Theory of Abrasive Wear Mechanism for FRP Composite

Indian Journal of Engineering & Materials Sciences '- " Vol. 1, October 1994, pp. 273-278 ' .,

, -, '

Theory of abrasive wear mechanism for FRP composite

Navin Chand", B Majumdarb & M Fahim" "Regional Research Laboratory (CSIR), Bhopal 462 026, India bGovernment Science College, Raipur 492 010, India

In fibre reinforced composites,residual thermal stressis build up becauseof a difference in thermal expansioncoefficients of the fibre and matrix. After abrasionprocess cooling takes place from high temperature.During this changein temperatureeach pan of heterogeneouscomposite system undergoes a different thermal contractionor expansionstrain giving rise to microstructuralresidual stresses. Spring network model has been used to define the abrasivewear mechanismin glassfibre reinforced polymer f composites.A theoritical wear equationis derived from the combinationof residual stressand fracture toughness.

Studies on wear mechanism of the fibre reinforced Model formulation polymer composite involve understanding of the Curtin and Scherl3 have studied brittle failure complex and undefined structure of composite, by using Spring network model. This model con- mainly composed of two heterogeneous materials. sists of different nodes connected to each other These studies assume significance in view of the with linearly elastic springs that have failure strain greater tribological importance of to these materi- associated with them. By varying the spring par- also Much investigations have been devoted tow- ameters, viz., spring equillibrium length, force con- ards the tribological studies of FRP materialsl-16. stant and displacement at which failure occurs, the Reinforcement of fibres complicates the structure disorder can be introduced in the system. of solid as a whole. This makes the problem cum- In case of FRP composite, the spacing between k bersome in investigating the mechanism responsi- the fibres is not uniform which always happen in ble for the wear of reinforced materials. Most of actual composite and hence a system is proposed the studies are concentrated on the sliding wear in which the disorder is supposed to be created in characteristics of glass fibre reinforced polymer the unstrained size of the element of the fibre. The composites7-9.Literature on abrasive wear studies approach is based on the fact that in initial stage of polymer composites is comparatively scarce when the material is removed, the spring constant and most of the work relates on either short or through which the molecules are attached is differ- continuous fibre reinforced compositeIO-12. ent from that of the material which is worn out in In this paper, abrasive wear mechanism of very the next subsequent stage, thereby, allowing dis- high weight fraction woven glass cloth reinforced order by virtue of spring parameters which vary polymer composites has been Teported. An at- from spring to spring in either correlated or un- tempt has also been made to analyse the genera- correlated manner. tion of residual stress during experiment and its Physically the whole picture is like that the ir- distribution in fibre reinforced polymer composite reducible material region which has been worn out in which molecules are assumed to be connected during the process exhibits distributed disorder. A with elastic springs. The wear mechanism on the spring snapping force law has been used because basis of Spring network model in FRP composites of the fact that these springs are not actually has also been defined. Stress intensity factor, K1C meant to represent interatomic bonds. is calculated based on the proposed concept. Since it is being assumed that fibres are not Moreover, a new relation between K1C and wear equally spaced in FRP composite, therefore, a volume is established proved that K IC depends on topological disorder appear just as in any real sys- particle size. tern. Conventionally, the topological disorder is .~-,,--"C

274 INDIAN J. ENG. MATER SCI.,OcrOBER 1994

not unimportant but spring to spring disorder ac- Moreover, the spherically symmetric nature of re- counts for all the disorder polymer composite. sidual stress makes it clear that the removal of the During the first 100 cycles of the experiment, material from bulk matrix consequently effects the " described elsewherel4, which takes about three mi- remaining residual stress fields in the vicinity. nutes, a small amount of material is worn out. It is Since disorder in the residual stress appears in the certain that the local temperature of the material scale of interparticle spacing the spring between which is in contact with abrasive paper will in- each particle and its neighbours can be identified crease. Due to this thermal gradient within the po- with microstructural features. Any failure of the lymer network a stress will be generated which physical region between neighbouring particles may be taken as one of the possible source of dis- would possibly lead to debonding of the interface order. This fact seems to be logical because there between particle and matrix. This phenomenon are clear evidences of the presence of residual would lead to cracking in the physical system stresses in a variety of composite materials. Con- which reflects non concentrated load transfer as clusively, Spring network model has been used to needed for Spring model in case of FRP compo- understand in detail the spatial variations of resid- site. A spring failure would then represent a de- uaI stresses that are expected during abrasion of bonded partIcle with a crack arrested in the inters- FRP composite. titial matrix region possibly in a lower residual During the second phase of experiment, the stress site during the removal of material. reinforced polymer matrix gives rise to residual In the Spring network model system it has been -..J stress as the polymer composite cools down by an assumed that physical disorder dominates over the amount of i\ 1; compared to room temperature or topological disorder because it leads to an open initial temperature of the composite. During this path for the study of microstructural features. In second phase, there will be a volume mismatch addition, the effects of topological disorder on a given by, partial basis can be studied by spring disorder i\ vi .model in a regular lattice network system. ~=i\a'i\T ...(1) In order to understand and interpret micros-

tructural features on the basis of the springs in ne- which can be calculated using simple elasticity the- twork ~odel, resid~al stress dis!ri~ution is int~o- orylS, where i\a is actually related to mismatch duced I~tO the. sl?nng ~haract~r!st~cs by allowmg between coefficients of thermal expansion of the fo! spatIal varI~tI?nS I.n eqwllibn~ len~, '0 matrix material and the remaining second phase Wl~OUt ~y vanatlons m th~ elastiCIty or failure particles in a polymer composite. ~tr~, .Er, m. the present physlcal.syste~. Ea.ch sp~- For the material used in the present study with- mg m Isola~on has no stres~ on It. This s~nng will ~ in the limit of experimental error for equal moduli have a resIdual stres~ dunng the abrasIv~ wear of glass fibre and resin matrix, stress fields can be process ~hen. c?nstramts of. the surroundmg ne- calculated where tangential stress field a is given twork SprIng IS Imposed on It. Consequently, any by TR variation in the equillibrium spring length, '0' ref- , lects that the distributions of interparticle spacings,

aTR = --~ 2 ...(ii) particle size and shapes and to some extent orient- 2(Rlro) ations related to the applied stress. Also the net

h . th uillib . I gth f h . R residual stress acting on a spring in present ne- w, ere ~ 0 IS e eq num en 0 t e SprIng ' twork system predommantly. depends upon, 0 va- "I

IS the radIus of sphencal partIcle bemg removed I f th ' ghb .. ..ues 0 e nel ounng SprIngs w hi cae h t th same from the matnx and ao IS equal to, tIme.. IS a dd .. Itlon al d . Isor d er p h YSIC. all Y present . m ao=E'i\a'i\.T ...(iii) the real polymer composite due to the closed proximity of other stressed particle. During the process of abrasive wear, firstly the Any variation in the distributed '0 values or re- stress applied is symmetric in nature, secondly, the sidual strain can be measured on the basis of Er, .. removal of the material always takes place along during deformation induced wear process. If the the same wear track and henceforth symmetric. As variations in '0 is characterised by distributed dis- such the distribution of the residual stress within order in i\,o and are small compared with Er then the bulk matrix after each phaSe of varying mode the distributed disorder is fairly unimportant be- would be symmetric in nature. Otherwise, cracks cause as soon as the first spring falls, the neigh- ;. in the bulk matrix would have been observed bouring springs can not support the transferred which is not seen in case of FRP composite. load during the removal of the material from the -.~' I ' J" : CHAND etal.: ABRASIVE WEAR MECHANISM OF FRP COMPOSI1E 275

bulk, even if they have some residual compressive is comprised of two material states, fibre makes stress, and the network fails completely. Alternat.. one material state while resin forms second state. ively, if variations in r 0 are comparable to f f then These two states represent two different material the distributed damage will be nucleated at low phases. applied stresses but no global failure occurs. At H Vs is volume of the solid, Vv is the volume of higher applied stresses crack propogation might be voids present in the composite, V is the volume visible and during this process the ultimate failure of fibres and V is the volume of p~lymer then to- must be sensitive to the complete full distribution tal volume, Vof p coItlposite is given by, of residual strains. Conclusively, for larger disor- der, when one or more spring failures take place V= Vy+ Vs in the bulk, it is equally likely that they will occur prior to any possible surface or bulk failure, or cracks start nucleating internally. V= V + V + V ...(1) To investigate the abrasive wear mechanism of y g p FRP materials through Spring network model, Depending on the loading regime, either V g or V p stress a 1 at which the first spring failure occurs, can be zero. During abrasion let the worn out vo- which basically correspond to first phase of elimi- lumes in these two material phases be yt and V2, nation of the material, maximum stress or failure respectively. These two volumes, can be shown stress, af and corresponding failure strain Ef conceptually as a hollow sphere model. The vo- ,, shouldMicrostructural be determined. Residual Stress in Polymer Ma- lumenl and ratios n2is givenby, of the two material-- phases denoted by

trix During Abrasion V V In a solid body residual stresses often exists nl =y and n2 =y 7'-~ ...(2) even in absence of external load. These stresses actually originates from the mismatch in perma- with the restriction that nent strain among different regions in the body. In ", this context, it is highly expected that residual n1 + n2= 1 ...(3) stresses,however, do localised in a microstructural region, such as grain, can also occur. The thermal Supposing that nl = n and n2= 1- 11,where n is contraction or expansion associated with a tem- restricted to the range, 0 ~ n ~ 1. For the general perature change during successive cycles of defor- theory, subscript denote a particular phase of the mation induced wear process is one of the domi- material. nant mechanism which ca:n create microstructural The ratio of the total pore volume V y to total-residual stresses. Ih the present heterogeneous sys- material volume J-:is the tbtal porosity, tern, each homogeneous part like a single phase region process a unique thermal expansion prop- !6=~ (4) erty. When any change in temperature takes place V ... during abrasion each part undergoes a different thermal contraction or expansion strain and mic- Denoting n + as an additional volume ratio of the rostructural residual streses can then be created. solid material phase 2, i.e., V p to total solid vo- In addition, phase transformation is another com- lume, V mon mechanism which can create microstructural s residual stresses. One of the most important ef- v: fects which can be attributed to residual stresses in n + = "if ...(6) brittle material such as polymer composite are s caused by micro,crack initiated by these stresses. Nevertheless microstructural residual stresses can where n+ is restricted to the range of 0 ~ n+ ~ 1. also influenc~ other properties of a material. It is, Th!s gives first solid material phase/solid volume therefore, highly desirable that in FRP composite, ratIo as residual stress will be a key factor in discuss~g the wear mechanism. ~ =~ ~ = 1 -n + v: v: ... (7) s s Calculation of Stress Intensity Factors FRP composite has flaws and voids initially. It Now, the amount of pore volume associated with 276 INDIAN J. ENG. M.Ai.rER.SCI., OcrOBER 1994 each of th~ two material phases is proportional to or, from ( 6), ., i n+

~=n+oVv n+[(~)+1] ~ n= and [( -!v:) +1 ] V;=(1-n+)-Vv ...(8) ~ which automatically follows that, this implies, n= n+ ...(14) Vv= ~ + V; ...(9) This identity will simplify the relationship to be derived for stressand strain. Alternatively,d fined the material phase porosities can be The b aSlC.. ffilXture ru 1es "lor stress and s t ram.. m e as, terms of their rates and the material phase ratio, v! n, during abrasive process as, f/JI v =~ cj=n(cjl)+(1-n)cj2 ...(15) and and i=n-i'+(1-n)i2 ...(16) ~ f/J2=~ ...(10) If. number of aspe~ties are N, i.e; hard pa~icle WIth an average dIameter dl, which determmes length of the wear path, i.e., asperity propagation or zone and further that aU asperities are large + V + '" enough to create voids around them during abra- f/J1 = -!non = ~ 0" sion under an external stress. n° V n The averagedistance, dt is given by, and (n/6)'/3od, dt= 1/3 ...(17) (11) Fv f/J2=(1-n+)oVv=(1-n+)-f/J ... (1- n)oV (1- n) where Fv= n/6.df.n is the volume fraction of ma- terial removed during abrasion. -+ On the basis of above equations, it can be proved The fractal dimension of worn out surface can that n and n+ are identical and hence f/J' and f/J2 be expressed by the microstructural parameters d are both equal to f/J. and dt,where dis the spring length. From Eq. (2),

vi Df=log(C,o~/d)... (18) n=- 10g(C2o~/d) V Similarly, for material phase 2, granularC1 and fractured C2 are constants.surface), C1 For = 1 and expansion C2 = 31/2. (inter r The relationship between fractal dimension Df n = ~ = ~~ = n + Vv+ V p ...(12) of the worn su.rfa~eand the plane strain fracture V v: + v: v: + V toughness,K1c ISgiven by, v s v s K1c=[C.E.XooUf.EJ1/2 ...(19) or :;, where. C is the constant associated with hardness, (~) Poisson's ratio, E is the Young's modulus, Xo is ~+v. v. the average sliding distance and dt is the length of n= ...(13) wear track. (~)+ 1 11 ~f and Ef.are similar to fail~re stress or failure ~ stram assummgthat Uf ~ Eo Ef still holds good. CHAND etal,: ABRASIVE WEAR MECHANISM OF FRP COMPOSITE 277

From Eq. (18), than Gaussian distribution exists and it will simply be the cumulant, ," Df=log-[(Cl/C);;kKlC] ...(20) x --2 log-[(C2/C) k-K1c] C(X)= J ~x)dx=exp( X) ...(25) -~ 23lIXI where kis a constant. Substituting the va'lue of d, , where, X~ O. The normalised first failure' stressis given by, D _log-[C1(3l/6)Fv/3_a:l/d] XI (~ro) g- (3l/6 )R/3_d /d ] ...(21) 01 = 1 + ...(26) f-lo [C 2 v 1 EffJ

where d is the length of the spring and d1 is the w~ere, XI is the averag~ value ?f themos~ n~gative size of the hard particle. X,m a network of N sprmgs, which then satisfIes Equating relation (18) and (21), (N+l)C(Xl)=1 ...(27)

K[c =~ exp[I/2-log(3l/6-Pv)1/3_(dl/ d)C] Solving XI using the asymptotic form for C(X), XI = In(N+ 1) -In(23l1/2 Ixl) yo where C is the Vicker's microhardness of the Such that .' composite. ...Xl=-(lnN)1/2 ...(28) First spnng breaking stress In the proposed spring network model, the var- In order to uriderstand the mechanism of wear iations in the first breaking stress, 01 with ~ro/Ef process during abrasion kinetic energy due to can be determined. If the concept of spring length, movement of hard particle in the' matrix has been ro is introduced in otherwise perfect lattice, it will balanced against the energy associated with the yield a residual strain on that spring of value say, new surface created in the process, taking in ac- count the effect of stored elastic (strain) energy (ro -"0) which is, however, present in present physical sys- ~E= -p- ...(22) tern due to topological disorder. Moreover, for quasistatic loading of the sample, during wear pro- where fJ is a lattice dependent constant and fJ= 3 cess, it is clear that th~ wear rate should be Co?-~ in a two dimensional triangular lattice. trolled by the po.tentIa~ an~6 surface energy, m By superposition, the strain E on that spring un- close accordance WIth Griffith ~eory. der an applied load strain will be equal to DuTlDg the process of abrasIve wear, the mean , size of the worn out particle can be obtained by E = E + ~ E minimising the total free energy density (F) with app respect to th e ':icquire. d surf ace area per urnt. vo- (r' -~ ) lume A. The surface energy density associated = Eapp-T ...(23) with the equillibrium worn out particle which turns out to be exactly twice the kinetic energy This spring will then fail at a normalised applied density that was supposedly available for causing strain such that E= Ef where, the consequence of wear of the material. the influence of neighbouring disordered spring A simple modest formulation will be able to has been omitted, which might be affected during correct this problem and will contribute towards each cycle of the successiveabrasion process. the effect of potential energy. It may be pointed Further, spring with smallest value of ro would out here that the sample under load undergoes then be the first spring in the network to fail. Thus with homogeneous dilatation, that the process is adia- the notation X, batic and that the compressibility effects can be ig- nored. Further condition is added that no particle r;) -ro can worn out unitl a critical stress is attained. x=-;;;:- ...(24) Relation betweenK1C and particle size-The to- (I tal kinetic energy for initiating the wear is given The probability of choosing a value more negative by, .. 278 INDIAN J. ENG. MATER. SCI.,OCTOBER 1994

~T=2/5JfN.p.i2a5 ...(29) a=2p1/3 ...(35) where, p is the mass density, N is the overall num- In general, the solution to Eq. (34) is, ber of chipped off particles, i is the strain rate -1/2 .~ (= t/3p) and a is the average size (radius) of the a- 2(a/3) sinh(f/J/3) ...(36) chipped off particle. where f/J = sinh -I P( 3/ a )3/2 when the parameter Now the particles, which are worn out during' , the process, upon their remoyal are stress free and .8(3/ a )3/2> > 1 and a = (2.8)1/3 all the stored elastic energy is available for creat- ing further wear track, i.e., on the other hand, if P( 3/ a )3/2< < 1

( 2) a=2p/a ~P=~ =4/3 JfR3 ~ ...(30) i.e., when low fracture toughness and high fracture

initiation stress which implies that in the last limit where k is the bulk modulus and R is the initial the final worn out particle size is essentially inde- radius of the dialating fibre. pendent of strain rate and proportional to square The surface energy associated with the worn of the ratio of the fracture toughness to the initia- out particle, is tion stress. r w = 4 Jf Na2 y Conclusion '1

=r(Rla) ...(31) The proposed model to understand the abrasive 1 wear mechanism in fibre reinforced polymer com- where r i is the initial surface energy on the worn posite depends upon the microstructural parame- out fibril. So that incremental surface energy ac- ters of the material, system in which material func- quired is, tion and the distribution of residual stress. It has been found that wear factor depends on stress in- -~r = rj(l- Ria) ...(32) tensity factor, Klc, which in turn is related to the .. Balancmg the change m energy of the system d ue size of worn out particle. to wear of particle during abrasion, References ~T=~p+~r 1 Archard J F,JAppIPhys, 24(1953)981.

; 2 BahadurS,ASMI,JLubrTechno/,100(1978)449. =r j (aIR)2 + Pi + ri (1- Ria) ...(33) 3 HallingJ, ASMI, J Lubr Techno/, 105 (1983) 212. .

4 Moore M A, Fundamentals of Friction and Wear of materi- ~ = 0 alSo edied by D A Rigney (ASM, Metals Park, OH, USA) 1981. which can be written as, 5 Tsukizoe T & Ohmae N, Fibre Sci Techno/,18 (1983) 265. a3+aa-2p=0 ...(34) 6 SungNH&SuhNP,Wear,53(1979)129. 7 Clerico M & PatiemoY, Wear,53 (1979)279. where, 8 BahadurS&ZhengY,Wear,137(1990)251. 9 Suh N P, Sin C H & Saka N, Fundamentalsof Tribology 2p 5(Oc)2 -.2 (MIT Press,USA), 1980,493. .. a=-+--;-and .8- 512 (K1clPct) 10 Lhymn C, TemplemeyerK E & DavIs P K, Composites, R 3pct 16(1985)127. 11 Ciri~oM, Pipes R B & Friedrich K, J Mater Sci, 22 (1987) and further, K = pC2 and surface energy 2481. 12 Tewari U S & Bijwe J, TribologyInternationa/, 24 (1991) Y =K IcI2pc2 13 CurtinWM&ScherHJ,MaterRes,5(3)(1990)535.247.

Wh.en th e sUrf ac~ e nergy of unworn.'. Particle ..(1993) can 14 ,Chand1603. N, Fahim M & H~ssainS G, J Mater Sci Leu, 12 ~ be Ignored and the stress requIred to 1ll1t1atebreak 15 EvansAG, Adv Ceram,21 (1976)171. up is insignificant a -.0 and the solution for Eq. 16 Griffith A A, Philos Trans Soc London A, 221 (1920) (34) is, 163.