An inverse problem for adhesive contact and non-direct evaluation of material properties for nanomechanics applications
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.
- 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)
School of Engineering, Cardiff University,
The Parade, Cardiff, CF24 3AA, UK
Institute for Problems in Materials Science,
Kiev 03142, Ukraine
Zoological Institute of the University of Kiel,
Kiel, D-24098, Germany
Faculty of Mechanics and Mathematics, Moscow State University,
Moscow, 119991, Russia
Moscow State Technical University of Radioengineering,
Electronics and Automation, Moscow, 119454, Russia
School of Engineering, Cardiff University,
The Parade, Cardiff, CF24 3AA, UK
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