Theoretical and experimental investigation of nanoindentation of polymers

• Applicants: Professor Dr.-Ing. Stefan Diebels; Professor Dr. Horst Vehoff
• Subject Area: Mechanics
• Term: from 2010 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 170769832

• Final Report Year: 2014

Final Report Abstract

In the work of this project, an analysis procedure to characterize polymers on the basis of nanoindentation has been developed using the finite element-based inverse method. The hyperelastic as well as viscoelastic properties of polymers have been evaluated using the obtained force-displacement data and taking into account the influence of friction, surface roughness, and adhesion effects. The project contains two phases: In the first phase, the nanoindentation of polymers has been studied with FEM computation. The influence of friction, surface roughness, and adhesion effects have been quantified numerically. A procedure has been developed to identify the hyperelastic and viscoelastic behavior of polymers. The accuracy and stability of the developed procedure have been proven using the strategy of parameters re-identification. In the second phase, the procedure and quantification knowledge obtained in the first stage have been applied to the real nanoindentation of the different polymers with an increasing rate-dependent property. The identified hyperelasticity and viscoelasticity from the nanoindentation force-displacement data, in which the influence of friction, surface roughness, and adhesion effects has been excluded, have been compared and verified with the results from macroindentation and uni/biaxial tensile tests. The investigation results ensure that it is possible to use the method developed in this project to accurately characterize polymers on the basis of nanoindentation. Furthermore, enough information has been obtained to allow us to deeply understand the relationship between the material models and the deformation forms in various experiments. The suggestions on the experimental setup supply an open window for the nanoindentation of polymers, in which it is extremely tricky to get accurate measurements. According to the numerical computation, the hyperelasticity behaviors of the polymer layers depend on the geometry-associated factors in nanoindentation. The most important advantage of this developed inverse procedure is that if the properties of the substrate are known, the penetration depth is not necessary to be constrained in order to accurately capture the properties of thin layers or coatings using nanoindentation. In the case of evaluating the viscoelasticity of polymer layers on the basis of nanoindentation, the choice of the loading history is important. It is better to split the behavior into basic elasticity and viscoelasticity, which can be identified using multistepwise monotonic testing and sinusoidal oscillatory testing, respectively. The friction between the indenter and the polymer layers can lead to a higher indentation force if the penetration depth becomes deeper without depending on the friction coefficient if it is larger than 0.4. However, if the penetration is shallow enough to avoid the influence of the substrate, the friction effect is negligible. The influence of the surface roughness on the identification results can be excluded by defining a new initial indentation point or by modeling the real rough surface with a multi-level protuberance-on-protuberance sine profile. The adhesion effect is modeled with the surface-based traction-separation law. This adhesive contact model does not only allow to exclude the adhesion influence, but also to quantify the adhesion forces in nanoindentation. Finally, the identification results from nano/macroindentation tests and uni/biaxial tensile tests have been compared to each other. The comparability of the identified hyperelasticity and viscoelasticity depends on the polymer type, constitutive model, deformation forms, and strain level.

Publications

• [2011]. ‘Numerical investigation of nanoindentation of viscoelastic polymer layers and parameter re-identification.’ PAMM, 11(1), pp. 765–766
  Chen, Z. & S. Diebels
  
• [2012]. ‘Modelling and parameter re-identification of nanoindentation of soft polymers taking into account effects of surface roughness.’ Computers and Mathematics with Applications, 64, pp. 2775–2786
  Chen, Z. & S. Diebels
  
• [2012]. ‘Nanoindentation of hyperelastic polymer layers at finite deformation and parameter re-identification.’ Arch. Appl. Mech., 82, pp. 1041–1056
  Chen, Z. & S. Diebels
  
• [2012]. ‘Surface Roughness Effects in Nanoindentation of Soft Polymers.’ PAMM, 12(1), pp. 297–298
  Chen, Z. & S. Diebels
  
• [2013]. ‘Identification of Finite Viscoelasticity and Adhesion Effects in Nanoindentation of a Soft Polymer by Inverse Method.’ Comput. Mater. Sci., 72, pp. 127–139
  Chen, Z., S. Diebels, N. J. Peter & A. S. Schneider
  
• [2013]. ‘Macroindentation of a soft polymer: Identification of hyperelasticity and validation by uni/biaxial tensile tests.’ Mech. Mater., 64, pp. 111–127
  Chen, Z., T. Scheffer, H. Seibert & S. Diebels
  
• [2013]. ‘Parameter re-identification in nanoindentation problems of viscoelastic polymer layers: small deformation.’ Zeitschrift für Angewandte Mathematik und Mechanik, 93, pp. 88–101
  Chen, Z. & S. Diebels
  
• [2014]. Nanoindentation testing of soft polymers: Computation, experiments and parameters identification. Ph.D. thesis, Universität des Saarlandes
  Chen, Z.
  
• [2014]. ‘Nanoindentation of Soft Polymers: Modeling, Experiments and Parameter Identification.’ Technische Mechanik, 34, pp. 166–189
  Chen, Z. & S. Diebels