Viscoelasticity

Abstract Polymer solids show viscoelasticity that is highly sensitive to varying temperature: these features are modelled for small strains using the theory of linear viscoelasticity, including time–temperature equivalence as observed in data. Creep is expressed in terms of a creep compliance, stress relaxation in terms of a stress relaxation modulus, and oscillatory response in terms of a complex modulus or compliance. These have been measured for many polymers and show characteristic features. The Boltzmann superposition principle then enables prediction of responses to other load sequences. Alternatively, a constitutive model of the material is employed: a set of linear differential equations relating stress, strain, and time, equivalent to combinations of springs and dashpots fitted to experimental data. A relaxation spectrum is usually required, equivalent to many springs and dashpots. The effect of temperature on polymer viscoelasticity usually exhibits time–temperature superposition, with shift factors following the Arrhenius equation or the Williams–Landel–Ferry (WLF) equation.