans. ASME (J. Appl. Mech.) 43 (1976) 630. Kravchuk, A. S. "On the Problem for Linearly and Nonlinearly Elastic Bodies of Finite Dimensions", Appl. Math. Mech. 41 (1977) 320. Chow, T. S. "Deformational Contact and F r i c t i o n on Viscoelastic Substrates", Wear 51 (1978) 355. Graham, G. A. C. "Viscoelastic Contact Problems with Friction", Int. J. Eng. S c i . 18 (1980) 191. Sabin, G. C. W.; Graham, G. A. C. "The Normal Aging Viscoelastic Contact Problem", Int. J. Eng. S c i . 18 (1980) 751. Aksel, N . ; Buggisch, H. "On the Problem of Contact between a Rigid Ball and a Viscoelastic Half-Space" (in German), Z. Angew. Math, u. Mech. (ZAMM) 62 (1982) 101. Johnson, K. L . "Adhesion at the Contact of Solids", i n : "Theoretical and Applied Mechanics"; Koiter, W. T., E d . ; North Holland, Amsterdam, 1977; 133. Mittmann, H . - U . ; Czaika, N . ; Czichos, H. "A New De vice for Simultaneous Measurement of F r i c t i o n Force, Normal Force and F r i c t i o n Coefficient", Wear 31 (1975) 179. Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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15.
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17. 18. 19. 20. 21.
Czichos, H . ; Feinle, P. "Tribological Behaviour of Thermoplastic, F i l l e d , and Glass-Fibre- Reinforced Polymers - Contact Deformation, F r i c t i o n and Wear, Surface Investigations", BAM Research Report 83, July 1982, 105 p. (Bundesanstalt fur Materialprüfung, Berlin-Dahlem) (in German). Becker, G. W., Schreuer, E . "Deformation Mechanics and Relaxation Behaviour", i n : "Structure and Physi c a l Behaviour of Polymers" (in German); Nitsche, R. and Wolf, Κ. Α . , Eds.; Springer, Berlin/Göttingen/Heidelberg, 1962; 331 f f . Ehrenstein, G. W. "Polymeric Materials" (in German); Hanser, München, 1978; 104 f f . Höhn, W.; Jungnickel, B.-J. "Structure and Relaxation Behaviour of Compressed Polyoxymethylene" (in German), Colloid and Polym. S c i . 260 (1982) 1093. Czichos, H. "Influence of Adhesive and Abrasive Mechanisms on the Tribological Behaviour of Thermoplastic Polymers", Wear 88 (1983) 27. Briscoe, B . J . "Wear of Polymers: An Essay on Fundamental Aspects", Tribology Int. 14 (1981) 231. Erhard, G. "Sliding F r i c t i o n of Polymer-Polymer Pairs" (in German), Jahrbuch VDI-Ges. Werkstofftechnik (Düsseldorf), 1981; 7.
DISCUSSION Q u e s t i o n b y P r o f e s s o r S. B a h a d u r , Iowa S t a t e U n i v e r s i t y : The v i s c o e l a s t i c e f f e c t i n d e f o r m a t i o n r e p o r t e d b y y o u i s s i m i l a r t o what h a s b e e n known f o r a l o n g t i m e i n wood. As s u c h t h e d e f o r m a t i o n v a l u e s i n l o a d i n g a n d unloading are d i f f e r e n t . Have y o u g i v e n a n y c o n s i d e r a t i o n how t h e s e r e s u l t s c o u l d be f a c t o r e d i n t o t h e a d h e s i o n t h e o r y o f f r i c t i o n w h i c h h a s a s o n e o f i t s components the r e a l area o f contact? Answer: T h e a i m o f t h e d e f o r m a t i o n e x p e r i m e n t s was t o study t h e i n f l u e n c e s o f p o s s i b l e v i s c o e l a s t i c and v i s c o p l a s t i c e f f e c t s on the H e r t z i a n c o n t a c t behaviour o f curved thermoplastic polymers. Because these experiments were p e r f o r m e d o n l y w i t h n o r m a l l o a d s we have n o t a t tempted t o e x t e n d t h e s e r e s u l t s t o s l i d i n g H e r t z i a n contacts. I n c o n t r a s t , t h e s t a t i c f r i c t i o n experiments r e p o r t e d i n t h i s p a p e r were p e r f o r m e d w i t h f l a t p o l y m e r polymer c o n t a c t s ( p i n - o n - d i s c c o n f i g u r a t i o n ) i n o r d e r t o keep i n these experiments t h e m e c h a n i c a l s t r e s s s i t u a t i o n as simple as p o s s i b l e . Question b y P r o f e s s o r D. Dowson, U n i v e r s i t y o f L e e d s : How was t h e l u b r i c a n t a p p l i e d i n t h e d e f o r m a t i o n studies? D i d t h e author observe any l u b r i c a n t entrapment w i t h i n t h e H e r t z i a n c o n t a c t zone i n t h e n o r m a l a p p r o a c h p r o c e s s ? Many a u t h o r s have r e p o r t e d t r a p p e d p o o l s o f l u b r i c a n t i n
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
1.
CZICHOS
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t h e c e n t r e o f H e r t z i a n c o n t a c t s when e l a s t i c s p h e r e s a r e loaded against f l a t surfaces i n t h epresence o f l i q u i d s .
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Answer: The l u b r i c a n t was a p p l i e d a s a t h i n b o u n d a r y film to thedisc surface. An e n t r a p m e n t o f l u b r i c a n t was n o t v i s i b l e i n o u r i n - s i t u m i c r o s c o p i c o b s e r v a t i o n s of t h e c o n t a c t zone. Question by Dr. B r i s c o e , I m p e r i a l C o l l e g e , London: I f e e l t h a t s u r f a c e f r e e e n e r g y i s n o t a good p a r a m e t e r to c o r r e l a t e w i t h s u r f a c e f r i c t i o n . Surface f r e e energy may be r e l a t e d t o c o h e s i v e e n e r g y d e n s i t y . There i s t o o much d a t a w h i c h c o n t r a d i c t s t h i s , e . g . (1) s t a t i c / d y n a m i c f r i c t i o n , (2) s p i n e f f e c t s , (3) t e m p e r a t u r e a n d v e l o c i t y dependence o f f r i c t i o n . Answer: I n c o n s i d e r i n g t h e r e s u l t s o f t h e f r i c t i o n ex p e r i m e n t s i t must be b o r n e i n m i n d t h a t o n l y t h e i n i t i a l s t a t i c f r i c t i o n , with a s l i d i n g d i s t a n c e o f l e s s than 500 μπι a n d n e g l i g i b l e i n f l u e n c e s o f v e l o c i t y a n d tempe r a t u r e was s t u d i e d . Because the m i c r o s c o p i c i n - s i t u ob servations o f thecontact interface revealed that the i n i t i a l s l i d i n g motion occured a t t h e a c t u a l i n t e r f a c e (without i n d i c a t i o n o f deformation o r m a t e r i a l t r a n s f e r effects) i t i s hypothesized that i n i t i a l s t a t i c f r i c t i o n i s t h e r e s i s t a n c e t o overcome i n t e r f a c i a l adhesion as c h a r a c t e r i z e d by t h e Dupré e q u a t i o n . Question b y Dr. R.C. C a v e s t r i , C o p e l a n d C o r p o r a t i o n , Sidney, Ohio: Have y o u c o n s i d e r e d t h e e f f e c t o f t h e d e n s i t y o f the polymers and p o s s i b l e c o r r e l a t i o n w i t h the s c a t t e r o f p i n - o n - d i s c data? Answer: The q u e s t i o n o f t h e i n f l u e n c e s o f p o l y m e r d e n s i t i e s was n o t c o n s i d e r e d i n t h i s p a p e r b u t i n a n o t h e r r e s e a r c h r e p o r t (see r e f . (15) ) . Q u e s t i o n b y Dr. D.H. B u c k l e y , NASA L e w i s R e s e a r c h C e n t e r , Cleveland: Don't t h e m o i s t u r e (50% r e l . h u m i d i t y ) o f y o u r e x p e r i m e n t a l e n v i r o n m e n t a l t e r t h e work o f a d h e s i o n and s h o u l d y o u e x p e c t t h e r e f o r e a c o r r e l a t i o n b e t w e e n f r i c t i o n a n d work o f a d h e s i o n ? Answer: The i n f l u e n c e o f m o i s t u r e a d s o r b e d b y t h e p o l y m e r s may i n d e e d have a n i n f l u e n c e o n t h e work o f adhesion. However, i n t h i s s t u d y o n l y t h e r a n k i n g o f data and n o t t h e i r a b s o l u t e v a l u e s i s c o n s i d e r e d . I t i s p o s s i b l e t h a t t h e e f f e c t o f m o i s t u r e i s one p o s s i b l e reason f o r theexperimentally observed s c a t t e r o f data. Question b y Dr. Y o u t i Kuo, X e r o x Company: What i s t h e r o l e o f shear i n your experiments and a n a l y s i s ? Answer: B e c a u s e t h e d e f o r m a t i o n e x p e r i m e n t s where p e r formed o n l y w i t h normal l o a d s and the c o n t a c t d e f o r m a t i o n
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.
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d i s p l a c e m e n t p e r p e n d i c u l a r t o t h e c o n t a c t i n t e r f a c e was e x p e r i m e n t a l l y m e a s u r e d , t h e r o l e o f s h e a r was n o t s t u d ied e x p l i c i t e l y .
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R E C E I V E D January 23, 1985
Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.