• Citer

Modelling "unusual" behaviour after strain reversal with hierarchical fractional models

par Verheulpen Heymans, Nicole ;Kitagawa, Masayoshi
Référence Rheologica acta, 43, 4, page (383-389)
Publication Publié, 2004-08

Article révisé par les pairs

• Détails
• Contenu

Résumé :

Various experiments involving strain reversal have been described by Kitagawa et al. For example, after initially loading and unloading a polymer sample, stress "relaxation" showed an initial increase in stress. This behaviour was called "Unusual Behaviour after Strain Reversal" or UBASR by Kitagawa et al., and attributed to an effect of non-linear behaviour. This behaviour is however similar in kind to thermal expansion occurring before contraction after an indirect quench as observed some years ago by Kovacs. We show here that this behaviour can also occur in the range of linear viscoelasticity, and it is then simply a result of fading memory. Such fading memory is particularly well described by models containing β elements, or springpots. In this paper, Kitagawa's data is analysed using a viscoelastic model containing springpots, described by a fractional differential constitutive equation. A novel method of integration based on Boltzmann superposition is developed. This method is shown to be applicable to non-linear viscoelasticity. The model affords a good phenomenological description of the changes in so-called "unusual" behaviour induced by non-linearity. © Springer-Verlag 2004.