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Nanoindentation of compliant materials using Berkovich tips and flat tips

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Abstract

Nanoindentation testing of compliant materials has recently attracted substantial attention. However, nanoindentation is not readily applicable to softer materials, as numerous challenges remain to be overcome. One key concern is the significant effect of adhesion between the indenter tip and the sample, leading to larger contact areas and higher contact stiffness for a given applied force relative to the Hertz model. Although the nano-Johnson–Kendall–Roberts (JKR) force curve method has demonstrated its capabilities to correct for errors due to adhesion, it has not been widely adopted, mainly because it works only with perfectly spherical tips. In this paper, we successfully extend the nano-JKR force curve method to include Berkovich and flat indenter tips by conducting numerical simulations in which the adhesive interactions are represented by an interaction potential and the surface deformations are coupled by using half-space Green’s functions discretized on the surface.

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References

  1. ISO standard 14577: Metallic materials—Instrumented indentation test for hardness and materials parameter. Part 1, part 2 and part 3, 2003; part 4, 2007.

  2. D.M. Ebenstein and L.A. Pruitt: Nanoindentation of biological materials. Nano Today 1, 26 (2006).

    Article  Google Scholar 

  3. D.M. Ebenstein: Nanoindentation of soft tissues and other biological materials. In Handbook of Nanoindentation with Biological Applications, M.L. Oyen, ed. (Pan Stanford Publishing, Singapore, 2010); p. 350.

    Google Scholar 

  4. J.D. Kaufman, G.J. Miller, E.F. Morgan, and C.M. Klapperich: Time-dependent mechanical characterization of poly(2-hydroxyethyl methacrylate) hydrogels using nanoindentation and unconfined compression. J. Mater. Res. 23, 1472 (2008).

    Article  CAS  Google Scholar 

  5. J.D. Kaufman and C.M. Klapperich: Surface detection errors cause overestimation of the modulus in nanoindentation on soft materials. J. Mech. Behav. Biomed. Mater. 2, 312 (2009).

    Article  Google Scholar 

  6. J. Deuschle, S. Enders, and E. Arzt: Surface detection in nanoindentation of soft polymers. J. Mater. Res. 22, 3107 (2007).

    Article  CAS  Google Scholar 

  7. M.R. Van Landingham, J.S. Villarrubia, W.F. Guthrie, and G.F. Meyers: Nanoindentation of polymers: An overview. Macromol. Symp. 167, 15 (2001).

    Article  Google Scholar 

  8. F. Carrillo, S. Gupta, M. Balooch, S.J. Marshall, G.W. Marshall, L. Pruitt, and C.M. Puttlitz: Nanoindentation of polydimethylsiloxane elastomers: Effect of crosslinking, work of adhesion, and fluid environment on elastic modulus. J. Mater. Res. 20, 2820 (2005).

    Article  CAS  Google Scholar 

  9. D.M. Ebenstein and K.J. Wahl: A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves. J. Colloid Interface Sci. 298, 652 (2006).

    Article  CAS  Google Scholar 

  10. S. Gupta, F. Carrillo, C. Li, L. Pruitt, and C. Puttlitz: Adhesive forces significantly affect elastic modulus determination of soft polymeric materials in nanoindentation. Mater. Lett. 61, 448 (2007).

    Article  CAS  Google Scholar 

  11. O. Franke, M. Goken, and A.M. Hodge: The nanoindentation of soft tissue: Current and developing approaches. JOM 60, 49 (2008).

    Article  CAS  Google Scholar 

  12. B. Tang and A.H.W. Ngan: Nanoindentation measurement of mechanical properties of soft solid covered by a thin liquid film. Soft Matter 5, 169 (2007).

    Article  CAS  Google Scholar 

  13. Y.F. Cao, D.H. Yang, and W. Soboyejoy: Nanoindentation method for determining the initial contact and adhesion characteristics of soft polydimethylsiloxane. J. Mater. Res. 20, 2004 (2005).

    Article  CAS  Google Scholar 

  14. J.C. Grunlan, X. Xinyun, D. Rowenhorst, and W.W. Gerberich: Preparation and evaluation of tungsten tips relative to diamond for nanoindentation of soft materials. Rev. Sci. Instrum. 72, 2804 (2001).

    Article  CAS  Google Scholar 

  15. J.K. Deuschle, G. Buerki, H.M. Deuschle, S. Enders, J. Michler, and E. Arzt: In situ indentation testing of elastomers. Acta Mater. 56, 4390 (2008).

    Article  CAS  Google Scholar 

  16. Z. Wang, A.A. Volinsky, and N.D. Gallant: Nanoindentation study of polydimethylsiloxane elastic modulus using Berkovich and flat punch tips. J. Appl. Polym. Sci. 132, 41384 (2015).

    Google Scholar 

  17. F. De Paoli and A.A. Volinsky: Obtaining full contact for measuring polydimethylsiloxane mechanical properties with flat punch nanoindentation. MethodsX 2, 374 (2015).

    Article  Google Scholar 

  18. C.M. Buffinton, K.J. Tong, R.A. Blaho, E.M. Buffinton, and D.M. Ebenstein: Comparison of mechanical testing methods for biomaterials: Pipette aspiration, nanoindentation, and macroscale testing. J. Mech. Behav. Biomed. Mater. 51, 367 (2015).

    Article  CAS  Google Scholar 

  19. K.J. Tong and D.M. Ebenstein: Comparison of spherical and flat tips for indentation of hydrogels. JOM 67, 713 (2015).

    Article  CAS  Google Scholar 

  20. J.C. Kohn and D.M. Ebenstein: Eliminating adhesion errors in nanoindentation of compliant polymers and hydrogels. J. Mech. Behav. Biomed. Mater. 20, 316 (2013).

    Article  CAS  Google Scholar 

  21. V.L. Ferguson, A.J. Bushby, and A. Boyde: Nanomechanical properties and mineral concentration in articular calcified cartilage and subchondral bone. J. Anat. 203, 191 (2003).

    Article  Google Scholar 

  22. P.L. Leong and E.F. Morgan: Measurement of fracture callus material properties via nanoindentation. Acta Biomaterialia 4, 1569 (2008).

    Article  CAS  Google Scholar 

  23. D.M. Ebenstein: Nano-JKR force curve method overcomes challenges of surface detection and adhesion for nanoindentation of a compliant polymer in air and water. J. Mater. Res. 28, 1026 (2011).

    Article  CAS  Google Scholar 

  24. F. Alisafaei, C-S. Han, and S.H.R. Sanei: On the time and indentation depth dependence of hardness, dissipation and stiffness in poly-dimethylsiloxane. Polym. Test. 32, 1220 (2013).

    Article  CAS  Google Scholar 

  25. C. Klapperich, L. Pruitt, and K. Komvopoulos: Nanomechanical properties of energetically treated polyethylene surfaces. J. Mater. Res. 17, 423 (2002).

    Article  CAS  Google Scholar 

  26. K.L. Johnson: Contact Mechanics (Cambridge University Press, Cambridge, 1985).

    Book  Google Scholar 

  27. W.C. Oliver and G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).

    Article  CAS  Google Scholar 

  28. F.M. Borodich and B.A. Galanov: Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation. Proc. R. Soc., Ser. A 464, 2759 (2008).

    Article  CAS  Google Scholar 

  29. E.S. Berkovich: Three-faced diamond pyramid for micro-hardness testing. Int. Diamond Rev. 11, 129 (1951).

    Google Scholar 

  30. I.A. Sneddon: The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965).

    Article  Google Scholar 

  31. D. Tabor: Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2 (1977).

    Article  CAS  Google Scholar 

  32. E. Barthel: Adhesive elastic contacts: JKR and more. J. Phys. D: Appl. Phys. 41, 163001 (2008).

    Article  CAS  Google Scholar 

  33. V.M. Muller, V.S. Yushchenko, and B.V. Derjaguin: On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid Interface Sci. 77, 91 (1980).

    Article  CAS  Google Scholar 

  34. J.A. Greenwood: Adhesion of elastic spheres. Proc. R. Soc. London, Ser. A 453, 1277 (1997).

    Article  CAS  Google Scholar 

  35. B.A. Galanov: Development of analytical and numerical methods for study of models of materials. In Report for the Project 7.06.00/001-92, 7.06.00/015-92. (Institute for Problems in Materials Science, Kiev, Ukrainian, 1993).

    Google Scholar 

  36. F.M. Borodich: Hertz type contact problems for power-law shaped bodies. In Contact Problems: The Legacy of L.A. Galin, G.M.L. Gladwell, ed. (Springer, Dordrecht, Netherlands, 2008); p. 261.

    Google Scholar 

  37. F.M. Borodich: The Hertz-type and adhesive contact problems for depth-sensing indentation. Adv. Appl. Mech. 47, 225 (2014).

    Article  Google Scholar 

  38. C. Jin, A. Jagota, and C-Y. Hui: An easy-to-implement numerical simulation method for adhesive contact problems involving asymmetric adhesive contact. J. Phys. D: Appl. Phys. 44, 405303 (2011).

    Article  CAS  Google Scholar 

  39. A.E. Giannakopoulos, P-L. Larsson, and R. Vestregaard: Analysis of Vickers indentation. Int. J. Solids Struct. 31, 2670 (1994).

    Article  Google Scholar 

  40. P-L. Larsson, A.E. Giannakopoulos, E. Soderlund, D.J. Rowcliffe, and R. Vestergaard: Analysis of Berkovich indentation. Int. J. Solids Struct. 33, 221 (1996).

    Article  Google Scholar 

  41. T. Chudoba and N. Jennett: Higher accuracy analysis of instrumented indentation data obtained with pointed indenters. J. Phys. D: Appl. Phys. 41, 215407 (2008).

    Article  CAS  Google Scholar 

  42. J.N. Israelachvili: Intermolecular and Surface Forces, 2nd ed. (Academic, San Diego, 1992).

    Google Scholar 

  43. C-Y. Hui, A. Jagota, S.J. Bennison, and J.D. Londono: Crack blunting and the strength of soft elastic solids. Proc. R. Soc. London, Ser. A 459, 1489 (2003).

    Article  Google Scholar 

  44. T. Tang, C.Y. Hui, A. Jagota, and M.K. Chaudhury: Thermal fluctuations limit the adhesive strength of compliant solids. J. Adhes. 82, 671 (2006).

    Article  CAS  Google Scholar 

  45. K.L. Johnson and J.A. Greenwood: An adhesion map for the contact of elastic spheres. J. Colloid Interface Sci. 192, 326 (1997).

    Article  CAS  Google Scholar 

  46. L. Kogut and I. Etsion: Adhesion in elastic-plastic spherical microcontact. J. Colloid Interface Sci. 261, 372 (2003).

    Article  CAS  Google Scholar 

  47. Y. Du, L. Chen, N.E. McGruer, G.G. Adams, and I. Etsion: A finite element model of loading and unloading of an asperity contact with adhesion and plasticity. J. Colloid Interface Sci. 312, 522 (2007).

    Article  CAS  Google Scholar 

  48. Z. Song and K. Komvopoulos: Adhesion-induced instabilities in elastic and elastic–plastic contacts during single and repetitive normal loading. J. Mech. Phys. Solids 59, 884 (2011).

    Article  Google Scholar 

  49. A. Jagota and C. Argento: An intersurface stress tensor. J. Colloid Interface Sci. 191, 326 (1997).

    Article  CAS  Google Scholar 

  50. N. Yu and A. Polycarpou: Adhesive contact based on the Lennard–Jones potential: A correction to the value of the equilibrium distance as used in the potential. J. Colloid Interface Sci. 278, 428 (2004).

    Article  CAS  Google Scholar 

  51. F.M. Borodich, B.A. Galanov, L.M. Keer, and M.M. Suarez-Alvarez: The JKR-type adhesive contact problems for transversely isotropic elastic solids. Mech. Mater. 75, 34 (2014).

    Article  Google Scholar 

  52. M. Fafard and B. Massicotte: Geometrical interpretation of the arc-length method. Comput. Struct. 46, 603 (1993).

    Article  Google Scholar 

  53. C. Jin, K. Khare, S. Vajpayee, S. Yang, A. Jagota, and C-Y. Hui: Adhesive contact between a rippled elastic surface and a rigid spherical indenter: From partial to full contact. Soft Matter 7, 10728 (2011).

    Article  CAS  Google Scholar 

  54. F.M. Borodich, B.A. Galanov, and M.M. Suarez-Alvarez: The JKR-type adhesive contact problems for power-law shaped axisymmetric punches. J. Mech. Phys. Solids 68, 14 (2014).

    Article  Google Scholar 

  55. R. Spolenak, S. Gorb, H. Gao, and E. Arzt: Effects of contact shape on biological attachments. Proc. R. Soc. London, Ser. A 461, 305 (2005).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  57. I.D. Johnston, D.K. McCluskey, C.K.L. Tan, and M.C. Tracey: Mechanical characterization of bulk Sylgard 184 for microfluidics and microengineering. J. Micromech. Microeng. 24, 035017 (2014).

    Article  CAS  Google Scholar 

  58. A. Sharfeddin, A.A. Volinsky, G. Mohan, and N.D. Gallant: Comparison of the macroscale and microscale tests for measuring elastic properties of polydimethylsiloxane. J. Appl. Polym. Sci. 132, 42680 (2015).

    Article  CAS  Google Scholar 

  59. K.R. Shull: Contact mechanics and the adhesion of soft solids. Mater. Sci. Eng., R 36, 1 (2002).

    Article  Google Scholar 

  60. Y.L. Yu, D. Sanchez, and N.S. Lu: Work of adhesion/separation between soft elastomers of different mixing ratios. J. Mater. Res. 30, 2702 (2015).

    Article  CAS  Google Scholar 

  61. R.L. Smith and G.E. Sutherland: Some notes on the use of a diamond pyramid for hardness testing. Iron Steel Inst. 1, 285 (1925).

    Google Scholar 

  62. F. Knoop, C.G. Peters, and W.B. Emerson: A sensitive pyramidal-diamond tool for indentation measurements. J. Res. Natl. Bur. Stand. 23, 39 (1939).

    Article  Google Scholar 

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ACKNOWLEDGMENTS

This work is supported by start-up funds provided by the Department of Mechanical Engineering at State University of New York at Binghamton. The nanoindenter used in this study was obtained through the support of the National Science Foundation (MRI-1040319). Conclusions and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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  1. Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY, 13902, USA

    Congrui Jin

  2. Department of Biomedical Engineering, Bucknell University, Lewisburg, Pennsylvania, 17837, USA

    Donna M. Ebenstein

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  1. Congrui Jin
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  2. Donna M. Ebenstein
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Correspondence to Congrui Jin.

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Jin, C., Ebenstein, D.M. Nanoindentation of compliant materials using Berkovich tips and flat tips. Journal of Materials Research 32, 435–450 (2017). https://doi.org/10.1557/jmr.2016.483

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