FACTA UN IVERSITATIS
Serie s: Mechanical Enginee ring Vol. 16, N o 1, 20 18, pp. 29 - 3 9
http s://doi.org/10.2 2190 /FUME 171226004P
© 2018 by Uni versi ty of Ni š, Serbia | C reativ e Com m on s Li cen ce: CC BY- NC - ND
Original scien tific pa per 
ADHESIVE WEAR : GENERALIZED RABINOWICZ’ CRITERI A
UDC 539.6
Valentin L. Popov
Ber l in Un i v e rs i t y of Tec h n ol og y , Ber l in , G er m an y
Abstra ct . In a re ce nt pape r in Natu re Com muni c at ion s , A gha bab ae i, W ar ne r and
M oli nari [ 5] us e d qua s i- mo le cul ar si m ul at ion s to c onfir m the cri ter ion fo r for mat io n of
de br is, pr opo s ed i n 19 58 by R abino wi cz [ 4] . The w or k of Agh aba bae i, Wa r ne r and
M oli nari imp ro v es our unde rs tand ing of adhe siv e we ar bu t at the sam e ti me puts ma ny
ne w que sti ons . The pr es ent pape r is dev ote d to the dis cus s io n of pos sibl e ge ne r al iz ation s
of the Rab in ow ic z-M olin ar i cri ter io n an d it s appl icat ion to a v ar ie ty of sy ste ms dif fer in g
by the inte rac ti ons i n th e i nt e rf ace and by the mate ria l pr oper tie s ( el asti c an d
el asto pl as ti c) and st ru c tu re ( hom ogen e ous and l ay e re d s y st ems ). A ge ne r al iz at io n of the
Rab in ow ic z-M oli nar i cr it e ri on fo r s yst ems wi th arbi tr ary c ompl ex cont ac t c onf ig ur atio n i s
su gge ste d w hic h doe s n ot use t he noti on of " as pe rit y ".
Key w ords : Plasticity, Ad hesion, Critical Leng th, Ad hesive Wear, Layered Systems,
Functio nally Grad ient Materials, Ra bin owicz’ Crit erion
1. I NT RODUCT I ON
Am o ng the basic tribo logical phenom ena of contact, adhesion, f riction, lubrication
an d w ear , w ear rem ai n s th e le as t sci ent if ic all y u nde rs tood . Thi s m ay be due to th e
com pl exi ty an d div er s it y of th e proce s s es le ad in g to w ear. In par ti cu lar , w ea r is not a pur el y
con tac t m ech ani cal ph eno m en on , bu t n ec es sar i ly al s o in cl ude s fr ac tur e ph en om en a w it h in
th e m ate ri al an d m ate ri al tran spo rt w it h th e res ul t in g v er y broa d pro bl em o f t he "t h ir d bod y ".
A t t h e sa me ti m e, w ear re ma ins on e of th e m ost im port an t tr ibol og ica l phe nom en a in
practice, affectin g all asp ects of our lives and current technologies. Wear signif icantly
determines the life time of m echanical system s; it is a key factor in m atters of technical
safety . W ear not only affects mach ines and m echanical constructions, it is e.g. also an
unsatis factorily solved problem in m edicine: Many implants , especially artificial j oints,
have to be rep laced after ap prox. 10 y ears. W ear is also an important issue in terms of

Receive d Decembe r 26, 20 17 / Acce pted Janu ary 29, 2 018
Corresponding author : Valentin L . Popov
Te chnisch e Univer sität B erl in, Sekr. C8 -4, Straße des 17. Jun i 13 5, D-10 623 Berli n
E-mail: v.popov @tu-berlin.de

30 V . POPO V
em ission of w ear particles into the environm ent (such as brakes and tires). In all of these
areas, very great efforts ar e undertaken to get wear under control. Up to now , this has
largely been done in a p urely em pirical way .
The m os t com m on basi s for w ear ca lc u l at i on s is f orm ed by a law w h i ch w as fo rm ul ate d
in 195 3 by Arc har d [1] and bea rs hi s na m e. Ac co rdi ng to Arc h ar d' s la w , th e w ear vol u m e is
pro por t io n al to th e sl id in g le n g th , th e no rm al for ce , an d in ver s el y prop or ti ona l to th e
h ar dn ess of the m ate ri al. Th e coe f f i ci en t of propo rt io n al ity is cal le d w ea r co ef fi ci ent . Bu t th e
dev il is i n prec i se ly t h is "coef fi cie n t", beca u s e em piri cal ly m ea s u re d va lu es of th e ad h es iv e
coe ff ici en t of w ear can dif fer by 7 dec i m al ord er s of m agn it u de [2] , w hi ch inv ali dat es th e
in fl u en ce of ha rdne ss. Ac cordi ng l y , gen era l rec om m en dat ion s m ade on th e bas is of th e
A rc h ar d’ s l a w hav e a ve ry lim it ed sc ope of appl ica bi l it y. For ex am pl e, th ere is a w ide l y
sp re ad opi n i on t h at the h i g h er th e ha rd n es s, th e low er th e w ear , si n ce th e ha rdn es s st an ds in
th e den om in ato r of the A rc h ar d ’s eq u at i on . Ho w ev er , Krag els ky [3] for m ul at ed an al m ost
ex act ly oppos it e pri nci ple for m in im iz in g w ear – th e pri nci ple of a pos iti ve ha rd n es s
g ra di en t, w hi ch st ate s tha t t h e su rf ac e la y ers m u s t be sof ter tha n th e low e r lay er s , oth erw is e
ca ta str oph ic w ea r occu rs. The se tw o st at em ent s, w hi ch see mi ng l y ex clu de each ot h er , bot h
h av e em pir i ca l c on fi rm at ion , w h i ch onl y em pha siz es t h at th e ph y si cs of t he w ea r proc es s h as
so f ar be en poor l y un der st ood a t i ts cor e.
In the last few decades, howev er, some idea s have bee n co ll ected which shed new
light on the phys ics o f wear. Thus, Molinari w ith collabo rators picked up and confirm ed
an old idea b y Rabinowicz (19 58), [ 4 ], ab out the phy sical m echanism that deter min es the
size o f the w ear particles and also controls the transition from m ild to catastro phic wear.
In the criterion of Rabinowicz and the theory of Molinari et al. based on that [5 ], it is the
interplay of plasticity and adhesion, which lead s to the ap pearance o f a characteristic
length : If a micro contact is smaller than th e characteristic length, it is plastically
deformed; if it is lar ger than the characteristic length, wear particles form. T he existence
of these two scenario s has b een independently confirm ed by P opov and Dim aki using the
m ethod of m ovable cellular autom ata and has been o bserved in m olecular dy namics
sim ulations [6]. Combin ed w ith ad vanced num erical sim ulation methods of contact
betw een rough surf aces [7], this new understanding advances the old idea of Rab inow icz
to a new parad igm [8].
The Ra bi n ow ic z-M ol i n ar i cri ter io n a ppl ies t o h om og en eou s sy st em s. Ho w ev er , the
su rf ac e reg ion of con tac ts in m os t low -w ea r te ch ni ca l s y st em s is not hom og ene ous . Thr ou gh
th e w ork of Ge rv e et al. [9 ] an d in th e la st deca de, es pe ci all y by M. Sc h er g e an d co- w ork ers
[ 10 ], the role of ver y th in ch em ic al ly m odi f ie d s u rf ace lay er s ha s been de m on s tr at ed f or
sy s te ms w ith "m i n im al w ea r" (in cl udi ng , for ex am ple , com bu s ti on eng in es) . Fu rth er , t h e
Ra bin ow i cz - Mo li nar i cri te ri on us es th e n oti on of “a sp er it y ”. How e v er , the dev elo pm en t of
th e con tac t m ech an ics of r ou gh s urf ace s h as sh ow n t h at th is not io n i s p oor ly def in ed . Th u s, it
is im port ant to s ea rch fo r f orm u l at i on s of th e sam e ph y si ca l prin cip le s w it h ou t us i n g th e
n ot io n of as pe ri t y . In th e pre s en t pape r, th e bas ic ph y si ca l id ea un derl y in g th e crit eri on of
Ra bin ow i cz - Mo li nar i w il l be a ppl ied t o h ete roge neo u s m edi a. Fu rth er , “ as per ity - fre e”
con cep ts w il l be d is cu ss ed.

A dhesive W ear: G ener alize d Rabi nowicz ' Criteria 31
2. R A BI NOWI CZ ' C RI TERI ON F OR F ORMAT IO N OF W EAR D EBRI S
2.1. Original R abinow icz' criterio n for homogeneous m edia
We st ar t w it h th e rep rod u ct ion of th e w el l-k now n der iv ati on of the Ra bi n ow ic z cri te ri on
[2, 4, 11 ] fo r a h om og en eou s m edi um . If tw o m icr o het erog ene i ti es col li de an d f orm a
w el ded brid g e, as su gg est ed by Bow den and Tabor [ 12 ], (s ee Fig . 1) th ey are plas tic all y
def orm ed, an d th e m ax im um st res s th at c an be ac h i ev ed is of t h e o rde r of th e ha rd n es s of th e
m ate ri al. In th is st ate , t h e s t ore d ela st ic ene rg y is pro por t io n al to th e th ird pow er of con t ac t
si ze:

3
2
0
2
σ D
G
U el 

. (1)
This energy can relax by crea ting a w ear particle. The process of detaching a w ea r
particle can, however, only occur if the stored elastic energy exceeds the energy

2
adh
U w D   

(2)
w hich is needed to create new free surfaces (w here  w is the w ork of adhesion per unit
area). It follows that only particles larger than some critical size can be d etached:

2
0
2 Gw
D 
 

. (3)

Fig. 1 Weld ed j oint of size D created d ue to contact and shear o f tw o asperities.
Note that the Eq. (3) p redicts only the existen ce of a lo w er b ound o f the size o f wear
particles. T hus, there also should be som e mechanism suppressing the ap pearance o f too
large particles. Rabinow icz d id not make any suggesti ons for such a m echanism .
How ever, a possible mechanism co uld be very sim ple and follow from the sam e E q. ( 3) .
Indeed, as noticed in [ 13 ], if some particle has size m uch larger than (3), it is energetically
favorable for it to disintegrate into two smaller ones. T his pr ocess can o nly continue until
the critical size (3 ) is r eached. T hus, the wear particles should all have a size o f the same
order of m agnitu de as the critical length giv en by Eq. (3 ) .
2.2. M odified Ra binowicz ' criter ion for frict ional intera ction in the interface
Co n s id er th e sa me aspe rit y con t ac t as sh ow n in Fi g. 1 , b u t a s su m e now t hat th e ta ng en tia l
st res s  nee de d to i n du ce m ac rosc opic re l ati v e s li din g o f a s pe ri ti es i s de term i n ed by t he f or ce
of f ri ct ion w ith t h e coef fi cie n t of f ri cti on  :  =  p , w h ere p is the pres su re ac ti ng in th e
con si de re d m icro con t ac t. The ela s t ic ene rg y st ored in t h e con tac t im m edia t el y bef ore gr os s
sl idi n g c an be est im ate d as

32 V . POPO V

3
2 2
2
μ D
G
p
U el 

(4)
and the criterion ( 3) is m odified as follows:

22
2 Gw
D p

 

. (5)
The m ain difference of this criter ion from the classical Rabinow icz' criterion is that the
critical asperity size d epends not o nly on m aterial par ameters b ut also on the pr essure in
that considered asperity. Howev er, even in this case th ere exists som e characteristic
asperity size w hich can be estimated by substituting in (5) the average pr essure in m icr o -
contacts, w hich in g ood ap pro xim atio n is given by [ 14 ]

*
1
2
p E z 

. (6)
The cr iterion for formation of particles thus takes the form

22
w
D Gz

 

, (7)
w it h th e add it ion al con str ai nt of (3), si n ce th e pre s s u re can not ex ce ed  0 . Thi s cri te ri on do es
n ot n ece ss ari l y as s u m e p la s ti c be h av iou r an d c an al s o b e ap pl ie d to pu re ly el as tic m ed ia .
2.3. M odified Ra binowicz ' criter ion for contact s wit h friction a nd adhesion
In th e pa per [ 15 ], a con tac t of t w o bod ie s h as be en co n s id er ed , w h i ch i n te ract by
adh es io n an d f ri ct ion fo rc es at the sa m e ti m e. In th e li mi t of ve ry st ron g bu t sh o rt ra n g ed
adh es iv e in te ra ct ion s, it ha s be en sh ow n th at th e cri tic al for ce at com ple t e s lidi ng is giv en by
th e s im ple equ at i on

22
,,
( ) ( ( ) )
x sl ip N J KR c c
F a F a a a         

, (8)
w he re F N, JK R ( a ) is th e n orm al f orc e ac co rd in g to t h e JKR - th eor y f or th e cor re sp on din g
pro f i le [ 16 , 17 ]. Thi s can be don e if
2 ,
/ ( ) / ( ) 1
c N J KR c
a F a a E h      

w h ic h is th e cas e
f or ty pica l m at er ia l para m ete rs of m et als an d jun cti ons lar g er th an abou t 1  m . In t h is cas e,
in th e f ir s t app ro x im at ion w e can ass um e th at th e su rfa ce s are pre s s ed ag ain st eac h oth er
w it h a con st an t an d hi gh adh es iv e pre s s u re  c . We th us hav e a con tac t w it h th e "fl ow st re ss "
 =   c , an d Eq. (3) is di re ct l y app l ic ab le w ith th e on ly s u bs tit u t io n of  0 =   c .
3. W EA R I N S YST EM S WI TH A S OFT S U RFA CE L A YER
Rabinow icz has formulated his criterion for h om ogeneous media. However, man y
tribological system s have a pronounced layered structure – either ar tificially designed or
developed during tribolo gical load ing. In the p resent p aper we rep eat the argum ents o f
Rabinow icz for such layered system s and find the co nditions for p lastic sm oothing and
particle d etachm ent in th is case. W e follow th e presentation of prep rint [ 18 ].

A dhesive W ear: G ener alize d Rabi nowicz ' Criteria 33
Consider an elastic m ed ium with elastic shear m o dulus G 0 covered w ith a soft
elastoplastic lay er of thickness h havin g shear modulus G c and the tangential y ield stress
 c . T his lay er can b e d eposited to the surface ar tificially or it can ap pear naturally thro ugh
m echanically induced chemical reactions of the base material w ith su rrounding su bstances
(lubricant, counter- body , air and so o n) [9 , 10 ]. Assu m e that d ue to normal loading and
tangential sliding a junction with the diameter D is formed, and that the Diameter D is
m uch larger than the thickness of the layer (the opposite ca se corr esponds to a
hom ogeneous medium and is covered by Eq. (3) ). T he co mponents of the stress tensor in
the near surroundings of the j unction will b e o f the or der of m agnitu de of  c . If the elastic
energy stored in the system is not enough for creating new surfaces with an area o f the
order of D 2 than the o nly po ssible p rocess w ill be p lastic smoothing as illustrated in detail
in the pap er [ 13 ]. In the o pposite case, the elastic energy can be relaxed by detaching of a
w ear particle. In the case of debris formation, tw o lim iting cases are possible:
3.1. Detachment in the base material
In this ca se, w e b asically can rep eat the line of argum ent of Rabinowicz. The stored
elastic ener gy has the ord er of (  c 2 /2 G 0 )  D 3 and the surface energy needed for formation
of a w ear p article is of the ord er of  w  D 2 w here  w is the work o f separation of the base
m aterial. T he formation of w ear par ticle is possible if (  c 2 /2 G 0 )  D 3 >  w  D 2 or

0 2
2
c
Gw
D 
 

(9)
w hich coincides with the Rabinowicz ’ criterio n ( 3) . T he o nly difference from the classical
criterion is that the elastic modulus and energy of separation are those of the base material
w hile the critical flow stress is that of the surf ace layer.
3.2. Detachment inside the surface lay er
In this case, the elastic energy w hic h is released due to particle detachm ent is on the
order o f (  c 2 /2 G c )  D 2 h and the energy needed for detachm ent  c D 2 , w here  c is the w o rk of
adhesion inside the soft lay er. T he form atio n o f p articles is thus po ssible if (  c 2 /2 G c )  D 2 h
>  c D 2 or

2
2 cc
c
c
G
hh 



. ( 10 )
In th is cas e, th e f u l f il m en t of cri te rion doe s not dep en d on th e dia m ete r of ju n ct ion bu t
dep en ds so le ly on th e thi ck ne s s of t h e lay er . If the thi ck ness of the lay er is sm al ler than the
cr iti cal one, h c , then f or ma t io n of pa rt icl es is no t pos si ble, inde pe nde ntl y of the si z e of
ju nc ti ons . N ot e th at in thi s c as e on ly th e p rop er ti es of th e s oft er s urf ace lay er d o pl ay a r ol e.
3.3. Criteria for fo rm ation of “flat ” and “spherica l” w ear part icles
L et u s co n s id er in de ta il t h e t r a ns i ti on b e t w ee n t h e c as es 1 a n d 2 di sc u ss e d in t h e p r e vi ou s
S ec ti on . A g a in c o n s i de r a ju n ct i o n w i t h s o m e p a rt ic u la r di am e te r D . Th e f o l lo w i n g ca se s ar e
p o s si b l e:

34 V . POPO V
1.
00
2
2
c
G
D 
 

but
2
2 cc
c
G
h 
 

.
In this case, formation of the in -lay er particles is not possible but formation of the b ase -
m aterial par ticles is possible. T his is the classical “R abinow icz case”.
2.
00
2
2
c
G
D 
 

but
2
2 cc
c
G
h 
 

.
(T his case is p ossible if the elastic m o dulus of the su rface layer is su ff iciently sm aller than
that of the base material). In this ca se, the formation of “bulk” par ticles is not p ossible but
surface-lay er flat wear particles can be formed.
3. In t h e gen era l cas e, on e cou ld su gg est t h e fo l lo w in g gen era li zed es tim at i on . A ssu m e
th at w e ha v e a jun cti on of diam et er D an d det ach ed is a par t ic l e of dia m ete r D and th ick ne s s
h. T hen, the elastic energy stored in the sy stem is on the order of

22
0
22
, fo r
2
, fo r
2
c
c
el
c
c
D h H h Hh
GG
U D H Hh
G
 
 

 
 
  
 



( 11 )
The energy needed for formation of th e above par ticle is on the order of

2
0
2
, fo r
, fo r
surf
c
D H h
U D H h
 

  



( 12 )
The formation of particles is possible if

22 2
0
0
22 2
, for
2
, f or
2
c
c
c c
c
D h H h D H h
GG
D H D H h
G
 
 
   
 
 
 
   



( 13 )
or

0 0 0
2
2
2 1 , for
2 , f or
c
c
cc
c
GG
H h H h
G
G
H H h
 

   
 

 
 
 
 


( 14 )
Let us display these relations graphically on th e plane ( H , h ) ,

A dhesive W ear: G ener alize d Rabi nowicz ' Criteria 35

Fig. 2 Schematic representation of conditions given by Eq. ( 14 ).
A com pletely “ w ear - less” sliding w ill occur if the follow ing tw o conditions are fulfilled:

2
2 cc
c
G
h 
 

( 15 )
and

0 0 0
2
2 []
c c c
c
D G G G      


. ( 16 )
Due to softness of the surface layer, the critical jun ction size can be m ade larg e
enough so that the only co ndition wh ich has to be observed would be that given by Eq.
( 15 ) . T his explains the p rinciple of “positive hardness gradient” as condition for wear -less
sliding, w hich w as form ulated by Kragelsk y [3 ].
Of course, even the p rocess of plastic sm oothing will lead to eff ective “w ea r” due to
“squeezing out” of the surface layer. Ho w ever, it was shown in [9] ( see also [ 11 ], §17 .5)
that in this case the effective w ea r rate is p ropo rtional to the square o f the r ati o of the
lay er thickness to the linear size L of the frictional contact zone. T he wear coefficient will
thus be on the order o f

2
adh
h
k L

 


( 17 )
and can assum e extremely small values. Note that the smaller is the thickness of the
surface lay er the sm aller is the w ear coefficient.

36 V . POPO V
4. A SPERI TY F REE C ONCEPT S F OR A DHESI VE W EA R
Ra bin ow i cz ' cri teri on is bas ed on th e not io n of "as perit y ". A n im port ant para m et er for
app l ic at ion of thi s cri teri on is the kn ow led g e of the "as pe ri ty si ze". Ho w ev er , it is w ide ly
re cog ni zed t h at th e n ot io n of as peri t y is a p oo rl y def i n ed no ti on f or rea l su rf ac es w h ic h of ten
h av e rou g h n es s on m an y le n g th sc ales . Ho w ev er , w i th out prop er ly def in i n g the si ze of an
as peri t y , th e Rab in ow ic z' cri te ri on ca nn ot be appl i ed . Lo ok in g at a con ta ct con fi g u ra ti on of
bod ie s w it h f ra ct al rou gh su rf ac es (F ig . 3) , w e s ee m ore or l es s c ont i n u ou s c l u s te rs of c on tac t
ar ea s in st ea d of se par at ed as peri tie s . We w ou ld li k e to su gg es t a "m odi fi ed Rab in ow icz ’
cr it erio n " w h i ch is larg ely in depe nde n t of th e def in i ti on of an as pe ri ty an d is bas ed on th e
id ea s f irs t pr opo s ed i n [ 19 ].

a) b)

c) d)
Fig. 3 Num erical simu lation of tangen tial contact between a rough surface and an elastic
half- space: a) the surface topograp hy ; b) contact ar ea at a given indentation depth.
Black colo r shows the stick regions and gray co lor the slip regions; c) T angential
stress distribution in the contact; d) tangential displacem ent of elastic half-space.
Black areas show a rigid-body translation and gray areas the slip regions.

A dhesive W ear: G ener alize d Rabi nowicz ' Criteria 37
Consider as illustration the contact o f r ough surfaces shown in Fig. 3 . A r ough sphere
w ith rough ness havin g the Hurst exponent 0.7 w as generated accord ing to the rules
described in [ 20 ]. T he indenter was pr essed into the elastic half-space and then moved
tangentially by a u x (0) sm aller than the displacement co rresponding to complete sliding
[ 21 ]. Bo th the norm al indentation and tang ential loading w er e sim ulated u sing the
Boundary Elemen t Method as d escribed in [ 7] . Unlike in [7 ], we assum ed that any tw o
points of bodies ar e in the stick state as long as the loca l stress is sm aller than a fixed
critical value,  c . After beginning of slip, the stress remained co nstant an d equal to  c , thus
m im icking elastic-ideally-plastic behavior in the contact interface. T he tangential contact
co mes into p lastic state b y o vercomin g the critical value  c which in this context p lays the
role of the " yield stress" used by Rabinow icz in Eq. (1 ).
Now consider a circular region centered at an arbitrary p oint w ith an arbitrary
diameter D . In Fig. 3b and 3 d, several exam p les o f such regions w ith different positions
and d ifferent diameters are show n with red circles . T he macro scopic tangential stress in
the selected circular ar ea is eq ual to  c , w here  is the " filling factor" defined as the ratio
of the r eal co ntact area in this circle to the area of the cir cle ~ D 2 . Assu m e further, that
configu ration of the contact in this area co rresponds to the plateau of the stiffness , as
described in [ 22 ] . Then the contact acts as a complete co ntact. T he elastic energy which
w ould be relea sed if a w ear p article with the charac teristic volum e ~ D 3 would detach, has
then the order of m agnitu de ((  c ) 2 /2G)  D 3 . If it is not enough for crea ting the free surface
of the order of D 2 , the detaching cannot happen. Thus the criterion for the possibility of
detaching a w ear particle with th e size D is ((  c ) 2 /2 G)  D 3 > D 2  w o r

2
2
()
c
Gw
D 
 

. ( 18 )
In th e mo s t g en eral cas e, ela sti c en erg y th at w il l be rel ax ed by deta ch in g the co n s id er ed
par t ic le, can b e es tim at ed a s

24
()
4 ( )
c
el
H
D
U Ga D



( 19 )
w here a H is the Ho lm- radius o f the considered contact configu ration [ 23 ]. T he condition
for particle d etachm ent can be w ritten as

2
2
2
2 ( ) ()
H c
D G w
aD

 

. ( 20 )
Generally, the dep endence of the Holm-radius on the diameter o f the circle can o nly be
determined numerically . Thus, this eq uation has to be evaluat ed using num er ical
sim ulations of contact and loca l stiff ness of v arious areas.
Note that for using Eqs. ( 19 ) and ( 20 ) there is no need to define w hat an asperity is.
By "p robing" various positions and d iameters, one can identify the material regions w hich
"can potentially p roduce w ear par ticles" . Ho w ever, in this co ncept the real co ntact ar ea
w ill p lay an essential r ole so that further ideas m ay be needed for deter m ination of a
robust criterio n which does not d epend o n fine details of the po w er density of the surface
roughness . A very interesting discussion of these aspects can be found in [ 24 ].

38 V . POPO V
5. C ON CL USI ONS
In the present pap er, w e applied the Rabinowicz-Molinari criterio n for formation of
w ear particles for a variety of sy stem s d ifferin g by the interactions in the interface and by
the materia l pr operties ( elastic and elastoplastic) and structure (homogen eous and layered
sy stem s). Of sp ecial interest is the result that in the system with a soft layer, no critical
size of contact does exist. Instead, there appears som e critical thickness. We further
discuss a generalization o f the Rabinowicz-Molinari cr iterion for sy stem s w ith ar bitrary
complex co ntact configuration. T his formulation does not use the notion of " asperity" and
autom atically includes "multi- contact" situations.
Acknowledg ement : The au thor thanks M. Popov fo r readin g th e draft p aper a nd for u seful
comments, J.-F. Molinari a nd R. Po hrt for interesting d iscussions rela ted to th e present pa per, and
Qiang Li for help with p reparatio n of Fi g. 3. The au thor ackno wledges finan cial supp ort of the
Deutsche Forschung sgemeinschaft (DFG PO 81 0 - 55 -1).
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A dhesive W ear: G ener alize d Rabi nowicz ' Criteria 39
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