Skip to main content
SpringerLink
Log in

Scale Effect in Mechanical Properties and Tribology

  • Chapter
Nanotribology and Nanomechanics

Summary

A model, which explains scale effects in mechanical properties and tribology is presented. Mechanical properties are scale dependent based on the strain gradient plasticity and the effect of dislocation-assisted sliding. Both single asperity and multiple asperity contacts are considered. The relevant scaling length is the nominal contact length — contact diameter for a single-asperity contact, and scan length for multiple-asperity contacts. For multiple asperity contacts, based on an empirical power-rule for scale dependence of roughness, contact parameters are calculated. The effect of load on the contact parameters and the coefficient of friction is also considered. During sliding, adhesion and two- and three-body deformation, as well as ratchet mechanism, contribute to the dry friction force. These components of the friction force depend on the relevant real areas of contact (dependent on roughness and mechanical properties), average asperity slope, number of trapped particles, and shear strength during sliding. Scale dependence of the components of the coefficient of friction is studied. A scale dependent transition index, which is responsible for transition from predominantly elastic adhesion to plastic deformation has been proposed. Scale dependence of the wet friction, wear, and interface temperature has been also analyzed. The proposed model is used to explain the trends in the experimental data for various materials at nanoscale and microscale, which indicate that nanoscale values of coefficient of friction are lower than the microscale values due to an increase of the three-body deformation and transition from elastic adhesive contact to plastic deformation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Bhushan. Handbook of Micro/Nanotribology. CRC, 2nd edition, 1999.

    Google Scholar 

  2. B. Bhushan. Nanoscale tribophysics and tribomechanics. Wear, 225–229:465–492, 1999.

    Article  Google Scholar 

  3. B. Bhushan. Springer Handbook of Nanotechnology. Springer, 2004.

    Google Scholar 

  4. B. Bhushan, J. N. Israelachvili, and U. Landman. Nanotribology: Friction, wear and lubrication at the atomic scale. Nature, 374:607–616, 1995.

    Article  CAS  Google Scholar 

  5. J. Ruan and B. Bhushan. Atomic-scale friction measurements using friction force microscopy: Part i — general principles and new measurement technique. ASME J. Tribol., 116:378–388, 1994.

    CAS  Google Scholar 

  6. B. Bhushan and A. V. Kulkarni. Effect of normal load on microscale friction measurements. Thin Solid Films, 278:49–56, 1996.

    Article  CAS  Google Scholar 

  7. R. W. Carpick, N. Agrait, D. F. Ogletree, and M. Salmeron. Measurement of interfacial shear (friction) with an ultrahigh vacuum atomic force microscope. J. Vac. Sci. Technol. B, 14:1289–1295, 1996.

    Article  CAS  Google Scholar 

  8. U. D. Schwarz, O. Zwörner, P. Köster, and R. Wiesendanger. Quantitative analysis of the frictional properties of solid materials at low loads. 1. carbon compounds. Phys. Rev. B, 56:6987–6996, 1997.

    Article  CAS  Google Scholar 

  9. B. Bhushan and S. Sundararajan. Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy. ActaMater., 46:3793–3804, 1998.

    CAS  Google Scholar 

  10. B. Bhushan and C. Dandavate. Thin-film friction and adhesion studies using atomic force microscopy. J. Appl. Phys., 87:1201–1210, 2000.

    Article  CAS  Google Scholar 

  11. H. Liu and B. Bhushan. Adhesion and friction studies of microelectromechanical systems/nanoelectromechanical systems materials using a novel microtriboapparatus. J. Vac. Sci. Technol. A, 21:1538–1538, 2003.

    Google Scholar 

  12. B. Bhushan, H. Liu, and S. M. Hsu. Adhesion and friction studies of silicon and hydrophobic and low friction films and investigation of scale effects. ASME J. Tribol., 126:583–590, 2004.

    Article  CAS  Google Scholar 

  13. A. W. Homola, J. N. Israelachvili, P. M. McGuiggan, and M. L. Gee. Fundamental experimental studies in tribology: The transition from interfacial friction of undamaged molecularly smooth surfaces to normal friction with wear. Wear, 136:65–83, 1990.

    Article  CAS  Google Scholar 

  14. V. N. Koinkar and B. Bhushan. Scanning and transmission electron microscopies of single-crystal silicon microworn/machined using atomic force microscopy. J. Mater. Res., 12:3219–3224, 1997.

    CAS  Google Scholar 

  15. X. Zhao and B. Bhushan. Material removal mechanisms of single-crystal silicon on nanoscale and at ultralow loads. Wear, 223:66–78, 1998.

    Article  CAS  Google Scholar 

  16. B. Bhushan. Introduction to Tribology. Wiley, 2002.

    Google Scholar 

  17. N. A. Fleck, G. M. Muller, M. F. Ashby, and J. W. Hutchinson. Strain gradient plasticity: Theory and experiment. Acta Metall. Mater., 42:475–487, 1994.

    Article  CAS  Google Scholar 

  18. W. D. Nix and H. Gao. Indentation size effects in crystalline materials: A law for strain gradient plasticity. J. Mech. Phys. Solids, 46:411–425, 1998.

    Article  CAS  Google Scholar 

  19. J. W. Hutchinson. Plasticity at the micron scale. Int. J. Solids Struct., 37:225–238, 2000.

    Article  Google Scholar 

  20. B. Bhushan and M. Nosonovsky. Scale effects in friction using strain gradient plasticity and dislocation-assisted sliding (microslip). Acta Mater., 51:4331–4345, 2003.

    Article  CAS  Google Scholar 

  21. B. Bhushan and M. Nosonovsky. Comprehensive model for scale effects in friction due to adhesion and two-and three-body deformation (plowing). Acta Mater., 52:2461–2474, 2004.

    Article  CAS  Google Scholar 

  22. B. Bhushan and M. Nosonovsky. Scale effects in dry and wet friction, wear, and interface temperature. Nanotechnol., 15:749–761, 2004.

    Article  CAS  Google Scholar 

  23. M. Nosonovsky and B. Bhushan. Scale effect in dry friction during multiple asperity contact. ASME J. Tribol., 127:37–46, 2005.

    Article  Google Scholar 

  24. H. Gao, Y. Huang, W. D. Nix, and J. W. Hutchinson. Mechanism-based strain-gradient plasticity — i. theory. J. Mech. Phys. Solids, 47:1239–1263, 1999.

    Article  Google Scholar 

  25. Y. Huang, H. Gao, W. D. Nix, and J. W. Hutchinson. Mechanism-based strain-gradient plasticity — ii. analysis. J. Mech. Phys. Solids, 48:99–128, 2000.

    Article  Google Scholar 

  26. Z. P. Bazant. Scaling of dislocation-based strain-gradient plasticity. J. Mech. Phys. Solids, 50:435–448, 2002.

    Article  Google Scholar 

  27. J. Friedel. Dislocations. Pergamon, 1964.

    Google Scholar 

  28. J. Weertman and J. R. Weertman. Elementary Dislocations Theory. MacMillan, 1966.

    Google Scholar 

  29. B. Bhushan and A. V. Koinkar. Nanoindentation hardness measurements using atomic force microscopy. Appl. Phys. Lett., 64:1653–1655, 1994.

    Article  CAS  Google Scholar 

  30. B. Bhushan, A. V. Kulkarni, W. Bonin, and J. T. Wyrobek. Nano/picoindentation measurement using a capacitive transducer system in atomic force microscopy. Philos. Mag., 74:1117–1128, 1996.

    CAS  Google Scholar 

  31. A. V. Kulkarni and B. Bhushan. Nanoscale mechanical property measurements using modified atomic force microscopy. Thin Solid Films, 290–291:206–210, 1996.

    Article  Google Scholar 

  32. N. Gane and J.M. Cox. tsnote hier Philos. Mag., 22:881, 1970.

    CAS  Google Scholar 

  33. M. A. Stelmashenko, M. G. Walls, L. M. Brown, and Y. V. Miman. Microindentation on W and Mo oriented single crystal an sem study. Acta Met. Mater., 41:2855–2865, 1993.

    Article  CAS  Google Scholar 

  34. K. W. McElhaney, J. J. Vlassak, and W. D. Nix. Determination of indenter tip geometry and indentation contact area of depth-sensing indentation experiments. J. Mater. Res., 13:1300–1306, 1998.

    CAS  Google Scholar 

  35. S. Sundararajan and B. Bhushan. Development of afmbased techniques to measure mechanical properties of nanoscale structures. Sensors Actuator A, 101:338–351, 2002.

    Article  Google Scholar 

  36. J. J. Weertman. Dislocations moving uniformly on the interface between isotropic media of different elastic properties. J. Mech. Phys. Solids, 11:197–204, 1963.

    Article  Google Scholar 

  37. K. L. Johnson. Adhesion and friction between a smooth elastic spherical asperity and a plane surface. Proc. R. Soc. London A, 453:163–179, 1997.

    CAS  Google Scholar 

  38. I. A. Polonsky and L. M. Keer. Scale effects of elastic-plastic behavior of microscopic asperity contact. ASME J. Tribol., 118:335–340, 1996.

    Google Scholar 

  39. V. S. Deshpande, A. Needleman, and E. Van der Giessen. Discrete dislocation plasticity modeling of short cracks in single crystals. Acta Mater., 51:1–15, 2003.

    Article  CAS  Google Scholar 

  40. R. A. Onions and J. F. Archard. The contact of surfaces having a random structure. J. Phys. D, 6:289–304, 1973.

    Article  Google Scholar 

  41. D. J. Whitehouse and J. F. Archard. The properties of random surfaces of significance in their contact. Proc. R. Soc. London A, 316:97–121, 1970.

    Google Scholar 

  42. J. A. Greenwood and J. B. P.Williamson. Contact of nominally flat surfaces. Proc. R. Soc. London A, 295:300–319, 1966.

    Article  CAS  Google Scholar 

  43. B. Bhushan. Contact mechanics of rough surfaces in tribology: Single asperity contact. Appl. Mech. Rev., 49:275–298, 1996.

    Google Scholar 

  44. B. Bhushan. Contact mechanics of rough surfaces in tribology: Multiple asperities contact. Tribol. Lett., 4:1–35, 1998.

    Article  Google Scholar 

  45. B. Bhushan and W. Peng. Contact modeling of multilayered rough surfaces. Appl. Mech. Rev., 55:435–480, 2002.

    Article  Google Scholar 

  46. A. Majumdar and B. Bhushan. Fractal model of elastic-plastic contact between rough surfaces. ASME J. Tribol., 113:1–11, 1991.

    Google Scholar 

  47. K. L. Johnson. Contact Mechanics. Clarendon, 1985.

    Google Scholar 

  48. E. Rabinowicz. Friction and Wear of Materials. Wiley, 2nd edition, 1995.

    Google Scholar 

  49. H. R. Clauser (Ed.). The Encyclopedia of Engineering Materials and Processes. Reinhold, 1963.

    Google Scholar 

  50. B. Bhushan and B. K. Gupta. Handbook of Tribology: Materials, Coatings, and Surface Treatments. McGraw-Hill, New York 1991; Krieger, Malabar, 1997.

    Google Scholar 

  51. B. Bhushan and S. Venkatesan. Mechanical and tribological properties of silicon for micromechanical applications: A review. Adv. Info. Storage Syst., 5:211–239, 1993.

    Google Scholar 

  52. INSPEC. Properties of Silicon. EMIS Data Rev. Ser. No. 4. INSPEC, Institution of Electrical Engineers, 2002.

    Google Scholar 

  53. J. E. Field (Ed.). The Properties of Natural and Synthetic Diamond. Academic, 1992.

    Google Scholar 

  54. B. Bhushan. Chemical, mechanical and tribological characterization of ultra-thin and hard amorphous carbon coatings as thin as 3.5 nm: Recent developments. Diam. Relat. Mater., 8:1985–2015, 1999.

    Article  CAS  Google Scholar 

  55. National Carbon Comp. The Industrial Graphite Engineering Handbook. National Carbon Company, 1959.

    Google Scholar 

  56. C. Bernhardt. Particle Size Analysis. Chapman Hall, 1994.

    Google Scholar 

  57. J. L. Devoro. Probability and Statistics for Engineering and the Sciences. Duxbury, 1995.

    Google Scholar 

  58. B. S. Everitt. The Cambridge Dictionary of Statistics. Cambridge Univ. Press, 1998.

    Google Scholar 

  59. D. Zwillinger and S. Kokoska. CRC Standard Probability and Statistics Tables and Formulas. CRC, 2000.

    Google Scholar 

  60. S. Wolfram. The Mathematica Book. Wolfram Media, 5th edition, 2003.

    Google Scholar 

  61. J. S. Bendet and A. G. Piersol. Engineering Applications of Correlation and Spectral Analysis. Wiley, 2nd edition, 1986.

    Google Scholar 

  62. R. D. Cadle. Particle Size — Theory and Industrial Applications. Reinhold, 1965.

    Google Scholar 

  63. G. Herdan. Small Particle Statistics. Butterworth, 1960.

    Google Scholar 

  64. Y. Xie and B. Bhushan. Effect of particle size, polishing pad and contact pressure in free abrasive polishing. Wear, 200:281–295, 1996.

    Article  CAS  Google Scholar 

  65. J. L. Xuan, H. S. Cheng, and R. J. Miller. Generation of submicrometer particles in dry sliding. ASME J. Tribol., 112:664–691, 1990.

    Article  Google Scholar 

  66. M. Mizumoto and K. Kato. Size distribution and number of wear particles generated by the abrasive sliding of a model asperity in the SEM-tribosystem, pages 523–530. Elsevier, 1992.

    Google Scholar 

  67. A. S. Shanbhag, H. O. Bailey, D. S. Hwang, C. W. Cha, N. G. Eror, and H. E. Rubash. Quantitative analysis of ultrahigh molecular weight polyethylene (uhmwpe) wear debris associated with total knee replacements. J. Biomed. Mater. Res., 53:100–110, 2000.

    Article  CAS  Google Scholar 

  68. T. M. Hunt. Handbook of Wear Debris Analysis and Particle Detection in Liquids. Elsevier Applied Science, 1993.

    Google Scholar 

  69. W. W. Seifert and V. C. Westcott. A method for the study of wear particles in lubricating oil. Wear, 21:27–42, 1972.

    Article  Google Scholar 

  70. D. Scott and V. C. Westcott. Predictive maintenance by ferrography. Wear, 44:173–182, 1977.

    Article  CAS  Google Scholar 

  71. D. P. Anderson. Wear Particle Atlas. Spectro Inc. Industrial Tribology Systems, 2nd edition, 1991.

    Google Scholar 

Download references

Authors
  1. Bharat Bhushan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Nosonovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Nanotribology Laboratory for Information storage and MEMS/NEMS, The Ohio State University, 206 W. 18th Ave., Coumbus, Ohio, 43210-1107, USA

    Bharat Bhushan

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bhushan, B., Nosonovsky, M. (2005). Scale Effect in Mechanical Properties and Tribology. In: Bhushan, B. (eds) Nanotribology and Nanomechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28248-3_16

Download citation

Publish with us

Policies and ethics

Search

Navigation