Determination of the Creep Parameters of Linear Viscoelastic Materials

Abstract

Creep process of linear viscoelastic materials is described by the integral equation of Boltzmann-Volterra in which creep kernel is approximated by Rabotnov’s fractional exponential function. The creep equation contains four unknown parameters:α, singularity parameter;β, fading parameter;λ, rheological parameter; andε0, conditionally instantaneous strain. Two-stage determination method of creep parameters is offered. At the first stage, taking into account weak singularity properties of Abel’s function at the initial moment of loading, parametersε0andαare determined. At the second stage, using already known parametersε0andα, parametersβandλare determined. Analytical expressions for calculating these parameters are obtained. An accuracy evaluation of the offered method with using experimentally determined creep strains of material Nylon 6 and asphalt concrete showed its high accuracy.

Determination of Nonlinear Creep Parameters for Hereditary Materials

“…It is known that the selection of kernel of the integral equation and determination of its parameters is one of the most responsible actions in the description of mechanical behavior of viscoelastic materials. As it has been said in our previous work [14], the most universal is creep kernel in the form of the fractional exponential function of Yu. N. Rabotnov [4][5][6]11].…”

Steady-State Creep of Asphalt Concrete

“…Previous works [14,22,23] showed that an asphalt concrete creep curve-as with most viscoelastic materials-had three characteristic stages: stage I of unsteady-state creep with decreasing rate; stage II of steady-state creep with a constant (minimum) rate; and stage III of accelerating creep with increasing rate which precedes failure. The above studies presented test results of asphalt concrete for creep with relatively narrow ranges of stress variation.…”

“…Therefore, the first and second stages of the creep curve are of main interest for mathematical description. The first stage of the creep curve for asphalt concrete was described with the use of Rabotnov's fractional exponential function [16] and was reported previously by the authors of Reference [14].…”

“…The strain ε 1 can be calculated by the methods described in [14]. Equations (3)- (5) allow the determination of the creep strain of asphalt concrete for the stage of steady-state creep (stage II) at the time moment t (t 1 < t ≤ t 2 ).…”

“…The strain 1  can be calculated by the methods described in [14]. Equations (3)- (5) • 2 σ= η ×ε , (6) where σ is stress; Additionally, for all considered stress variation limit, we can write the Equation (6) in the following form:…”