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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 23 января 2020 г.
Аннотация:А. V. Khokhlov. ON THE ABILITY OF THE RABOTNOV NON-LINEAR RELATION FOR VISCOELASTIC MATERIALS TO SIMULATE STRESS-STRAIN CURVES WITH A DECREASING SEGMENT
The Rabotnov physically non-linear constitutive equation with two arbitrary (increasing) material functions for elasto-viscoplastic materials is studied analytically in order to outline the set of basic rheological effects it can simulate, to clarify the material functions governing abilities, to indicate application field of the relation and to develop identification techniques. Under minimal primary restrictions on two material functions, the general equation of the stress-strain curves family produced by the model at constant strain rates is derived and analyzed in uni-axial case. The main qualitative properties of the stress-strain curves and their dependence on a strain rate and material functions are examined and compared to typical properties of test stress-strain curves of elasto-viscoplastic materials and to the properties of stress-strain curves generated by the Boltzmann-Volterra linear viscoelasticity theory (with arbitrary creep compliance). The last one have been generalized to formulate the Rabotnov relation and so the inherited properties and the new properties acquired due to the introduction of the second material function governing non-linearity are in the focus of attention. In particular, it is proved that the stress-strain curves family increases monotonously as strain rate parameter grow and converges to limit curve (instantaneous or equilibrium) as strain rate tends to zero or infinity. Two-sided bounds for stress-strain curves and conditions for their monotonicity with respect to strain or for existence of maximum are obtained. It is shown that the Rabotnov constitutive equation is able to simulate (qualitatively) deformation softening of materials, i.e. a non-monotone behavior and existence of a decreasing segment of stress-strain curves in tensile tests under constant strain rate condition. The linear viscoelasticity theory fails to do it as it generates only increasing and convex-up stress-strain curves.
***** Keywords: viscoelasticity, physical non-linearity, constant strain rate tests, stress-strain curves, positive rate sensitivity, equilibrium stress-strain curve, softening