A Fatigue-Abrasive Wear Mechanism for Polymeric Surfaces - ACS

5 A Fatigue-Abrasive Wear Mechanism for Polymeric Surfaces T. S. Chow

Downloaded by FUDAN UNIV on April 3, 2017 | http://pubs.acs.org Publication Date: September 12, 1985 | doi: 10.1021/bk-1985-0287.ch005

Webster Research Center, Xerox Corporation, Webster, NY 14580

A model based on a fatigue-abrasive wear mechanism has been developed for calculating the wear of polymeric surfaces due to its interaction with small particles and a foam roller. The wear is related to the contact deformation and fatigue resistance which are determined and expressed in terms of material, geometrical and process parameters. The material parameters are the modulus, yield strength and hardness of particles and polymers, the frictional coefficient, the foam modulus and the fatigue behavior of polymers. The geometrical and process parameters are the normal load, particle size, foam roll radius, surface velocity of foam roller and surface coverage of particles. The analysis and calculation reveal the weak dependence of the foam modulus on wear which benefits the investigation of the direct interaction between the small particles and polymeric surface and the understanding of its wear mechanism. A model i s p r e s e n t e d which d e s c r i b e s t h e wear o f p o l y m e r i c s u r f a c e s i n c o n t a c t w i t h s m a l l p a r t i c l e s and a foam r o l l . Wear i s d e f i n e d as t h e p r o g r e s s i v e l o s s o f m a t e r i a l from t h e s u r f a c e as a consequence o f r e l a t i v e m o t i o n . Two p r i m a r y wear mechanisms can be i d e n t i f i e d when p a r t i c l e s t r a v e l on a s u r f a c e w h i l e under compression o f a foam r o l l . These a r e a b r a s i v e wear which i s caused by t h e m i c r o - c u t t i n g and l o n g i t u d i n a l s c r a t c h i n g by p a r t i c l e s between t h e p o l y m e r i c s u r f a c e and foam and f a t i g u e wear r e s u l t i n g from the accumulated damage caused by c y c l i c s t r e s s i n g and d e f o r m a t i o n s i m i l a r t o t h e m e c h a n i c a l fatigue. Other mechanisms, such as a d h e s i v e wear and c o r r o s i v e wear, a r e c o n s i d e r e d t o be l e s s i m p o r t a n t i n t h i s problem and a r e n o t e x p l i c i t l y i n c l u d e d i n t h e a n a l y s i s . The wear i s r e l a t e d t o t h e c o n t a c t s t r e s s , d e f o r m a t i o n , s u r f a c e coverage o f p a r t i c l e and f a t i g u e r e s i s t a n c e , each o f which i s determined and e x p r e s s e d i n terms o f the m a t e r i a l , 0097-6156/ 85/ 0287-0067S06.00/ 0 © 1985 American Chemical Society

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

68

CONTROL

geometric and p r o c e s s parameters. The m a t e r i a l parameters i n c l u d e the compression modulus, h a r d n e s s , and f a t i g u e r e s i s t a n c e of the polymer; the compression modulus, y i e l d s t r e n g t h , and f r i c t i o n a l c o e f f i c i e n t f o r the p a r t i c l e ; and the compression modulus f o r the foam. The p r o c e s s parameters c o n s i d e r e d are the l o a d , p a r t i c l e s i z e , foam r o l l r a d i u s , v e l o c i t i e s of the foam r o l l e r and s u r f a c e and the number of c y c l e s . A n a l y s i s and c a l c u l a t i o n are c a r r i e d out t o i n v e s t i g a t e the f u n c t i o n a l b e h a v i o r of these v a r i a b l e s and s e r v e d as the b a s i s u n d e r s t a n d i n g the p h y s i c s of the i n t e r a c t i o n wear.


Theory When s m a l l p a r t i c l e s move on a p o l y m e r i c s u r f a c e w h i l e b e i n g compressed by a r o t a t i n g foam r o l l (see F i g u r e 1 ) , the s u r f a c e i s s u b j e c t e d t o c y c l i c s t r e s s e s . The accumulated damage of the s u r f a c e due t o a b r a s i o n by p a r t i c l e s i n i t i a t e s c r a c k s which propagate i n c r e m e n t a l l y and e v e n t u a l l y l e a d t o a f r a c t u r e of the s u r f a c e l a y e r . A l t h o u g h a g r e a t d e a l o f r e s e a r c h i s ongoing i n the a r e a of f r i c t i o n and wear ( 1-4), the wear problem i s much too complex t o t r e a t c o m p l e t e l y r i g o r o u s l y . The p r e s s u r e d i s t r i b u t i o n i n s i d e the c o n t a c t zone, the d i s t r i b u t i o n of p a r t i c l e s on the s u r f a c e and the p a r t i c l e s i z e d i s t r i b u t i o n are not c o n s i d e r e d . C o r r e s p o n d i n g mean v a l u e s are a p p l i e d . C o n t r i b u t i o n s from the m i c r o - c u t t i n g and s u r f a c e roughness t o the shear s t r e s s e s on the s u r f a c e are combined w i t h the frictional coefficient. A new parameter c a l l e d the e f f e c t i v e f r i c t i o n a l c o e f f i c i e n t ( μ ) i s defined. When the s t r a i n ( o r s t r e s s ) l e v e l i s i n s u f f i c i e n t t o generate c r a z e s , the f a t i g u e l i f e i s e v a l u a t e d as a f u n c t i o n of s t r a i n ( ε ) , r e s u l t i n g i n the c o n v e n t i o n a l S-N curve of the form (5) 3

2N = ( ε / ε ) , f o r ε > ε ο cr

(1)

9

where Ν i s the number of c y c l e s t o f a i l u r e , 3 i s the c o e f f i c i e n t of fatigue resistance, ε i s p r o p o r t i o n a l t o the f a i l u r e s t r a i n i n t e n s i l e t e s t s and ε i s the c r i t i c a l s t r a i n below which f a t i g u e does not o c c u r . Parameters ε , ε and 3 are determined from the S-N cr ο · curve. The f a t i g u e r e s i s t a n c e 3 i s an i n t r i n s i c p r o p e r t y w h i c h c h a r a c t e r i z e s the m a t e r i a l r e s i s t a n c e t o r e p e a t e d l o a d i n g , ε is a s t r o n g e r f u n c t i o n of m o l e c u l a r weight than i s 3 a t room tempera ture^). For polycarbonate^), we have 3 =3.6, ε =0.435 and c =0.0085. ° C o n t i n u i n g w i t h the concept of f a t i g u e - a b r a s i v e wear mechanism, the volume of m a t e r i a l removed from a s u r f a c e , V , by a p a r t i c l e i s j c J wear' d e f i n e d as cr

J

V

wear

= V, /N def

r

(2)

C

where ^ i s the deformed volume of s u r f a c e caused by t r a v e l i n g p a r t i c l e . E l i m i n a t i n g Ν from Eqs. (1) and ( 2 ) , the t h i c k n e s s of the s u r f a c e b e i n g worn away, A h, by p a r t i c l e s w i t h s u r f a c e coverage, Φ , is Δ h = 2 φ (V

2

./π R ) der J J

0

( ε/ ε ) o

3

, for ε > ε

cr

(3)



5. C H O W

Fatigue-Abrasive

Wear Mechanism

F i g u r e 1.

C o n t a c t geometry.


69

P O L Y M E R W E A R A N D ITS C O N T R O L

70

where R^ i s the average p a r t i c l e r a d i u s . The wear, Δ h, i s z e r o f o r ε < ε which r a r e l y happens i n any p r a c t i c a l range o f a p p l i c a t i o n . I n e q u a t i o n ( 3 ) , t h e c o n t a c t s t r a i n , ε , has t o be determined by a n a l y z i n g l o a d t r a n s f e r s from t h e foam "** p a r t i c l e s u r f a c e and t h e e l a s t i c and/or p l a s t i c deformations i n s i d e the c o n t a c t zones. I n the end r e s u l t , b o t h ε and V, a r e d e r i v e d i n terms o f m a t e r i a l and der p r o c e s s parameters. c

7

Determination

o f Wear


When p a r t i c l e s move on a s u r f a c e w h i l e under a r o t a t i n g and compressed foam r o l l , the s u r f a c e i s s u b j e c t e d t o normal ( σ ) and shear ( τ ) stresses. The t o t a l c o n t a c t s t r e s s can be determined from a s t r a i n energy r e l a t i o n s h i p . o 2

/ 2 E ,

=

2 / 2 E

+ T 2 / 2 G

( 4 )

total l ° 'l l 2 where E E / ( l - v ) and s u b s c r i p t 1 i d e n t i f i e s t h e p o l y m e r i c sub strate. Ε i s Young's modulus, G i s the shear modulus and i s Poisson*s r a t i o . Ε' may be t r e a t e d as the compression modulus. I n the case o f i s o t r o p i c m a t e r i a l s , E / G = 2 / l ( l - v )= 3 f o r common p o l y mers w i t h ν =1/3. Eq. (4) reduces t o the f a m i l i a r von M i s e s y i e l d c r i t e r i o n under p l a s t i c y i e l d c o n d i t i o n s ^ ) , and serves t o d e s c r i b e the l o c a l _ s t r a i n energy. A s i m p l i f y i n g assumption i s t h a t =p^ and τ = μ i n the c o n t a c t zone. Thus Eq. (4) becomes , =

v

f

0

ε

/ E

=^otal

r
V l

where ρ i s the mean p r e s s u r e between the p a r t i c l e and s u b s t r a t e and μ i s d e f i n e d as the e f f e c t i v e f r i c t i o n c o e f f i c i e n t . Three main f a c t o r s c o n t r i b u t e t o the f r i c t i o n generated between u n l u b r i c a t e d p a r t i c l e s and s u r f a c e i n r e l a t i v e m o t i o n . The f i r s t f a c t o r i s the a b r a s i o n and m i c r o c u t t i n g , the second f a c t o r i s t h e a d h e s i o n which i s a pure s u r f a c e c o n t r i b u t i o n and the t h i r d i s d e s c r i b e d as d e f o r m a t i o n w h i c h i s a b u l k term. I t i s ( J i f f i c u l t t o p r e d i c t μ b u t i t i s known that μ > 1 f o r abrasive_wear. The mean p r e s s u r e ρ can be r e l a t e d t o the mean p r e s s u r e p^ between the foam r o l l and substrate(8^) P= 3

2

,

a ( R / a ) 5 = [4Ε· Ε' /3π(Ε» Ε )] 3

3

2

1

3

1 +

3

2

/

3

( α ^ )

1

/

3

(6)

1

where Ε ^ i s the compression modulus o f t h e p a r t i c l e and α c h a r a c terizes the i n t e r a c t i o n o f p a r t i c l e s . For large values of φ, α ^ Ι / φ. I n t r o d u c i n g the s u b s c r i p t 2 t o i d e n t i f y t h e foam r o l l s , the mean p r e s s u r e (p«)> foam s e m i - c o n t a c t l e n g t h (a^)» foam r a d i u s (R^), compression modulus ( E ) and t h e l o a d p e r u n i t l e n g t h ( F ) a p p l i e d t o foam r o l l e r can be r e l a t e d by H e r t z ' s e q u a t i o n . When p a r t i c l e s move i n t h e gap between the foam and s u b s t r a t e under c o m p r e s s i o n , the a b r a s i v e p a r t i c l e s deform the s u r f a c e and the volume o f d e f o r m a t i o n i s o b t a i n e d by a g e o m e t r i c a l c o n s i d e r a t i o n , 1

V

def= *

h

l V

3

( 7 )

h

where h^ i s the depth o f s u r f a c e

penetration,

a =(2R h^) 3

3


i s the

5. C H O W

Fatigue-Abrasive

71

Wear Mechanism

p a r t i c l e c o n t a c t r a d i u s and I i s the d i s t a n c e t r a v e l e d by p a r t i c l e s i n the compression mode a f t e r C number o f o p e r a t i n g c y c l e s ( n o t t o be c o n f u s e d w i t h number o f c y c l e s Ν t o f a t i g u e f a i l u r e ) . Since E'^ > > E t h e p a r t i c l e can be assumed t o have the same v e l o c i t y as the foam V = R ω , we o b t a i n 1

2

2

I =C(V +V )t=C(V +V ) a / V 2

1

2

1

2

(8)

2

where

i s t h e s u r f a c e v e l o c i t y and t i s the time. D u r i n g p l a s t i c d e f o r m a t i o n , the p e n e t r a t i o n depth f o r a s p h e r i c a l contact i s i n v e r s e p r o p o r t i o n a l t o t h e m a t e r i a l hardness (R)(2,3). present s i t u a t i o n


I

n

t

n

e

h /h =H /H 1

3

3

(9)

1

where the s u b s c r i p t s 1 and 3 a r e f o r the s u b s t r a t e and p a r t i c l e , r e s p e c t i v e l y . S i n c e the a b r a s i v e p a r t i c l e s a r e assumed t o be s o f t e r than p o l y m e r i c s u b s t r a t e s , the normal l o a d (P) i s equal t o A 11^(2) and the r e a l area o f c o n t a c t A^=2 π R J i ^ . The normal l o a d a t which the p l a s t i c d e f o r m a t i o n o f a compressée! p a r t i c l e takes p l a c e i s r e l a t e d t o the p a r t i c l e y i e l d s t r e s s (Y^) by r

P=ÏÏR^Y

(10)

3

Thus h

3

= R

Y

/ 2 H

3 3

(

3

Eqs. (9) and (11) l e a d substrates h

l

=

R

Y

/

3 3

2

H

t o the s u r f a c e

penetration

U

)

expression f o r

(

l

1

2

)

S u b s t i t u t i n g Eqs. (8) and (12) i n t o Eq. ( 7 ) , the r e s u l t i s V

def

=

C

(

1

+

V

l

/

V

2

}

a

R

2

3

2

(

Y

/

3

H

l

)

1

,

5

/

6

(

1

3

)

Combining Eqs. ( 3 ) , ( 5 ) , (6) and ( 1 3 ) , the t h i c k n e s s o f a p o l y m e r i c s u r f a c e b e i n g worn away i s g i v e n by Δ Η - Ο Φ β ( 1 + ν 1 / ν 2 ) ( Y / H ) ' [ (1+3^ ) ^ / ^ E 1

2

3

5

2

1

3

,

o

1

3

3

/ 3 * (14)

with ,

,

,

; - [4Ε Ε /π(Ε +Ε' ) ] ( a F / 2 a ) 3

1

3

1

3

1 / 3

2

and a =2(FR / π Ε ' ) ^ 2

2

2

Discussion C o n s i d e r the wear o f a p o l y c a r b o n a t e surface. The m a t e r i a l and p r o c e s s parameters i n v o l v e d i n t h e c a l c u l a t i o n a r e t a b u l a t e d i n T a b l e I u n l e s s o t h e r w i s e s p e c i f i e d . F i g u r e 2 r e v e a l s t h a t the compression


72


Table I . M a t e r i a l and P r o c e s s Parameters Modulus

Yield

5

(10 p s i ) Polycarbonate(l) Foam(2)

4.0 5xl0"

Stress

Others

3

(10 psi) Η

χ

= 20

V^=10 i n / s e c

5

R =0.94 i n . 2

1

2.65

9.5

2

2.65

7.0

R =5.5 y m

3

2.10

7.0

y =1.75

4

0.75

5.0

Φ =4.55%

CO

Partiel


ω=500 rpm

Ί

1 1 Γ AFTER IOK CYCLES

10

20 30 40 FOAM MODULUS (E2, PSI)

3

2.S

ι 025

01

ω aioh 0.05h

F i g u r e 2.

50

Wear as a f u n c t i o n o f foam modulus and p a r t i c l e properties. F=0.205 l b / i n . ; F=0.256 l b / i n . The numbers r e p r e s e n t t h e p a r t i c l e s d e f i n e d i n Table I .


5.

CHOW

Fatigue-Abrasive

73

Wear Mechanism

modulus o f foam has v e r y l i t t l e e f f e c t on the wear o f p o l y m e r i c s u r f a c e , on the o t h e r hand the p r o p e r t i e s o f p a r t i c l e have a v e r y s t r o n g e f f e c t . T h i s i s m a i n l y due t o the h i g h r a t i o P~/p ^ 0 ( 1 0 ) and ρ ^ 0 ( 1 p s i ) . The weak dependence o f the compression modulus o f the foam r o l l on wear b e n e f i t s the i n v e s t i g a t i o n o f the d i r e c t i n t e r a c t i o n between the s m a l l p a r t i c l e s and p o l y m e r i c s u r f a c e . D u r i n g the wear measurement, the compression modulus o f a g i v e n foam can i n c r e a s e i n time w i t h an i n c r e a s e o f trapped p a r t i c l e s which has l i t t l e i n f l u e n c e on wear. We found t h a t the c a l c u l a t e d curves i n F i g u r e 2 compare reasonably w e l l w i t h t h e measured wear r a n g e ( ^ ) from 0.7 t o 1.4 ym/10K c y c l e s f o r type 1-3 p a r t i c l e s . F i g u r e 3 i l l u s t r a t e s how the wear v a r i e s w i t h the hardness and modulus o f polymer s u b s t r a t e . F i g u r e 4 shows t h a t the wear i n c r e a s e s d r a s t i c a l l y w i t h an i n c r e a s e o f the e f f e c t i v e f r i c t i o n a l c o e f f i c i e n t ( μ ) between the p a r t i c l e and p o l y m e r i c s u r f a c e . As was mentioned e a r l i e r , the f r i c t i o n μ depends not o n l y on the b u l k and s u r f a c e p r o p e r t i e s o f m a t e r i a l s i n c o n t a c t but a l s o on such parameters as c o n t a c t geometry and s u r f a c e roughness. The d i r e c t d e t e r m i n a t i o n o f μ from the f i r s t p r i n c i p l e has y e t t o be e s t a b l i s h e d . The p r e s e n t model can be used t o e s t i m a t e i t s v a l u e from experiment. When a s u r f a c e becomes smoother and h a r d e r , t h e e f f e c t i v e f r i c t i o n a l c o e f f i c i e n t u s u a l l y decreases and so does the wear.


9

F i g u r e 3.

Wear versus the modulus and hardness o f p o l y m e r i c substrates. Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


74


1.25

1.50

1.75

2.00

2.25

EFFECTIVE FRICTION BETWEEN RARTICLE AND SURFACE F i g u r e 4.

Wear v e r s u s the e f f e c t i v e f r i c t i o n a l

coefficient.

Literature Cited 1.

Moore, D.F. "Principles and Applications of Tribology", Pergamon Press, 1975. 2. Bowden, F.P.; Tabor, D "Friction and Lubrication of Solids", Clarendon Press, Oxford (1964). 3. Kragelsky, I.V.; Dobychin, M.N.; Kombalov, V.S. "Friction and Wear", Pergamon Press, 1982. 4. Chow, T.S. Wear 1978 51, 355. 5. Sauer, J.Α.; Foden, E; Morrow, D.R. Polym. Engr. Sci. 1977 17, 246. 6. Rabinowitz, S; Beardmore, P. J. Mater, Sci. 1974 9, 81. 7. Ward, I.M. "Mechanical Properties of Solid Polymers", Wiley, N.Y., 1971. 8. Landau, L.D.; Lifshitz, E.M. "Theory of Elasticity", AddisonWesley, Reading, Mass. 1957. 9. Penwell, R.C.; Chow, T.S. unpublished data. RECEIVED January 23, 1985 Lee; Polymer Wear and Its Control ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

A Fatigue-Abrasive Wear Mechanism for Polymeric Surfaces - ACS

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