An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications

• Autorzy: F.M. Borodich , B.A. Galanov , S.N. Gorb , M.Y. Prostov , Y.I. Prostov , M.M. Suarez-Alvarez
• Języki publikacji: EN

Abstrakty

EN

We show how the values of the effective elastic modulus of contacting solids and the work of adhesion, that are the crucial material parameters for application of theories of adhesive contact to nanomechanics, may be quantified from a single test using a non-direct approach (the Borodich-Galanov (BG) method). Usually these characteristics are not determined from the same test, e.g. often sharp pyramidal indenters are used to determine the elastic modulus from a nanoindentation test, while the work of adhesion is determined from a different test by the direct measurements of pull-off force of a sphere. The latter measurements can be greatly affected by roughness of contacting solids and they are unstable due to instability of the load-displacement diagrams at tension. The BG method is 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. Various aspects related to solving the inverse problem for adhesive contact and experimental evaluation of material properties for nanomechanics applications are discussed. It is shown that the BG method is simple and robust. Some theoretical aspects of the method are discussed and the BG method is developed by application of statistical approaches to experimental data. The advantages of the BG method are demonstrated by its application to soft polymer (polyvinylsiloxane) samples.

Słowa kluczowe

EN

Molecular adhesion; nano-mechanics; nanoindentation; soft polymers and biological materials; inverse problems; BG method

Kategorie tematyczne

• 68.35.Np: Adhesion(for polymer adhesion, see 82.35.Gh: for cell adhesion, see 87.17.Rt in biological physics)
• 82.35.Gh: Polymers on surfaces; adhesion(see also 68.35.Np Adhesion in surfaces and interfaces)
• 68.35.Md: Surface thermodynamics, surface energies(see also 05.70.Np Interface and surface thermodynamics in statistical physics, thermodynamics and nonlinear dynamical systems; 65.40.gp Surface energy in thermal properties of condensed matter)
• 46.55.+d: Tribology and mechanical contacts(see also 81.40.Pq Friction, lubrication and wear in materials science; 62.20.Qp Friction, tribology and hardness in mechanical properties of solids)
• 68.35.Gy: Mechanical properties; surface strains(for strain induced piezoelectric fields, see 77.65.Ly; for strain effects on ferroelectric phase transitions, see 77.80.bn)
• 81.70.Bt: Mechanical testing, impact tests, static and dynamic loads(see also 62.20.M- Structural failure of materials; 46.50.+a Fracture mechanics, fatigue, and cracks)

• 74B99: None of the above, but in this section
• 74M15: Contact
• 74G75: Inverse problems
• 74E99: None of the above, but in this section
• 74A55: Theories of friction (tribology)

• Wydawca: De Gruyter Open
• Czasopismo: Nanoscale Systems: Mathematical Modeling, Theory and Applications
• Rocznik: 2012
• Tom: 1
• Strony: 80-92

Daty

otrzymano

2012-10-01

poprawiono

2012-11-15

zaakceptowano

2012-11-16

online

2012-11-26

Twórcy

autor

F.M. Borodich

• School of Engineering, Cardiff University,
  The Parade, Cardiff, CF24 3AA, UK

autor

B.A. Galanov

• Institute for Problems in Materials Science,
  Kiev 03142, Ukraine

autor

S.N. Gorb

• Zoological Institute of the University of Kiel,
  Kiel, D-24098, Germany

autor

M.Y. Prostov

• Faculty of Mechanics and Mathematics, Moscow State University,
  Moscow, 119991, Russia

autor

Y.I. Prostov

• Moscow State Technical University of Radioengineering,
  Electronics and Automation, Moscow, 119454, Russia

autor

M.M. Suarez-Alvarez

• School of Engineering, Cardiff University,
  The Parade, Cardiff, CF24 3AA, UK

Bibliografia

• B. Derjaguin. Untersuchungen über die Reibung und Adhäsion, IV. Theorie des Anhaftens kleiner Teilchen. Kolloid Zeitschrift, 69, 155–164 (1934).
• B.V. Deryagin, N.A. Krotova and V.P. Smilga. Adhesion of Solids. Consultants Bureau, New York, London, (1978).
• J.A. Greenwood. Adhesion of elastic spheres. Proc. R. Soc. Ser. A, 453, 1277–1297 (1997).
• D. Maugis. Contact, Adhesion and Rupture of Elastic Solids. Springer Verlag, Berlin, (2000).
• K. Kendall. Molecular Adhesion and its Applications: The Sticky Universe. Kluwer Academic, New York, (2001).
• A.O. Sergici, G.G. Adams and S. Muftu. Adhesion in the contact a spherical indenter with a layered elastic half-space. J. Mech. Phys. Solids, 54, 1843–1861 (2006).
• W.K. Liu, S. Jun and D. Qian. Computational nanomechanics of materials. J. Comput. Theor. Nanoscience, 5, 970–996 (2008).
• G.I. Barenblatt and P.J.M. Monteiro. Scaling laws in nanomechanics. Physical Mesomechanics, 13 , 245–248 (2010). [WoS]
• E.R. Beach, G.W.Tormoen, J. Drelich and R. Han. Pull-off force measurements between rough surfaces by atomic force microscopy. J. Coll. Interfac. Sci., 247, 84–99 (2002).
• D.K. Owens and R.C. Wendt. Estimation of the surface free energy of polymers. J. Appl. Polym. Sci., 13, 1741–1747 (1969).
• W. Wu, R.F. Giese and C.J. van Oss. Evaluation of the Lifshitz-Van der Waals/acid-base approach to determine surface tension components. Langmuir, 11, 379–382 (1995).
• B.V. Derjaguin, A.S. Titijevskaia, I.I. Abrikossova and A.D. Malkina. Investigations of the forces of interaction of surfaces in different media and their application to the problem of colloid stability. Discuss. Faraday Soc., 18, 24–41 (1954).
• J.N. Israelachvili and D. Tabor. The measurement of Van Der Waals dispersion forces in the range 1.5 to 130 nm. Proc. R. Soc. Ser. A 331, 19–38 (1972).
• W.W. Merrill, A.V. Pocius, B.V. Thakker and M. Tirrell. Direct measurement of molecular level adhesion forces between biaxially oriented solid polymer films. Langmuir, 7, 1975–1980 (1991).
• K.J. Wahl, S.A.S. Asif, J.A. Greenwood and K.L. Johnson. Oscillating adhesive contacts between micron-scale tips and compliant polymers. J. Colloid. Interface Sci., 296 , 178–188 (2006).
• F.M. Borodich and B.A. Galanov. Non-direct estimations of adhesive and elastic properties of materials by depthsensing indentation. Proc. R. Soc. Ser. A, 464, 2759–2776 (2008).
• F.M. Borodich, B.A. Galanov, S.N. Gorb, M.I. Prostov, Y.I. Prostov and M.M. Suarez-Alvarez. Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres. Applied Physics A: Materials Science & Processing, 108, 13–18 (2012).
• G.N. Kalei. Some results of microhardness test using the depth of impression. Mashinovedenie, 4, 105–107 (1968).
• G. Binnig, C.F. Quate and C. Gerber. Atomic force microscope. Phys. Rev. Lett., 56 , 930–933 (1986).
• Y. Jiao, S. Gorb and M. Scherge. Adhesion measured on the attachment pads of Tettigonia viridissima (Orthoptera, insecta). The Journal of Experimental Biology, 203, 1887–1895 (2000).
• D.C. Lin, E.K. Dimitriadis and F. Horkay. Robust strategies for automated AFM force curve analysis - II. Adhesioninfluenced indentation of soft, elastic materials. J. Biomechanical Eng., 129, 904–912 (2007). [WoS]
• S.I. Bulychev, V.P. Alekhin, M.K. Shorshorov, A.P. Ternovskii and G.D. Shnyrev. Determination of Young’s modulus according to indentation diagram. Industrial Lab., 41, 1409–1412 (1975).
• F.M. Borodich and L.M. Keer. Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int. J. Solids Struct., 41, 2479–2499 (2004).
• F.M. Borodich and L.M. Keer. Evaluation of elastic modulus of materials by adhesive (no-slip) nanoindentation. Proc. R. Soc. Ser. A, 460, 507–514 (2004).
• F.M. Borodich, L.M. Keer and C.J. Korach. Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes. Nanotechnology, 14, 803–808 (2003). [Crossref]
• M.M.Chaudhri and Y.Y. Lim. Nanoindentation techniques: A critical assessment of the current methods of data analysis. Key Engineering Materials, 345 - 346 1107–1114. (2007).
• F.M. Borodich. Contact problems at nano/microscale and depth sensing indentation techniques. Materials Science Forum, 662, 53–76 (2011).
• E.V. Gorb and S.N. Gorb. Contact mechanics at the insect-plant interface. How do insects stick and how do plants prevent this? In: F.M. Borodich (ed.) Scaling in Solid Mechanics, Springer, Berlin, pp. 243–252 (2009).
• F.M. Borodich and B.A. Galanov. Self-similar problems of elastic contact for non-convex punches. J. Mech. Phys. Solids, 50, 2441–2461 (2002).
• A.N. Tikhonov and V.Y. Arsenin. Solutions of Ill-Posed Problems. Wiley, New York, (1977).
• A. Tarantola. Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM, Philadelphia, (2004).
• P.C. Hansen and D.P. Oleary. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comp., 14, 1487–1503 (1993).
• S. Gorb, M. Varenberg, A. Peressadko and J. Tuma. Biomimetic mushroom-shaped fibrillar adhesive microstructure. J. R. Soc. Interface, 4, 271–275 (2007). [WoS]

Identyfikatory

DOI

10.2478/nsmmt-2012-0006