Ž .Wear 225–229 1999 205–214

Transitions between two-body and three-body abrasive wear: influenceof test conditions in the microscale abrasive wear test

R.I. Trezona ), D.N. Allsopp, I.M. HutchingsUniÕersity of Cambridge, Department of Materials Science and Metallurgy, Pembroke Street, Cambridge, CB2 3QZ, UK

Abstract

Ž .The microscale abrasive wear test also known as the ball-cratering wear test is generally considered to be a three-body wear test.Ž . Ž .Nevertheless, different test conditions can produce either two-body grooving or three-body rolling wear mechanisms. The wearŽ . Žmechanisms and wear rates were investigated over a range of loads 0.1 to 5.0 N , slurry concentrations 0.000031 to 0.24 volume

. Ž .fraction abrasive and abrasive materials SiC, Al O and diamond . It was found that for each abrasive, a transition from grooving to2 3

rolling wear could be identified with a critical ratio of load to slurry concentration. The wear rate varied with concentration, with amaximum at intermediate slurry concentrations. The classification of abrasive wear into two-body and three-body mechanisms is

wdiscussed with reference to the problems noted by Gates J.D. Gates, Two-body and three-body abrasion: a critical discussion, Wear 215Ž . x1998 139–146 . q 1999 Elsevier Science S.A. All rights reserved.

Keywords: Abrasive wear; Grooving wear; Rolling wear; Ball-cratering

1. Introduction

w xThe ball-cratering microscale abrasive wear test 1,2 isan example of a test method which produces an imposed

w xwear scar geometry 3 . In this method, a sphere of radiusR is rotated against a specimen in the presence of a slurryof fine abrasive particles. The geometry of the wear scar isassumed to reproduce the spherical geometry of the ball,and the wear volume may then be calculated by measure-ment of either the crater diameter or its depth. For ho-mogenous bulk materials, the wear volume, V, can berelated to the total distance of sliding, S, and the normalload on the contact, N, by a simple model for abrasive

w xwear 4 which is equivalent to the Archard equation forsliding wear:

VskSN 1Ž .3 Ž .y1where k is the ‘wear coefficient’ with units m N m ;

the abrasive wear resistance is defined as ky1 and hasŽ . y3units N m m . The usefulness of k as a measure of the

abrasive wear response of the material is thus limited tosituations in which the wear volume is directly propor-tional to both the load and sliding distance.

) Corresponding author. Fax: q 44-1223334567; e-mail:rit1001@cus.cam.ac.uk

For a wear scar of spherical geometry in an initiallyplane specimen, the wear volume may be calculated from

Žthe crater dimensions i.e., surface chordal diameter b or.depth h :

p b4

Vf for b<R 2aŽ .64R

Vfp h2R for h<R 2bŽ .

The method may be extended to coated systems, and thewear coefficients of both the coating and substrate may be

w xdetermined from a single test 1,5 . The method may alsobe extended to specimen surfaces with compound curva-

w xture using suitable expressions for the wear volume 6 .Several variants of the experimental apparatus exist,

which can be divided into two categories: ‘free ball’machines, in which the ball is driven by friction from adrive shaft against which it rests, and in which the loadapplied to the sample is essentially due to the weight of the

w xball 1,2 ; and ‘fixed ball’ machines, in which the ball isŽdriven positively for example, by being clamped between

.coaxial rotating shafts and the sample is loaded againstthe ball with the desired normal force by a lever armarrangement.

0043-1648r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved.Ž .PII: S0043-1648 98 00358-5

( )R.I. Trezona et al.rWear 225–229 1999 205–214206

Published results from this test, and from the essentiallyw xsimilar dimple-grinder test 5 , have used abrasive slurries

y3 w xof SiC at 0.75 g cm 1 , diamond at approximately 0.01y3 w xg cm 7 , or diamond of unspecified standard concentra-w xtion 5 . Loads of between 0.05 and 0.35 N have been used

w x1,2,5,7,8 . There is clearly a wide range of test conditionsin use, but to date there has been no systematic report ofthe effect of slurry concentration and composition, or ofnormal load. Published micrographs of the wear cratertopography show that the wear mechanisms for the dilutediamond slurries are predominantly two-body parallelgrooving, whereas the mechanisms seen with the moreconcentrated SiC slurries are predominantly associated withthree-body wear by rolling particles, with no apparent

w xdirectionality to the topography 1,2,5,7,8 .A study was therefore carried out into the effects of

slurry concentration, abrasive material and applied normalload on the mechanism and rate of wear in the microscaleabrasive wear test.

2. Experimental methods

Tests were performed with two different fixed-ball ma-chines. The first was constructed in this laboratory andallows continuous measurement of the depth of the wearscar during the test, without requiring it to be interrupted.This machine was used for mapping the wear mechanismsand investigating the effect of slurry concentration. The

Ž .apparatus is shown schematically in Fig. 1 a . The ball isdriven positively by a shaft, and the sample is held hori-zontally beneath the ball, pressed upwards against it by alever arm with dead weight loading. The wear depth waslogged and plotted by computer, and observed continuallyduring the test to confirm the smooth progress of wear.However, the final wear volume was determined frommeasurements of the scar diameter by optical microscopy,and in some cases also by optical profilometry. The wearvolume was calculated from the measured crater diameter

Ž .via Eq. 2a .The other instrument is a commercial Plint TE-66 mi-

croscale abrasion tester which allows more accurate con-Ž .trol of the normal load to an accuracy of "0.01 N and is

Ž .illustrated schematically in Fig. 1 b . The ball is drivenpositively by a shaft. The sample is mounted vertically ona pivoted L-shaped arm and is loaded against the ball by adead weight hanging from the horizontal lever. The wearvolume was calculated from the diameter of the wear scar

Ž .via Eq. 2a . This method was used to investigate theeffects of both total sliding distance and normal load onthe wear volume. For the sliding distance experiments,sequential tests at a range of sliding distances were carriedout at different locations on the specimen.

Fig. 1. The two microscale abrasion test machines employed in this work.

Hard martensitic steel bearing balls were used, 25.40mm in diameter, with a hardness of 990"40 HV. Theballs were treated before use to produce fine surfacepitting. This modification has been shown to be necessaryin order to achieve consistent results on materials softerthan the ball, as the pits aid in the entrainment of the

w xabrasive into the contact 9 . All tests were performed onŽtool steel specimens 1.0 wt.% C; 1.2 wt.% Mn: 0.2 wt.%

.Si: 0.5 wt.% Cr; 0.15 wt.% V; 0.5 wt.% W , quenched andtempered to a hardness of 775"10 HV, then ground andpolished by conventional metallographic methods.

Abrasive slurries of SiC, Al O and diamond particles2 3

suspended in distilled water were used, at various concen-trations between 0.0001 and 1.0 g of abrasive per cubiccentimetre of water. The SiC and Al O abrasives were2 3

grade F1200, with mean particle sizes of 4.25 and 4.97mm, respectively, and the diamond abrasive had a meanparticle size of 3.05 mm, all determined by laser granulom-etry. The slurries were agitated continuously throughouteach test to prevent settling of the abrasive particles. Alltests were performed with a sliding speed of 0.05 m sy1

and total sliding distances of 15 to 75 m. The slurries werefed on to the top of the ball throughout the test at a rate ofapproximately 0.25 cm3 miny1. A range of normal loadsfrom 0.1 to 5.0 N was used.

( )R.I. Trezona et al.rWear 225–229 1999 205–214 207

Fig. 2. SEM image of the worn surface of a quenched and tempered tool steel produced by microscale abrasion at a normal load of 0.25 N with a 0.0009Ž y3 .volume fraction 0.003 g cm 3 mm diamond slurry. This surface is typical of those produced at high loads and low slurry concentrations.

The worn samples were examined by optical mi-croscopy, scanning electron microscopy and optical pro-filometry.

3. Results

3.1. Wear mechanism transitions

A two-body grooving wear mechanism was found to bedominant at high loads andror low slurry concentrations

for all abrasives tested. This process occurs in the mi-croscale abrasion test when a significant proportion of theparticles embed in the surface of the ball bearing and actas fixed indenters, producing a series of fine parallelgrooves in the specimen surface. Examination of such

Ž .wear scars by SEM Fig. 2 indicates that the grooves aresteep-sided and correspond well in size with the abrasiveparticles. This suggests that the grooves are formed by theabrasive particles and not by asperities on the surface ofthe ball. The dominant mechanism at low loads andror

Fig. 3. SEM image of the worn surface of quenched and tempered tool steel produced by microscale abrasion at a normal load of 0.25 N with a 0.237Ž y3 .volume fraction 1.0 g cm F1200 SiC slurry. This surface is typical of those produced at low loads and high slurry concentrations.

( )R.I. Trezona et al.rWear 225–229 1999 205–214208

Fig. 4. Wear mechanism map for ball crater microscale abrasion of toolsteel by F1200 SiC slurry.

high slurry concentrations was a three-body process, inwhich the abrasive particles do not embed, but roll be-tween the two surfaces producing a heavily deformed,multiply indented wear surface with no evident surfacedirectionality. A scanning electron micrograph of a typicalthree-body wear surface formed in the tool steel is shownin Fig. 3. At intermediate loads andror slurry concentra-tions some of the wear scars displayed a mixed character,with two-body grooving in the centre and three-bodyrolling at the sides.

Wear mechanism maps, in terms of the applied load andslurry concentration for SiC, Al O and diamond, are2 3

shown in Figs. 4–6. The transition between two-bodygrooving and three-body rolling was found to occur at anapproximately constant ratio of load to volume fraction forthe SiC and Al O abrasives for loads up to 1.0 N; the2 3

ratio loadrvolume fraction was approximately 7 for SiCand approximately 5 for the Al O . For the diamond2 3

abrasive, there was a much wider variation in this ratio,although the average value was also approximately 5.

3.2. Wear Õolumes

The variation of wear volume with slurry concentrationwas studied for the SiC abrasive and is shown in Fig. 7. Itwas nonlinear, exhibiting a maximum in wear volume at

y3 Ž .0.1–0.2 g cm volume fraction 0.03–0.06 for the loads

Fig. 5. Wear mechanism map for ball crater microscale abrasion of toolsteel by F1200 alumina slurry.

Fig. 6. Wear mechanism map for ball crater microscale abrasion of toolsteel by 3 mm diamond slurry.

studied. At low slurry concentrations the wear volume wasalmost independent of load, depending predominantly onslurry concentration.

The effect of the total sliding distance on the volume ofwear was investigated for both mechanisms by using very

Ž . Žlow volume fractions0.015 and very high volume.fractions0.189 F1200 SiC slurries to ensure two-body

grooving and three-body rolling respectively. The resultsare plotted in Figs. 8 and 9. The total wear volume wasfound to be directly proportional to the sliding distance, in

Ž .agreement with the prediction of Eq. 1 .The effect of the normal load on the wear volume per

unit sliding distance was also studied for both three-bodyrolling and two-body grooving mechanisms, by using the

Ž . Žsame high volume fractions0.189 and low volume.fractions0.015 SiC slurry concentrations to try and en-

sure that the mechanism stayed the same over the completerange of loads employed. A much greater range of loadswas investigated for three-body rolling wear than for two-body grooving wear, because it was not possible to obtainwell-formed spherical craters for loads greater than 0.5 Nunder the conditions used to ensure grooving wear condi-tions. A mechanism by which slurry is not fully entrainedinto the wear contact but instead flows round the sides has

w xbeen described previously 9 . This mechanism leads to

Fig. 7. Variation of wear volume after 30 m sliding with slurry concentra-tion and applied load in the microscale abrasion test; F1200 SiC abrasiveslurry against tool steel.

( )R.I. Trezona et al.rWear 225–229 1999 205–214 209

Fig. 8. Variation of wear volume with sliding distance for three-bodyŽ y3 .rolling abrasion; 0.189 volume fraction 0.75 g cm F1200 SiC abra-

sive slurry against tool steel at a load of 0.25 N.

nonspherical wear scars, characterised by a ridge of speci-men material in the centre of the scar, parallel to thesliding direction. Such ridges were present in all thetwo-body grooving wear scars produced at loads of over

Ž0.5 N, and also in some produced at lower loads as.indicated in Fig. 11 .

Fig. 10 shows the wear volume per unit sliding distanceas a function of normal load for the higher slurry concen-tration. Despite the use of a concentrated slurry, the wearscar produced at a normal load of 5 N displayed a surfacetopography characteristic of the two-body grooving wearmechanism and was also generally nonspherical, with aridge of specimen material in the centre of the scar. Thewear scar at 3 N was spherical in general form and itswear surface was mainly characteristic of three-bodyrolling, but it displayed some evidence of two-body groov-ing. However, under all the other loads employed at thisslurry concentration, the dominant wear mechanism wasthree-body rolling. These data suggest that the wear vol-

Ž .ume per unit sliding distance VrS is directly propor-Ž .tional to the normal load N for three-body rolling abra-Ž .sion in agreement with Eq. 1 .

Fig. 11 is a plot of the wear volume per unit slidingdistance as a function of normal load for the lower slurry

Ž .concentration volume fractions0.015 . All the wear scarsdisplayed a two-body grooving wear surface, although

Fig. 9. Variation of wear volume with sliding distance for two-bodyŽ y3 .grooving abrasion; 0.015 volume fraction 0.05 g cm F1200 SiC

abrasive slurry against tool steel at a load of 0.10 N.

Fig. 10. Variation of wear volume per unit sliding distance with normalŽload for three-body rolling abrasion; 0.189 volume fraction 0.75 g

y3 .cm F1200 SiC abrasive slurry against tool steel; various slidingdistances from 12 to 24 m.

some were ridged and nonspherical; these have been plot-ted as a different data set. The variation of the wearvolume of the spherical two-body grooving scars with loadappears to be nonlinear, in disagreement with the predic-

Ž .tions of Eq. 1 , and is better described by a power lawfunction with an exponent of load of 0.62 than by a linearfit. There is no clear relationship between normal load andwear volume per unit sliding distance for the ridged wearscars.

4. Discussion

4.1. Wear mechanism transitions

The dependence of the wear mechanism on load andabrasive concentration can be explained by an adaptation

w xof an existing model; Williams and Hyncica 10 showedthat an abrasive particle between two surface undergoes atransition from grooving to rolling at a critical value ofDrh where D is the particle major axis and h is the

Ž .separation of the surfaces Fig. 12 . In their work, thesurface separation h was determined by hydrodynamiclubrication conditions; in the present case, the surfaces are

Fig. 11. Variation of wear volume per unit sliding distance with normalŽload for two-body grooving abrasion; 0.015 volume fraction 0.05 g

y3 .cm F1200 SiC abrasive slurry against tool steel; constant slidingdistance of 32 m.

( )R.I. Trezona et al.rWear 225–229 1999 205–214210

Fig. 12. The geometry of a single abrasive particle is described byw xparameters D and b , after Williams and Hyncica 10 .

not supported by a significant hydrodynamic pressure, andso the separation is determined by the load and by thenumber of particles within the contact, or equivalently, theload per particle. If the contact contains many particlesunder a low load, each particle will indent the surfacesonly lightly, and so Drhf1. For a typical angular parti-

Ž . w xcle geometry bs558 the critical ratio is 1.74 10 , andso at low loads, rolling wear is produced. If the contactcontains a few heavily loaded particles they will indent thesurface more deeply, making Drh)1.74, and groovingwear results.

Let us assume that the surfaces are of equal hardness,with H sH sH. Then the indentation depths of theA B

particle will also be equal; asb. The particle hardness isassumed to be large compared with the surface hardness.

At the transition, the inclination of the particle tends tow x908 10 , so hfDy2 a.

For a pyramidal indentation, for instance a Vickersindentation, the surface diagonal length d is proportionalto the depth a; and the hardness is defined by

PHA 3Ž .2d

where p is the load on the indenter, i.e., the mean load perparticle. It can readily be shown that p depends on thetotal load N, the projected area of the wear contact A, andthe volume fraction of abrasive Õ, in the following way:

ND2

pA 4Ž .AÕ

'Therefore hsDyB prH where B is a constant for agiven indenter geometry.

At the transition Drh is constant, andy1D B p

s 1y 5Ž .(ž /h D H

Ž .'Therefore BrD prH is expected to have a constantvalue at the transition between wear mechanisms.

This model predicts that the wear mechanism will de-pend upon the load per particle p, the length of the majoraxis of the particle D, the hardness of the surfaces H, andthe constant B, which may be interpreted as a ‘geometry

Žfactor’ dependent on the particle shape. The critical value

of Drh, and therefore of the expression above, dependsw x .on the particle shape as defined by the angle b 10 . We

therefore expect different transition values for differentabrasive particle sizes and shapes.

The model is consistent with the results reported in thisstudy: a transition in wear mechanism is observed as thevolume fraction of abrasive or the normal load, and hencethe load per particle, is changed; and the transition value isdependent on the abrasive used.

The effects of particle size and surface hardness haveyet to be fully investigated.

4.2. Wear Õolumes

A large and nonlinear variation in the wear rate wasŽ .observed as the slurry concentration was changed Fig. 7 ;

test results using different slurry concentrations are there-fore not directly comparable. The rate of change of wearrate was greatest for high loads at abrasive volume frac-

Ž y3 .tions above approximately 0.003 0.01 g cm .At very low slurry concentrations, the wear volume is

seen to be almost independent of load, contrary to theŽ .linear dependence of Eq. 1 . This is to be expected, as one

of the assumptions in the derivation of the equation is thatan increase in load causes the particle to embed moredeeply. Clearly, assuming that the particles do not fracture,there must come a point where each particle is fullyembedded, and any additional load must be supported by ahydrodynamic film andror by asperities on the surfaceitself. An increase in load will therefore not increase thevolume of material removed by abrasion; the wear coeffi-cient can only be increased by increasing the number ofparticles in the contact, by raising the slurry concentration.

4.2.1. Sliding distanceAny simple model for the volume of material removed

by abrasive action will predict that the wear volume shouldbe directly proportional to the total distance that the two

Ž Ž ..surfaces have slid over each other Eq. 1 , i.e., that thewear volume per unit sliding distance does not change.However, in the case of the microscale abrasion test andother wear tests in which the size of the wear contactincreases with sliding distance, it is not at all obvious thatthe wear volume per unit sliding distance should necessar-

w xily remain constant 3 .During a microscale abrasion test, the area of the wear

contact is continually increasing and consequently, thenominal pressure on the contact is continually decreasing.This means that, assuming the concentration of the slurryin the contact does not change, the load per abrasive

Ž Ž ..particle decreases as the wear volume increases Eq. 4 .Even if the slurry concentration in the contact does change,it is still likely that the load per particle will vary in someway with wear volume. Thus, in order for the wear volumeper unit sliding distance to be independent of the sliding

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distance, it must also be independent of the load perabrasive particle.

Independence of the wear rate on load per particle isŽ . w xindeed a feature of Rabinowicz’s derivation of Eq. 1 4 .

In this approach, both the load per particle, and thecross-sectional area of the groove in the wearing surfacecreated by each particle, depend directly on the number ofparticles in the contact. Thus, for higher load per particlevalues, there must be fewer particles, each of which re-moves a larger cross-sectional area volume of material sothat the total volume of material removed is the same.However, the results plotted in Fig. 7 suggest that, formicroscale abrasion, the load per particle does have aneffect on the wear rate; there is significant variation in thewear volume as the slurry concentration changes. The onlyway in which the slurry concentration can affect the wearprocess is by altering the actual concentration of abrasivein the wear contact. This is significant because it hadpreviously been suggested that the actual concentration ofabrasive in the wear contact was independent of the slurry

w xconcentration 1 .As the slurry concentration and thus the load per abra-

sive particle has been shown to affect the wear rate in theŽ .microscale abrasion test Fig. 7 , the wear volume per unit

sliding distance would not be expected be independent ofsliding distance. Figs. 8 and 9 show the variation of wearvolume with sliding distance for a 0.189 volume fractionŽ y3 .0.75 g cm SiC slurry at 0.25 N and a 0.015 volume

Ž y3 .fraction 0.05 g cm SiC slurry at 0.10 N, producingthree-body rolling and two-body grooving conditions re-spectively. It is surprising to see that the wear volume perunit sliding distance does, in fact, remain remarkablyconstant. However, an explanation for this apparent contra-diction can be offered by further reference to Fig. 7.

The variation of wear volume with slurry volume frac-tion is smaller for lower loads, only changing by a factorof about 3 over the complete range of concentrations for aload of 0.25 N; an even smaller variation would be ex-pected for 0.1 N. For the three-body rolling regime of the0.25 N plot, the crater volume changes by a factor of about2 with a change in volume fraction of abrasive by a factorof 15. For the two-body grooving regime, the wear volumechanges by a factor of 3, for a change in volume fractionof abrasive by a factor of 1000.

Since the load per particle is inversely proportional toŽ Ž ..the volume fraction of abrasive in the slurry Eq. 4 , it

follows that although the wear rate does depend on theload per particle, it is not very sensitive to it, especially atlower loads, and plots of wear volume against slidingdistance may well be expected to appear linear if the range

Žof wear volumes involved is relatively small since theprojected area of the contact is proportional to the square

.root of the wear volume for these shallow scars . Forinstance, for three-body rolling behaviour in Fig. 8, thewear volume changes only by a factor of 4, so the contactarea and thus the load per particle change only by a factor

Ž Ž ..of 2 Eq. 4 . For the two-body grooving case shown inFig. 9, the contact area also changes only by a factor ofabout 2.

4.2.2. Normal loadŽ .Eq. 1 also predicts that abrasive wear volume should

be directly proportional to the load on the wear contact.The data presented in Figs. 10 and 11 suggest that volumeis proportional to load for three-body rolling but that fortwo-body grooving, wear volume is proportional to apower of load lower than one.

It is interesting to note, however, that the linear trend-line through the data for three-body rolling in Fig. 10 doesnot pass through the origin of the plot. There is also aslight discontinuity between the values at 0.75 N and 1.0N. The ‘linear’ section of Fig. 10 has been replotted in Fig.13 to indicate the sliding distance at which each test wasconducted. It does appear that there is a slight discontinu-ity, not just between 0.75 N and 1.0 N, but also at everypoint at which the sliding distance was changed. This iswhat might be expected since the wear volume per unitsliding distance is weakly dependent on the sliding dis-tance as discussed above.

Another important feature of the results plotted in Fig.10 is that at 5 N load the wear mechanism was two-bodygrooving rather than three-body rolling, and that at 3 N thewear scar displayed a mixed character. This confirms thata transition between the two mechanisms will occur even

Ž .at very high slurry concentrations 0.189 volume fractionif a sufficiently high load is used.

It has been shown in Fig. 7 that for two-body groovingwear with slurries of very low abrasive volume fractionŽ .below 0.003 the wear volume is almost independent ofthe normal load. This has been explained by total embed-ding of the abrasive particles when there are very few ofthem in the contact. For three-body rolling abrasion, thevolume does appear to be proportional to the load. How-ever, there is a transitional two-body grooving regime inwhich the applied load has some effect on the wearvolume, but is not directly proportional to it. For SiC

Fig. 13. Variation of wear volume per unit sliding distance with normalload for three-body rolling abrasion; the sliding distance at which each set

Žof tests was carried out has been included; 0.189 volume fraction 0.75 gy3 .cm F1200 SiC abrasive slurry against tool steel.

( )R.I. Trezona et al.rWear 225–229 1999 205–214212

slurries this regime lies between 0.003 and 0.030 volumefraction.

It can be seen from Fig. 11 that at an abrasive volumefraction of 0.015 the wear volume is proportional to loadto the power of about 0.6. In terms of the Rabinowicz

Ž .derivation of Eq. 1 , the increase in load has caused theparticles to embed more deeply, but the correspondingincrease in material removal is not as great as would beexpected. This may be because at such a relatively lowabrasive volume fraction, the particles are being embeddeddeeply enough so that they no longer behave as thegeometrically self-similar indenters assumed in the deriva-tion of the equation.

4.2.3. Ridged wear scarsUnder the conditions used to investigate the effect of

load for two-body grooving abrasion, the wear scars oftendid not form properly, displaying a ridged topography. The

w xformation of these ridges has been discussed before 9 andit was concluded that they are a feature of the entrainmentof abrasive into the wear contact. It was shown thattendency for ridge formation depends on the hardness ofthe specimen material and the surface condition of the ball.In the present work it has been shown that ridge formationis also more likely at higher loads and lower slurry concen-

Ž .trations Figs. 10 and 11 . It has previously been estab-w xlished 9 that a ridge will form if abrasive cannot get into

the wear contact at the start of the test. This explains whyridges are likely to form for a higher applied load andlower slurry concentration as both these effects will makeit more difficult for slurry to be entrained at the start of thetest.

4.3. Classification of abrasion

The classification of abrasive wear into the categories‘two-body abrasion’ and ‘three-body abrasion’ is widely

w xused 11 and will be familiar to most readers. The originof these terms comes from the application of systems

w xanalysis to abrasion 12,13 . The systems analysis ap-proach seeks to break down a phenomenon into a list ofinputs and outputs. The process by which the inputs aretransformed into the outputs is treated, initially, as a ‘blackbox’. Thus, for two-body abrasion the inputs are the twosurfaces that interact: the first body, which is the bodywhose wear is of the most concern, and the second body, acounterface which is in motion relative to the first bodyand in direct or indirect contact with it such that forcesmay be transmitted between the two bodies. In three-bodyabrasion, the inputs are the two surfaces, the first andsecond bodies as described before, and a third body whichcomprises any solid materials, entirely separate from thefirst two bodies, which might be present at the interfacebetween the first and second bodies. It can readily be seenthat according to the original, systems analysis definition,microscale abrasion with an abrasive slurry is a three-body

abrasion process irrespective of the experimental condi-tions employed.

However, the current dominant interpretation of thedifference between two- and three-body abrasion differsfrom the original distinction derived from systems analysisw x11 . In this dominant view, two-body abrasion is a processin which particles or asperities are rigidly attached to thesecond body whereas in three-body abrasion, the abrasiveparticles are loose and free to roll. Two-body abrasionconditions are expected to produce higher wear rates thanthree-body conditions because the contact between theabrasive particle and the wearing surface is sliding ratherthan rolling. Under this classification, microscale abrasionis considered to be a two-body abrasion process underconditions in which the abrasive becomes embedded in thecounterface and a three-body abrasion process when theabrasive particles do not embed and are able to rollbetween the two surfaces.

Clearly, there is a discrepancy between the interpreta-tion obtained from the literal, systems analysis approachand the interpretation most commonly used. In a recent

w xpaper, Gates 11 cites several more examples where theapplication of the current dominant interpretation leads toinconsistencies. For example, a shovel digging into a pileof loose rock is considered as a three-body interactioneven though there is no separate counterface present as asecond body. The dry sandrrubber wheel abrasion testŽ . w xDSRWAT 14 is considered to produce three-body abra-sion. However, in this test, particles are, to some extent,gripped by the rubber and may not be free to rotate,producing unexpectedly high wear rates for three-bodyabrasion. Also, the case of free-flowing sand or gravelsliding down a chute is often regarded as two-body eventhough the particles may be rolling and the wear rates canbe very low.

These difficulties arise from the use of the terms two-and three-body to distinguish between situations in whichthe abrasive particles are fixed to the counterface, produc-ing grooves, or free, so that they roll between the twosurfaces, irrespective of the actual number of bodies in-volved. The terms two-body abrasion and three-body abra-sion would be better used in their original, systems analy-sis sense to describe the number of different inputs in anabrasion situation. The current dominant usage of theseterms, however, is mechanistic, describing the behaviourof the particles in the wear contact, rather than situation-based.

It is thus the opinion of the current authors that newterms should be adopted that describe the behaviour of theabrasive particles. Abrasive wear processes in which theparticles are fixed to the counterface would be described as‘grooving abrasive wear’ and abrasive wear processes inwhich the abrasive is able to roll between the two surfaceswould be described as ‘rolling abrasive wear’. However, itis possible for abrasive particles to slide over a surfaceproducing grooves even if they are not held by a counter-

( )R.I. Trezona et al.rWear 225–229 1999 205–214 213

Ž .face gravel sliding down a chute, for instance so thefollowing more complete definitions are suggested:

GrooÕing abrasiÕe wearAn abrasive wear process in which effectively the same

region of the abrasive particle or asperity is in contact withthe wearing surface throughout the process. Wear surfacesproduced by grooving abrasion are characterised by groovesparallel to the direction of sliding.

Rolling abrasiÕe wearAn abrasive wear process in which the region of the

abrasive particle in contact with the wearing surface iscontinually changing. Wear surfaces produced by rollingabrasion are characterised by a heavily deformed, multiplyindented appearance and little or no directionality.

In many abrasive wear situations it is likely that carefulexamination of the wear surface would be required inorder to determine whether grooving wear or rolling wearis occurring; in this sense, the classification scheme out-lined above is at a disadvantage with respect to alternatives

w xbased on the severity of the wear 11 since a change inwear severity is more readily identifiable to an engineerwithout specialist equipment. However, the classificationof abrasive wear into grooving wear and rolling wear hasthe key advantage of being a direct reference to the wearprocess rather than either the situation that causes thatprocess or its secondary manifestations. In the microscaleabrasion work presented in this paper, it has been shown inFigs. 4–6 that relatively small changes in test conditionsŽ .in this case, load and slurry concentration can lead totransitions between grooving wear and rolling wear. Thereare a range of conditions, near the transition between wearprocesses, for which it would not be possible, just fromknowledge of the wear situation, to determine how thewear was occurring. Also, because grooving wear occursat lower slurry concentrations in microscale abrasion, thewear rate, or wear severity, associated with grooving wear,is not necessarily any higher than that produced by rolling

Ž .abrasion Fig. 7 and it is thus not always possible todetermine how the wear is occurring just by reference tothe severity of wear.

5. Conclusions

Ž .1 In the microscale abrasion test, both ‘two-body’grooving and ‘three-body’ rolling mechanisms can be pro-duced in a nominally three-body situation, by varying theparameters of normal load, volume fraction of abrasive inthe slurry, and abrasive type.

Ž .2 The operating wear mechanism has been mapped fora range of normal loads and volume fractions, for threedifferent abrasives; the grooving mechanism dominated athigh loads and low abrasive volume fractions and therolling mechanism dominated at low loads and high abra-sive volume fractions.

Ž .3 The transition between the two wear mechanismsoccurs at an approximately constant ratio of normal load toslurry volume fraction for the SiC and Al O abrasives,2 3

while for the diamond abrasive there was a wider variationin the ratio, but a similar mean value. The exact value ofthis ratio at the transition depends on the abrasive used. Anexisting model for abrasive wear has been adapted todescribe the wear situation encountered in the microscaleabrasion test. This model is able to account for the wearmechanism transition and its dependence on the load,abrasive volume fraction and abrasive type.

Ž .4 The wear rate in this test varies with abrasivevolume fraction in a nonlinear way, with the most severewear at intermediate concentrations. At low volume frac-tions the wear rate is influenced predominantly by theslurry concentration; the normal load is a much weakerfactor than at high slurry volume fractions.

Ž .5 For the rolling wear mechanism, the wear volume isproportional to the normal load, in accordance with the

Ž .classical Archard wear equation 1 . For the grooving wearmechanism, the wear volume is proportional to somepower of load lower than one.

Ž .6 The wear rate in this test is found in practice to bealmost constant with sliding distance, in accordance with

Ž .the classical Archard wear equation 1 , for both groovingand rolling wear mechanisms, despite the change in con-tact conditions during the test. This is thought to bebecause the wear rate is not highly sensitive to the load perparticle.

Ž .7 The consequence for microscale abrasive wear test-ing is that values of the wear coefficient are only directlycomparable if obtained under the same conditions of abra-sive type and abrasive volume fraction. Values obtained atdifferent loads, but with identical slurries are comparableonly for the rolling wear mechanism. Values obtained atdifferent sliding distances but otherwise identical condi-tions are likely to be comparable for both wear mecha-nisms.

Ž .8 It is suggested that the terms ‘grooving abrasivewear’ and ‘rolling abrasive wear’ should be adopted forthe description of abrasive wear mechanisms, to producean entirely unambiguous replacement for the terms ‘two-body abrasive wear’ and ‘three-body abrasive wear’, dueto the contradictory interpretations of the latter terms in theliterature.

Acknowledgements

This work was supported via the CASE studentshipscheme by the Engineering and Physical Sciences Re-

Ž .search Council, MultiArc UK and the Ford Motor Com-pany. We would also like to acknowledge the work ofKeith Rutherford and Gary Chapman in the design andconstruction of the depth-sensing microscale abrasion ap-paratus.

( )R.I. Trezona et al.rWear 225–229 1999 205–214214

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