Scale effects in friction of single–asperity contacts. I. From concurrent slip to single–dislocation–assisted slip

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Hurtado Juan A. and Kim Kyung–Suk 1999Scale effects in friction of single–asperity contacts. I. From concurrent slip to single–dislocation–assisted slipProc. R. Soc. Lond. A.4553363–3384http://doi.org/10.1098/rspa.1999.0455SectionRestricted accessResearch articleScale effects in friction of single–asperity contacts. I. From concurrent slip to single–dislocation–assisted slip Juan A. Hurtado Juan A. Hurtado Division of Engineering, Brown University, Providence, RI 02912, USA Google Scholar Find this author on PubMed Search for more papers by this author and Kyung–Suk Kim Kyung–Suk Kim Division of Engineering, Brown University, Providence, RI 02912, USA Google Scholar Find this author on PubMed Search for more papers by this author Juan A. Hurtado Juan A. Hurtado Division of Engineering, Brown University, Providence, RI 02912, USA Google Scholar Find this author on PubMed Search for more papers by this author and Kyung–Suk Kim Kyung–Suk Kim Division of Engineering, Brown University, Providence, RI 02912, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:08 September 1999https://doi.org/10.1098/rspa.1999.0455AbstractA micromechanical dislocation model of frictional slip between two asperities is presented. The model suggests that when the contact radius is smaller than a critical value, the friction stress is constant, of the order of the theoretical shear strength, in agreement with reported atomic force microscope (AFM) friction experiments. However, at the critical value there is a transition beyond which the friction stress decreases with increasing area, until it reaches the second transition where the friction stress gradually becomes independent of the contact size. This is in contrast to previous theories, which assume that the friction stress is always independent of the size. The present model also predicts that the mechanisms of slip are size dependent. Before the first transition, the constant friction stress is associated with concurrent slip without the aid of dislocation motion. The first transition corresponds to the minimum contact size at which a single dislocation loop is nucleated and sweeps through the whole contact interface, resulting in a single–dislocation–assisted (SDA) slip. This mechanism is predicted to prevail for a wide range of contact sizes, from 10 nm to 10 µm in radius for typical dry adhesive contacts; however, there are no available experimental data in this size range. The second transition is found to be caused by the effective Peierls stress which stabilizes the dislocation loop within the contact region, resulting in dislocation pile–ups. Beyond the second transition, slip is assisted by cooperative glide of dislocations in the pile–up. For sufficiently large contacts the mechanism of cooperative glide induces a size–independent friction stress, in agreement with observations in surface force apparatus (SFA) friction experiments. This paper (Part I) addresses the first transition: from concurrent slip to SDA slip. The second transition is analysed in a companion paper (Part II). Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Choi S, Mai N and Nguyen V (2021) Dislocation nucleation and segregation under adhesive contact of a nano-asperity coating on a crystalline solid, European Journal of Mechanics - A/Solids, 10.1016/j.euromechsol.2021.104311, 89, (104311), Online publication date: 1-Aug-2021. Brazil O and Pharr G (2021) Direct observation of partial interface slip in micrometre-scale single asperity contacts, Tribology International, 10.1016/j.triboint.2020.106776, 155, (106776), Online publication date: 1-Mar-2021. Markenscoff X (2021) “Volume collapse” instabilities in deep-focus earthquakes: A shear source nucleated and driven by pressure, Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2021.104379, 152, (104379), Online publication date: 1-Jul-2021. Monti J and Robbins M (2020) Sliding Friction of Amorphous Asperities on Crystalline Substrates: Scaling with Contact Radius and Substrate Thickness, ACS Nano, 10.1021/acsnano.0c06241, 14:12, (16997-17003), Online publication date: 22-Dec-2020. Zhao K and Aghababaei R (2020) Interfacial plasticity controls material removal rate during adhesive sliding contact, Physical Review Materials, 10.1103/PhysRevMaterials.4.103605, 4:10 Das D and Chasiotis I (2020) Sliding of adhesive nanoscale polymer contacts, Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2020.103931, 140, (103931), Online publication date: 1-Jul-2020. Giannoukos K and Salonitis K (2020) Study of the mechanism of friction on functionally active tribological Polyvinyl Chloride (PVC) – Aggregate composite surfaces, Tribology International, 10.1016/j.triboint.2019.105906, 141, (105906), Online publication date: 1-Jan-2020. (2018) Friction and Contact of Solid Interfaces Dynamics and Control of Robotic Manipulators with Contact and Friction, 10.1002/9781119422518.ch3, (45-113) Malekan A and Rouhani S (2018) Model of contact friction based on extreme value statistics, Friction, 10.1007/s40544-018-0215-9, 7:4, (327-339), Online publication date: 1-Aug-2019. Brink T and Molinari J (2019) Adhesive wear mechanisms in the presence of weak interfaces: Insights from an amorphous model system, Physical Review Materials, 10.1103/PhysRevMaterials.3.053604, 3:5 Bjerremand C, Larsen J and Hinge M (2017) Macroscale Load and Temperature Dependency on High-Friction Poly(Styrene-co-Butyl Methacrylate)-Coated Paper, Tribology Letters, 10.1007/s11249-017-0965-y, 66:1, Online publication date: 1-Mar-2018. Izmailov V and Novoselova M (2018) On the Temperature Effect on the Parameters of the Specific Friction Force of Metals, Journal of Friction and Wear, 10.3103/S1068366618040062, 39:4, (289-293), Online publication date: 1-Jul-2018. (2018) Bibliography Surface and Interfacial Forces 2e, 10.1002/9783527804351.refs, (381-429) Stone T and Hammi Y (2018) Nickel Powder Metal Modeling Illustrating Atomistic-Continuum Friction Laws Integrated Computational Materials Engineering (ICME) for Metals, 10.1002/9781119018377.ch13, (447-464) (2018) Friction Surface and Interfacial Forces 2e, 10.1002/9783527804351.ch9, (251-296) Huang G and Yan J (2017) A mechanical model for the adhesive contact with local sliding induced by a tangential force, Acta Mechanica Solida Sinica, 10.1016/j.camss.2017.07.008, 30:4, (369-373), Online publication date: 1-Aug-2017. Ghaednia H, Wang X, Saha S, Xu Y, Sharma A and Jackson R (2017) A Review of Elastic–Plastic Contact Mechanics, Applied Mechanics Reviews, 10.1115/1.4038187, 69:6, Online publication date: 1-Nov-2017. Sharp T, Pastewka L, Lignères V and Robbins M (2017) Scale- and load-dependent friction in commensurate sphere-on-flat contacts, Physical Review B, 10.1103/PhysRevB.96.155436, 96:15 Song H, Deshpande V and Van der Giessen E (2016) Discrete dislocation plasticity analysis of loading rate-dependent static friction, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472:2192, Online publication date: 1-Aug-2016. Sheng Chen G and Liu X (2016) Friction Friction Dynamics, 10.1016/B978-0-08-100285-8.00003-1, (91-159), . Miguel F, Müller R, Rosenkranz A, Mathur S and Mücklich F (2016) Analysis and modelling of the dry-sliding friction and wear behaviour of electrodeposited Ni and Ni-matrix-nanocomposite films, Wear, 10.1016/j.wear.2015.11.006, 346-347, (87-98), Online publication date: 1-Jan-2016. Sethuramiah A and Kumar R (2016) Tribology in Perspective Modeling of Chemical Wear, 10.1016/B978-0-12-804533-6.00001-9, (1-23), . Gao Z, Zhang W and Gao Y (2016) Scale dependence of interface dislocation storage governing the frictional sliding of single asperities, Modelling and Simulation in Materials Science and Engineering, 10.1088/0965-0393/24/6/065010, 24:6, (065010), Online publication date: 1-Aug-2016. Sharp T, Pastewka L and Robbins M (2016) Elasticity limits structural superlubricity in large contacts, Physical Review B, 10.1103/PhysRevB.93.121402, 93:12 Vanni M (2015) Accurate modelling of flow induced stresses in rigid colloidal aggregates, Computer Physics Communications, 10.1016/j.cpc.2015.02.022, 192, (70-90), Online publication date: 1-Jul-2015. Shimizu T, Yang M and Manabe K (2015) Classification of mesoscopic tribological properties under dry sliding friction for microforming operation, Wear, 10.1016/j.wear.2015.01.050, 330-331, (49-58), Online publication date: 1-May-2015. Varini N, Vanossi A, Guerra R, Mandelli D, Capozza R and Tosatti E (2015) Static friction scaling of physisorbed islands: the key is in the edge, Nanoscale, 10.1039/C4NR06521B, 7:5, (2093-2101) Ciavarella M (2015) Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited, Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2015.08.002, 84, (313-324), Online publication date: 1-Nov-2015. VASU T and BHANDAKKAR T (2015) Semi-analytical solution to plane strain loading of elastic layered coating on an elastic substrate, Sadhana, 10.1007/s12046-015-0418-y, 40:7, (2221-2238), Online publication date: 1-Oct-2015. Dikken R, Van der Giessen E and Nicola L (2015) Plastic shear response of a single asperity: a discrete dislocation plasticity analysis, Philosophical Magazine, 10.1080/14786435.2015.1102982, 95:34, (3845-3858), Online publication date: 2-Dec-2015. Perfilyev V, Moshkovich A, Lapsker I, Laikhtman A and Rapoport L (2014) Dislocation Structure and Stick–Slip Phenomenon, Tribology Letters, 10.1007/s11249-014-0358-4, 55:2, (295-301), Online publication date: 1-Aug-2014. (2014) Fundamentals of contact mechanics and friction Handbook of Friction-Vibration Interactions, 10.1533/9780857094599.71, (71-152), . Dai L, Sorkin V, Sha Z, Pei Q, Branicio P and Zhang Y (2014) Molecular Dynamics Simulations on the Frictional Behavior of a Perfluoropolyether Film Sandwiched between Diamond-like-Carbon Coatings, Langmuir, 10.1021/la404680v, 30:6, (1573-1579), Online publication date: 18-Feb-2014. Paggi M and Carpinteri A (2013) Size-Scale Effects on the Friction Coefficient: From Weak Faults at the Planetary Scale to Superlubricity at the Nanoscale Recent Advances in Contact Mechanics, 10.1007/978-3-642-33968-4_5, (67-84), . Dong Y, Li Q and Martini A (2013) Molecular dynamics simulation of atomic friction: A review and guide, Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, 10.1116/1.4794357, 31:3, (030801), Online publication date: 1-May-2013. Hanke S, Petri J and Johannsmann D (2013) Partial slip in mesoscale contacts: Dependence on contact size, Physical Review E, 10.1103/PhysRevE.88.032408, 88:3 Cheong W and Yong A (2013) Probing the Complexities of Friction in Submicron Contacts Between Two Pristine Surfaces Nano-tribology and Materials in MEMS, 10.1007/978-3-642-36935-3_8, (199-213), . Korayem M, Zakeri M and Taheri M (2013) Simulation of Two-Dimensional Nanomanipulation of Particles Based on the HK and LuGre Friction Models, Arabian Journal for Science and Engineering, 10.1007/s13369-013-0594-1, 38:6, (1573-1585), Online publication date: 1-Jun-2013. Huang G and Svendsen B (2013) Model of mismatched contact for dislocation generation during coalescence of grains, Philosophical Magazine Letters, 10.1080/09500839.2012.762466, 93:4, (246-253), Online publication date: 1-Apr-2013. Onal C, Ozcan O and Sitti M (2012) Automated Tip-Based 2-D Mechanical Assembly of Micro/Nanoparticles Feedback Control of MEMS to Atoms, 10.1007/978-1-4419-5832-7_4, (69-108), . Stone T and Horstemeyer M (2012) Length scale effects of friction in particle compaction using atomistic simulations and a friction scaling model, Journal of Nanoparticle Research, 10.1007/s11051-012-1121-0, 14:9, Online publication date: 1-Sep-2012. Korayem M, Taheri M and Zakeri M (2012) Sensitivity analysis of nanoparticles manipulation based on different friction models, Applied Surface Science, 10.1016/j.apsusc.2011.12.024, 258:18, (6713-6722), Online publication date: 1-Jul-2012. Annett J, Gao Y, Cross G, Herbert E and Lucas B (2011) Mesoscale friction anisotropy revealed by slidingless tests, Journal of Materials Research, 10.1557/jmr.2011.270, 26:18, (2373-2378), Online publication date: 28-Sep-2011. Wahl K (2011) Macroscale to Microscale Tribology Micro- and Nanoscale Phenomena in Tribology, 10.1201/b11211-3, (5-22), Online publication date: 19-Oct-2011. Mylvaganam K and Zhang L (2011) Micro/nano tribology Tribology for Engineers, 10.1533/9780857091444.121, (121-160), . Dong Y, Li Q, Wu J and Martini A (2011) Friction, slip and structural inhomogeneity of the buried interface, Modelling and Simulation in Materials Science and Engineering, 10.1088/0965-0393/19/6/065003, 19:6, (065003), Online publication date: 1-Sep-2011. Eriten M, Polycarpou A and Bergman L (2011) Physics-based modeling for fretting behavior of nominally flat rough surfaces, International Journal of Solids and Structures, 10.1016/j.ijsolstr.2011.01.028, 48:10, (1436-1450), Online publication date: 1-May-2011. Ananthakrishna G and Kumar J (2010) Correlation between stick-slip frictional sliding and charge transfer, Physical Review B, 10.1103/PhysRevB.82.075414, 82:7 Landolsi F, Sun Y, Lu H, Ghorbel F and Lou J (2010) Regular and reverse nanoscale stick-slip behavior: Modeling and experiments, Applied Surface Science, 10.1016/j.apsusc.2009.10.107, 256:8, (2577-2582), Online publication date: 1-Feb-2010. Prokopovich P, Perni S, Piccirillo C, Pratten J, Parkin I and Wilson M (2009) Frictional properties of light-activated antimicrobial polymers in blood vessels, Journal of Materials Science: Materials in Medicine, 10.1007/s10856-009-3882-2, 21:2, (815-821), Online publication date: 1-Feb-2010. Lhernould M, Berke P, Massart T, Régnier S and Lambert P (2009) Variation of the Electrostatic Adhesion Force on a Rough Surface due to the Deformation of Roughness Asperities During Micromanipulation of a Spherical Rigid Body, Journal of Adhesion Science and Technology, 10.1163/156856109X434026, 23:9, (1303-1325), Online publication date: 1-Jan-2009. Agrawal R, Moldovan N and Espinosa H (2009) An energy-based model to predict wear in nanocrystalline diamond atomic force microscopy tips, Journal of Applied Physics, 10.1063/1.3223316, 106:6, (064311), Online publication date: 15-Sep-2009. Johnson S and Williams J (2009) Sub-discretized surface model with application to contact mechanics in multi-body simulation, Powder Technology, 10.1016/j.powtec.2009.03.006, 193:3, (319-331), Online publication date: 1-Aug-2009. Li Q and Kim K (2008) Micromechanics of friction: effects of nanometre-scale roughness, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464:2093, (1319-1343), Online publication date: 8-May-2008. Stone T, Horstemeyer M, Hammi Y and Gullett P (2008) Contact and friction of single crystal nickel nanoparticles using molecular dynamics, Acta Materialia, 10.1016/j.actamat.2008.03.044, 56:14, (3577-3584), Online publication date: 1-Aug-2008. Paris M, Haddab Y, Lutz P and Rougeot P (2008) Practical characterisation of the friction force for the positioning and orientation of micro-components 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems, 10.1109/IROS.2008.4650726, 978-1-4244-2057-5, (931-936) Chen S, Xu G and Soh A (2008) Robust Nanoadhesion Under Torque, Tribology Letters, 10.1007/s11249-008-9301-x, 29:3, (235-239), Online publication date: 1-Mar-2008. He X (2008) Adhesion Dynamics in Probing Micro- and Nanoscale Thin Solid Films, Mathematical Problems in Engineering, 10.1155/2008/742569, 2008, (1-18), . Sümer B and Sitti M (2008) Rolling and Spinning Friction Characterization of Fine Particles Using Lateral Force Microscopy Based Contact Pushing, Journal of Adhesion Science and Technology, 10.1163/156856108X295527, 22:5-6, (481-506), Online publication date: 1-Jan-2008. Chen S, Yan C and Soh A (2008) Non-slipping JKR model for transversely isotropic materials, International Journal of Solids and Structures, 10.1016/j.ijsolstr.2007.08.013, 45:2, (676-687), Online publication date: 1-Jan-2008. Xu D, Ravi-Chandar K and Liechti K (2008) On scale dependence in friction: Transition from intimate to monolayer-lubricated contact, Journal of Colloid and Interface Science, 10.1016/j.jcis.2007.09.086, 318:2, (507-519), Online publication date: 1-Feb-2008. Jones R (2005) A Greenwood-Williamson Model of Small-Scale Friction, Journal of Applied Mechanics, 10.1115/1.2172269, 74:1, (31-40), Online publication date: 1-Jan-2007. Deshpande V, Balint D, Needleman A and Giessen E (2006) Size effects in single asperity frictional contacts, Modelling and Simulation in Materials Science and Engineering, 10.1088/0965-0393/15/1/S09, 15:1, (S97-S108), Online publication date: 1-Jan-2007. Yu H, Shrotriya P, Gao Y and Kim K (2007) Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation, Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2006.09.003, 55:3, (489-516), Online publication date: 1-Mar-2007. Nosonovsky M and Bhushan B (2007) Multiscale friction mechanisms and hierarchical surfaces in nano- and bio-tribology, Materials Science and Engineering: R: Reports, 10.1016/j.mser.2007.09.001, 58:3-5, (162-193), Online publication date: 1-Nov-2007. Wang M, Xu D, Ravi-Chandar K and Liechti K (2007) On the Development of a Mesoscale Friction Tester, Experimental Mechanics, 10.1007/s11340-006-0653-6, 47:1, (123-131), Online publication date: 1-Feb-2007. Deshpande V, Needleman A and Van Der Giessen E (2007) Chapter 71 Discrete Dislocation Plasticity Modeling of Contact and Friction , 10.1016/S1572-4859(07)80003-9, (1-46), . Shi X and Polycarpou A (2006) Adhesive Effects on Dynamic Friction for Unlubricated Rough Planar Surfaces, Journal of Tribology, 10.1115/1.2345392, 128:4, (841-850), Online publication date: 1-Oct-2006. Ali S and Sahoo P (2006) Adhesive friction for elastic–plastic contacting rough surfaces using a scale-dependent model, Journal of Physics D: Applied Physics, 10.1088/0022-3727/39/4/018, 39:4, (721-729), Online publication date: 21-Feb-2006. Gao Y and Bower A Rough Surface Plasticity and Adhesion across Length Scales Nanomechanics of Materials and Structures, 10.1007/1-4020-3951-4_27, (277-287) Gao Y, Lucas B, Hay J, Oliver W and Pharr G (2006) Nanoscale incipient asperity sliding and interface micro-slip assessed by the measurement of tangential contact stiffness, Scripta Materialia, 10.1016/j.scriptamat.2006.05.006, 55:7, (653-656), Online publication date: 1-Oct-2006. Stevens F, Langford S and Dickinson J (2006) Tribochemical wear of sodium trisilicate glass at the nanometer size scale, Journal of Applied Physics, 10.1063/1.2166646, 99:2, (023529), Online publication date: 15-Jan-2006. Balint D, Deshpande V, Needleman A and Van der Giessen E (2006) Discrete dislocation plasticity analysis of the wedge indentation of films, Journal of the Mechanics and Physics of Solids, 10.1016/j.jmps.2006.07.004, 54:11, (2281-2303), Online publication date: 1-Nov-2006. Adams G and Müftü S (2005) Improvements to a scale-dependent model for contact and friction, Journal of Physics D: Applied Physics, 10.1088/0022-3727/38/9/012, 38:9, (1402-1409), Online publication date: 7-May-2005. Cho M, Kim S, Lim D and Jang H (2005) Atomic scale stick-slip caused by dislocation nucleation and propagation during scratching of a Cu substrate with a nanoindenter: a molecular dynamics simulation, Wear, 10.1016/j.wear.2005.01.002, 259:7-12, (1392-1399), Online publication date: 1-Jul-2005. Deshpande V, Needleman A and Van der Giessen E (2005) Size dependence of energy storage and dissipation in a discrete dislocation plasticity analysis of static friction, Materials Science and Engineering: A, 10.1016/j.msea.2005.01.078, 400-401, (393-396), Online publication date: 1-Jul-2005. Sari O, Adams G and Mu¨ftu¨ S (2005) Nano-Scale Effects in the Sliding and Rolling of a Cylinder on a Substrate, Journal of Applied Mechanics, 10.1115/1.1831291, 72:5, (633-640), Online publication date: 1-Sep-2005. Yang W, Wang H and Huang Y (2004) Abnormal Tribological Behavior of Multiwalled Nanotube Rafts Part I: Aligned Rafts, Journal of Engineering Materials and Technology, 10.1115/1.1867980, 127:4, (383-392), Online publication date: 1-Oct-2005. Carpick R, Flater E, Sridharan K, Ogletree D and Salmeron M (2004) Atomic-scale friction and its connection to fracture mechanics, JOM, 10.1007/s11837-004-0291-3, 56:10, (48-52), Online publication date: 1-Oct-2004. Houston J (2004) Interfacial Force Microscopy: Selected Applications Applied Scanning Probe Methods, 10.1007/978-3-642-35792-3_2, (41-73), . Bhushan B and Nosonovsky M (2004) Comprehensive model for scale effects in friction due to adhesion and two- and three-body deformation (plowing), Acta Materialia, 10.1016/j.actamat.2004.01.038, 52:8, (2461-2474), Online publication date: 1-May-2004. Ajayi O, Ludema K, Hammerberg J and Lee Holian B (2004) Simulation Methods for Interfacial Friction in Solids Surface Modification and Mechanisms, 10.1201/9780203021545.ch18, Online publication date: 30-Apr-2004. Deshpande V, Needleman A and Van der Giessen E (2004) Discrete dislocation plasticity analysis of static friction, Acta Materialia, 10.1016/j.actamat.2004.03.018, 52:10, (3135-3149), Online publication date: 1-Jun-2004. Bhushan B and Nosonovsky M (2003) Scale effects in friction using strain gradient plasticity and dislocation-assisted sliding (microslip), Acta Materialia, 10.1016/S1359-6454(03)00261-1, 51:14, (4331-4345), Online publication date: 1-Aug-2003. Adams G, Mu¨ftu¨ S and Azhar N (2003) A Scale-Dependent Model for Multi-Asperity Contact and Friction, Journal of Tribology, 10.1115/1.1573232, 125:4, (700-708), Online publication date: 1-Oct-2003. He G and Robbins M (2003) Scale Effects and the Molecular Origins of Tribological Behavior Nanotribology, 10.1007/978-1-4615-1023-9_4, (29-44), . Ecke S and Butt H (2001) Friction between Individual Microcontacts, Journal of Colloid and Interface Science, 10.1006/jcis.2001.7959, 244:2, (432-435), Online publication date: 1-Dec-2001. Hurtado J and Kim K (1999) Scale effects in friction of single–asperity contacts. II. Multiple–dislocation–cooperated slip, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 455:1989, (3385-3400), Online publication date: 8-Sep-1999. Kim K (2006) Nano and Micro Mechanical Measurement of Interaction Forces Between Solid Surfaces, Key Engineering Materials, 10.4028/www.scientific.net/KEM.326-328.1, 326-328, (1-4) Cheong W (2014) Sliding Systems: Nanofriction and Nanowear Simulations Dekker Encyclopedia of Nanoscience and Nanotechnology, Third Edition, 10.1081/E-ENN3-120024162, (4544-4559) Clegg W, Vandeperre L and Pitchford J (2006) Energy Changes and the Lattice Resistance, Key Engineering Materials, 10.4028/www.scientific.net/KEM.317-318.271, 317-318, (271-276) Wang J, Yuan W, Bian J and Wang G (2020) A semi-analytical model for the scale-dependent friction of nanosized asperity, Journal of Physics Communications, 10.1088/2399-6528/abbae7, 4:9, (095026) Wang H, Ni Y and Lu H (2014) Quasicontinuum Analysis of Dislocation Propagation during Nanocontact, Advanced Materials Research, 10.4028/www.scientific.net/AMR.941-944.470, 941-944, (470-478) This Issue08 September 1999Volume 455Issue 1989 Article InformationDOI:https://doi.org/10.1098/rspa.1999.0455Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/09/1999Published in print08/09/1999 License: Citations and impact Keywordsdry frictionsingle asperityfrictional slipscale effectsadhesive contactdislocation model