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David by Edited 14853 NY F Polytechnique Ecole wear adhesive Aghababaei of Ramin origins debris-level the On seiycnat.I a hw htdbi atce omol at only form particles debris that at shown formation was debris It controls that contacts. scale asperity length debris identi- critical the wear a by a of (19) of fication addressed recently formation was the question to This When lead particle? 18): collision (4, asperity Archard an by does posed question long-standing a chal- gradual lenges further a observation reporting This by smoothing. formation asperity debris atom-by-atom wear of chal- origins and (15–17) the experiments lenge (12–14) wear are (AFM) simulations origins microscope wear force microscopic atomic Single-asperity their (11). and unclear empirical, still fully remain tions (10). friction) of normal law to first proportional Amontons’ force (i.e., tangential force a proportional and volume wear distance a sliding assumes fol- one to observation if third two first The the 9). from (2, proportional lows load be to normal observed macroscopic is the contact to of by area understood real be the then that can noting sur- observation second elevated of The area between 3). real (2, the contact contact with the of associated consequently that result is and arguing direct asperities face a by is The rationalized process 5–8). commonly wear (3, is experimentally observation observed first dis- and inter- sliding and fric- (5) and discussed 1860 the in force mittently Reye to by frictional hypothesized proportional of first is was product which volume tance), the wear wear (i.e., Archard’s the work i.e., (iii) tional interface, and wear the 4), (i.e., (3, to rate law normal wear acting the macro- load the (ii) to scopic proportional independent 3), linearly is is (2, distance) sliding debris) contact per volume of wear area of apparent volume the of total (i) load, (i.e., applied volume of range exper- wear certain wear a of within series showed, systematic that a iments with mid-1900s the in occurred T nanotribology a ´ nttt fCvlEngineering, Civil of Institute ept h asg fmr hn5 er,teewa rela- wear these years, 50 than more of passage the Despite a vrtocnuiso itr 1.Sbtnilprogress Substantial (1). history of centuries “wear,” as two known surfaces, over sliding at has loss material of study he | deiewear adhesive ed ´ rl eLuan,C 05Luan,Sizrad and Switzerland; Lausanne, 1015 CH Lausanne, de erale ´ a,b ee .Warner H. Derek , cl oyehiu F Polytechnique Ecole ´ | friction | erdbi particle debris wear c n Jean-Franc¸oisMolinari and , ed ´ rl eLuan,C 05Luan,Switzerland; Lausanne, 1015 CH Lausanne, de erale ´ | 1073/pnas.1700904114/-/DCSupplemental at online information supporting contains article This Submission. 1 Direct PNAS a is article This interest. of supervised conflict J.-F.M. no declare discussions; paper. authors the the The wrote J.-F.M. in and D.H.W., participated R.A., J.-F.M. and and research; the D.H.W., R.A., data; lyzed and potentials the of Details wear analyzed. 3D and of process simulated dia- formation is developed The particles used. recently developed are a newly (20) and potential and mond (19) potentials 2D interatomic leads of model size set junction 3D A the formation. that debris so wear chosen to was here simu- all discussed of lations junctions configuration smaller the asper- and Accordingly, larger particles plastically. with smoothing debris size, wear junction forming recent critical junctions our a ity in exists shown surface there As flat (19), surfaces. atomistically study opposing an on properties. with asperities contact two interfacial in and asperity and single bulk a configurations, i.e., geometrical and distinct two size, spanned conditions, simulations boundary The and size, contact shape system sliding in asperity of differing simulations performed, multimillion-atom were of set large A Results understanding. on this contextualized of then basis are macro- the models and and microscopic observations always wear Discrepant is that scopic particle volume. such debris its a creation to create debris proportional to required for tan- work the distance tangential controlling sliding the factor, and governing the force be gential to junc- evalu- found asperity be is contacting size can The tion debris particles. factor. wear empirical debris individual any wear of without ated, volume i.e., the level, that rela- fundamental shows wear It most above-mentioned the the at and on tions wear focusing by of contact, quantification sliding the during detached is material much macro- of origins the relations. studying wear materials and observed detached particles scopically debris of of amount form opens the the finding in quantifying This of properties. interfacial possibility and the is bulk which size, of junction function critical a a above sizes with junctions contact uhrcnrbtos ..dsge eerh ..cridotsmltos ..ana- R.A. simulations; out carried R.A. research; designed R.A. contributions: Author c owo orsodnesol eadesd mi:jean-francois.molinari@epfl.ch. Email: addressed. be should correspondence whom To colo ii n niomna niern,CrelUiest,Ithaca, University, Cornell Engineering, Environmental and Civil of School in ogohsc,pyis n engineering. applica- and with physics, ability, geophysics, predictive to tions increased drastically mod- wear with new developing els for possibility the open results observations. The experimental understood previously not unifies and study the This disconnected work. that frictional the empir- discloses via any factor, without ical It estimated be particles. can most volume the particle wear detached at i.e., surface, level, solids from fundamental detachment material of ori- gins microscopic mainly long-standing the remains reveals study wear This of empirical. 19th understanding the scientific losses in the indus- progress century, energy considerable and and Despite economic, consequences. material environmental, trial of serious amount with huge annually, a causes Wear Significance nprdb hsfidn 1) hsrpr ist drs how address to aims report this (19), finding this by Inspired a,b,1 b nttt fMtrasSineadEngineering, and Science Materials of Institute . www.pnas.org/lookup/suppl/doi:10. NSEryEdition Early PNAS | f6 of 1

ENGINEERING corresponding physical properties and critical junction size are tions with different asperity shapes. On the whole, the behavior presented in Methods (see also SI Appendix, Fig. S1 and Table observed in the simulations is consistent with the classical pic- S1). In all cases, the simulations represent the dry adhesive slid- ture of adhesive wear hypothesized from experimental observa- ing of identical materials at a constant temperature to reduce the tions (21–24). Recent small-scale wear experiments on ceram- complexity of the model and subsequent analysis. Details of the ics and rocks (25, 26) confirm the formation of cylindrical and simulations are given in Methods and SI Appendix, Fig. S2 and spherical wear debris particles. We make the distinction that this Table S2. work is focused on wear by fracture-induced debris formation, as Universal features are apparent in all simulations despite the opposed to surface folding and delamination (23) mechanisms variety of parameters and configurations examined (Fig. 1). Ini- that may occur at different scales and/or under different wear tially, a strong adhesive bond (junction) forms between contact- conditions, e.g., abrasive wear. ing asperities. Subsequent sliding leads to the buildup of tan- gential forces and stored elastic energy (Fig. 1 E–H). During Wear Is Predictive at Debris Level. Inspired by Archard’s wear this phase, the junction grows by localized inelastic deforma- model (4) [V = k(N × S)/H ], we first examine the relationship tion (SI Appendix, Fig. S3), until crack nucleation and growth between the debris particle volume, V , and the product of the ensues at the two corners of the junction loaded in tension. With applied normal force, N , and sliding distance, S (Fig. 2A), with subsequent sliding, the forces transmitted across the junction H being the material hardness and k being a proportionality con- decrease as the cracks grow, ultimately creating a debris parti- stant (i.e., the wear coefficient). S is taken as the sliding dis- cle. SI Appendix, Fig. S4 depicts a similar observation in simula- tance at which the tangential force returns to zero (Fig. 1). In

A E

B F

C G

D H

Fig. 1. Debris formation at the asperity level. Snapshots at different sliding distance S of multimillion-atom simulations of debris formation and corre- sponding forces evolutions in (A) asperity-flat with 2D model potential, (B) colliding asperities with 2D model potential (P1), (C) colliding asperities with 3D model potential (P4), and (D) colliding asperities with diamond potential (20). See Methods for detail of potentials (see also SI Appendix, Fig. S1 and Table S1). The coloring of atoms is artificial and added for better visualization of the particle formation. E–H plot, for A–D respectively, the applied normal loads and tangential forces that are carried by the junction. The work done by the tangential force (i.e., the area under the tangential force–sliding distance curve) is also shown as a function of sliding distance. SI Appendix, Fig. S3 presents the corresponding stress evolution during debris formation. Snapshots of more simulations with different initial asperity shapes are provided in SI Appendix, Fig. S4.

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1700904114 Aghababaei et al. Downloaded by guest on September 29, 2021 Downloaded by guest on September 29, 2021 cl,adtemxmmjnto iedrn erscreation al. debris et Aghababaei a during size junction maximum spher- the or consider- cylindrical and volume circular, (i.e., its ical), shape from particle computed idealized an 3A particle, ing Fig. debris the size. of junction wear eter the the and between relationship size the particle Following examined contact. we of area hypothesis, vol- real Based this the wear with contact. the correlated that of directly is hypothesized area ume (4) Archard apparent observation, the this of on independent wear the is that volume show (2–4) experiments wear macroscopic Volume. duction, Debris Dictates Size Junction size. junction asperity between the exam- relation and the we volume i.e., particle formation, findings, tangential the debris debris these to the of kinematics proportional understand that the is better way ine particle To a debris volume. such a slid- debris create in and to linked profile required force be work the must Thus, distance that 1). slid- simulations ing (Fig. of that performed set over the been profile across have variable force highly the are distance and ing creation particle debris for in discussion a this as elaborated of is result 19) (8, remarkable Eq. of most emergence the The work. is coefficients empirical any where ,teability the ), S2 and S1 Tables and S4 Eq. and of S2 (see Figs. conditions Appendix, loading SI and size, and of configurations properties, interfacial set geometrical and the bulk in Considering varying strength. performed, shear simulations junction adhesive the and 2B), (Fig. work this 1/τ in of performed related simulations constant are quantities proportionality two a these Remarkably, level, with particles. debris the debris at resultant that, tangential found of between we volume relationship the the and examined we work volume 28), wear 27, and a 25, work (7, of tangential observations the between laboratory correlation macroscopic (τ linear (ii) strength and shear formation junction cle the of importance of absence the (see in force even normal particle applied debris an a can form asperities and opposing adhere, two collide, that unexpected considering not level, the is asperity with result the This at simulations potential. of interfacial groups and bulk on same focusing correlation when even a creation, obervations, wear macroscopic Eq. between of the prediction in presented with the is of the simulations contrast Plot underestimates two (B) of prediction analysis correlation. Archard’s detailed direct the A no that level. with debris shows the scatter It at of considered. unity degree is of large coefficient thickness wear a layer volume. a show atomic providing debris sets single measured data a individual the simulations, the versus 2D addition, For In 1). volume. (Fig. debris zero to returns force 2. Fig. ncnrs otetneta ok h ldn itnerequired distance sliding the work, tangential the to contrast In u eetsuy(9 htrvae h critical the revealed that (19) study recent our (i) by Inspired τ 1 lto h rhr’ oe rdcin (N prediction, model Archard’s the of Plot (A) level. debris at prediction Wear ersnstelse ftebl aeilserstrength shear material bulk the of lesser the represents oetmt h oueo erdbi atce without particles debris wear of volume the estimate to V and N × S sntosre o igedbi particle debris single for observed not is V = 1 i.S5). Fig. Appendix, SI rma nryblneviewpoint balance energy an from R B Fds τ hw httepooe oe a siaetedbi oue ihu n supinadeprclfactors, empirical and assumption any without volume, debris the estimate can model proposed the that shows , IAppendix. SI sdsusdi h Intro- the in discussed As costewd ag of range wide the across oprstediam- the compares ndbi parti- debris on ) [1] h aeili oni rprinlt h ucinsz.Our size. junction the to the proportional of is junction which worn asperity to is depth an the material assumption that from the implies the assumption forms upon This particle diameter. built same debris is a pre- rates, for that successful wear quite macroscopic proven has dicting which (4), model Archard’s Discussion rough- and properties, nonlin- material of adhesion, degree parameters. of ness the function where a con- load, is the normal earity between applied (36, relation and nonlinear multiasperity area a and tact confirm 35) that 34, contacts (29, 37) single in (see observations 33) recent also (32, area loading shear contact and real also adhesion the (31). interfacial effect, geometry nor- on asperity’s geometrical depends the the the to by to proportional affected addition not largely In is is the and asperity as load single of understood, mal a range be of the can area across finding contact observed This is (SI performed. level relation debris simulations No the S6). at Fig. hardness applied the Appendix, the by and normalized size force, junction normal maximum the between correlation event. contact asperity volume an debris from the result of will indication that accurate an a provide across can transmitted junction force junction the tangential maximum at the that observed inelastic- indicates the is with that also consistent change) (see limit, shape shear (permanent elastic ity junction its the to that loaded indicates is result This studies. (30) experimental proportional- of a a with constant find quantities We ity two 3B). these (Fig. between event relation creation linear debris force a tangential maximum during and encountered size junction maximum the tween central a is (4). which model debris, wear the Archard’s of of the volume tenet between the correlation junction and direct area maximum a contact observe the real we to words, debris other equal a In create cross-section size. to grow a then of which having nucleation edges, particle the its from by cracks determined junction of is pair the that the a i.e., size maximum examined, across a been to have configuration grows of that simulations geometric independent of being and range formation parameters particle material the debris to of attributed size, is junction kinematics correspondence maximum particular one-to-one the a This of as simulation. configurations same and parameters the the debris be of independent the to of found diameter is the particle Remarkably, measurement. size tion See event. osdrn rhr’ lsia oe,w loeaiethe examine also we model, classical Archard’s Considering be- relationship the studied we observation, this Following IAppendix SI × S )/H hsresult this 3A, Fig. with Together S3). Fig. Appendix, SI esstemaue ersvlm,cmue netangential once computed volume, debris measured the versus i.S7 Fig. Appendix, SI τ .Ti euti ossetwith consistent is result This S10). and S9 Figs. , nacrac opeiu ueia 2)and (29) numerical previous to accordance in , is 9adS10. and S9 Figs. Appendix, SI o ute eal ntejunc- the on details further for NSEryEdition Early PNAS 1, R | Fds/τ f6 of 3

ENGINEERING Fig. 3. Junction size dictates debris volume. (A) Comparison of the debris size and the maximum asperity junction size. Debris size is computed from the debris volume considering an idealized debris particle shape (i.e., circular, cylindrical or spherical). The maximum junction size is geometrically measured across the junction once the tangential force reaches a maximum. Horizontal error bars show the maximum and minimum of junction size (Methods and SI Appendix, Fig. S7). The plot shows a direct correlation between the junction and debris sizes; this confirms that debris volume V is proportional to d3 (or d2 for 2D cases), where d represents the maximum junction size. This observation supports Archard’s assumption that the depth to which the material is worn is proportional to the junction size (see also SI Appendix, Figs. S10 and S11). This result also rationalizes the macroscopic observation (2–4) that the wear rate is independent of the apparent contact area. (B) Plot of the junction size estimation via the tangential force Fmax /τ versus the measured junction size at maximum tangential force; τ represents the junction shear strength. For 3D simulations, an idealized circular junction area is assumed, to obtain the size of junctions. This figure confirms that the junction size can be accurately predicted via the tangential force. As a result, the maximum frictional force correlates with d2 (or d for 2D cases). SI Appendix, Fig. S3 also shows that the shear stress during debris formation is limited by the junction shear strength.

simulations have confirmed this assumption across a wide range eter of the debris particle. Although our simulation data (Fig. 1) of conditions (Fig. 3), if one takes the maximum asperity junc- and the literature (8) make it clear that Archard’s assumption is tion size observed in the simulations to be the junction size to an approximation of the real case, the data presented here show which Archard referred. However, our simulations show that the that this is a good approximation, provided one considers the asperity-level junction size cannot be solely approximated by the maximum asperity junction size and the tangential force trans- applied normal load, due to the collision of opposing asperities, mitted through the junction at its maximum size (SI Appendix, the presence of interfacial adhesion, and the role of plastic shear- Fig. S8). More precisely, Fig. 2 shows that V = R Fds/τ, which ing. Instead, the tangential load is shown to be a good indicator can be written as V = (Fmax × S )/τ by defining an effective R eff of the asperity junction size. This finding is in agreement with sliding distance, Seff = Fds/Fmax . Then, using the results of observations in recent studies (29, 30, 35, 36, 38) that show that, Fig. 3, we arrive at Seff = (π/4)d and Seff = (2/3)d for the cre- although friction force is always linear with the real contact area ation of a cylindrical and a spherical debris particle of diame- at any length scale, the relation between the normal load and the ter d, a result similar to Archard’s assumption that the sliding real contact area is largely influenced by the roughness parame- distance required to create a debris particle from an asperity ters and interfacial adhesion. junction was equal to the diameter of the debris particle. Given The above argument also explains the discrepancy between that both Fmax and Seff can be written in terms of the maximum the asperity-level observation made here and the macroscopi- junction size, we assert that the maximum asperity junction size cally observed linear correlation between wear volume and the during a contact event is the fundamental parameter controlling applied normal force (3, 4). Although our simulations confirm both the wear volume and wear rate at the single debris scale. a correlation between the wear volume and real contact area, An important component of Archard’s model is the propor- this discrepancy can be attributed to the absence of a correla- tionality factor, i.e., wear coefficient, k. Archard introduced this tion between the real contact area and the normal load at single- parameter to the model as the probability factor describing the asperity contacts. However, it was shown (39, 40) that a linear likelihood that a given asperity contact would create a debris par- correlation between the normal load and the real contact area ticle. This assertion is consistent with our recent work, where we can be recovered via multiasperity contact models. Accordingly, showed that only junctions above a critical size lead to debris the macroscopically observed linear relation between the wear particles (19). However, our recent work was not sufficient to volume and the normal force may be reconstructed via multi- determine that k is solely a probability factor. However, when asperity contact models (39–41). It has been shown (29, 35) that our previous results are taken together with those presented sliding between surfaces with low roughness and high adhesion here, the modeling suggests that it is necessary and sufficient (e.g., asperity-level contact) is an adhesion-controlled process, in that the wear coefficient k corresponds to the probability of a which normal force is a sublinear function of real contact area given asperity contact event leading to debris particle formation. and tangential force. On the other hand, the sliding between More precisely, Archard’s model suggests (4) a wear coefficient surfaces with large roughness and low interfacial adhesion [e.g., of unity at the single debris level, a value that is confirmed by our macroscopic multiasperity contacts (39–41)] is a load-controlled simulations. process, in which both the normal and tangential forces are pro- Considering that typical values of k measured in laboratory portional to the contact area (i.e., Amontons’ friction law). In tests are orders of magnitude smaller than 1, the asperity con- such conditions, the wear volume is expected to correlate with tacts that will lead to the formation of wear debris particles (the both the normal and tangential forces (see also SI Appendix, ones studied in this manuscript) are far outnumbered by con- Fig. S5). tacts that do not. We believe that this discrepancy can be rec- To arrive at the volume of material worn per distance slide, onciled by recalling that only junctions above a critical size will Archard assumed that the sliding distance required to create a lead to debris particles (19), noting that ordinary macroscopic debris particle from an asperity junction was equal to the diam- contacts are expected to contain a wide range of junction sizes

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Physical and Potentials Interatomic Methods junc- of statistics wear the sizes. adhesive given clusters contact, the tion rough predicting sliding finding for for This (19). basis coefficient size fundamental junction critical a junc- the asperity provides than when larger level, debris is the size atomistic at tion unity in confirm of level we coefficient a addition, wear debris In a offers single experiments. wear finding the AFM This at and simulations volume. wear debris quantify the and, to predict size at junction pathway cannot that, normal the result, the shown on a adhesion, depend also linearly high as is not of does It presence component force the junction. applied tangential in a the and by level by carried asperity can done load volume work the debris the of wear via the quantified consequently, be and, simula- size, controls directly Our debris size work. junction the asperity frictional the and that demonstrate area, tions contact real wear the the volume, between relations wear exper- macroscopic of observed origins imentally microscopic long-standing the reveals study This Conclusion junction of contacts. multiasperity analysis in statistical probability and also size and asperities particles contacting debris of between resultant importance that interaction critical dur- the the assume surfaces highlights the investigating to hypothesis into This rate unreasonable sliding. some not at ing reabsorb is will it particles debris Furthermore, 43). (42, i.S1 properties. Fig. mechanical Appendix, coarse-grained SI indepen- corresponding properties and inelastic parameters potentials. of tials properties. the influence 10% elastic of the to of all study up dently for to properties 3.5 us elastic to allow constant equal potentials ensures is factor which 1. potential, The the of width the and distance, bond and rium scale, length interaction the the where .Bwe P ao 13)Teae fcnatbtensainr n between and stationary between contact of area The (1939) D Tabor FP, Bowden 9. process. transformation wear. energy Adhesive an (1995) as E Wear Rabinowicz (1978) J 8. Fohl H, wear. Uetz and Friction 7. (1947) zapfenreibung. EJW der Whittaker theorie surfaces. Zur 6. flat (1860) of T rubbing Reye and wear. Contact 5. (1953) adhesive JF of Archard law empirical 4. the On (1952) CD Strang JT, Burwell 3. current. without contacts metallic in wear Frictional (1946) R Holm 2. specific the on alloys, various the on observations and Experiments (1803) C Hatchett 1. tion. 275–282. surfaces. moving 125–166. pp 18–28. 232–242. pp York), New (Springer, R Holm ed to estab- present appointed the council, mint. and Majesty’s kingdom, privy His this of of of constitution coins committee and the the lishment of made state of report the a lords consideration of into the substance take the honourable Being right gold. the of wear to comparative the on and gravity, hsRvB Rev Phys V r (r cut , ε) aaee ensteptnilctf aisadcontrols and radius cutoff potential the defines parameter 53:2101–2113. = rcMt hsEgSci Eng Phys Math Proc ε hw h orsodn netto epnefr2D for response indentation corresponding the shows        0  c 1 ε 1 r 6 stedpho h oeta el and well; potential the of depth the is 3 − + alsS n S2 and S1 Tables Appendix, SI e −α(r c 2 r rcinadWa fMaterials of Wear and Friction c 2 2 1 −r + to o 169:391–413. Nature ) c  3 c 2 4 r + − e Civilingenieur Der J r parameters; are hlsTasRScLond Soc R Trans Philos c 159:541. 1 4 1.r r r setnieydsusdin discussed extensively As cut a Nanotechnol Nat < plPhys Appl J ≤ o 1.r ≤ r o r e cdRA R Acad Mem Wear ≤ r 4:235–255. lcrclContacts, Electrical o Wly e York), New (Wiley, 24:981–988. rsn poten- present r steequilib- the is cut plPhys Appl J tan These strain. 49:253–264. , 93:43–194. 8:81–82. α controls 1699 [2] 23: 7 osanB at A(08 tmsi eri igeaprt ldn contact. sliding asperity single a in wear transi- Atomistic of (2008) MA application Lantz the B, On Gotsmann (2010) RW 17. Carpick MA, Lantz B, review. Gotsmann A TDB, tips: Jacobs microscopy force 16. atomic Tersoff of nanotribology characteristics modified Wear of (2014) Simulations A K-H (2008) Chung GS (2013) Grest 15. YW MJ, Stevens Zhang CD, Lorenz V, M, Chandross Sorkin 14. QX, Pei PS, Branicio ZD, Sha 13. 3 u P(93 h eaiainter fwear. of theory delamination The (1973) NP Suh 23. the (1960) of GK analysis Fleming theoretical A 22. metals: unlubricated between Friction (1955) AP bond-order Green empirical Screened 21. (2013) M Moseler P, Gumbsch A, adhesive Klemenz controls L, scale Pastewka length Critical 20. (2016) J-F conditions. Molinari unlubricated DH, under Warner R, metals Aghababaei of wear 19. The (1956) W Hirst JF, Archard 18. h ws ainlSineFudto Gat126,Cnatmcaisof mechanics Contact 162569, surfaces). (Grant rough Foundation Science National Swiss the spherical ACKNOWLEDGMENTS. or cylindrical and 2D in circular (i.e., 3D). considering in shape by volume particle debris consid- idealized the is from an computed thickness the directly layer and is atomic debris size single in Debris a tangential ered. atoms simulations, of corresponding 2D number For the the volume. of once atomic product the (i.e., as zero) regime reaches steady-state force the horizontal at of (see terms 3 sured in and Fig. reported in minimum and bars the measured error 50) are con- (49, sizes measuring junction conductance, for maximum thermal/electrical approach using atoms experimental bonded area the of by tact (48). number Inspired area the junction. as bonded the estimated the at is define size to junction considered the are Accordingly, potential interfacial the of Data. Simulations of Compilation steps. (47). time software 100 Ovito every by considered. averaged layers. visualized are are thermostat are 1 fs and simulations Fig. boundary 1 All in rigid of shown for step profiles considered time force is a Tangential nm and 1 ps of simula- 1 thickness is diamond of A unit) For length parameter layers. reduced damping thermostat (in a numeri- and 5 tions, for of boundary used thickness rigid are A for unit) 19). time considered ref. reduced also algorithm in (see Verlet load. (both integration a 0.0025 applied cal and of and 0.05 step velocity, of time a sliding parameter with damping dimension, a system potentials, the model For for study this in ,adgoerclcngrtos(.. igeaprt ver- asperity single asperities). (i.e., interlocking configurations sus geometrical and sine; S4), half Fig. and rectangular, Appendix, triangular, segment, circular semi- partial (i.e., and fixed shapes circular asperity (i.e., initial conditions pressure), boundary applied fixed size, versus box displacement simulation the of independent junction are welded a consider we simulations. 1D), 3D Fig. the in of shown all (e.g., for simulation simulations S4 the 3D Fig. for of Appendix, d cost colli- ∼10 (SI computational the enormous junction both the welded simulations, Noting a 2D modeled. and the asperities In this between thermostat. of sion outside Langevin just a layers thin using (see two region along examined enforced was were Temperature conditions S2). Fig. boundary fixed and pressure o imn iuain,teAOITC irr 2)i sdaogwith applied along were velocity (46). used sliding the is a LAMMPS in and (20) condition software boundary library periodic ATOMISTICA dynamics A LAMMPS. the molecular simulations, the diamond For using Conditions. performed Boundary were and Loading, Geometry, Simulation well modified a 19). with ref. potentials also (see of used set is different depth control To a 20. adhesion, ref. from interfacial taken parame- the are Potential screening properties used. physical a is corresponding breaking, and using with bond ters simulations enhanced brittle modeling diamond (45), for For (20) potential function 19). Tersoff ref. the also atoms, (see multimillion potentials model 3D and epromdalresto iuain,wihcnre htteresults the that confirmed which simulations, of set large a performed We insaeter oaoi-cl wear. atomic-scale to theory state tion Manuf Eng Precis J models. tip probe realistic with carbon. diamond-like hydrogenated 146–150. and pure for potential h hss(nvBiihClmi,Vancouver). Columbia, British (Univ thesis PhD faces. model. junction Si-C. for potentials mechanisms. wear Sci Eng Phys Math Lett Rev x ieto o l ftesmltos nthe In simulations. the of all for direction 101:125501. rcMt hsEgSci Eng Phys Math Proc 236:397–410. a Commun Nat hsRvB Rev Phys oe ucinaayi ftefito n ero ealcsur- metallic of wear and friction the of analysis junction Model 15:2219–2230. .FM n ..akoldefiaca upr from support financial acknowledge R.A. and J.-F.M. .Tevlm fdbi smea- is debris of volume The S7). Fig. Appendix, SI al S2 Table Appendix, SI 87:205410. Langmuir 7:11816. ufc tm ihntectf radius cutoff the within atoms Surface rblLett Tribol 228:191–204. 24:1240–1246. Wear 39:257–271. NSEryEdition Early PNAS y 25:111–124. hw h oee range covered the shows ieto,bt constant both direction, optMtrSci Mater Comput l simulations All IAppendix, SI | are A) f6 of 5 Phys Proc 67: Int SI

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