Journal of Materials Science

, Volume 48, Issue 9, pp 3479–3485 | Cite as

Nanoscale mechanical characterization of PMMA by AFM nanoindentation: a theoretical study on the time-dependent viscoelastic recovery

  • Y. H. Ding
  • X. H. Deng
  • X. Jiang
  • P. Zhang
  • J. R. Yin
  • Y. Jiang


Temperature-dependent indent recovery of polymethyl methacrylate is depicted by atomic force microscopy. The viscoelastic indent recovery is predicted by a numerical model based on the Boussinesq elastic theory. From the perspective of an elastic solution, viscoelastic solution for stress and displacement field is constructed through the analysis of the elasticity–viscoelasticity corresponding theory. The findings also illustrate the effect of loading condition, elastic modulus, and viscosity on the viscoelastic recovery rate.


Atomic Force Microscopy PMMA Recovery Rate Viscoelastic Material PMMA Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The financial supports from the National Natural Science Foundation of China (No. 51002128), National Science Foundation for Post-doctoral Scientists of China (No. 2012M511737), Foundation for Department of Science and Technology of Hunan Province (No. 2011FJ3218) and Natural Science Foundation of Xiangtan University (No. 2011XZX19) are greatly acknowledged.


  1. 1.
    Tranchida D, Sperotto E, Chateauminois A, Schonherr H (2011) Macromolecules 44:368CrossRefGoogle Scholar
  2. 2.
    Bei H, Lu ZP, George EP (2004) Phys Rev Lett 93:125504CrossRefGoogle Scholar
  3. 3.
    Jager A, Lackner R (2009) Strain 45:45CrossRefGoogle Scholar
  4. 4.
    Herbert EG, Oliver WC, Pharr GM (2008) J Phys D Appl Phys 41:074021CrossRefGoogle Scholar
  5. 5.
    Shi X, Croll SG (2010) J Coat Technol Res 7:73CrossRefGoogle Scholar
  6. 6.
    Tweedie CA, Van Vliet KJ (2006) J Mater Res 21:3029CrossRefGoogle Scholar
  7. 7.
    Du B, Tsui OKC, Zhang Q, He T (2001) Langmuir 17:3286CrossRefGoogle Scholar
  8. 8.
    Strojny A, Xia X, Tsou A, Gerberich WW (1998) J Adhes Sci Technol 12:1299CrossRefGoogle Scholar
  9. 9.
    Zhao MH, Ye ZZ, Mao SX (2009) Phys Rev Lett 102:45502CrossRefGoogle Scholar
  10. 10.
    Kumar R, Narasimhan R (2004) Curr Sci 87:1088Google Scholar
  11. 11.
    VanLandingham MR, Chang NK, Drzal PL, White CC, Chang SH (2005) J Polym Sci Part B Polym Phys 43:1794CrossRefGoogle Scholar
  12. 12.
    Briscoe BJ, Sebastian KS (1996) Proc R Soc Lond Ser A Math Phys Eng Sci 452:439CrossRefGoogle Scholar
  13. 13.
    Briscoe BJ, Fiori L, Pelillo E (1999) J Phys D Appl Phys 31:2395CrossRefGoogle Scholar
  14. 14.
    Oyen ML, Cook RF (2003) J Mater Res 18:139CrossRefGoogle Scholar
  15. 15.
    Oyen ML (2006) Philos Mag 86:5625CrossRefGoogle Scholar
  16. 16.
    Briscoe BJ, Pelillo E, Ragazzi F, Sinha SK (1998) Polymer 39:2161CrossRefGoogle Scholar
  17. 17.
    Puttick KE (2001) J Phys D Appl Phys 11:595CrossRefGoogle Scholar
  18. 18.
    Hinz M, Kleiner A, Hild S, Marti O, Durig U, Gotsmann B, Drechsler U, Albrecht TR, Vettiger P (2004) Eur Polym J 40:957CrossRefGoogle Scholar
  19. 19.
    Anand L, Ames NM (2006) Int J Plast 22:1123CrossRefGoogle Scholar
  20. 20.
    Lee EH, Radok JRM (1960) J Appl Mech 27:438CrossRefGoogle Scholar
  21. 21.
    Bembey AK, Oyen ML, Bushby AJ, Boyde A (2006) Philos Mag 86:5691CrossRefGoogle Scholar
  22. 22.
    Seltzer R, Mai YW (2008) Eng Fract Mech 75:4852CrossRefGoogle Scholar
  23. 23.
    Vandamme M, Ulm FJ (2006) Int J Solids Struct 43:3142CrossRefGoogle Scholar
  24. 24.
    Giannakopoulos AE (2006) J Mech Phys Solids 54:1305CrossRefGoogle Scholar
  25. 25.
    Shimizu S, Yanagimoto T, Sakai M (1999) J Mater Res 14:4075CrossRefGoogle Scholar
  26. 26.
    Selvadurai APS (2009) Int J Eng Sci 47:1339CrossRefGoogle Scholar
  27. 27.
    Cheng L, Xia X, Scriven LE, Gerberich WW (2005) Mech Mater 37:213CrossRefGoogle Scholar
  28. 28.
    Hung C, Chen RH, Lin CR (2002) Int J Adv Manuf Technol 20:230CrossRefGoogle Scholar
  29. 29.
    Lu H, Wang B, Ma J, Huang G, Viswanathan H (2003) Mech Time Depend Mater 7:189CrossRefGoogle Scholar
  30. 30.
    Wei PJ, Shen WX, Lin JF (2008) J Non Cryst Solids 354:3911CrossRefGoogle Scholar
  31. 31.
    Feng G, Ngan AHW (2002) J Mater Res 17:660CrossRefGoogle Scholar
  32. 32.
    Torquato S, Gibiansky LV, Silva MJ, Gibson LJ (1998) Int J Mech Sci 40:71CrossRefGoogle Scholar
  33. 33.
    Lee SS, Westmann RA (1995) Int J Numer Methods Eng 38:607CrossRefGoogle Scholar
  34. 34.
    Ge S, Pu Y, Zhang W, Rafailovich M, Sokolov J (2000) Phys Rev Lett 85:2340CrossRefGoogle Scholar
  35. 35.
    Xie FC, Zhang HF, Lee FK, Du BY, Tsui OKC, Yokoe Y, Tanaka K, Takahara A, Kajiyama T, He TB (2002) Macromolecules 35:1491CrossRefGoogle Scholar
  36. 36.
    Forrest JA, Dalnoki-Veress K, Stevens JR, Dutcher JR (1996) Phys Rev Lett 77:2002CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Y. H. Ding
    • 1
  • X. H. Deng
    • 1
  • X. Jiang
    • 1
  • P. Zhang
    • 1
  • J. R. Yin
    • 1
  • Y. Jiang
    • 1
  1. 1.Institute of Rheology MechanicsXiangtan UniversityHunanChina

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