Tribology Letters

, 67:30 | Cite as

Contact Area and Shear Stress in Repeated Single-Asperity Sliding of Steel on Polymer

  • Xian-Qiang PeiEmail author
  • Leyu Lin
  • Alois K. Schlarb
  • Roland Bennewitz
Original Paper


A model for the contact area of a single asperity sliding in a groove after repeated cycles is presented. Based only on the asperity geometry and on data from friction experiments, the model predicts the area of the asymmetric elliptical contact of the asperity sliding in its own groove. It thus allows to determine the shear stress of the steel–polymer couple in the relevant geometry without need for further microscopy of indenter or groove. The model was validated by experiments with an indenter manufactured from slide bearing steel and polyether-ether ketone (PEEK) as substrate. In experiments of 1000 repeated cycles, the contact area was found to vary with varying load and sliding velocity, while the shear stress was 20.5 MPa at a normal pressure of 50–70 MPa, independent of velocity when friction heating is still negligible. Model and experimental confirmation advance single-asperity friction experiments into an efficient method to extract shear stress and contact area for an understanding of sliding friction in metal-polymer contacts.


Asperity scratching Contact area Shearing PEEK 



The authors acknowledge financial support of the German Research Foundation (Deutsche Forschungsgemeinschaft) on the projects BE 4238/7-2 and SCHL 280/22-2, Evonik Industries AG, Germany, for the donation of the experimental materials, and thank Eduard Arzt for the continuous support of this project. The authors are also grateful to Karl-Peter Schmitt of INM for his help in tribological tests.


  1. 1.
    Bowden, F.P., Moore, A.J.W., Tabor, D.: The ploughing and adhesion of sliding metals. J. Appl. Phys. 14(2), 80–91 (1943). CrossRefGoogle Scholar
  2. 2.
    Gane, N., Bowden, F.P.: Microdeformation of solids. J. Appl. Phys. 39(3), 1432–1435 (1968). CrossRefGoogle Scholar
  3. 3.
    Iqbal, T., Yasin, S., Luckham, P.F., Ramzan, N., Mohsin, M.: Scratch deformations of poly (ether ether ketone) composites. Fibers Polym. 15(5), 1042–1050 (2014). CrossRefGoogle Scholar
  4. 4.
    Jiang, H., Browning, R., Sue, H.-J.: Understanding of scratch-induced damage mechanisms in polymers. Polymer. 50(16), 4056–4065 (2009). CrossRefGoogle Scholar
  5. 5.
    Krupička, A., Johansson, M., Hult, A.: Use and interpretation of scratch tests on ductile polymer coatings. Prog. Org. Coat. 46(1), 32–48 (2003). CrossRefGoogle Scholar
  6. 6.
    Briscoe, B.J., Evans, P.D., Lancaster, J.K.: Single point deformation and abrasion of γ-irradiated poly(tetrafluoroethylene). J. Phys. D 20(3), 346 (1987)CrossRefGoogle Scholar
  7. 7.
    Woldman, M., Van Der Heide, E., Tinga, T., Masen, M.A.: The influence of abrasive body dimensions on single asperity wear. Wear. 301(1–2), 76–81 (2013). CrossRefGoogle Scholar
  8. 8.
    Hadal, R.S., Misra, R.D.K.: Scratch deformation behavior of thermoplastic materials with significant differences in ductility. Mater. Sci. Eng. A. 398(1–2), 252–261 (2005). CrossRefGoogle Scholar
  9. 9.
    Rajesh, J.J., Bijwe, J.: Investigations on scratch behaviour of various polyamides. Wear. 259(1–6), 661–668 (2005). CrossRefGoogle Scholar
  10. 10.
    Bermudez, M.D., Brostow, W., Carrion-Vilches, F.J., Cervantes, J.J., Pietkiewicz, D.: Wear of thermoplastics determined by multiple scratching. e-Polymers 001 (2005)Google Scholar
  11. 11.
    Pei, X.-Q., Lin, L.-Y., Schlarb, A.K., Bennewitz, R.: Novel experiments reveal scratching and transfer film mechanisms in the sliding of the PEEK/steel tribosystem. Tribol. Lett. 63(3), 1–9 (2016). CrossRefGoogle Scholar
  12. 12.
    Bowden, F.P., Tabor, D.: The area of contact between stationary and between moving surfaces. Proc. R. Soc. Lond. 169(938), 391–413 (1939)CrossRefGoogle Scholar
  13. 13.
    D7027-13, A: Standard Test Method for Evaluation of Scratch Resistance of Polymeric Coatings and Plastics Using an Instrumented Scratch Machine. ASTM International, West Conshohocken (2013)
  14. 14.
    Gauthier, C., Lafaye, S., Schirrer, R.: Elastic recovery of a scratch in a polymeric surface: experiments and analysis. Tribol. Int. 34(7), 469–479 (2001). CrossRefGoogle Scholar
  15. 15.
    Lafaye, S., Gauthier, C., Schirrer, R.: Analysis of the apparent friction of polymeric surfaces. J. Mater. Sci. 41(19), 6441–6452 (2006). CrossRefGoogle Scholar
  16. 16.
    Malzbender, J., den Toonder, J.M.J., Balkenende, A.R., de With, G.: Measuring mechanical properties of coatings: a methodology applied to nano-particle-filled sol–gel coatings on glass. Mater. Sci. Eng. 36(2), 47–103 (2002). CrossRefGoogle Scholar
  17. 17.
    Puttock, M.J., Thwaite, E.G.: Elastic compression of spheres and cylinders at point and line contact. National Standards Laboratory Technical Paper No. 25 Commonwealth Scientific and Industrial Research Organization, Australia (1969)Google Scholar
  18. 18.
    Pei, X.-Q., Bennewitz, R., Kasper, C., Tlatlik, H., Bentz, D., Becker-Willinger, C.: Tribological synergy of filler components in multi-functional polyimide coatings. Adv. Eng. Mater. 19(1), 1600363 (2017)CrossRefGoogle Scholar
  19. 19.
    Villat, C., Ponthiaux, P., Pradelle-Plasse, N., Grosgogeat, B., Colon, P.: Initial sliding wear kinetics of two types of glass ionomer cement: a tribological study. Biomed. Res. Int. (2014). CrossRefGoogle Scholar
  20. 20.
    Jiang, H., Browning, R., Fincher, J., Gasbarro, A., Jones, S., Sue, H.-J.: Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins. Appl. Surf. Sci. 254(15), 4494–4499 (2008). CrossRefGoogle Scholar
  21. 21.
    Zhang, G., Liao, H., Li, H., Mateus, C., Bordes, J.M., Coddet, C.: On dry sliding friction and wear behaviour of PEEK and PEEK/SiC-composite coatings. Wear. 260(6), 594–600 (2006). CrossRefGoogle Scholar
  22. 22.
    Rzatki, F.D., Barboza, D.V.D., Schroeder, R.M., Barra, G.M.d.O., Binder, C., Klein, A.N., de Mello, J.D.B.: Effect of surface finishing, temperature and chemical ageing on the tribological behaviour of a polyether ether ketone composite/52100 pair. Wear. 332–333, 844–854 (2015). CrossRefGoogle Scholar
  23. 23.
    Schroeder, R., Torres, F.W., Binder, C., Klein, A.N., de Mello, J.D.B.: Failure mode in sliding wear of PEEK based composites. Wear. 301(1–2), 717–726 (2013). CrossRefGoogle Scholar
  24. 24.
    Chen, F., Ou, H., Gatea, S., Long, H.: Hot tensile fracture characteristics and constitutive modelling of polyether-ether-ketone (PEEK). Polym. Testing. 63, 168–179 (2017). CrossRefGoogle Scholar
  25. 25.
    Laux, K.A., Jean-Fulcrand, A., Sue, H.J., Bremner, T., Wong, J.S.S.: The influence of surface properties on sliding contact temperature and friction for polyetheretherketone (PEEK). Polymer. 103, 397–404 (2016). CrossRefGoogle Scholar
  26. 26.
    Bowden, F.P., Tabor, D.: Friction, lubrication and wear: a survey of work during the last decade British. J. Appl. Phys. 17(12), 1521–1544 (1966)Google Scholar
  27. 27.
    McGhee, E.O., Pitenis, A.A., Urueña, J.M., Schulze, K.D., McGhee, A.J., O’Bryan, C.S., Bhattacharjee, T., Angelini, T.E., Sawyer, W.G.: In situ measurements of contact dynamics in speed-dependent hydrogel friction. Biotribology. 13, 23–29 (2018). CrossRefGoogle Scholar
  28. 28.
    Stuart, B.H., Briscoe, B.J.: The effect of crystallinity on the scratch hardness of poly(ether ether ketone). Polym. Bull. 36(6), 767–771 (1996). CrossRefGoogle Scholar
  29. 29.
    Bowden, F.P., Tabor, D.: The Friction and Lubrication of Solids, (Vol. 2). Clarendon Press, Oxford (1964)Google Scholar
  30. 30.
    Briscoe, B.J., Stuart, B.H., Sebastian, S., Tweedale, P.J.: The failure of poly (ether ether ketone) in high speed contacts. Wear 162–164, 407–417 (1993). CrossRefGoogle Scholar
  31. 31.
    Popov, V.: Contact Mechanics and Friction: Physical Principles and Applications (Vol. 55), Springer, Amsterdam (2010)CrossRefGoogle Scholar
  32. 32.
    Bellemare, S., Dao, M., Suresh, S.: The frictional sliding response of elasto-plastic materials in contact with a conical indenter. Int. J. Solids Struct. 44(6), 1970–1989 (2007). CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Xian-Qiang Pei
    • 1
    • 2
    Email author
  • Leyu Lin
    • 2
  • Alois K. Schlarb
    • 2
    • 3
    • 4
  • Roland Bennewitz
    • 1
  1. 1.INM-Leibniz Institute for New MaterialsSaarbrückenGermany
  2. 2.Chair of Composite Engineering (CCe)Technische Universität KaiserslauternKaiserslauternGermany
  3. 3.Research Center OPTIMASTechnische Universität KaiserslauternKaiserslauternGermany
  4. 4.Qingdao University of Science and TechnologyQingdaoPeople’s Republic of China

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