Simulation of hydrostatic pressure influence on creep curves and poisson’s ratio of rheonomic materials under tension using the rabotnov non-linear hereditary relation | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 24 > №3 / 2018 / Pages: 407-436

Simulation of hydrostatic pressure influence on creep curves and poisson’s ratio of rheonomic materials under tension using the rabotnov non-linear hereditary relation


The Rabotnov physically non-linear constitutive equation for non-aging elasto-viscoplastic materials with four material functions is studied analytically in order to outline the set of basic rheological phenomena which it can simulate, to clarify the material functions governing abilities, to indicate application field of the relation and to develop identification and verification techniques. The relation is quasi-linear, it doesn’t involve the third invariants of stress and strain tensors and implies that their hydrostatic and deviatoric parts don’t depend on each other. Assuming minimal restrictions on material functions of the relation, general properties of the creep curves for shear, volumetric, axial and lateral strains generated by the model under uni-axial tension and constant hydrostatic pressure are analyzed. Conditions for creep curves monotonicity and for existence of extrema and sign changes of strains, the Poisson ratio (lateral contraction ratio in creep) evolution in time, evolution of the strain triaxiality ratio (which is equal to volumetric strain divided by deviatoric strain) and their dependences on pressure and tensile stress levels and material functions characteristics are studied. Taking into account the pressure influence and volumetric creep (governed by two material functions of the model) is proved to affect strongly the qualitative behavior and characteristic features of longitudinal creep curves and the Poisson ratio evolution and its range. In particular, it is proved that the Rabotnov relation is able to simulate non-monotone behavior and sign changes of lateral strain and Poisson’s ratio under constant tensile load (even if the pressure is zero) and the longitudinal strain may start to decrease provided the pressure level is high enough. The expressions for Poisson’s ratio via the strain triaxiality ratio and in terms of tensile stress and pressure levels and material functions of the model are derived. Assuming material functions are arbitrary, general bounds for the Poisson ratio range are obtained and the influence of pressure level is studied. Additional restrictions on material functions and stress levels are derived to provide negative values of Poisson’s ratio. Conditions for its increase or decrease and for its non-dependence on time are found. It is proved that, for any fixed tensile load, the higher the pressure level is the more creep curves for volumetric, axial and lateral strains shift down along the strain axis and the Poisson ratio decreases at any time moment. The qualitative properties of the theoretic creep curves families and Poisson’s ratio produced by the constitutive equation are compared to typical properties of test creep curves of elasto-viscoplastic materials under hydrostatic pressure in order to reveal a set of necessary phenomenological restrictions which should be imposed on material functions to provide an adequate description of typical effects. A number of specific features and quantitative characteristics of the theoretic creep curves are found that can be employed as indicators of the constitutive relation applicability (or non-applicability) for simulation of a material behavior which are convenient to check in creep tests with various levels of pressure and tensile stress. The specific properties and restrictions of the model with zero dilatational creep compliance which simulates a material exhibiting purely elastic volumetric deformation are considered.