Abstract
Work of adhesion is the crucial material parameter for application of theories of adhesive contact. It is usually determined by experimental techniques based on the direct measurements of pull-off force of a sphere. These measurements are unstable due to instability of the load-displacement diagrams at tension, and they can be greatly affected by roughness of contacting solids. We show how the values of work of adhesion and elastic contact modulus of materials may be quantified using a new indirect approach (the Borodich–Galanov (BG) method) based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Using numerical simulations it is shown that the BG method is simple and robust. The crucial difference between the proposed method and the standard direct experimental techniques is that the BG method may be applied only to compressive parts of the force-displacements curves. Finally, the work of adhesion and the elastic modulus of soft polymer (polyvinylsiloxane) samples are extracted from experimental load-displacement diagrams.
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References
K. Kendall, Molecular Adhesion and its Applications: The Sticky Universe (Kluwer Academic, New York, 2001)
E.R. Beach, G.W. Tormoen, J. Drelich, R. Han, Pull-off force measurements between rough surfaces by atomic force microscopy. J. Colloid Interface Sci. 247, 84 (2002)
D.K. Owens, R.C. Wendt, Estimation of the surface free energy of polymers. J. Appl. Polym. Sci. 13, 1741 (1969)
W. Wu, R.F. Giese, C.J. van Oss, Evaluation of the Lifshitz–Van der Waals/acid–base approach to determine surface tension components. Langmuir 11, 379 (1995)
B.V. Derjaguin, N.A. Krotova, V.P. Smilga, Adhesion of Solids (Nauka, Moscow, 1973)
K.J. Wahl, S.A.S. Asif, J.A. Greenwood, K.L. Johnson, Oscillating adhesive contacts between micron-scale tips and compliant polymers. J. Colloid Interface Sci. 296, 178 (2006)
D.M. Ebenstein, 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)
S. Vajpayee, Ch.-Y. Hui, A. Jagota, Model-independent extraction of adhesion energy from indentation experiments. Langmuir 24, 9401 (2008)
F.M. Borodich, B.A. Galanov, Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation. Proc. R. Soc. A 464, 2759 (2008)
F.M. Borodich, Contact problems at nano/microscale and depth sensing indentation techniques. Mater. Sci. Forum 662, 53 (2011)
S.I. Bulychev, V.P. Alekhin, M.Kh. Shorshorov, A.P. Ternovskii, G.D. Shnyrev, Determining Young’s modulus from the indentor penetration diagram. Ind. Lab. 41, 1409 (1975)
F.M. Borodich, L.M. Keer, Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int. J. Solids Struct. 41, 2479 (2004)
F.M. Borodich, L.M. Keer, Evaluation of elastic modulus of materials by adhesive (no-slip) nano-indentation. Proc. R. Soc. Ser. A 460, 507 (2004)
G.N. Kalei, Some results of microhardness test using the depth of impression. Mashinovedenie 4, 105 (1968)
G. Binnig, C.F. Quate, Ch. Gerber, Atomic force microscope. Phys. Rev. Lett. 56, 930 (1986)
D. Maugis, Contact, Adhesion and Rupture of Elastic Solids (Springer, Berlin, 2000)
B.A. Galanov, O.N. Grigor’ev, Adhesion and wear of diamond. Part I. Modelling. Preprint. Institute Prob. Mat. Sci., Nat. Ac. Sci. Ukraine, Kiev, pp. 1–14 (1994)
R.W. Carpick, N. Agraït, D.F. Ogletree, M. Salmeron, Measurement of interfacial shear (friction) with an ultrahigh vacuum atomic force microscope. J. Vac. Sci. Technol. B 14, 1289 (1996)
F.M. Borodich, Hertz type contact problems for power-law shaped bodies, in Contact Problems. The Legacy of L.A. Galin, ed. by L.A. Galin, G.M.L. Gladwell (Springer, New York, 2008), p. 261
F.M. Borodich, L.M. Keer, C.J. Korach, Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes. Nanotechnology 14, 803 (2003)
Y. Jiao, S. Gorb, M. Scherge, Adhesion measured on the attachment pads of Tettigonia viridissima (Orthoptera, insecta). J. Exp. Biol. 203, 1887 (2000)
D.C. Lin, E.K. Dimitriadis, F. Horkay, Robust strategies for automated AFM force curve analysis, II: adhesion-influenced indentation of soft, elastic materials. J. Biomech. Eng. 129, 904 (2007)
E.V. Gorb, S.N. Gorb, Contact mechanics at the insect-plant interface. How do insects stick and how do plants prevent this, in Scaling in Solid Mechanics, ed. by F.M. Borodich (Springer, Berlin, 2009), p. 243
F.M. Borodich, B.A. Galanov, Self-similar problems of elastic contact for non-convex punches. J. Mech. Phys. Solids 50, 2441 (2002)
S. Gorb, M. Varenberg, A. Peressadko, J. Tuma, Biomimetic mushroom-shaped fibrillar adhesive microstructure. J. R. Soc. Interface 4, 271 (2007)
J.A. Greenwood, Adhesion of elastic spheres. Proc. R. Soc. A 453, 1277 (1997)
R.W. Carpick, D.F. Ogletree, M. Salmeron, A general equation for fitting contact area and friction vs load measurements. J. Colloid Interface Sci. 211, 395 (1999)
Acknowledgements
This work was initiated in the framework of the ADHESINT International Network supported by the Leverhulme Trust. It was also partly supported by the SPP 1420 priority program of the German Science Foundation (DFG) “Biomimetic Materials Research: Functionality by Hierarchical Structuring of Materials” (project GO 995/9-1).
In 2007, one of the authors (FB) delivered the first presentation of the BG method. After the presentation, Professor J.R. Willis (DAMTP, University of Cambridge) advised to develop an algorithm for checking the validity of the BG method and Professor K.L. Johnson (Department of Engineering, University of Cambridge) suggested to think about determination of the zero reference point on displacement axis. The authors are very grateful for these stimulating discussions and advise.
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Borodich, F.M., Galanov, B.A., Gorb, S.N. et al. Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres. Appl. Phys. A 108, 13–18 (2012). https://doi.org/10.1007/s00339-012-6982-7
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DOI: https://doi.org/10.1007/s00339-012-6982-7