SPECIFIC FEATURES OF STRESS-STRAIN CURVES AT CONSTANT STRESS RATE OR STRAIN RATE YIELDING FROM LINEAR VISCOELASTICITY
The qualitative analysis of linear integral constitutive equation of viscoelasticity with an arbitrary creep compliance function is continued. General equation and basic properties of quasi-static theoretic stress-strain curves (SSC) at constant stress rate are analytically studied herein and compared with properties of SSC at constant strain rate. It is proved for any increasing creep function that: 1) every SSC is an increasing and convex-up function of time (without extremum or inflection points); 2) SSC rise up as stress rate increase; 3) the instantaneous and longterm equilibrium moduli (i.e. the limit values of SSC derivative at zero and infinity points) don’t depend on a stress rate; 4) SSC family of any regular model converges uniformly to the linear function (instantaneous SSC of the model) as stress rate tends to infinity; SSC family of any non-regular model converges to vertical line; 5) if stress rate tends to zero, SSC family descends and converges uniformly to the linear function with the slope equal to equilibrium modulus (it may be zero if relaxation modulus tends to zero at infinity). All these properties are also proved to be valid for SSC at constant strain rate. Three main three classes of linear models (i.e. regular, unbounded and singular) are considered and distinctive features of their SSC are marked. It is proved for any regular model that SSC at a constant stress rate lies higher than its SSC at the corresponding constant strain rate (equal to the stress rate divided by the model instantaneous modulus). General properties and peculiarities of SSC families and their dependence on creep function parameters are illustrated by examination of classical rheological models. The specific features of SSC (and other basic curves) of the linear integral constitutive equation are highlighted that can indicate its applicability or non-applicability being compared with the list of typical properties of a certain material test curves. The list of indicators helps to check linear theory abilities to provide an adequate description of basic rheological phenomena and typical test curves of viscoelastoplastic materials.