Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range Part 1: constitutive equations

• Published in: Continuum mechanics and thermodynamics Vol. 29; no. 5; pp. 1027 - 1046
• Main Author: Kari, Leif
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017; Springer Nature B.V
• Subjects: Aging; Chains (polymeric); Classical and Continuum Physics; Cleavage; Computational fluid dynamics; Constitutive equations; Constitutive relationships; Damage; Differential equations; Engineering Thermodynamics; Evolution; Heat and Mass Transfer; Mathematical models; Natural rubber; Original Article; Physics; Physics and Astronomy; Polymers; Relaxation time; Rubber; Stiffness; Stress relaxation; Structural Materials; Temperature dependence; Theoretical and Applied Mechanics; Vibration; Vibration isolators; Viscoelasticity; Fractional differential equation; Doolittle equation; Fractional free volume; William–Landel–Ferry function; Mittag-Leffler function; Chemically and physically ageing
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-017-0569-7

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William–Landel–Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.