A method of viscoelastic properties identification for surface layers of elastomers based on nanodynamic indentation

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Abstract

A theoretical and experimental method is poroposed for identification of mechanical properties of the surface layers of highly elastic materials by the results of their dynamic indentation for small depths (nanoDMA). The method is based on an approximate solution of the contact problem for a rigid ball in contact with a deformable specimen, the contact being loaded by an oscillating normal force. The specimen is modeled by a linear viscoelastic half-space with the relaxation kernel presented as a sum of exponential terms. The method allows one to determine sets of parameters defining the relaxation and creep functions of a material in a time interval corresponding to the experimental range of frequencies, as well as to calculate the dynamic storage and loss moduli for each frequency. The application of the method is shown by an example of the analysis of the mechanical properties of surface layers for two types of frost-resistant rubber (butadiene-nitrile and isoprene) depending on the degree of wear of their surfaces. It is established that the wear of surfaces of the rubbers under investigation leads to an increase of the surface layers stiffness and to a decrease in their relaxation properties; these changes are more pronounced for rubber based on nitrile butadiene than for that based on isoprene.

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About the authors

Y. Y. Makhovskaya

Ishlinsky Institute for Problems in Mechanics of RAS

Author for correspondence.
Email: makhovskaya@mail.ru
Russian Federation, Moscow

A. V. Morozov

Ishlinsky Institute for Problems in Mechanics of RAS

Email: morozovalexei@mail.ru
Russian Federation, Moscow

K. S. Kravchuk

NRC “KURCHATOV INSTITUTE” – TISNCM

Email: kskrav@gmail.com
Russian Federation, Moscow, Troitsk

References

  1. Ferry J.D. Viscoelastic Properties of Polymers. NY: Wiley, 1961. 482 p.
  2. Goryacheva I.G., Makhovskaya Yu.Yu., Morozov A.V., Stepanov F.I. Friction of Elastomers. Modeling and Experiment (Institute for Computer Science, Moscow-Izhevsk, 2017) [in Russian].
  3. Oliver W.C., Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments // J Mater Res. 1992. V. 7. № 6. P. 1564–1583.
  4. Asif S.A.S., Wahl K.J., Colton R.J. Nanoindentation and contact stiffness measurement using force modulation with a capacitive load-displacement transducer // Review of Scientific Instruments. 1999. V. 70. № 5. P. 2408–2413.
  5. Herbert E.G., Oliver W.C., Pharr G.M. Nanoindentation and the dynamic characterization of viscoelastic solids // J Phys D Appl Phys. 2008. V. 41. № 7. P. 074021.
  6. Pharr G.M., Oliver W.C., Brotzen F.R. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation // J Mater Res. 1992. Vol. 7. № 3. P. 613–617.
  7. Igarashi T. et al. Nanorheological Mapping of Rubbers by Atomic Force Microscopy // Macromolecules. 2013. V. 46. № 5. P. 1916–1922.
  8. Pittenger B. et al. Nanoscale DMA with the Atomic Force Microscope: A New Method for Measuring Viscoelastic Properties of Nanostructured Polymer Materials // JOM. 2019. V. 71. № 10. P. 3390–3398.
  9. Huang G., Wang B., Lu H. Measurements of Viscoelastic Functions of Polymers in the Frequency-Domain Using Nanoindentation // Mech Time Depend Mater. 2004. V. 8. № 4. P. 345–364.
  10. Cheng Y.-T., Ni W., Cheng C.-M. Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids // Phys Rev Lett. 2006. V. 97. № 7. P. 075506.
  11. Nikfarjam M. et al. Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy // Beilstein Journal of Nanotechnology. 2018. V. 9. P. 1116–1122.
  12. Greenwood J.A. Contact between an axisymmetric indenter and a viscoelastic half-space // Int J Mech Sci. 2010. V. 52. № 6. P. 829–835.
  13. Wayne Chen W. et al. Semi-Analytical Viscoelastic Contact Modeling of Polymer-Based Materials // J Tribol. 2011. V. 133. № 4.
  14. Rabotnov Yu.N. Creep of Structural Elements. Moscow: Nauka, 1966. 752 p. [in Russian].
  15. Johnson K.L. Contact Mechanics. Cambridge: Cambrige University Press, 1985.
  16. Christensen R.M. Theory of Viscoelasticity. An Introduction New York: Acad. Press, 1971.
  17. Sneddon I. Fourier Transforms, New York: McGraw Hill, 1951.
  18. Haiat G., Phan Huy M.C., Barthel E. The adhesive contact of viscoelastic spheres // J. Mech Phys Solids. 2003. V. 51. № 1. P. 69–99.
  19. Argatov I.I., Popov V.L. Rebound indentation problem for a viscoelastic half‐space and axisymmetric indenter — Solution by the method of dimensionality reduction // ZAMM – Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 2016. V. 96. № 8. P. 956–967.
  20. Morozov A.V., Bukovskiy P.O. Method of Constructing a 3D Friction Map for a Rubber Tire Tread Sliding Over a Rough Surface // Journal of Friction and Wear. 2018. V. 39. № 2.
  21. Morozov A.V., Makhovskaya Y.Y., Kravchuk K.S. Influence of Adhesive Properties and Surface Texture of Laminated Plywood on Rubber Friction // Journal of Friction and Wear. 2021. V. 42. № 4.
  22. Baumgaertel M., Winter H.H. Determination of discrete relaxation and retardation time spectra from dynamic mechanical data // Rheol Acta. 1989. V. 28. № 6. P. 511–519.
  23. Grosch K.A. The relation between the friction and visco-elastic properties of rubber // Proc R Soc Lond A Math Phys Sci. 1963. V. 274. № 1356. P. 21–39.

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2. Fig. 1. The scheme of contacting during the nanodome test.

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3. Figure 2. Diagram of parallel connected elements illustrating the material model in differential form (3.5).

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4. Fig. 3. Typical dependences of the load P [mN] (a) and displacement c [µm] (b) on the time t [s] during the nanoDMA test, as well as a diagram of the applied load (c) taking into account the processes of preloading and unloading of the test material (BNKS-18).

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5. Fig. 4. Dependence of the accumulation modules E ' [MPa] and losses E" [MPa] on the oscillation frequency f [Hz] for BNKS-18 (a) and SKI-3 (b), where 1 is the unworn rubber surface, 2 is Str = 4 km and 3 is Str = 20 km.

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6. Fig. 5. Graphs of relaxation nuclei G(t) and creep K(t), t[c] for BNKS-18 (a, c) and SKI-3 (b,d), where 1 is the unworn rubber surface, 2 is Str = 4 km and 3 is Str = 20 km.

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