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

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Supplementary files

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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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