Acta Mechanica Solida Sinica

, Volume 32, Issue 1, pp 1–16 | Cite as

Plastic Effect on the Sliding Inception Between a Cylinder and a Rigid Flat

  • S. Zhang
  • J. Huan
  • H. Song
  • X. LiuEmail author
  • Y. G. WeiEmail author


The effects of material plasticity and local slip on the sliding inception of asperity are studied in the present work. Firstly, a semi-analytical solution is derived under the full-stick condition to analyze the effect of material plasticity on sliding friction. Then, a friction model with contact stiffness criterion is proposed to study the cases from partial-slip condition to full-stick condition. Finite element simulations with the provided model are used to present the friction map. The friction coefficient of full-stick interface converges at a stable value, approximately 0.3. Plasticity saturation appears as the normalized contact interference \(\omega ^{*}\) is larger than 3. A transition mechanism from slip-dominated to yield-dominated takes place in the sliding process. The simulation results are compared with the semi-analytical solution.


Material yielding Local slip Contact stiffness criterion Finite element simulation 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11772334, 11432014, 11672301), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040501) and the State Key Laboratory of Structural Analysis for Industrial Equipment (DUT Grant No. GZ15116).


  1. 1.
    Mindlin RD. Compliance of elastic bodies in contact. ASME J Appl Mech. 1949;16:259–68.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Hamilton GM. Explicit equations for the stresses beneath a sliding spherical contact. Proc Inst Mech Eng Part C Mech Eng Sci. 1983;197C:53–9.CrossRefGoogle Scholar
  3. 3.
    Chang WR, Etsion I, Bogy DB. Static friction coefficient model for metallic rough surfaces. ASME J Tribol. 1988;110:57–63.CrossRefGoogle Scholar
  4. 4.
    Kogut L, Etsion I. A semi-analytical solution for the sliding inception of a spherical contact. ASME J Appl Mech. 2003;125:499–505.Google Scholar
  5. 5.
    Brizmer V, Kligerman Y, Etsion I. The effect of contact conditions and material properties on the elasticity terminus of a spherical contact. Int J Solids Struct. 2006;43:5736–49.CrossRefzbMATHGoogle Scholar
  6. 6.
    Brizmer V, Zait Y, Kligerman Y, Etsion I. The effect of contact conditions and material properties on elastic-plastic spherical contact. J Mech Mater Struct. 2006;1:865–79.CrossRefzbMATHGoogle Scholar
  7. 7.
    Zait Y, Kligerman Y, Etsion I. Unloading of an elastic-plastic spherical contact under stick contact condition. Int J Solids Struct. 2010;47:990–7.CrossRefzbMATHGoogle Scholar
  8. 8.
    Etsion I, Kligerman Y, Kadin Y. Unloading of an elastic-plastic loaded spherical contact. Int J Solids Struct. 2005;42:3716–29.CrossRefzbMATHGoogle Scholar
  9. 9.
    Ronen S, Goltsberg R, Etsion I. A comparison of stick and slip contact conditions for a coated sphere compressed by a rigid flat. Friction. 2017;5:326–38.CrossRefGoogle Scholar
  10. 10.
    Brizmer V, Kligerman Y, Etsion I. Elastic-plastic spherical contact under combined normal and tangential loading in full stick. Tribol Lett. 2007;25:61–70.CrossRefGoogle Scholar
  11. 11.
    Wu A, Shi X. Numerical investigation of adhesive wear and static friction based on the ductile fracture of junction. ASME J Appl Mech. 2013;80(4):041032.CrossRefGoogle Scholar
  12. 12.
    Shi X, Wu A, Zhu CM, Qu SX. Effects of load configuration on partial slip contact between an elastic-plastic sphere and a rigid flat. Tribol Int. 2013;61:120–8.CrossRefGoogle Scholar
  13. 13.
    Wu A, Shi X, Polycarpou AA. An elastic-plastic spherical contact model under combined normal and tangential loading. ASME J Appl Mech. 2012;79(5):051001.CrossRefGoogle Scholar
  14. 14.
    Shi X. On slip inception and static friction for smooth dry contact. ASME J Appl Mech. 2014;81(12):121005.CrossRefGoogle Scholar
  15. 15.
    Bhushan B. Contact mechanics of rough surfaces in tribology: multiple asperity contact. Tribol Lett. 1998;4:1–35.CrossRefGoogle Scholar
  16. 16.
    Hodge PG. Plastic analysis of structures. New York: McGraw-Hill Book Company; 1959.zbMATHGoogle Scholar
  17. 17.
    Owen DRJ, Hinton E. Finite elements in plasticity: theory and practice. Swansea: Pineridge Press LTD.; 1980.zbMATHGoogle Scholar
  18. 18.
    Liu G, Zhu J, Yu L, Wang QJ. Elasto-plastic contact of rough surfaces. Tribol Trans. 2001;44:437–43.CrossRefGoogle Scholar
  19. 19.
    Lin LP, Lin JF. A new method for elastic-plastic contact analysis of a deformable sphere and a rigid flat. ASME J Tribol. 2006;128:221–9.CrossRefGoogle Scholar
  20. 20.
    Zhao B, Zhang S, Wang QF, Zhang Q, Wang P. Loading and unloading of a power-law hardening spherical contact under stick contact condition. Int J Mech Sci. 2015;94–95:20–6.CrossRefGoogle Scholar
  21. 21.
    Jackson RL, Green I. A finite element study of elastoplastic hemispherical contact against a rigid flat. ASME J Tribol. 2005;127:343–54.CrossRefGoogle Scholar
  22. 22.
    Shi X, Zou Y, Fang H. Numerical investigation of the three-dimensional elastic-plastic sloped contact between two hemispheric asperities. ASME J Appl Mech. 2016;83(10):101004.CrossRefGoogle Scholar
  23. 23.
    Vermeulen PJ, Johnson KL. Contact of nonspherical elastic bodies transmitting tangential forces. ASME J Appl Mech. 1964;31:338–40.CrossRefzbMATHGoogle Scholar
  24. 24.
    Jahnke E, Emde F. Tables of functions with formulae and curves. New York: Dover Publications; 1945.zbMATHGoogle Scholar
  25. 25.
    Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1985.CrossRefzbMATHGoogle Scholar
  26. 26.
    Tian H, Saka N. Finite element analysis of an elastic-plastic two-layer half-space: sliding contact. Wear. 1991;148:261–85.CrossRefGoogle Scholar
  27. 27.
    Kogut L, Etsion I. Elastic-plastic contact analysis of a sphere and a rigid flat. ASME J Appl Mech. 2002;69:657–62.CrossRefzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  1. 1.LNM, Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.Department of Mechanical EngineeringJohns Hopkins UniversityBaltimoreUSA
  3. 3.College of EngineeringPeking UniversityBeijingChina
  4. 4.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

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