Analysis of properties of ramp stress relaxation curves produced by the Rabotnov non-linear hereditary theoryстатья
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
Аннотация:The Rabotnov nonlinear constitutive equation for non-aging elasto-viscoplastic materials containing two material functions is studied analytically to elucidate the set of basic rheological phenomena which it is able to simulate, to outline the areas of material functions influence, to indicate application field of the relation and to find the ways of its identification and fitting. General properties and specific features of the theoretic relaxation curves generated by the model under ramp deformation programs up to a given strain level are investigated in uni-axial case assuming material functions of the relation are arbitrary. The properties dependences on rise time magnitude, on strain rate at initial stage and on the material functions are analyzed. Stress rate jump at final point of a ramp stage, monotonicity and convexity intervals of relaxation curves, their asymptotic behavior at infinity and conditions for convergence to zero of the deviation from the relaxation curve under instantaneous (step) deformation to the same strain level with time tending to infinity are examined. Two-sided bounds are obtained for ramp relaxation curves and for deviation from the relaxation curve under step loading. The uniform convergence of the theoretic ramp relaxation curves family (with fixed strain level) to the relaxation curve under step loading with the rise time tending to zero is proved.
The qualitative features of theoretic relaxation curves are compared to typical properties of test relaxation curves of elasto-viscoplastic materials and the necessary phenomenological restrictions are revealed that should be imposed on material functions to provide an adequate description of typical test relaxation curves. A few effects are pointed out that the model can’t simulate whatever material functions are taken. The analysis reveals several characteristic features of the theoretic stress relaxation curves that can be employed as the relation applicability (or non- applicability) indicators which are convenient for check in ramp relaxation tests. The ways of the relation identification are outlined. The arsenal of capabilities of the Rabotnov nonlinear constitutive relation and its applicability scope are compared to capabilities of the Boltzmann-Volterra linear viscoelasticity theory which was generalized to formulate the Rabotnov relation. We elucidate the inherited properties and the properties acquired due to the introduction of the second material function providing a sort of physical non-linearity
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Keywords: elastoviscoplasticity, physical non-linearity, stress relaxation curves, ramp tests, rise time influence, bounds for ramp relaxation curves, asymptotics, convergence, fading memory, applicability indicators, identification